Number 95 December 2005

NEWSLETTEROF THE

N E W Z E A L A N D M A T H E M A T I C A L S O C I E T Y

Contents

Publisherrsquos Notice 2

Editorial 3

Presidentrsquos Column 5

Local News 6

Centrefold (George Szekeres) 20

Features 25

Minutes 27

Book Reviews 29

Conferences 31

Notices 33

Mathematical Miniature 28 39

1

Contents

Contents

PUBLISHERrsquoS NOTICE 3

EDITORIAL 4

PRESIDENTrsquoS COLUMN 6

LOCAL NEWS 7

FEATURES 26

MINUTES 28

BOOK REVIEWS 30

CONFERENCES 32

NOTICES 34

2

NZMS Newsletter No 95

PUBLISHERrsquoS NOTICE

This newsletter is the official organ of the New Zealand Mathematical Society Inc This issue was assembled by FionaRichmond and printed at Massey University The official address of the Society is

The New Zealand Mathematical Societyc- The Royal Society of New ZealandPO Box 598 Wellington New Zealand

However correspondence should normally be sent to the Secretary

Winston SweatmanInstitute of Information and Mathematical SciencesMassey UniversityPrivate Bag 102 904North Shore Mail CentreAucklandwsweatmanmasseyacnz

NZMS Council and Officers

President Professor Gaven Martin (Massey University Albany)Incoming Vice President Associate Professor Mick Roberts (Massey University Albany)Secretary Dr Winston Sweatman (Massey University Albany)Treasurer Dr Tammy Smith (Massey University Palmerston North)Councillors Dr Michael Albert (University of Otago) to 2006

Dr Shaun Hendy (Industrial Research Limited) to 2007Dr Warren Moors (The University of Auckland) to 2006Dr Rick Beatson (University of Canterbury) to 2008Dr Tammy Smith (Massey University Palmerston North) to 2008Dr Winston Sweatman (Massey University Albany) to 2007

Membership Secretary Dr John Shanks (University of Otago)Newsletter Editor Professor Robert McLachlan (Massey University Palmerston North)Legal Adviser Dr Peter Renaud (University of Canterbury)Archivist Emeritus Professor John Harper (Victoria University of Wellington)Visitor Liaison Dr Stephen Joe (The University of Waikato)Publications Convenor Dr David McIntyre (The University of Auckland)Webmaster Dr Stephen Joe (The University of Waikato)

Newsletter Correspondents

Sub-EditorsBook reviews Associate Professor Bruce van-Brunt (Massey University Palmerston North))Mathematical Miniatures Emeritus Professor John Butcher (The University of Auckland)

Honorary CorrespondentsMurray Black Mathematics (Auckland University of Technology)Michael Doherty Statistics NZ (Wellington)Lenette Grant Mathematics and Statistics (University of Otago)David Harte Statistics and Operations Research (Victoria University of Wellington)Shaun Hendy Industrial Research Ltd (Lower Hutt)Stephen Joe Mathematics (The University of Waikato)Geoff Jones Statistics (Massey University Palmerston North)Ken Louie AgResearch (Ruakura)Ben Martin Mathematics (University of Canterbury)Mark McGuinness Mathematics (Victoria University of Wellington)Judi McWhirter Statistics (The University of Waikato)Donald Nield Engineering Science (The University of Auckland)Aroon Parshotam Landcare (Palmerston North)Alona Ben-Tal Mathematics (Massey University Albany)Garry Tee Mathematics (The University of Auckland)Wynand Verwoerd Mathematics and Statistics (Lincoln University)Marijcke Vlieg-Hulstman Mathematics (Massey University Palmerston North)

Web SitesThe homepage of the New Zealand Mathematical Society is

httpwwwmathwaikatoacnzNZMSNZMShtml (Webmaster stephenjmathwaikatoacnz)

The newsletter is available at httpIFSmasseyacnzmathnewsNZMSnewsshtml

Editorial enquiries and items for submission to this journal should be submitted as text or LATEX files to

rmclachlanmasseyacnz

ISSN 0110-0025

3

NZMS Newsletter No 95

PUBLISHERrsquoS NOTICE

This newsletter is the official organ of the New Zealand Mathematical Society Inc This issue was assembled by FionaRichmond and printed at Massey University The official address of the Society is

The New Zealand Mathematical Societyc- The Royal Society of New ZealandPO Box 598 Wellington New Zealand

However correspondence should normally be sent to the Secretary

Winston SweatmanInstitute of Information and Mathematical SciencesMassey UniversityPrivate Bag 102 904North Shore Mail CentreAucklandwsweatmanmasseyacnz

NZMS Council and Officers

President Professor Gaven Martin (Massey University Albany)Incoming Vice President Associate Professor Mick Roberts (Massey University Albany)Secretary Dr Winston Sweatman (Massey University Albany)Treasurer Dr Tammy Smith (Massey University Palmerston North)Councillors Dr Michael Albert (University of Otago) to 2006

Dr Shaun Hendy (Industrial Research Limited) to 2007Dr Warren Moors (The University of Auckland) to 2006Dr Rick Beatson (University of Canterbury) to 2008Dr Tammy Smith (Massey University Palmerston North) to 2008Dr Winston Sweatman (Massey University Albany) to 2007

Membership Secretary Dr John Shanks (University of Otago)Newsletter Editor Professor Robert McLachlan (Massey University Palmerston North)Legal Adviser Dr Peter Renaud (University of Canterbury)Archivist Emeritus Professor John Harper (Victoria University of Wellington)Visitor Liaison Dr Stephen Joe (The University of Waikato)Publications Convenor Dr David McIntyre (The University of Auckland)Webmaster Dr Stephen Joe (The University of Waikato)

Newsletter Correspondents

Sub-EditorsBook reviews Associate Professor Bruce van-Brunt (Massey University Palmerston North))Mathematical Miniatures Emeritus Professor John Butcher (The University of Auckland)

Honorary CorrespondentsMurray Black Mathematics (Auckland University of Technology)Michael Doherty Statistics NZ (Wellington)Lenette Grant Mathematics and Statistics (University of Otago)David Harte Statistics and Operations Research (Victoria University of Wellington)Shaun Hendy Industrial Research Ltd (Lower Hutt)Stephen Joe Mathematics (The University of Waikato)Geoff Jones Statistics (Massey University Palmerston North)Ken Louie AgResearch (Ruakura)Ben Martin Mathematics (University of Canterbury)Mark McGuinness Mathematics (Victoria University of Wellington)Judi McWhirter Statistics (The University of Waikato)Donald Nield Engineering Science (The University of Auckland)Aroon Parshotam Landcare (Palmerston North)Alona Ben-Tal Mathematics (Massey University Albany)Garry Tee Mathematics (The University of Auckland)Wynand Verwoerd Mathematics and Statistics (Lincoln University)Marijcke Vlieg-Hulstman Mathematics (Massey University Palmerston North)

Web SitesThe homepage of the New Zealand Mathematical Society is

httpwwwmathwaikatoacnzNZMSNZMShtml (Webmaster stephenjmathwaikatoacnz)

The newsletter is available at httpIFSmasseyacnzmathnewsNZMSnewsshtml

Editorial enquiries and items for submission to this journal should be submitted as text or LATEX files to

rmclachlanmasseyacnz

ISSN 0110-0025

3

EDITORIAL

EDITORIAL

AVE ATQUE VALE

The mathematics scene in New Zealand has changed enormously since I godwits return joined Masseyin 1994 Then there was a single maths conference in a year the Colloquium now more than 10 ayear are reported in the Newsletter plus several one-day meetings In the early 1990s there were 2 or 3PhD graduates per year Since 1997 there have been more than 14 per year In 1994 the only avenuefor significant research funding was the Public Good Science Fund which famously had no category forpure research in 2005 the Marsden Fund awarded $29m to 9 projects in the mathematical sciencesand the NZIMA awarded $12m to its semester programmes scholarships Maclaurin Fellows and smallgrants In the 2003 PBRF round mathematics scored well with 134 of staff rated A second only tophilosophy (Our average score of 36510 was ranked only 12th out of 41 subjects however) Of 222maths and stats staff 88 were rated A or B of 388 CSISIT staff 103 were rated A or B In otherwords every team of 4 AB staff in the country could each receive $80Kyear in research funding plusanother $80K from their PBRF earnings Pretty good

And yet (in the midst of life we are in death) somehow Irsquom still worried All this largesse and activityis fantastic for those of us who are involved in it but meanwhile the more basic concerns of our professionremain unfixed A quick rehearsal falling or uncertain rolls insufficient maths required in other quanti-tative degrees not enough maths teachers with maths degrees EFTS-grabbing within universities notenough maths graduates full stop These problems faced by maths departments around the world butin New Zealandrsquos funding system they have an immediate financial impact on us Moreover the fundingmodel imposes no reward for the quality of the education students receive quite the opposite How wouldour graduates fare if they were tested and ranked internationally To take just a single observation Inoted while at La Trobe University Melbourne (not one of Australiarsquos best but ranked similarly toMassey) that their engineering students have finished all of introductory differential equations by the endof their first yearmdashmaterial that is in our second year DE paper which is not even required for engineersApart from periodic textbook changes papers cut for efficiency and a glacial spread of computing andweb resources I have hardly noticed any changes in teaching since 1994

We could be called to task by either of our bill-payers the students and the government Australiahas just completed its first assessment of teaching and learning at Australiarsquos 38 universities distributing$50m to the top 15 The rankings were brutal with some strong research universities faring well (Mel-bourne ranked 3rd UQ 5th ANU 7th) and others very badly (UNSW 32nd Adelaide 36th) Many smalluniversities and former polytechs did well (Each university was ranked from 1 to 38 for graduatesrsquo viewsof the enhancement of their generic skills of teaching quality and of their overall satisfaction with theiruniversity program the percentage of graduates in full-time employment those continuing to furtherfull-time study drop-out rates and pass rates and the 7 ranks averaged) These results partly echo thesituation in the United States where in response to the statement lsquoThe professor makes the subject comealiversquo the small teaching-oriented liberal arts colleges like Reed scored at the top while all the famousresearch universities scored at the bottom Research-led teaching

The AMS took on (OK talked about) all these problems in its 1999 report Towards Excellence Lead-ing a Mathematics Department in the 21st Century (at wwwamsorgtowardsexcellence) The mathdepartment at UCLA was one of the case studies of successful departments 35 of all UCLA graduatesare in math one of the highest percentages in the US On closer inspection most of these studentsare studying operations research applied math computation teaching actuarial science managementhistory of science or premed Only 10 of their students (a class of 17) were actually majoring inlsquomathematicsrsquo In other words the department has been successful by hanging onto lots of turf not bypromoting traditional mathematics

With only a little squeak of reluctance I can see that this has to be the way to go UCLA also hosts theInstitute for Pure and Applied Mathematics one of several maths research institutes established recentlyLook at their schedule of semester-long programmes in 2000 genomicsgeometrically-based motions in2001 conformal field theorylarge scale networks in 2002 nanotechnologysymplectic geometry in 2003inverse problemsproteomics in 2004 multiscale geometry amp analysiscomputational astrophysics in2005 multiscale in material and biosciencecells amp materials in 2006 internet securityrandom shapesThe programmes of the NZIMA are scarcely less applied All around the world the groups that arereaching out and building bridges are thriving while the others are dying Speaking at a recent NSF

4

NZMS Newsletter No 95

Workshop on Math Majors (12805) James Keener from the University of Utah (and colleague of ourown James Sneyd) described his own math biology program and summed up by saying that

bull Interdisciplinarity (not only in Math Biology) has the potential to help revitalize mathematics

bull The current traditional academic culture does not encouragereward interdisciplinarity It is nottreasured and nourished Rather it is often viewed with suspicion andor disdain

bull Warning As interdisciplinary mathematics grows (and it will) mathematics departments mustdecide how to encourage this growth opportunity or they will lose it If not Mathematics thenwhere

Clearly this is already happening Even at the recent NZ Mathematics Colloquium 16 out of 59 talkswere on biology The real challenge will be to make the public and the students know that itrsquos happeningand to make them part of it

I thought I would find a contrary view in Gian-Carlo Rotarsquos Ten lessons for the survival of a mathe-matics department (found in his 1997 book Indiscrete Thoughts) remembering his statement that lsquomath-ematics is not and will never be flakyrsquo In other words backs against the wall Not quite

Flakiness is nowadays creeping into the sciences like a virus through a computer and it maybe the present threat to our civilisation Mathematics can save the world from the invasion ofthe flakes by unmasking them and by contributing some hard thinking You and I know thatmathematics is not and will never be flaky by definition This is the biggest chance we havehad in a long while to make a lasting contribution to the well-being of Science Let us not botchit as we did with the few other chances we have had in the past

If of thy mortal good thou art bereftAnd of thy slender store two loaves alone to thee are leftSell one and with the doleBuy hyacinths to feed thy soul

Bio- inter- nano- multi- these will be our bread but mathematics will remain our hyacinths

Robert McLachlanMassey University Palmerston North

5

PRESIDENTrsquoS COLUMN

PRESIDENTrsquoS COLUMN

Wersquore all going to die Avian influenza (Panicus tabloidus) is about to sweep the world or at least untilthe lighter British newspapers find something else to sensationalize As I write this I am on overseasleave in the Zoology Department of Oxford University and everybody including BBC TV is turning upto find out about bird flu Eventual death is the only event that occurs with probability one I think thatfollows from the Borel-Cantelli Lemma but what does bird flu have to do with mathematics Questionsof when how and how many cases are flying around and quantitative answers are demanded To do thisrequires some sort of mathematical model and we are then up against the common misconceptions Itdoesnrsquot matter that the human virus does not yet exist so nobody really knows how it will behave acomputer should be able to predict what is going to happen Isnrsquot that modeling Never mind wherethe parameters came from or what assumptions are made look at the results The best bet is thatsomething similar to the H5N1 virus that killed 20ndash40 million (according to the scientific literature but50ndash100 million according to the papers) in the 1918 pandemic will emerge A model can be set-up usingthat assumption as long as the basis is made explicit and modifications are made as better informationbecomes available But a model requires a computer and some graphical output to be believed at whichstage the decision makers get carried away with the results and forget to question the assumptions Thesolution of a differential equation is often seen as too theoretical a view reinforced when assumptionsare explicit and perhaps questionable

I wasted two days on what should be a lesson for the lsquocomputers are modelingrsquo brigade last week butthey are not usually NZMS members so they wonrsquot benefit from hearing the tale As part of a Matlabprogram I was computing the eigenvalues of three different matrices I was doing this because they arosein different parts of the model and I have a non-trivial proof that they have the same spectrum Myproblem was that Matlab calculated different eigenvalues for each The time was wasted checking andrechecking my analytic result then carefully checking the code then trying to come up with programmodifications to provoke the computer into confessing where the error was Finally I noticed a subscriptlsquoirsquo coded as a lsquo1rsquo in a dense part of the program and fixing this made the eigenvalues coincide Thelesson is that with either lsquoirsquo or lsquo1rsquo in the program all the results produced were totally reasonable I didnrsquothave complex numbers of people infected or flu behaving in an un-flu-like manner Without the extramathematics no warning bells would have sounded With a flashy front-end I could have convinced thepolicymakers into advocating bad decisions How many computer simulation results look reasonable butare produced by a program with a similar gremlin in its interior meaning that the results are rubbish

The NZMS has just honoured two applied mathematicians that are definitely not of the lsquocompute andrunrsquo camp By the time you read this Gaven Martin NZMS Incoming Vice-President will have pre-sented two NZMS research awards at the RSNZ Awards Dinner The awards go to James Sneyd of TheUniversity of Auckland ldquofor extensive and celebrated contributions in mathematical biology demonstrat-ing approaches that combine originality with biological realismrdquo and to Robert McLachlan of MasseyUniversity ldquofor creative pioneering work leading to deep advances in the theory of geometric numericalintegration and its application in the study of dynamical systemsrdquo Our congratulations go to Jamesand Robert for this recognition of their outstanding contributions to mathematics But therersquos moreWe are not alone in our recognition James Sneyd has been made a Fellow of the Royal Society of NewZealand The RSNZ describe him as ldquoone of the worldrsquos leading mathematical biologists His modellingis characterised by ingenuity technical prowess and a clear understanding of biological phenomena at anappropriate level of detailrdquo Robert McLachlan has also received the Individual Researcher Award fromMassey University for 2005 the universityrsquos website states that ldquoHe is acknowledged by leading figuresin the field as simply brilliant and there can be no question about the high regard that he is held in byhis peersrdquo

The NZMS has two new fellows Igor Boglaev and Kee Teo both of Massey University in PalmersonNorth I would like to congratulate Igor and Kee on their achievements and thank the committee forgiving their time to assess the applications The NZMS council has also decided to make John Shanksof the University of Otago an Honorary Member of the Society in recognition of his many years of workas the membership secretary Our thanks go to John for his efforts on our behalf

A final bouquet to Robert McLachlan for editing the NZMS newsletter since 2000 This is his lastissue and he deserves our thanks for the outstanding way in which he has carried out the task

Mick Roberts

6

NZMS Newsletter No 95

LOCAL NEWS

AGRESEARCH

Kumar Vetharaniam travelled to the USA in Julywhere he was an invited speaker at the Ameri-can Dairy Science Associationrsquos Lactation BiologySymposium in the ADSA-ASAS-CSAS Joint Meet-ing Cincinnati Ohio July 24ndash28 2005

The title of his talk was lsquoPeak and persistencythe mathematics of the lactation curversquo reportingon joint work with S R Davis and E S Kolver

Rajiv Chaturvedi also visited the USA recentlyand writes

I recently attended two conferences whichbrought to focus the continuing role mathematicsand modeling has been playing in biological sci-ences

The first one was the Sixth International Con-ference on Systems Biology held from October 19ndash24 2005 in Boston Massachusetts USA (web sitehttpcsbimiteduicsb-2005) Held jointlyat the Harvard Medical and the MIT the con-ference comprised of invited and contributed talksand posters tutorials and workshops The sub-ject areas covered a wide range of tools and tech-niques for purposes ranging from bringing organi-zation into the explosive growth of data in biologi-cal sciences to predictive application of mathemat-ical techniques My presentation in this conferencewas ldquoNetwork modeling of symbiotic metabolic in-teractions of Ryegrass and its Endophyterdquo by Ra-jiv Chaturvedi Tanya Soboleva Anthony Parsonsand Susanne Rasmussen (all from AgResearch Lim-ited)

The second conference I attended was the bian-nual ldquoBiocomplexityrdquo workshops organized by aconsortium of universities in Indiana USA Thistime its theme was ldquoApplications of Methods ofStochastic Systems and Statistical Physics in Bi-ologyrdquo and it was held at University of NotreDame Notre Dame IN USA from October 28ndash30 2005 (web site httpwwwndedusimicsbwrkshp2005html) The deliberations ranged fromdiscussing theoretical properties of mathematicalmodels that have been used in many biologicalproblems to application of these models to explainbiological observations I talked about the applica-tion of a hybrid model that I had worked on ear-lier for skeletal patterning of an avian limb bud inthe Limb Development workshop that was held atthe end of the conference This model combines astochastic discrete model for cells and a determinis-tic continuum model for diffusible morphogens witha regulatory network to describe the complex bio-

logical phenomena of skeletal patterning in a grow-ing limb domain

Ken Louie

THE UNIVERSITY OFAUCKLAND

Department of Computer Science

Dr Beryl Plimmer has been the Director of Pro-grammes and now she has been appointed asSenior Lecturer in Human Computer InteractionBeryl has particular interests in pen-based inter-faces and particularly in the use of sketch-basedapproaches to early design of computer systems

Jim Warren has arrived to take up his appoint-ment as Professor of Health Informatics Thatis a joint position in Computer Science and theSchool of Population Health and he will be basedat Tamaki Campus

Bakh Khousssainov has been elected a Fellow ofthe Royal Society of New Zealand

John Hosking has been Head of Department fortwo terms and Robert Amor will succeed him on1 February 2006

Reinhard Klette and Robert Amor were hostedat the Microsoft Research Asia Faculty Summit2005 in China at the end of October

Alexei Drummond and Dr David Bryant (Math-ematics) have received a Marsden Fund grant of$555000 for their research project on ldquoThe statis-tics of phylogenetic networksrdquo Hans Guesgenhas been awarded a one-year grant from Kiwi-plan Ltd for a project on optimization of packingdesigns Both of the Departmentrsquos major FRSTgrants (Clark Thomborson and John Grundy plusJohn Hosking) have obtained rollover for an ad-ditional year John Hosking Janet Copsey andStephen Whiteside have received a VCUDF Grantof $100000 for ldquoRaising strategic understandingand application of ICT at The University of Auck-landrdquo

Dr Bodo Rosenhahn has been a Postdoctoral Fel-low at CITR for two years At the 27th annualDAGM symposium (of the German Austrian andSwiss Associations for Pattern Recognition) hispaper ldquoA system for marker-less human motion es-timationrdquo reported on joint research of ComputerScience and Sports Sciences at Tamaki campus(in collaboration with Universitaet Saarbruecken)That paper was awarded the Main DAGM Prize2005 ldquoin appreciation of outstanding work effortand enthusiasm shown in the preparation and pre-sentation of the paperrdquo In November Bodo became

7

PRESIDENTrsquoS COLUMN

PRESIDENTrsquoS COLUMN

Wersquore all going to die Avian influenza (Panicus tabloidus) is about to sweep the world or at least untilthe lighter British newspapers find something else to sensationalize As I write this I am on overseasleave in the Zoology Department of Oxford University and everybody including BBC TV is turning upto find out about bird flu Eventual death is the only event that occurs with probability one I think thatfollows from the Borel-Cantelli Lemma but what does bird flu have to do with mathematics Questionsof when how and how many cases are flying around and quantitative answers are demanded To do thisrequires some sort of mathematical model and we are then up against the common misconceptions Itdoesnrsquot matter that the human virus does not yet exist so nobody really knows how it will behave acomputer should be able to predict what is going to happen Isnrsquot that modeling Never mind wherethe parameters came from or what assumptions are made look at the results The best bet is thatsomething similar to the H5N1 virus that killed 20ndash40 million (according to the scientific literature but50ndash100 million according to the papers) in the 1918 pandemic will emerge A model can be set-up usingthat assumption as long as the basis is made explicit and modifications are made as better informationbecomes available But a model requires a computer and some graphical output to be believed at whichstage the decision makers get carried away with the results and forget to question the assumptions Thesolution of a differential equation is often seen as too theoretical a view reinforced when assumptionsare explicit and perhaps questionable

I wasted two days on what should be a lesson for the lsquocomputers are modelingrsquo brigade last week butthey are not usually NZMS members so they wonrsquot benefit from hearing the tale As part of a Matlabprogram I was computing the eigenvalues of three different matrices I was doing this because they arosein different parts of the model and I have a non-trivial proof that they have the same spectrum Myproblem was that Matlab calculated different eigenvalues for each The time was wasted checking andrechecking my analytic result then carefully checking the code then trying to come up with programmodifications to provoke the computer into confessing where the error was Finally I noticed a subscriptlsquoirsquo coded as a lsquo1rsquo in a dense part of the program and fixing this made the eigenvalues coincide Thelesson is that with either lsquoirsquo or lsquo1rsquo in the program all the results produced were totally reasonable I didnrsquothave complex numbers of people infected or flu behaving in an un-flu-like manner Without the extramathematics no warning bells would have sounded With a flashy front-end I could have convinced thepolicymakers into advocating bad decisions How many computer simulation results look reasonable butare produced by a program with a similar gremlin in its interior meaning that the results are rubbish

The NZMS has just honoured two applied mathematicians that are definitely not of the lsquocompute andrunrsquo camp By the time you read this Gaven Martin NZMS Incoming Vice-President will have pre-sented two NZMS research awards at the RSNZ Awards Dinner The awards go to James Sneyd of TheUniversity of Auckland ldquofor extensive and celebrated contributions in mathematical biology demonstrat-ing approaches that combine originality with biological realismrdquo and to Robert McLachlan of MasseyUniversity ldquofor creative pioneering work leading to deep advances in the theory of geometric numericalintegration and its application in the study of dynamical systemsrdquo Our congratulations go to Jamesand Robert for this recognition of their outstanding contributions to mathematics But therersquos moreWe are not alone in our recognition James Sneyd has been made a Fellow of the Royal Society of NewZealand The RSNZ describe him as ldquoone of the worldrsquos leading mathematical biologists His modellingis characterised by ingenuity technical prowess and a clear understanding of biological phenomena at anappropriate level of detailrdquo Robert McLachlan has also received the Individual Researcher Award fromMassey University for 2005 the universityrsquos website states that ldquoHe is acknowledged by leading figuresin the field as simply brilliant and there can be no question about the high regard that he is held in byhis peersrdquo

The NZMS has two new fellows Igor Boglaev and Kee Teo both of Massey University in PalmersonNorth I would like to congratulate Igor and Kee on their achievements and thank the committee forgiving their time to assess the applications The NZMS council has also decided to make John Shanksof the University of Otago an Honorary Member of the Society in recognition of his many years of workas the membership secretary Our thanks go to John for his efforts on our behalf

A final bouquet to Robert McLachlan for editing the NZMS newsletter since 2000 This is his lastissue and he deserves our thanks for the outstanding way in which he has carried out the task

Mick Roberts

6

NZMS Newsletter No 95

LOCAL NEWS

AGRESEARCH

Kumar Vetharaniam travelled to the USA in Julywhere he was an invited speaker at the Ameri-can Dairy Science Associationrsquos Lactation BiologySymposium in the ADSA-ASAS-CSAS Joint Meet-ing Cincinnati Ohio July 24ndash28 2005

The title of his talk was lsquoPeak and persistencythe mathematics of the lactation curversquo reportingon joint work with S R Davis and E S Kolver

Rajiv Chaturvedi also visited the USA recentlyand writes

I recently attended two conferences whichbrought to focus the continuing role mathematicsand modeling has been playing in biological sci-ences

The first one was the Sixth International Con-ference on Systems Biology held from October 19ndash24 2005 in Boston Massachusetts USA (web sitehttpcsbimiteduicsb-2005) Held jointlyat the Harvard Medical and the MIT the con-ference comprised of invited and contributed talksand posters tutorials and workshops The sub-ject areas covered a wide range of tools and tech-niques for purposes ranging from bringing organi-zation into the explosive growth of data in biologi-cal sciences to predictive application of mathemat-ical techniques My presentation in this conferencewas ldquoNetwork modeling of symbiotic metabolic in-teractions of Ryegrass and its Endophyterdquo by Ra-jiv Chaturvedi Tanya Soboleva Anthony Parsonsand Susanne Rasmussen (all from AgResearch Lim-ited)

The second conference I attended was the bian-nual ldquoBiocomplexityrdquo workshops organized by aconsortium of universities in Indiana USA Thistime its theme was ldquoApplications of Methods ofStochastic Systems and Statistical Physics in Bi-ologyrdquo and it was held at University of NotreDame Notre Dame IN USA from October 28ndash30 2005 (web site httpwwwndedusimicsbwrkshp2005html) The deliberations ranged fromdiscussing theoretical properties of mathematicalmodels that have been used in many biologicalproblems to application of these models to explainbiological observations I talked about the applica-tion of a hybrid model that I had worked on ear-lier for skeletal patterning of an avian limb bud inthe Limb Development workshop that was held atthe end of the conference This model combines astochastic discrete model for cells and a determinis-tic continuum model for diffusible morphogens witha regulatory network to describe the complex bio-

logical phenomena of skeletal patterning in a grow-ing limb domain

Ken Louie

THE UNIVERSITY OFAUCKLAND

Department of Computer Science

Dr Beryl Plimmer has been the Director of Pro-grammes and now she has been appointed asSenior Lecturer in Human Computer InteractionBeryl has particular interests in pen-based inter-faces and particularly in the use of sketch-basedapproaches to early design of computer systems

Jim Warren has arrived to take up his appoint-ment as Professor of Health Informatics Thatis a joint position in Computer Science and theSchool of Population Health and he will be basedat Tamaki Campus

Bakh Khousssainov has been elected a Fellow ofthe Royal Society of New Zealand

John Hosking has been Head of Department fortwo terms and Robert Amor will succeed him on1 February 2006

Reinhard Klette and Robert Amor were hostedat the Microsoft Research Asia Faculty Summit2005 in China at the end of October

Alexei Drummond and Dr David Bryant (Math-ematics) have received a Marsden Fund grant of$555000 for their research project on ldquoThe statis-tics of phylogenetic networksrdquo Hans Guesgenhas been awarded a one-year grant from Kiwi-plan Ltd for a project on optimization of packingdesigns Both of the Departmentrsquos major FRSTgrants (Clark Thomborson and John Grundy plusJohn Hosking) have obtained rollover for an ad-ditional year John Hosking Janet Copsey andStephen Whiteside have received a VCUDF Grantof $100000 for ldquoRaising strategic understandingand application of ICT at The University of Auck-landrdquo

Dr Bodo Rosenhahn has been a Postdoctoral Fel-low at CITR for two years At the 27th annualDAGM symposium (of the German Austrian andSwiss Associations for Pattern Recognition) hispaper ldquoA system for marker-less human motion es-timationrdquo reported on joint research of ComputerScience and Sports Sciences at Tamaki campus(in collaboration with Universitaet Saarbruecken)That paper was awarded the Main DAGM Prize2005 ldquoin appreciation of outstanding work effortand enthusiasm shown in the preparation and pre-sentation of the paperrdquo In November Bodo became

7

NZMS Newsletter No 95

LOCAL NEWS

AGRESEARCH

Kumar Vetharaniam travelled to the USA in Julywhere he was an invited speaker at the Ameri-can Dairy Science Associationrsquos Lactation BiologySymposium in the ADSA-ASAS-CSAS Joint Meet-ing Cincinnati Ohio July 24ndash28 2005

The title of his talk was lsquoPeak and persistencythe mathematics of the lactation curversquo reportingon joint work with S R Davis and E S Kolver

Rajiv Chaturvedi also visited the USA recentlyand writes

I recently attended two conferences whichbrought to focus the continuing role mathematicsand modeling has been playing in biological sci-ences

The first one was the Sixth International Con-ference on Systems Biology held from October 19ndash24 2005 in Boston Massachusetts USA (web sitehttpcsbimiteduicsb-2005) Held jointlyat the Harvard Medical and the MIT the con-ference comprised of invited and contributed talksand posters tutorials and workshops The sub-ject areas covered a wide range of tools and tech-niques for purposes ranging from bringing organi-zation into the explosive growth of data in biologi-cal sciences to predictive application of mathemat-ical techniques My presentation in this conferencewas ldquoNetwork modeling of symbiotic metabolic in-teractions of Ryegrass and its Endophyterdquo by Ra-jiv Chaturvedi Tanya Soboleva Anthony Parsonsand Susanne Rasmussen (all from AgResearch Lim-ited)

The second conference I attended was the bian-nual ldquoBiocomplexityrdquo workshops organized by aconsortium of universities in Indiana USA Thistime its theme was ldquoApplications of Methods ofStochastic Systems and Statistical Physics in Bi-ologyrdquo and it was held at University of NotreDame Notre Dame IN USA from October 28ndash30 2005 (web site httpwwwndedusimicsbwrkshp2005html) The deliberations ranged fromdiscussing theoretical properties of mathematicalmodels that have been used in many biologicalproblems to application of these models to explainbiological observations I talked about the applica-tion of a hybrid model that I had worked on ear-lier for skeletal patterning of an avian limb bud inthe Limb Development workshop that was held atthe end of the conference This model combines astochastic discrete model for cells and a determinis-tic continuum model for diffusible morphogens witha regulatory network to describe the complex bio-

logical phenomena of skeletal patterning in a grow-ing limb domain

Ken Louie

THE UNIVERSITY OFAUCKLAND

Department of Computer Science

Dr Beryl Plimmer has been the Director of Pro-grammes and now she has been appointed asSenior Lecturer in Human Computer InteractionBeryl has particular interests in pen-based inter-faces and particularly in the use of sketch-basedapproaches to early design of computer systems

Jim Warren has arrived to take up his appoint-ment as Professor of Health Informatics Thatis a joint position in Computer Science and theSchool of Population Health and he will be basedat Tamaki Campus

Bakh Khousssainov has been elected a Fellow ofthe Royal Society of New Zealand

John Hosking has been Head of Department fortwo terms and Robert Amor will succeed him on1 February 2006

Reinhard Klette and Robert Amor were hostedat the Microsoft Research Asia Faculty Summit2005 in China at the end of October

Alexei Drummond and Dr David Bryant (Math-ematics) have received a Marsden Fund grant of$555000 for their research project on ldquoThe statis-tics of phylogenetic networksrdquo Hans Guesgenhas been awarded a one-year grant from Kiwi-plan Ltd for a project on optimization of packingdesigns Both of the Departmentrsquos major FRSTgrants (Clark Thomborson and John Grundy plusJohn Hosking) have obtained rollover for an ad-ditional year John Hosking Janet Copsey andStephen Whiteside have received a VCUDF Grantof $100000 for ldquoRaising strategic understandingand application of ICT at The University of Auck-landrdquo

Dr Bodo Rosenhahn has been a Postdoctoral Fel-low at CITR for two years At the 27th annualDAGM symposium (of the German Austrian andSwiss Associations for Pattern Recognition) hispaper ldquoA system for marker-less human motion es-timationrdquo reported on joint research of ComputerScience and Sports Sciences at Tamaki campus(in collaboration with Universitaet Saarbruecken)That paper was awarded the Main DAGM Prize2005 ldquoin appreciation of outstanding work effortand enthusiasm shown in the preparation and pre-sentation of the paperrdquo In November Bodo became

7

LOCAL NEWS

the Chair of a research group at the Max-Planck In-stitute in Saarbruecken and he intends to maintainhis links with our Department

Yang Jia has completed his PhD on ldquoFast StringParsing and its Application in Information andSimilarity Measurementrdquo and Linjiang Yu hascompleted his PhD on ldquoPartially Supervised Tex-ture Segmentation and Retrievalrdquo

Nodira Khoussainova now aged 18 is the daugh-ter of Muharram and Bakh both of whom are nowoverseas on leave After graduating BSc with 1st-class honours in computer science Nodira gained aresearch internship at Microsoft headquarters Sheis now in the first year of doctoral studies at theUniversity of Washington In Auckland the NorthHarbour Club Tower presents AIMES Awards toyoung people (aged 25 or younger) from North Har-bour who have shown exceptional talent in the artsinformation technology and science music educa-tion and sport The Khoussainov family came backto Auckland for the 2005 AIMES Awards whichwere presented at the Bruce Mason Centre on Oc-tober 8th Nodira received the overall award for ex-cellence and also the award for excellence in infor-mation technology and computer science totalling$17000

Seminars

Veikko Keranen ldquoAbelian pattern-free wordsrdquo

Peter Gacs ldquoUniform tests of algorithmicrandomness over a general spacerdquo

Simson Garfinkel ldquoJohnny 2 a user test ofkey continuity management with SMIMEand Outlook Expressrdquo

Gyori Sandor ldquoTree algorithm for collisionresolutionrdquo

Paul Vitanyi ldquoAutomatic meaning discoveryusing Googlerdquo

Osmar Zaiane ldquoThe potential of associativeclassifiersrdquo

Rebecca Weber ldquoKurtz 2-randomnessrdquo

Professor Douglas Bridges (University ofCanterbury) ldquoApartness on latticesrdquo

Anirban Majumdar ldquoManufacturing opaquepredicates for control-flow obfuscationrdquo

Faith Ellen Fich ldquoHow hard is it to take asnapshotrdquo

Garry J Tee

Department of Mathematics

Dr Antonius Frederick Maria ter Elst (EindhovenUniversity of Technology) has accepted the offer ofa Lectureship in our Department We expect to seehim in the new year

Bill Barton spent two days visiting Polytechnicsand Universities in Singapore for the Faculty of Sci-ence investigating possible articulation of studentsfrom those institutions

Anthony Blaom had been on unpaid parentalleave for a year and he has decided not to returnto the Department He has been appointed as Hon-orary Researcher

David Bryant (amp Alexei Drummond in the De-partment of Computer Science) have won a Mars-den Research Grant of $555000 for their projecton ldquoThe statistics of phylogenetic networksrdquo

Bruce Calvert has received a $4500 grant fromthe Staff Research Fund for ldquoWinner-take-all neu-ral networksrdquo

Colin Fox has received a $5000 research grantfrom ISAT Linkages Fund for ldquoMeshing multigridand MCMCrdquo Colin Fox amp James Sneyd have re-ceived a $9000 grant from the Staff Research Fundfor ldquoModelling the contraction of airway smoothmusclerdquo

David Gauld has won a Marsden Research Grantof $390000 for his project on ldquoDynamics on non-metrisable surfaces and manifoldsrdquo He gave twoinvited lectures at the 9th Galway Topology Collo-quium in Belfast and his 1982 book ldquoDifferentialTopology An Introductionrdquo has been republishedby Dover in its reprint series

Rod Gover has received a Researchersrsquo StrategicSupport Initiative Award of $49100

Sina Greenwood has received a New StaffUARC Grant of $6500 Sina Greenwood Han-nah Bartholomew amp Colleen McMurchy-Pilkington(Faculty of Education) won $3472 from the EqualOpportunities Office for a longitudinal study ofMaori mathematics students in Northland

Mike Meylan has received a New Staff UARCGrant of $8600 for ldquoWave scattering by infinite andsemi-infinite arraysrdquo

Boris Pavlov has received a research grant fromISAT Linkages Fund for ldquoTransport properties andmathematical modelling of quantum networksrdquoand he gave an invited lecture at the College ofSciences Massey University

Philip Sharp has received a $1750 grant from theStaff Research Fund for ldquoMulti-pole methods forsimulating the solar systemrdquo

8

NZMS Newsletter No 95

Jozef Siran has received a grant from the StaffResearch Fund

Arkadii Slinko has become a founding memberof the ARC Economic Design Network which re-ceived funding ($AU300000 per year) from theAustralian Research Council for the next five yearsHe will be a semi-funded invited speaker at the2nd Pan-Pacific Conference on Game Theory onNovember 24ndash26 at Taipei

James Sneyd has been elected a Fellow of theRoyal Society of New Zealand and he has beenawarded a research grant from the Universityof Massachusetts Medical Center James Sneydamp Robert McLachlan (Massey University) havejointly won the NZMS Research Award for 2005James Sneyd amp Colin Fox have received a $9000grant from the Staff Research Fund for ldquoModellingthe contraction of airway smooth musclerdquo

Mike Thomas returned from leave during whichhe gave seminars or workshops at the Chinese HighSchool of Singapore University of Swansea War-wick University Open University Plymouth Uni-versity and the University of Grenoble He haswon a $20k+ grant to use the Universityrsquos nuclearMagnetic Resonance Imaging machine to examinebrain functioning of people while they do mathe-matical tasks He is linking with people in Psychol-ogy and a researcher in Turin And Mike has beenappointed as ldquoSpecialist Adviserrdquo to the PBRF Re-view panels on Mathematics Education

Shixiao Wang has received a grant from the NewStaff Research Fund

A Departmental professorsrsquo committee has allo-cated grants to Bill Barton Colin Fox Sina Green-wood Vivien Kirk Mike Meylan Philip SharpArkadii Slinko Steve Taylor and Mike Thomas to-talling $27000

Visitors

Professor Len Bos (University of Calgary)

Dr Andreas Cap (University of Vienna)

Dr Heiko Dietrich (Technische Universitaet zuBraunschweig)

Professor Bettina Eick (TechnischeUniversitaet zu Braunschweig)

Professor George Havas (University ofQueensland)

Dr Frank Himstedt (Munich University ofTechnology)

Dr Carolyn Kieran (University of Quebec aMontreal)

Dr Ville Kolehmainen (University of KuopioFinland)

Dr Martin Macaj (Comenius University)

Professor John Mason (Open University)

Professor Mike Newman (ANU)

Professor Cheryl Praeger (UWA)

Dr Anne Watson (Oxford University)

Professor Wolfgang Willems (UniversitaetMagdeburg)

Professor Mariusz Wodzicki (University ofCalifornia - Berkeley)

William Rowan Hamiltonrsquos 200th birthdaywas celebrated around the world on 3 August2005 Hamiltonrsquos sister Sydney Margaret Hamil-ton (1811ndash1889) became his principal astronomi-cal assistant She settled in Auckland in 1875 andwas befriended by Sir George Grey who was thenstudying quaternions

The NZMS and the New Zealand Institute ofPhysics sponsored a public lecture by Garry Teeon William Rowan Hamilton given on Hamiltonrsquos200th birthday That lecture was repeated at TheUniversity of Waikato on October 27 A Librarydisplay was set up in The University of AucklandGeneral Library (for July and August) includingcopies of some of the very rich collection of Hamil-tonrsquos manuscripts and publications in AucklandCity Central Library

Our Department hosted the 2005 Albany-Auckland-Waikato Applied Mathematics Day onFriday September 9 The following lectures weregiven

Dr Garry Tee ldquoSurface integrals overellipsoidal segmentrdquo

Inga Wang ldquoA model for smooth musclecontractions in the lungrdquo

Basil Sinescu ldquoGood rank-1 lattice rules basedon the general weighted star discrepancyrdquo

Professor Graeme Wake (Massey University(Albany)) ldquoA model of transientcell-growthrdquo

Elan Gin ldquoCellular calcium and buffersrdquo

Leng Leng Lim ldquoModelling of volcanic ashfallrdquo

Professor John Butcher ldquoTowards efficientgeneral linear methodsrdquo

9

LOCAL NEWS

We took advantage of the presence of a number ofvisitors at The University of Auckland to hold a 2-day workshop on Group Theory on November 1 and2 That meeting acknowledged the 65th birthdayon November 2 of one of our frequent visitors andcollaborators Professor Charles Leedham-Greenfrom Queen Mary College University of London

The following lectures were presented at theWorkshop

Professor Marston Conder (Auckland)ldquoConnectedness of generating sets for finitegroupsrdquo

Professor Bettina Eick (TechnischeUniversitaet zu Braunschweig) ldquoPeriodicityand the automorphism group conjecturerdquo

Dr Ben Martin (University of Canterbury)ldquoCoclass p-adic integration and eliminationof imaginariesrdquo

Professor Mike Newman (ANU) ldquoGroupswith exactly three involutionsrdquo

Professor George Havas (University ofQueensland) ldquo4-Engel groups are locallynilpotentrdquo

Professor Gaven Martin (Massey University(Albany)) ldquoAutomorphisms of hyperbolicgroups and open maps of manifoldsrdquo

Dr Andre Nies (Department of ComputerScience) ldquoGroups with finite descriptionsrdquo

Dr Henrik Baarnhielm (London)ldquoConstructive recognition of the Suzukigroupsrdquo

Associate Professor Jozef Siran (Auckland)ldquoRegular maps on a given surfacemdasha surveyrdquo

The Workshop concluded with a special lectureby

Charles Leedham-Green entitled ldquoApologiapro vita suardquo

We welcome Laura Ciobanu to the Departmentas a University of Auckland Postdoctoral Fellowfor two years She is a a recent graduate of Rut-gers University and her research interests are inalgebra Caroline Poisard has been appointed to apost-doctoral position for one year starting in Jan-uary She will work with Bill Barton in the area ofEthnomathematics

Mala Nataraj has enrolled for a PhD concerningVedic Mathematics and Garry Nathan has enrolled

for a PhD on Undergraduate Conceptions of Rea-soning and Proof

Matthew Auger and Elan Gin have beenawarded UoA guaranteed doctoral scholarships

On November 4 the prominent businessmanMichael Erceg was flying a business associatefrom Auckland to Queenstown The helicopterdisappeared in very stormy conditions and 15 dayslater the wreckage was found near Raglan DavidGauld had sent the following message around ourDepartment

Dear colleagues

Perhaps not many of you are aware that the miss-ing businessman Mike Erceg was a student in theDepartment as well as a colleague

Mike completed his BSc(Hons) and MSc degreesin this Department gaining a Fowlds MemorialPrize for the top masters student in the Facultyof Science in his year before heading to the Univer-sity of California at Berkeley where he completedhis PhD in Functional Analysis in 1981 After hisreturn to New Zealand he taught part-time in theDepartment for several years and at least one ofour colleagues recalls with fondness his graduatecourse in Functional Analysis taught to him byMike When his work in the family vineyard be-came too onerous he stopped teaching in the De-partment

More recently with a group of Industrial Math-ematics staff I visited Mikersquos business premiseswhere we investigated whether some sort of projectfor the IM Programme might be set up there Hepaid a return visit to the Tamaki Campus with anumber of his staff to talk to IM students

Mike was a welcoming and gracious host whenwe visited him and I for one am very saddened byhis disappearance last Friday

Regards

David Gauld

Seminars

Professor Winfried Kohnen (Heidelberg)ldquoOn infinite product expansions of modularfunctionsrdquo

Dr Jana Siagiova ldquoApplications of coverings inCayley maps and in the degree-diameterproblemrdquo

Professor David Gauld ldquoMOPping uprdquo

10

NZMS Newsletter No 95

Dr Primoz Potocnik ldquoTetravalentedge-transitive graphs and related topicsrdquo

Dr Tsukasa Yashiro ldquoDiagrammaticapproaches to surface-knots - 1-handles andtriple pointsrdquo

Dr Anthony D Blaom ldquoThe ghost ofsymmetry in a curved worldrdquo

Professor Mariusz Wodzicki (University ofCaliforniamdashBerkeley) ldquoExotic tracesrdquo

Dr Sina Greenwood ldquoCharacterisingcontinuous functions on connected compactspacesrdquo

Professor Wolfgang Willems (UniversitaetMagdeburg) ldquoSome open problems inmodular representation theoryrdquo ldquoAre cycliccodes asymptotically goodrdquo and ldquoA surveyof problems and methods in coding theoryrdquo

Dr Frank Himstedt (TU Munich)ldquoLow-dimensional representations ofSteinbergrsquos triality groupsrdquo

Dr Sasa Radomirovic (Rutgers University)ldquoCusp forms over function fields and modularsymbolsrdquo

Dr Andreas Cap (University of Vienna)ldquoInfinitesimal automorphisms anddeformations of parabolic geometriesrdquo

Professor Cheryl Praeger (UWA) ldquoGroupsprobability algorithms computing withgiantsrdquo

Dr Laura Ciobanu ldquoFixed subgroups in freegroupsrdquo

Professor CK Raju (University of BhopalIndia) ldquoSeries expansions and thecomputation of Pi in India from Aryabhattato Yuktideepikardquo and ldquoThe Indian origins ofthe calculus and its transmission to Europeprior to Newton and Leibniz Part 2 Lessonsfor mathematics educationrdquo

Christopher Hay ldquoMetrizability of compactconvex sets under certain criteriardquo

Dr Hyuck Chung ldquoModelling timber-basedfloor structuresrdquo

David Choquenot (Landcare Research)ldquoMathematical models and wildlifepopulation dynamicsrdquo

Daniel Watzenig (Graz University ofTechnology) ldquoElectrical capacitancetomography at Graz University ofTechnology state-space representations andparticle filteringrdquo

Dr Carlo Laing (Massey University (Albany))ldquoEquation-free modelling some neuralexamplesrdquo

Dr David Bryant ldquo Continuous and (mostly)tractable models for the variation ofevolutionary ratesrdquo

Dr Emily Lane (UCLA) ldquoWave-currentinteractions and shore-connected barsrdquo

Professor Roman Nedela (Slovak Academy ofSciences) ldquoEnumeration of maps andhypermaps with given genus and givennumber of edgesrdquo

Garry J Tee

Department of Statistics

Russell Millar appeared on the television programldquoJohn Campbell Liverdquo in early July His briefingwas to tell the audience the probability of winningLottomdashalthough we all know that if Russell reallyhad inside Lotto information wersquod be advertisingfor a new lecturer The segment was created byJacqui Brown and her crew and was filmed in a lec-ture theatre on the Tamaki campus The style waslight-hearted but nonetheless demonstrated somesolid statistical points including conditional prob-abilities and misuse of the ldquolaw of averagesrdquo Rus-sellrsquos night of fame has been recorded for posterityand it will be played in our first-year lectures foryears to come

Russell Millar and Marti Anderson have been di-viding their time between Perth Auckland andAlaska in their work on fisheries and multivariateecological analysis

The Rodent Invasion Research Group spent atotal of two weeks rat-catching in the Bay of Is-lands With the Department of ConservationSteven Miller helped set up the traps then thenext week Rachel Fewster went to bag the rats withStephen Cope as cameraman The trip was excep-tionally successful with a total of 360 rats baggedfor the DNA project

Doctoral student James Russell spent time inBrazil to give a student finalist talk at the Soci-ety for Conservation Biology He then travelled toOregon for the Association of Pacific Rim Univer-sities Annual Doctoral Students Conference on the

11

LOCAL NEWS

multidisciplinary theme ldquoMoving Towards a Sus-tainable Futurerdquo A paper on ldquoIntercepting thefirst rat ashorerdquo written by James Russell andothers from the Rodent Invasion ProjectResearchGroup (DR Towns SH Anderson amp MN Clout)tells of a rat which was released on Motuhoropapa(one of the uninhabited Noises Islands) which thenswam 400 metres to the island Otata That pa-per was published in NATURE 437(7062) p1107and it has attracted attention around the worldThe story was run by over 100 international newsagencies from the UK Independent to WashingtonNational Public Radio and it also included a fea-ture on NZ TV news

Tim Langlois has gained his PhD for his thesisldquoInfluence of reef-associated predators on adjacentsoft-sediment communitiesrdquo He has been based atthe Leigh Marine Laboratory Yuichi Hirose hascompleted his PhD

An NZIMA Postgraduate Scholarship has beenawarded to Adam Smith for a Masters thesisproject at The University of Auckland (from July2005) on the statistical validation of the NZ MarineEnvironment Classification under the supervisionof Drs Marti Anderson and Clinton Duffy MikeManning who is studying for his MSc while work-ing for NIWA in Wellington appeared on ldquo60 Min-utesrdquo in April in a piece about the satellite taggingof white sharks

IASS 55 was organised and run by this Depart-ment and held at the Maritime Museum in Auck-land New Zealand Alastair Scott chaired some ofthe sessions CR Rao spoke to a packed room inthis Department In his talk he covered a historyof statistics

From June 2 to 7 the SRTL-4 conference washeld at Grafton Hall It was organised largely byRoss Parsonage and Maxine Pfannkuch along withinput from Dani Ben-Zvi Joan Garfield and oth-ers Rachel Cunliffe Ross Ihaka Chris Wild MikeForster and Ilze Ziedins attended ISI 55 in SydneyAustralia

Seminars

Dr Beatrix Jones (Massey University(Albany)) ldquoFitting and interpreting sparseGaussian graphical models forhigh-dimensional datardquo

Associate Professor David Whittaker (TheUniversity of Waikato) ldquoThe state of the artin the generation of efficient statisticaldesignsrdquo

Associate Professor Russell Millar ldquoLocalsensitivity of Bayesian inference to priors anddatardquo

Dr W Paul Malcolm (ANU) ldquoNew Gaussianmixture techniques for filtering andsmoothing of discrete-time Gauss-Markovjump Markov systemsrdquo

Dr Stephane Guindon (BioinformaticsInstitute) ldquoStatistical modelling of thenatural selection processes acting on proteinsequencesrdquo

Dr Ross Ihaka ldquoColour me carefullyrdquo

Dr Roger Marshall (School of PopulationHealth Epidemiology and Biostatistics)ldquoUse of scaled rectangle diagrams to visualizecategorical data with particular reference toclinical and epidemiological datardquo

Professor Goeran Kauermann (University ofBielefeldUNSW) ldquoPenalized splinesmoothing and generalized linear mixedmodelsmdashsome theory and applicationsrdquo

Garry J Tee

UNIVERSITY OF CANTERBURY

Department of Mathematics and Statistics

Dr Mike Plank will be taking up a position as Lec-turer from 2006 Mike does mathematical mod-elling especially of problems arising from biologyIn current joint work with David Wall and TimDavid (Engineering) he is studying the early stagesof cardiovascular disease by modelling blood flow inthe human body He finished his PhD at the Uni-versity of Leeds in 2003 then began a postdoctoraljob here in February 2004 Mike has already beenmaking himself useful around the place and he is awelcome addition to the department

Another current Postdoctoral Fellow Dr Si-mona Vıta will be staying here for a further yearHer new position is supported by the FoRSTNZScience amp Technology ldquoBridge to Employmentrdquoscheme

Dr Paul Mullowney is a recent arrival He starteda two-year university-funded postdoctoral fellow-ship in June 2005 Paul is working with Alex Jameson stochasticity in biological processes He com-pleted his PhD on dynamical systems and fluid me-chanics at the University of Colorado at Boulder in2004

Professor Ian Stewart who is well knownas a mathematician and an expositor visited

12

NZMS Newsletter No 95

Christchurch in September He delivered a keynotespeech at the New Zealand Association of Mathe-matics Teachers Biennial Conference as well as giv-ing a departmental colloquium

Douglas Bridges was awarded a standard Mars-den grant for his project ldquoConstructive reversemathematicsrdquo The project has two main aimsto classify constructive theorems according tothe proof principles that are necessary to estab-lish them and to classify essentially nonconstruc-tive theorems according to the nonconstructiveproof principles that they require for their proofBen Martin and Gerhard Rohrle (Southampton)were awarded a standard Marsden grant for theirproject ldquoA geometric approach to reductive alge-braic groupsrdquo They will use geometric techniquesto study reductive algebraic groups and their sub-groups and the way in which they act on theirassociated buildings

Rick Beatson was an invited speaker at the SIAMconference on Geometric Design and Computingin Phoenix Arizona in OctoberNovember Dou-glas Bridges and Simona Vıta visited Munich towork with Peter Schuster and Josef Berger andspoke at the Computability amp Complexity in Anal-ysis meeting in Kyoto in August In SeptemberMike Steel gave talks in Canada UC Berkeley andat the Mathematical Biosciences Institute in Ohiowhich hosted a special workshop on Phylogeneticsand Self-Organization in Ecology The 10th an-nual phylogenetics meeting will be held in Kaik-oura from 12ndash17 February 2006 Ben Martin gavea talk at the November Group Theory workshopat the University of Auckland which was held tocelebrate the 65th birthday of Charles Leedham-Green

Professor Dominic Welsh (University of Oxford)is currently visiting as part of the University ofCanterbury and University of Oxford exchange pro-gram The exchange is teaching-based and as aresult Dominic has been lecturing second yeargraph theory as well as a fourth year matroidtheory course Other recent and current visitorsinclude Tanja Gernhard (University of Munich)Dr Granville Tunnicliffe-Wilson (Lancaster Univer-sity) Dr Emily Lane (UCLA) Dr Jon Pitchford(University of York) and Professor Minoru Murata(Tokyo Institute of Technology)

John Hannah organised a sequence of mathemat-ical enrichment talks for schoolpupils during thesecond half of the year The talks covered topicsranging from complexity in computing to algebra topatterns and pictures In a talk on proof in mathe-matics a well-known ldquoproofrdquo was presented of theproposition that Girls are Evil The audience waschallenged to give a proof in a similar spirit that

Boys are Evil Here is the winning entry by JamieMcCloskey and Joan McArdle

BOYS ARE EVIL

Let us start with the singular of the gender ieBOY We find that the inverse of BOY is YOB (iefrom right to left) So we have

BOYminus1 = YOB

We all know that in order to behave in a yobbishfashion the yob must be alive

YOB = LIVE

Now we can invert both sides as follows

YOBminus1 = LIVEminus1

On calculating the inverses of each side we areleft with

BOY = EVIL

So we have proven that BOY = EVIL Let usmultiply both sides by two

2 BOY = 2 EVIL

This can be reduced to

BOYS = 2 EVIL

We feel we ought to be awarded the prize for thisbecause not only have we proven that boys are evilwe have proven they are more evil than evil mdash infact they are too evil

The prize was a $20 book token

Seminars

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoAbstract tubesrdquo

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoUse of gene expressioncomparisons for classification of tissuesamplesrdquo

Dr Christopher Paul Tuffley (University ofCalifornia Davis) ldquoFinite subset spaces ofthe circlerdquo

Dr Stefan Grunewald (University ofCanterbury) ldquoThin quartet setsrdquo

Dr Thomas Forster (University of Cambridge)ldquoDe-linearising Ehrenfeucht-Mostowskirdquo

Professor Ian Stewart (University ofWarwick) ldquoNetwork models of sympatricspeciationrdquo

Dr WP Malcolm (Australian NationalUniversity) ldquoState and mode estimation fordiscrete time-jump Markov systemsrdquo

13

LOCAL NEWS

Dr Granville Tunnicliffe Wilson (LancasterUniversity) ldquoAssessment of empiricalnon-linear time series prediction toolsrdquo

Professor Michael McAleer (University ofWestern Australia) ldquoGeneralizedautoregressive conditional correlation scalarBEKK and indirect DCCrdquo

Liam Wagner (University of Queensland)ldquoRepresentations of finite groups andpre-monoidal categoriesrdquo

Ben Martin

MASSEY UNIVERSITY

Institute of Fundamental Sciences(Palmerston North)

Mathematics

Partir cest mourir a peu

From Dean Halford

ldquoGillian Thornley is retiring after nearly 26 yearsat Massey University having joined the mathemat-ics staff in 1980 when Brian Hayman was Headof Department Following her graduation with aFirst Class Honours MSc from the University ofCanterbury in 1963 Gillian obtained a PhD inmetric differential geometry from the Universityof Toronto in 1965 under the supervision of Pro-fessors Hanno Rund and Ray Vanstone She re-turned to New Zealand where she lectured for twoyears at the University of Canterbury before mar-rying John Thornley and taking up a lectureshipat the Trinidad campus of the University of theWest Indies Then it was back to Nelson whereGillian and Johnrsquos children Louise and Matthewwere born and where Gillian did some part-timeteaching at Nelson Polytechnic In 1973 the familymoved to Wellington where Gillian obtained mostlypart-time positions in Wellington College of Educa-tion Wellington Polytechnic Victoria Universityand held a research position in the Department ofMines

Gillian has had an outstanding career She ishighly respected by staff and students as a top-levelteacher winning three Institute of FundamentalSciencesrsquo Distinguished Teaching Awards Furtherdistinction was the invitation from The Universityof Auckland to deliver the 1996 Aldis Lecture heraddress was entitled From Descartes to Aldis andBeyond A Geometrical History Gillian has givenfine support and encouragement to all of her stu-dents her personal qualities of patience integrity

fairness and professionalism are almost legendaryGillianrsquos research interests lie mainly in differentialgeometry in particular the study of Finsler spacesbut her work on gender issues in mathematics ed-ucation led her to publish and speak at overseasconferences

Gillianrsquos professionalism has been exercised inthe wider community where she has given much tothe development of mathematics and mathematicseducation For 14 years from 1978 to 1992 Gilliancontributed to the activities of the New ZealandMathematical Society in several roles becomingPresident of the Society for two years in 1989 Shewill be remembered for her wise and capable leader-ship during a challenging period and representedthe Society at the IMU meeting in Kobe Japanwhere she was the only woman president presentIndeed Gillian is the only woman President of theNZMS since it was founded in 1974 In 1997 shewas elected a Fellow of the New Zealand Mathe-matical Society and in December 2004 the Societyawarded Gillian Honorary Membership status

In addition to the Mathematics Department andnumerous boards and committees at Massey Uni-versity Gillian has also contributed much to theManawatu Mathematics Teachersrsquo Association Al-ways this was characterized by her superb organi-zational skills her grasp of the mathematics cur-riculum her concern for student welfare and herrepresentation of women in academia

Gillianrsquos professionalism depth of experiencesuperior teaching skills and guidance on studentmatters will be widely missed We wish her a longand happy retirementrdquo

Alas we also had to say farewell to ProfessorAndrew Vince His sunny nature will be missed andalso his excellent contribution towards our teachingprogramme and research

Charles Little has itchy feet again and will be go-ing on an yearrsquos sabbatical to the Federal Univer-sity of Mato Groso do Sul Campo Grande BrazilHe will be visiting Marcelo de Cavallo DesejamosBarbara e Charles um tempo agradavel em Brasil

On a more happy noteCongratulations to

bull Kee Teo and Tammy Smith for securing aMassey University award ldquoFund for Innovationand Excellence in Teachingrdquo for the projectldquoDeveloping MathsFirst A web-based systemto enhance first year mathematics teachingand learningrdquo Last year they were also suc-cessful in obtaining a grant

bull Gillian Thornley and Igor Boglaev who havebeen made Fellows of the New Zealand Math-ematics Society

14

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

NZMS Newsletter No 95

Jozef Siran has received a grant from the StaffResearch Fund

Arkadii Slinko has become a founding memberof the ARC Economic Design Network which re-ceived funding ($AU300000 per year) from theAustralian Research Council for the next five yearsHe will be a semi-funded invited speaker at the2nd Pan-Pacific Conference on Game Theory onNovember 24ndash26 at Taipei

James Sneyd has been elected a Fellow of theRoyal Society of New Zealand and he has beenawarded a research grant from the Universityof Massachusetts Medical Center James Sneydamp Robert McLachlan (Massey University) havejointly won the NZMS Research Award for 2005James Sneyd amp Colin Fox have received a $9000grant from the Staff Research Fund for ldquoModellingthe contraction of airway smooth musclerdquo

Mike Thomas returned from leave during whichhe gave seminars or workshops at the Chinese HighSchool of Singapore University of Swansea War-wick University Open University Plymouth Uni-versity and the University of Grenoble He haswon a $20k+ grant to use the Universityrsquos nuclearMagnetic Resonance Imaging machine to examinebrain functioning of people while they do mathe-matical tasks He is linking with people in Psychol-ogy and a researcher in Turin And Mike has beenappointed as ldquoSpecialist Adviserrdquo to the PBRF Re-view panels on Mathematics Education

Shixiao Wang has received a grant from the NewStaff Research Fund

A Departmental professorsrsquo committee has allo-cated grants to Bill Barton Colin Fox Sina Green-wood Vivien Kirk Mike Meylan Philip SharpArkadii Slinko Steve Taylor and Mike Thomas to-talling $27000

Visitors

Professor Len Bos (University of Calgary)

Dr Andreas Cap (University of Vienna)

Dr Heiko Dietrich (Technische Universitaet zuBraunschweig)

Professor Bettina Eick (TechnischeUniversitaet zu Braunschweig)

Professor George Havas (University ofQueensland)

Dr Frank Himstedt (Munich University ofTechnology)

Dr Carolyn Kieran (University of Quebec aMontreal)

Dr Ville Kolehmainen (University of KuopioFinland)

Dr Martin Macaj (Comenius University)

Professor John Mason (Open University)

Professor Mike Newman (ANU)

Professor Cheryl Praeger (UWA)

Dr Anne Watson (Oxford University)

Professor Wolfgang Willems (UniversitaetMagdeburg)

Professor Mariusz Wodzicki (University ofCalifornia - Berkeley)

William Rowan Hamiltonrsquos 200th birthdaywas celebrated around the world on 3 August2005 Hamiltonrsquos sister Sydney Margaret Hamil-ton (1811ndash1889) became his principal astronomi-cal assistant She settled in Auckland in 1875 andwas befriended by Sir George Grey who was thenstudying quaternions

The NZMS and the New Zealand Institute ofPhysics sponsored a public lecture by Garry Teeon William Rowan Hamilton given on Hamiltonrsquos200th birthday That lecture was repeated at TheUniversity of Waikato on October 27 A Librarydisplay was set up in The University of AucklandGeneral Library (for July and August) includingcopies of some of the very rich collection of Hamil-tonrsquos manuscripts and publications in AucklandCity Central Library

Our Department hosted the 2005 Albany-Auckland-Waikato Applied Mathematics Day onFriday September 9 The following lectures weregiven

Dr Garry Tee ldquoSurface integrals overellipsoidal segmentrdquo

Inga Wang ldquoA model for smooth musclecontractions in the lungrdquo

Basil Sinescu ldquoGood rank-1 lattice rules basedon the general weighted star discrepancyrdquo

Professor Graeme Wake (Massey University(Albany)) ldquoA model of transientcell-growthrdquo

Elan Gin ldquoCellular calcium and buffersrdquo

Leng Leng Lim ldquoModelling of volcanic ashfallrdquo

Professor John Butcher ldquoTowards efficientgeneral linear methodsrdquo

9

LOCAL NEWS

We took advantage of the presence of a number ofvisitors at The University of Auckland to hold a 2-day workshop on Group Theory on November 1 and2 That meeting acknowledged the 65th birthdayon November 2 of one of our frequent visitors andcollaborators Professor Charles Leedham-Greenfrom Queen Mary College University of London

The following lectures were presented at theWorkshop

Professor Marston Conder (Auckland)ldquoConnectedness of generating sets for finitegroupsrdquo

Professor Bettina Eick (TechnischeUniversitaet zu Braunschweig) ldquoPeriodicityand the automorphism group conjecturerdquo

Dr Ben Martin (University of Canterbury)ldquoCoclass p-adic integration and eliminationof imaginariesrdquo

Professor Mike Newman (ANU) ldquoGroupswith exactly three involutionsrdquo

Professor George Havas (University ofQueensland) ldquo4-Engel groups are locallynilpotentrdquo

Professor Gaven Martin (Massey University(Albany)) ldquoAutomorphisms of hyperbolicgroups and open maps of manifoldsrdquo

Dr Andre Nies (Department of ComputerScience) ldquoGroups with finite descriptionsrdquo

Dr Henrik Baarnhielm (London)ldquoConstructive recognition of the Suzukigroupsrdquo

Associate Professor Jozef Siran (Auckland)ldquoRegular maps on a given surfacemdasha surveyrdquo

The Workshop concluded with a special lectureby

Charles Leedham-Green entitled ldquoApologiapro vita suardquo

We welcome Laura Ciobanu to the Departmentas a University of Auckland Postdoctoral Fellowfor two years She is a a recent graduate of Rut-gers University and her research interests are inalgebra Caroline Poisard has been appointed to apost-doctoral position for one year starting in Jan-uary She will work with Bill Barton in the area ofEthnomathematics

Mala Nataraj has enrolled for a PhD concerningVedic Mathematics and Garry Nathan has enrolled

for a PhD on Undergraduate Conceptions of Rea-soning and Proof

Matthew Auger and Elan Gin have beenawarded UoA guaranteed doctoral scholarships

On November 4 the prominent businessmanMichael Erceg was flying a business associatefrom Auckland to Queenstown The helicopterdisappeared in very stormy conditions and 15 dayslater the wreckage was found near Raglan DavidGauld had sent the following message around ourDepartment

Dear colleagues

Perhaps not many of you are aware that the miss-ing businessman Mike Erceg was a student in theDepartment as well as a colleague

Mike completed his BSc(Hons) and MSc degreesin this Department gaining a Fowlds MemorialPrize for the top masters student in the Facultyof Science in his year before heading to the Univer-sity of California at Berkeley where he completedhis PhD in Functional Analysis in 1981 After hisreturn to New Zealand he taught part-time in theDepartment for several years and at least one ofour colleagues recalls with fondness his graduatecourse in Functional Analysis taught to him byMike When his work in the family vineyard be-came too onerous he stopped teaching in the De-partment

More recently with a group of Industrial Math-ematics staff I visited Mikersquos business premiseswhere we investigated whether some sort of projectfor the IM Programme might be set up there Hepaid a return visit to the Tamaki Campus with anumber of his staff to talk to IM students

Mike was a welcoming and gracious host whenwe visited him and I for one am very saddened byhis disappearance last Friday

Regards

David Gauld

Seminars

Professor Winfried Kohnen (Heidelberg)ldquoOn infinite product expansions of modularfunctionsrdquo

Dr Jana Siagiova ldquoApplications of coverings inCayley maps and in the degree-diameterproblemrdquo

Professor David Gauld ldquoMOPping uprdquo

10

NZMS Newsletter No 95

Dr Primoz Potocnik ldquoTetravalentedge-transitive graphs and related topicsrdquo

Dr Tsukasa Yashiro ldquoDiagrammaticapproaches to surface-knots - 1-handles andtriple pointsrdquo

Dr Anthony D Blaom ldquoThe ghost ofsymmetry in a curved worldrdquo

Professor Mariusz Wodzicki (University ofCaliforniamdashBerkeley) ldquoExotic tracesrdquo

Dr Sina Greenwood ldquoCharacterisingcontinuous functions on connected compactspacesrdquo

Professor Wolfgang Willems (UniversitaetMagdeburg) ldquoSome open problems inmodular representation theoryrdquo ldquoAre cycliccodes asymptotically goodrdquo and ldquoA surveyof problems and methods in coding theoryrdquo

Dr Frank Himstedt (TU Munich)ldquoLow-dimensional representations ofSteinbergrsquos triality groupsrdquo

Dr Sasa Radomirovic (Rutgers University)ldquoCusp forms over function fields and modularsymbolsrdquo

Dr Andreas Cap (University of Vienna)ldquoInfinitesimal automorphisms anddeformations of parabolic geometriesrdquo

Professor Cheryl Praeger (UWA) ldquoGroupsprobability algorithms computing withgiantsrdquo

Dr Laura Ciobanu ldquoFixed subgroups in freegroupsrdquo

Professor CK Raju (University of BhopalIndia) ldquoSeries expansions and thecomputation of Pi in India from Aryabhattato Yuktideepikardquo and ldquoThe Indian origins ofthe calculus and its transmission to Europeprior to Newton and Leibniz Part 2 Lessonsfor mathematics educationrdquo

Christopher Hay ldquoMetrizability of compactconvex sets under certain criteriardquo

Dr Hyuck Chung ldquoModelling timber-basedfloor structuresrdquo

David Choquenot (Landcare Research)ldquoMathematical models and wildlifepopulation dynamicsrdquo

Daniel Watzenig (Graz University ofTechnology) ldquoElectrical capacitancetomography at Graz University ofTechnology state-space representations andparticle filteringrdquo

Dr Carlo Laing (Massey University (Albany))ldquoEquation-free modelling some neuralexamplesrdquo

Dr David Bryant ldquo Continuous and (mostly)tractable models for the variation ofevolutionary ratesrdquo

Dr Emily Lane (UCLA) ldquoWave-currentinteractions and shore-connected barsrdquo

Professor Roman Nedela (Slovak Academy ofSciences) ldquoEnumeration of maps andhypermaps with given genus and givennumber of edgesrdquo

Garry J Tee

Department of Statistics

Russell Millar appeared on the television programldquoJohn Campbell Liverdquo in early July His briefingwas to tell the audience the probability of winningLottomdashalthough we all know that if Russell reallyhad inside Lotto information wersquod be advertisingfor a new lecturer The segment was created byJacqui Brown and her crew and was filmed in a lec-ture theatre on the Tamaki campus The style waslight-hearted but nonetheless demonstrated somesolid statistical points including conditional prob-abilities and misuse of the ldquolaw of averagesrdquo Rus-sellrsquos night of fame has been recorded for posterityand it will be played in our first-year lectures foryears to come

Russell Millar and Marti Anderson have been di-viding their time between Perth Auckland andAlaska in their work on fisheries and multivariateecological analysis

The Rodent Invasion Research Group spent atotal of two weeks rat-catching in the Bay of Is-lands With the Department of ConservationSteven Miller helped set up the traps then thenext week Rachel Fewster went to bag the rats withStephen Cope as cameraman The trip was excep-tionally successful with a total of 360 rats baggedfor the DNA project

Doctoral student James Russell spent time inBrazil to give a student finalist talk at the Soci-ety for Conservation Biology He then travelled toOregon for the Association of Pacific Rim Univer-sities Annual Doctoral Students Conference on the

11

LOCAL NEWS

multidisciplinary theme ldquoMoving Towards a Sus-tainable Futurerdquo A paper on ldquoIntercepting thefirst rat ashorerdquo written by James Russell andothers from the Rodent Invasion ProjectResearchGroup (DR Towns SH Anderson amp MN Clout)tells of a rat which was released on Motuhoropapa(one of the uninhabited Noises Islands) which thenswam 400 metres to the island Otata That pa-per was published in NATURE 437(7062) p1107and it has attracted attention around the worldThe story was run by over 100 international newsagencies from the UK Independent to WashingtonNational Public Radio and it also included a fea-ture on NZ TV news

Tim Langlois has gained his PhD for his thesisldquoInfluence of reef-associated predators on adjacentsoft-sediment communitiesrdquo He has been based atthe Leigh Marine Laboratory Yuichi Hirose hascompleted his PhD

An NZIMA Postgraduate Scholarship has beenawarded to Adam Smith for a Masters thesisproject at The University of Auckland (from July2005) on the statistical validation of the NZ MarineEnvironment Classification under the supervisionof Drs Marti Anderson and Clinton Duffy MikeManning who is studying for his MSc while work-ing for NIWA in Wellington appeared on ldquo60 Min-utesrdquo in April in a piece about the satellite taggingof white sharks

IASS 55 was organised and run by this Depart-ment and held at the Maritime Museum in Auck-land New Zealand Alastair Scott chaired some ofthe sessions CR Rao spoke to a packed room inthis Department In his talk he covered a historyof statistics

From June 2 to 7 the SRTL-4 conference washeld at Grafton Hall It was organised largely byRoss Parsonage and Maxine Pfannkuch along withinput from Dani Ben-Zvi Joan Garfield and oth-ers Rachel Cunliffe Ross Ihaka Chris Wild MikeForster and Ilze Ziedins attended ISI 55 in SydneyAustralia

Seminars

Dr Beatrix Jones (Massey University(Albany)) ldquoFitting and interpreting sparseGaussian graphical models forhigh-dimensional datardquo

Associate Professor David Whittaker (TheUniversity of Waikato) ldquoThe state of the artin the generation of efficient statisticaldesignsrdquo

Associate Professor Russell Millar ldquoLocalsensitivity of Bayesian inference to priors anddatardquo

Dr W Paul Malcolm (ANU) ldquoNew Gaussianmixture techniques for filtering andsmoothing of discrete-time Gauss-Markovjump Markov systemsrdquo

Dr Stephane Guindon (BioinformaticsInstitute) ldquoStatistical modelling of thenatural selection processes acting on proteinsequencesrdquo

Dr Ross Ihaka ldquoColour me carefullyrdquo

Dr Roger Marshall (School of PopulationHealth Epidemiology and Biostatistics)ldquoUse of scaled rectangle diagrams to visualizecategorical data with particular reference toclinical and epidemiological datardquo

Professor Goeran Kauermann (University ofBielefeldUNSW) ldquoPenalized splinesmoothing and generalized linear mixedmodelsmdashsome theory and applicationsrdquo

Garry J Tee

UNIVERSITY OF CANTERBURY

Department of Mathematics and Statistics

Dr Mike Plank will be taking up a position as Lec-turer from 2006 Mike does mathematical mod-elling especially of problems arising from biologyIn current joint work with David Wall and TimDavid (Engineering) he is studying the early stagesof cardiovascular disease by modelling blood flow inthe human body He finished his PhD at the Uni-versity of Leeds in 2003 then began a postdoctoraljob here in February 2004 Mike has already beenmaking himself useful around the place and he is awelcome addition to the department

Another current Postdoctoral Fellow Dr Si-mona Vıta will be staying here for a further yearHer new position is supported by the FoRSTNZScience amp Technology ldquoBridge to Employmentrdquoscheme

Dr Paul Mullowney is a recent arrival He starteda two-year university-funded postdoctoral fellow-ship in June 2005 Paul is working with Alex Jameson stochasticity in biological processes He com-pleted his PhD on dynamical systems and fluid me-chanics at the University of Colorado at Boulder in2004

Professor Ian Stewart who is well knownas a mathematician and an expositor visited

12

NZMS Newsletter No 95

Christchurch in September He delivered a keynotespeech at the New Zealand Association of Mathe-matics Teachers Biennial Conference as well as giv-ing a departmental colloquium

Douglas Bridges was awarded a standard Mars-den grant for his project ldquoConstructive reversemathematicsrdquo The project has two main aimsto classify constructive theorems according tothe proof principles that are necessary to estab-lish them and to classify essentially nonconstruc-tive theorems according to the nonconstructiveproof principles that they require for their proofBen Martin and Gerhard Rohrle (Southampton)were awarded a standard Marsden grant for theirproject ldquoA geometric approach to reductive alge-braic groupsrdquo They will use geometric techniquesto study reductive algebraic groups and their sub-groups and the way in which they act on theirassociated buildings

Rick Beatson was an invited speaker at the SIAMconference on Geometric Design and Computingin Phoenix Arizona in OctoberNovember Dou-glas Bridges and Simona Vıta visited Munich towork with Peter Schuster and Josef Berger andspoke at the Computability amp Complexity in Anal-ysis meeting in Kyoto in August In SeptemberMike Steel gave talks in Canada UC Berkeley andat the Mathematical Biosciences Institute in Ohiowhich hosted a special workshop on Phylogeneticsand Self-Organization in Ecology The 10th an-nual phylogenetics meeting will be held in Kaik-oura from 12ndash17 February 2006 Ben Martin gavea talk at the November Group Theory workshopat the University of Auckland which was held tocelebrate the 65th birthday of Charles Leedham-Green

Professor Dominic Welsh (University of Oxford)is currently visiting as part of the University ofCanterbury and University of Oxford exchange pro-gram The exchange is teaching-based and as aresult Dominic has been lecturing second yeargraph theory as well as a fourth year matroidtheory course Other recent and current visitorsinclude Tanja Gernhard (University of Munich)Dr Granville Tunnicliffe-Wilson (Lancaster Univer-sity) Dr Emily Lane (UCLA) Dr Jon Pitchford(University of York) and Professor Minoru Murata(Tokyo Institute of Technology)

John Hannah organised a sequence of mathemat-ical enrichment talks for schoolpupils during thesecond half of the year The talks covered topicsranging from complexity in computing to algebra topatterns and pictures In a talk on proof in mathe-matics a well-known ldquoproofrdquo was presented of theproposition that Girls are Evil The audience waschallenged to give a proof in a similar spirit that

Boys are Evil Here is the winning entry by JamieMcCloskey and Joan McArdle

BOYS ARE EVIL

Let us start with the singular of the gender ieBOY We find that the inverse of BOY is YOB (iefrom right to left) So we have

BOYminus1 = YOB

We all know that in order to behave in a yobbishfashion the yob must be alive

YOB = LIVE

Now we can invert both sides as follows

YOBminus1 = LIVEminus1

On calculating the inverses of each side we areleft with

BOY = EVIL

So we have proven that BOY = EVIL Let usmultiply both sides by two

2 BOY = 2 EVIL

This can be reduced to

BOYS = 2 EVIL

We feel we ought to be awarded the prize for thisbecause not only have we proven that boys are evilwe have proven they are more evil than evil mdash infact they are too evil

The prize was a $20 book token

Seminars

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoAbstract tubesrdquo

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoUse of gene expressioncomparisons for classification of tissuesamplesrdquo

Dr Christopher Paul Tuffley (University ofCalifornia Davis) ldquoFinite subset spaces ofthe circlerdquo

Dr Stefan Grunewald (University ofCanterbury) ldquoThin quartet setsrdquo

Dr Thomas Forster (University of Cambridge)ldquoDe-linearising Ehrenfeucht-Mostowskirdquo

Professor Ian Stewart (University ofWarwick) ldquoNetwork models of sympatricspeciationrdquo

Dr WP Malcolm (Australian NationalUniversity) ldquoState and mode estimation fordiscrete time-jump Markov systemsrdquo

13

LOCAL NEWS

Dr Granville Tunnicliffe Wilson (LancasterUniversity) ldquoAssessment of empiricalnon-linear time series prediction toolsrdquo

Professor Michael McAleer (University ofWestern Australia) ldquoGeneralizedautoregressive conditional correlation scalarBEKK and indirect DCCrdquo

Liam Wagner (University of Queensland)ldquoRepresentations of finite groups andpre-monoidal categoriesrdquo

Ben Martin

MASSEY UNIVERSITY

Institute of Fundamental Sciences(Palmerston North)

Mathematics

Partir cest mourir a peu

From Dean Halford

ldquoGillian Thornley is retiring after nearly 26 yearsat Massey University having joined the mathemat-ics staff in 1980 when Brian Hayman was Headof Department Following her graduation with aFirst Class Honours MSc from the University ofCanterbury in 1963 Gillian obtained a PhD inmetric differential geometry from the Universityof Toronto in 1965 under the supervision of Pro-fessors Hanno Rund and Ray Vanstone She re-turned to New Zealand where she lectured for twoyears at the University of Canterbury before mar-rying John Thornley and taking up a lectureshipat the Trinidad campus of the University of theWest Indies Then it was back to Nelson whereGillian and Johnrsquos children Louise and Matthewwere born and where Gillian did some part-timeteaching at Nelson Polytechnic In 1973 the familymoved to Wellington where Gillian obtained mostlypart-time positions in Wellington College of Educa-tion Wellington Polytechnic Victoria Universityand held a research position in the Department ofMines

Gillian has had an outstanding career She ishighly respected by staff and students as a top-levelteacher winning three Institute of FundamentalSciencesrsquo Distinguished Teaching Awards Furtherdistinction was the invitation from The Universityof Auckland to deliver the 1996 Aldis Lecture heraddress was entitled From Descartes to Aldis andBeyond A Geometrical History Gillian has givenfine support and encouragement to all of her stu-dents her personal qualities of patience integrity

fairness and professionalism are almost legendaryGillianrsquos research interests lie mainly in differentialgeometry in particular the study of Finsler spacesbut her work on gender issues in mathematics ed-ucation led her to publish and speak at overseasconferences

Gillianrsquos professionalism has been exercised inthe wider community where she has given much tothe development of mathematics and mathematicseducation For 14 years from 1978 to 1992 Gilliancontributed to the activities of the New ZealandMathematical Society in several roles becomingPresident of the Society for two years in 1989 Shewill be remembered for her wise and capable leader-ship during a challenging period and representedthe Society at the IMU meeting in Kobe Japanwhere she was the only woman president presentIndeed Gillian is the only woman President of theNZMS since it was founded in 1974 In 1997 shewas elected a Fellow of the New Zealand Mathe-matical Society and in December 2004 the Societyawarded Gillian Honorary Membership status

In addition to the Mathematics Department andnumerous boards and committees at Massey Uni-versity Gillian has also contributed much to theManawatu Mathematics Teachersrsquo Association Al-ways this was characterized by her superb organi-zational skills her grasp of the mathematics cur-riculum her concern for student welfare and herrepresentation of women in academia

Gillianrsquos professionalism depth of experiencesuperior teaching skills and guidance on studentmatters will be widely missed We wish her a longand happy retirementrdquo

Alas we also had to say farewell to ProfessorAndrew Vince His sunny nature will be missed andalso his excellent contribution towards our teachingprogramme and research

Charles Little has itchy feet again and will be go-ing on an yearrsquos sabbatical to the Federal Univer-sity of Mato Groso do Sul Campo Grande BrazilHe will be visiting Marcelo de Cavallo DesejamosBarbara e Charles um tempo agradavel em Brasil

On a more happy noteCongratulations to

bull Kee Teo and Tammy Smith for securing aMassey University award ldquoFund for Innovationand Excellence in Teachingrdquo for the projectldquoDeveloping MathsFirst A web-based systemto enhance first year mathematics teachingand learningrdquo Last year they were also suc-cessful in obtaining a grant

bull Gillian Thornley and Igor Boglaev who havebeen made Fellows of the New Zealand Math-ematics Society

14

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

LOCAL NEWS

We took advantage of the presence of a number ofvisitors at The University of Auckland to hold a 2-day workshop on Group Theory on November 1 and2 That meeting acknowledged the 65th birthdayon November 2 of one of our frequent visitors andcollaborators Professor Charles Leedham-Greenfrom Queen Mary College University of London

The following lectures were presented at theWorkshop

Professor Marston Conder (Auckland)ldquoConnectedness of generating sets for finitegroupsrdquo

Professor Bettina Eick (TechnischeUniversitaet zu Braunschweig) ldquoPeriodicityand the automorphism group conjecturerdquo

Dr Ben Martin (University of Canterbury)ldquoCoclass p-adic integration and eliminationof imaginariesrdquo

Professor Mike Newman (ANU) ldquoGroupswith exactly three involutionsrdquo

Professor George Havas (University ofQueensland) ldquo4-Engel groups are locallynilpotentrdquo

Professor Gaven Martin (Massey University(Albany)) ldquoAutomorphisms of hyperbolicgroups and open maps of manifoldsrdquo

Dr Andre Nies (Department of ComputerScience) ldquoGroups with finite descriptionsrdquo

Dr Henrik Baarnhielm (London)ldquoConstructive recognition of the Suzukigroupsrdquo

Associate Professor Jozef Siran (Auckland)ldquoRegular maps on a given surfacemdasha surveyrdquo

The Workshop concluded with a special lectureby

Charles Leedham-Green entitled ldquoApologiapro vita suardquo

We welcome Laura Ciobanu to the Departmentas a University of Auckland Postdoctoral Fellowfor two years She is a a recent graduate of Rut-gers University and her research interests are inalgebra Caroline Poisard has been appointed to apost-doctoral position for one year starting in Jan-uary She will work with Bill Barton in the area ofEthnomathematics

Mala Nataraj has enrolled for a PhD concerningVedic Mathematics and Garry Nathan has enrolled

for a PhD on Undergraduate Conceptions of Rea-soning and Proof

Matthew Auger and Elan Gin have beenawarded UoA guaranteed doctoral scholarships

On November 4 the prominent businessmanMichael Erceg was flying a business associatefrom Auckland to Queenstown The helicopterdisappeared in very stormy conditions and 15 dayslater the wreckage was found near Raglan DavidGauld had sent the following message around ourDepartment

Dear colleagues

Perhaps not many of you are aware that the miss-ing businessman Mike Erceg was a student in theDepartment as well as a colleague

Mike completed his BSc(Hons) and MSc degreesin this Department gaining a Fowlds MemorialPrize for the top masters student in the Facultyof Science in his year before heading to the Univer-sity of California at Berkeley where he completedhis PhD in Functional Analysis in 1981 After hisreturn to New Zealand he taught part-time in theDepartment for several years and at least one ofour colleagues recalls with fondness his graduatecourse in Functional Analysis taught to him byMike When his work in the family vineyard be-came too onerous he stopped teaching in the De-partment

More recently with a group of Industrial Math-ematics staff I visited Mikersquos business premiseswhere we investigated whether some sort of projectfor the IM Programme might be set up there Hepaid a return visit to the Tamaki Campus with anumber of his staff to talk to IM students

Mike was a welcoming and gracious host whenwe visited him and I for one am very saddened byhis disappearance last Friday

Regards

David Gauld

Seminars

Professor Winfried Kohnen (Heidelberg)ldquoOn infinite product expansions of modularfunctionsrdquo

Dr Jana Siagiova ldquoApplications of coverings inCayley maps and in the degree-diameterproblemrdquo

Professor David Gauld ldquoMOPping uprdquo

10

NZMS Newsletter No 95

Dr Primoz Potocnik ldquoTetravalentedge-transitive graphs and related topicsrdquo

Dr Tsukasa Yashiro ldquoDiagrammaticapproaches to surface-knots - 1-handles andtriple pointsrdquo

Dr Anthony D Blaom ldquoThe ghost ofsymmetry in a curved worldrdquo

Professor Mariusz Wodzicki (University ofCaliforniamdashBerkeley) ldquoExotic tracesrdquo

Dr Sina Greenwood ldquoCharacterisingcontinuous functions on connected compactspacesrdquo

Professor Wolfgang Willems (UniversitaetMagdeburg) ldquoSome open problems inmodular representation theoryrdquo ldquoAre cycliccodes asymptotically goodrdquo and ldquoA surveyof problems and methods in coding theoryrdquo

Dr Frank Himstedt (TU Munich)ldquoLow-dimensional representations ofSteinbergrsquos triality groupsrdquo

Dr Sasa Radomirovic (Rutgers University)ldquoCusp forms over function fields and modularsymbolsrdquo

Dr Andreas Cap (University of Vienna)ldquoInfinitesimal automorphisms anddeformations of parabolic geometriesrdquo

Professor Cheryl Praeger (UWA) ldquoGroupsprobability algorithms computing withgiantsrdquo

Dr Laura Ciobanu ldquoFixed subgroups in freegroupsrdquo

Professor CK Raju (University of BhopalIndia) ldquoSeries expansions and thecomputation of Pi in India from Aryabhattato Yuktideepikardquo and ldquoThe Indian origins ofthe calculus and its transmission to Europeprior to Newton and Leibniz Part 2 Lessonsfor mathematics educationrdquo

Christopher Hay ldquoMetrizability of compactconvex sets under certain criteriardquo

Dr Hyuck Chung ldquoModelling timber-basedfloor structuresrdquo

David Choquenot (Landcare Research)ldquoMathematical models and wildlifepopulation dynamicsrdquo

Daniel Watzenig (Graz University ofTechnology) ldquoElectrical capacitancetomography at Graz University ofTechnology state-space representations andparticle filteringrdquo

Dr Carlo Laing (Massey University (Albany))ldquoEquation-free modelling some neuralexamplesrdquo

Dr David Bryant ldquo Continuous and (mostly)tractable models for the variation ofevolutionary ratesrdquo

Dr Emily Lane (UCLA) ldquoWave-currentinteractions and shore-connected barsrdquo

Professor Roman Nedela (Slovak Academy ofSciences) ldquoEnumeration of maps andhypermaps with given genus and givennumber of edgesrdquo

Garry J Tee

Department of Statistics

Russell Millar appeared on the television programldquoJohn Campbell Liverdquo in early July His briefingwas to tell the audience the probability of winningLottomdashalthough we all know that if Russell reallyhad inside Lotto information wersquod be advertisingfor a new lecturer The segment was created byJacqui Brown and her crew and was filmed in a lec-ture theatre on the Tamaki campus The style waslight-hearted but nonetheless demonstrated somesolid statistical points including conditional prob-abilities and misuse of the ldquolaw of averagesrdquo Rus-sellrsquos night of fame has been recorded for posterityand it will be played in our first-year lectures foryears to come

Russell Millar and Marti Anderson have been di-viding their time between Perth Auckland andAlaska in their work on fisheries and multivariateecological analysis

The Rodent Invasion Research Group spent atotal of two weeks rat-catching in the Bay of Is-lands With the Department of ConservationSteven Miller helped set up the traps then thenext week Rachel Fewster went to bag the rats withStephen Cope as cameraman The trip was excep-tionally successful with a total of 360 rats baggedfor the DNA project

Doctoral student James Russell spent time inBrazil to give a student finalist talk at the Soci-ety for Conservation Biology He then travelled toOregon for the Association of Pacific Rim Univer-sities Annual Doctoral Students Conference on the

11

LOCAL NEWS

multidisciplinary theme ldquoMoving Towards a Sus-tainable Futurerdquo A paper on ldquoIntercepting thefirst rat ashorerdquo written by James Russell andothers from the Rodent Invasion ProjectResearchGroup (DR Towns SH Anderson amp MN Clout)tells of a rat which was released on Motuhoropapa(one of the uninhabited Noises Islands) which thenswam 400 metres to the island Otata That pa-per was published in NATURE 437(7062) p1107and it has attracted attention around the worldThe story was run by over 100 international newsagencies from the UK Independent to WashingtonNational Public Radio and it also included a fea-ture on NZ TV news

Tim Langlois has gained his PhD for his thesisldquoInfluence of reef-associated predators on adjacentsoft-sediment communitiesrdquo He has been based atthe Leigh Marine Laboratory Yuichi Hirose hascompleted his PhD

An NZIMA Postgraduate Scholarship has beenawarded to Adam Smith for a Masters thesisproject at The University of Auckland (from July2005) on the statistical validation of the NZ MarineEnvironment Classification under the supervisionof Drs Marti Anderson and Clinton Duffy MikeManning who is studying for his MSc while work-ing for NIWA in Wellington appeared on ldquo60 Min-utesrdquo in April in a piece about the satellite taggingof white sharks

IASS 55 was organised and run by this Depart-ment and held at the Maritime Museum in Auck-land New Zealand Alastair Scott chaired some ofthe sessions CR Rao spoke to a packed room inthis Department In his talk he covered a historyof statistics

From June 2 to 7 the SRTL-4 conference washeld at Grafton Hall It was organised largely byRoss Parsonage and Maxine Pfannkuch along withinput from Dani Ben-Zvi Joan Garfield and oth-ers Rachel Cunliffe Ross Ihaka Chris Wild MikeForster and Ilze Ziedins attended ISI 55 in SydneyAustralia

Seminars

Dr Beatrix Jones (Massey University(Albany)) ldquoFitting and interpreting sparseGaussian graphical models forhigh-dimensional datardquo

Associate Professor David Whittaker (TheUniversity of Waikato) ldquoThe state of the artin the generation of efficient statisticaldesignsrdquo

Associate Professor Russell Millar ldquoLocalsensitivity of Bayesian inference to priors anddatardquo

Dr W Paul Malcolm (ANU) ldquoNew Gaussianmixture techniques for filtering andsmoothing of discrete-time Gauss-Markovjump Markov systemsrdquo

Dr Stephane Guindon (BioinformaticsInstitute) ldquoStatistical modelling of thenatural selection processes acting on proteinsequencesrdquo

Dr Ross Ihaka ldquoColour me carefullyrdquo

Dr Roger Marshall (School of PopulationHealth Epidemiology and Biostatistics)ldquoUse of scaled rectangle diagrams to visualizecategorical data with particular reference toclinical and epidemiological datardquo

Professor Goeran Kauermann (University ofBielefeldUNSW) ldquoPenalized splinesmoothing and generalized linear mixedmodelsmdashsome theory and applicationsrdquo

Garry J Tee

UNIVERSITY OF CANTERBURY

Department of Mathematics and Statistics

Dr Mike Plank will be taking up a position as Lec-turer from 2006 Mike does mathematical mod-elling especially of problems arising from biologyIn current joint work with David Wall and TimDavid (Engineering) he is studying the early stagesof cardiovascular disease by modelling blood flow inthe human body He finished his PhD at the Uni-versity of Leeds in 2003 then began a postdoctoraljob here in February 2004 Mike has already beenmaking himself useful around the place and he is awelcome addition to the department

Another current Postdoctoral Fellow Dr Si-mona Vıta will be staying here for a further yearHer new position is supported by the FoRSTNZScience amp Technology ldquoBridge to Employmentrdquoscheme

Dr Paul Mullowney is a recent arrival He starteda two-year university-funded postdoctoral fellow-ship in June 2005 Paul is working with Alex Jameson stochasticity in biological processes He com-pleted his PhD on dynamical systems and fluid me-chanics at the University of Colorado at Boulder in2004

Professor Ian Stewart who is well knownas a mathematician and an expositor visited

12

NZMS Newsletter No 95

Christchurch in September He delivered a keynotespeech at the New Zealand Association of Mathe-matics Teachers Biennial Conference as well as giv-ing a departmental colloquium

Douglas Bridges was awarded a standard Mars-den grant for his project ldquoConstructive reversemathematicsrdquo The project has two main aimsto classify constructive theorems according tothe proof principles that are necessary to estab-lish them and to classify essentially nonconstruc-tive theorems according to the nonconstructiveproof principles that they require for their proofBen Martin and Gerhard Rohrle (Southampton)were awarded a standard Marsden grant for theirproject ldquoA geometric approach to reductive alge-braic groupsrdquo They will use geometric techniquesto study reductive algebraic groups and their sub-groups and the way in which they act on theirassociated buildings

Rick Beatson was an invited speaker at the SIAMconference on Geometric Design and Computingin Phoenix Arizona in OctoberNovember Dou-glas Bridges and Simona Vıta visited Munich towork with Peter Schuster and Josef Berger andspoke at the Computability amp Complexity in Anal-ysis meeting in Kyoto in August In SeptemberMike Steel gave talks in Canada UC Berkeley andat the Mathematical Biosciences Institute in Ohiowhich hosted a special workshop on Phylogeneticsand Self-Organization in Ecology The 10th an-nual phylogenetics meeting will be held in Kaik-oura from 12ndash17 February 2006 Ben Martin gavea talk at the November Group Theory workshopat the University of Auckland which was held tocelebrate the 65th birthday of Charles Leedham-Green

Professor Dominic Welsh (University of Oxford)is currently visiting as part of the University ofCanterbury and University of Oxford exchange pro-gram The exchange is teaching-based and as aresult Dominic has been lecturing second yeargraph theory as well as a fourth year matroidtheory course Other recent and current visitorsinclude Tanja Gernhard (University of Munich)Dr Granville Tunnicliffe-Wilson (Lancaster Univer-sity) Dr Emily Lane (UCLA) Dr Jon Pitchford(University of York) and Professor Minoru Murata(Tokyo Institute of Technology)

John Hannah organised a sequence of mathemat-ical enrichment talks for schoolpupils during thesecond half of the year The talks covered topicsranging from complexity in computing to algebra topatterns and pictures In a talk on proof in mathe-matics a well-known ldquoproofrdquo was presented of theproposition that Girls are Evil The audience waschallenged to give a proof in a similar spirit that

Boys are Evil Here is the winning entry by JamieMcCloskey and Joan McArdle

BOYS ARE EVIL

Let us start with the singular of the gender ieBOY We find that the inverse of BOY is YOB (iefrom right to left) So we have

BOYminus1 = YOB

We all know that in order to behave in a yobbishfashion the yob must be alive

YOB = LIVE

Now we can invert both sides as follows

YOBminus1 = LIVEminus1

On calculating the inverses of each side we areleft with

BOY = EVIL

So we have proven that BOY = EVIL Let usmultiply both sides by two

2 BOY = 2 EVIL

This can be reduced to

BOYS = 2 EVIL

We feel we ought to be awarded the prize for thisbecause not only have we proven that boys are evilwe have proven they are more evil than evil mdash infact they are too evil

The prize was a $20 book token

Seminars

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoAbstract tubesrdquo

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoUse of gene expressioncomparisons for classification of tissuesamplesrdquo

Dr Christopher Paul Tuffley (University ofCalifornia Davis) ldquoFinite subset spaces ofthe circlerdquo

Dr Stefan Grunewald (University ofCanterbury) ldquoThin quartet setsrdquo

Dr Thomas Forster (University of Cambridge)ldquoDe-linearising Ehrenfeucht-Mostowskirdquo

Professor Ian Stewart (University ofWarwick) ldquoNetwork models of sympatricspeciationrdquo

Dr WP Malcolm (Australian NationalUniversity) ldquoState and mode estimation fordiscrete time-jump Markov systemsrdquo

13

LOCAL NEWS

Dr Granville Tunnicliffe Wilson (LancasterUniversity) ldquoAssessment of empiricalnon-linear time series prediction toolsrdquo

Professor Michael McAleer (University ofWestern Australia) ldquoGeneralizedautoregressive conditional correlation scalarBEKK and indirect DCCrdquo

Liam Wagner (University of Queensland)ldquoRepresentations of finite groups andpre-monoidal categoriesrdquo

Ben Martin

MASSEY UNIVERSITY

Institute of Fundamental Sciences(Palmerston North)

Mathematics

Partir cest mourir a peu

From Dean Halford

ldquoGillian Thornley is retiring after nearly 26 yearsat Massey University having joined the mathemat-ics staff in 1980 when Brian Hayman was Headof Department Following her graduation with aFirst Class Honours MSc from the University ofCanterbury in 1963 Gillian obtained a PhD inmetric differential geometry from the Universityof Toronto in 1965 under the supervision of Pro-fessors Hanno Rund and Ray Vanstone She re-turned to New Zealand where she lectured for twoyears at the University of Canterbury before mar-rying John Thornley and taking up a lectureshipat the Trinidad campus of the University of theWest Indies Then it was back to Nelson whereGillian and Johnrsquos children Louise and Matthewwere born and where Gillian did some part-timeteaching at Nelson Polytechnic In 1973 the familymoved to Wellington where Gillian obtained mostlypart-time positions in Wellington College of Educa-tion Wellington Polytechnic Victoria Universityand held a research position in the Department ofMines

Gillian has had an outstanding career She ishighly respected by staff and students as a top-levelteacher winning three Institute of FundamentalSciencesrsquo Distinguished Teaching Awards Furtherdistinction was the invitation from The Universityof Auckland to deliver the 1996 Aldis Lecture heraddress was entitled From Descartes to Aldis andBeyond A Geometrical History Gillian has givenfine support and encouragement to all of her stu-dents her personal qualities of patience integrity

fairness and professionalism are almost legendaryGillianrsquos research interests lie mainly in differentialgeometry in particular the study of Finsler spacesbut her work on gender issues in mathematics ed-ucation led her to publish and speak at overseasconferences

Gillianrsquos professionalism has been exercised inthe wider community where she has given much tothe development of mathematics and mathematicseducation For 14 years from 1978 to 1992 Gilliancontributed to the activities of the New ZealandMathematical Society in several roles becomingPresident of the Society for two years in 1989 Shewill be remembered for her wise and capable leader-ship during a challenging period and representedthe Society at the IMU meeting in Kobe Japanwhere she was the only woman president presentIndeed Gillian is the only woman President of theNZMS since it was founded in 1974 In 1997 shewas elected a Fellow of the New Zealand Mathe-matical Society and in December 2004 the Societyawarded Gillian Honorary Membership status

In addition to the Mathematics Department andnumerous boards and committees at Massey Uni-versity Gillian has also contributed much to theManawatu Mathematics Teachersrsquo Association Al-ways this was characterized by her superb organi-zational skills her grasp of the mathematics cur-riculum her concern for student welfare and herrepresentation of women in academia

Gillianrsquos professionalism depth of experiencesuperior teaching skills and guidance on studentmatters will be widely missed We wish her a longand happy retirementrdquo

Alas we also had to say farewell to ProfessorAndrew Vince His sunny nature will be missed andalso his excellent contribution towards our teachingprogramme and research

Charles Little has itchy feet again and will be go-ing on an yearrsquos sabbatical to the Federal Univer-sity of Mato Groso do Sul Campo Grande BrazilHe will be visiting Marcelo de Cavallo DesejamosBarbara e Charles um tempo agradavel em Brasil

On a more happy noteCongratulations to

bull Kee Teo and Tammy Smith for securing aMassey University award ldquoFund for Innovationand Excellence in Teachingrdquo for the projectldquoDeveloping MathsFirst A web-based systemto enhance first year mathematics teachingand learningrdquo Last year they were also suc-cessful in obtaining a grant

bull Gillian Thornley and Igor Boglaev who havebeen made Fellows of the New Zealand Math-ematics Society

14

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

NZMS Newsletter No 95

Dr Primoz Potocnik ldquoTetravalentedge-transitive graphs and related topicsrdquo

Dr Tsukasa Yashiro ldquoDiagrammaticapproaches to surface-knots - 1-handles andtriple pointsrdquo

Dr Anthony D Blaom ldquoThe ghost ofsymmetry in a curved worldrdquo

Professor Mariusz Wodzicki (University ofCaliforniamdashBerkeley) ldquoExotic tracesrdquo

Dr Sina Greenwood ldquoCharacterisingcontinuous functions on connected compactspacesrdquo

Professor Wolfgang Willems (UniversitaetMagdeburg) ldquoSome open problems inmodular representation theoryrdquo ldquoAre cycliccodes asymptotically goodrdquo and ldquoA surveyof problems and methods in coding theoryrdquo

Dr Frank Himstedt (TU Munich)ldquoLow-dimensional representations ofSteinbergrsquos triality groupsrdquo

Dr Sasa Radomirovic (Rutgers University)ldquoCusp forms over function fields and modularsymbolsrdquo

Dr Andreas Cap (University of Vienna)ldquoInfinitesimal automorphisms anddeformations of parabolic geometriesrdquo

Professor Cheryl Praeger (UWA) ldquoGroupsprobability algorithms computing withgiantsrdquo

Dr Laura Ciobanu ldquoFixed subgroups in freegroupsrdquo

Professor CK Raju (University of BhopalIndia) ldquoSeries expansions and thecomputation of Pi in India from Aryabhattato Yuktideepikardquo and ldquoThe Indian origins ofthe calculus and its transmission to Europeprior to Newton and Leibniz Part 2 Lessonsfor mathematics educationrdquo

Christopher Hay ldquoMetrizability of compactconvex sets under certain criteriardquo

Dr Hyuck Chung ldquoModelling timber-basedfloor structuresrdquo

David Choquenot (Landcare Research)ldquoMathematical models and wildlifepopulation dynamicsrdquo

Daniel Watzenig (Graz University ofTechnology) ldquoElectrical capacitancetomography at Graz University ofTechnology state-space representations andparticle filteringrdquo

Dr Carlo Laing (Massey University (Albany))ldquoEquation-free modelling some neuralexamplesrdquo

Dr David Bryant ldquo Continuous and (mostly)tractable models for the variation ofevolutionary ratesrdquo

Dr Emily Lane (UCLA) ldquoWave-currentinteractions and shore-connected barsrdquo

Professor Roman Nedela (Slovak Academy ofSciences) ldquoEnumeration of maps andhypermaps with given genus and givennumber of edgesrdquo

Garry J Tee

Department of Statistics

Russell Millar appeared on the television programldquoJohn Campbell Liverdquo in early July His briefingwas to tell the audience the probability of winningLottomdashalthough we all know that if Russell reallyhad inside Lotto information wersquod be advertisingfor a new lecturer The segment was created byJacqui Brown and her crew and was filmed in a lec-ture theatre on the Tamaki campus The style waslight-hearted but nonetheless demonstrated somesolid statistical points including conditional prob-abilities and misuse of the ldquolaw of averagesrdquo Rus-sellrsquos night of fame has been recorded for posterityand it will be played in our first-year lectures foryears to come

Russell Millar and Marti Anderson have been di-viding their time between Perth Auckland andAlaska in their work on fisheries and multivariateecological analysis

The Rodent Invasion Research Group spent atotal of two weeks rat-catching in the Bay of Is-lands With the Department of ConservationSteven Miller helped set up the traps then thenext week Rachel Fewster went to bag the rats withStephen Cope as cameraman The trip was excep-tionally successful with a total of 360 rats baggedfor the DNA project

Doctoral student James Russell spent time inBrazil to give a student finalist talk at the Soci-ety for Conservation Biology He then travelled toOregon for the Association of Pacific Rim Univer-sities Annual Doctoral Students Conference on the

11

LOCAL NEWS

multidisciplinary theme ldquoMoving Towards a Sus-tainable Futurerdquo A paper on ldquoIntercepting thefirst rat ashorerdquo written by James Russell andothers from the Rodent Invasion ProjectResearchGroup (DR Towns SH Anderson amp MN Clout)tells of a rat which was released on Motuhoropapa(one of the uninhabited Noises Islands) which thenswam 400 metres to the island Otata That pa-per was published in NATURE 437(7062) p1107and it has attracted attention around the worldThe story was run by over 100 international newsagencies from the UK Independent to WashingtonNational Public Radio and it also included a fea-ture on NZ TV news

Tim Langlois has gained his PhD for his thesisldquoInfluence of reef-associated predators on adjacentsoft-sediment communitiesrdquo He has been based atthe Leigh Marine Laboratory Yuichi Hirose hascompleted his PhD

An NZIMA Postgraduate Scholarship has beenawarded to Adam Smith for a Masters thesisproject at The University of Auckland (from July2005) on the statistical validation of the NZ MarineEnvironment Classification under the supervisionof Drs Marti Anderson and Clinton Duffy MikeManning who is studying for his MSc while work-ing for NIWA in Wellington appeared on ldquo60 Min-utesrdquo in April in a piece about the satellite taggingof white sharks

IASS 55 was organised and run by this Depart-ment and held at the Maritime Museum in Auck-land New Zealand Alastair Scott chaired some ofthe sessions CR Rao spoke to a packed room inthis Department In his talk he covered a historyof statistics

From June 2 to 7 the SRTL-4 conference washeld at Grafton Hall It was organised largely byRoss Parsonage and Maxine Pfannkuch along withinput from Dani Ben-Zvi Joan Garfield and oth-ers Rachel Cunliffe Ross Ihaka Chris Wild MikeForster and Ilze Ziedins attended ISI 55 in SydneyAustralia

Seminars

Dr Beatrix Jones (Massey University(Albany)) ldquoFitting and interpreting sparseGaussian graphical models forhigh-dimensional datardquo

Associate Professor David Whittaker (TheUniversity of Waikato) ldquoThe state of the artin the generation of efficient statisticaldesignsrdquo

Associate Professor Russell Millar ldquoLocalsensitivity of Bayesian inference to priors anddatardquo

Dr W Paul Malcolm (ANU) ldquoNew Gaussianmixture techniques for filtering andsmoothing of discrete-time Gauss-Markovjump Markov systemsrdquo

Dr Stephane Guindon (BioinformaticsInstitute) ldquoStatistical modelling of thenatural selection processes acting on proteinsequencesrdquo

Dr Ross Ihaka ldquoColour me carefullyrdquo

Dr Roger Marshall (School of PopulationHealth Epidemiology and Biostatistics)ldquoUse of scaled rectangle diagrams to visualizecategorical data with particular reference toclinical and epidemiological datardquo

Professor Goeran Kauermann (University ofBielefeldUNSW) ldquoPenalized splinesmoothing and generalized linear mixedmodelsmdashsome theory and applicationsrdquo

Garry J Tee

UNIVERSITY OF CANTERBURY

Department of Mathematics and Statistics

Dr Mike Plank will be taking up a position as Lec-turer from 2006 Mike does mathematical mod-elling especially of problems arising from biologyIn current joint work with David Wall and TimDavid (Engineering) he is studying the early stagesof cardiovascular disease by modelling blood flow inthe human body He finished his PhD at the Uni-versity of Leeds in 2003 then began a postdoctoraljob here in February 2004 Mike has already beenmaking himself useful around the place and he is awelcome addition to the department

Another current Postdoctoral Fellow Dr Si-mona Vıta will be staying here for a further yearHer new position is supported by the FoRSTNZScience amp Technology ldquoBridge to Employmentrdquoscheme

Dr Paul Mullowney is a recent arrival He starteda two-year university-funded postdoctoral fellow-ship in June 2005 Paul is working with Alex Jameson stochasticity in biological processes He com-pleted his PhD on dynamical systems and fluid me-chanics at the University of Colorado at Boulder in2004

Professor Ian Stewart who is well knownas a mathematician and an expositor visited

12

NZMS Newsletter No 95

Christchurch in September He delivered a keynotespeech at the New Zealand Association of Mathe-matics Teachers Biennial Conference as well as giv-ing a departmental colloquium

Douglas Bridges was awarded a standard Mars-den grant for his project ldquoConstructive reversemathematicsrdquo The project has two main aimsto classify constructive theorems according tothe proof principles that are necessary to estab-lish them and to classify essentially nonconstruc-tive theorems according to the nonconstructiveproof principles that they require for their proofBen Martin and Gerhard Rohrle (Southampton)were awarded a standard Marsden grant for theirproject ldquoA geometric approach to reductive alge-braic groupsrdquo They will use geometric techniquesto study reductive algebraic groups and their sub-groups and the way in which they act on theirassociated buildings

Rick Beatson was an invited speaker at the SIAMconference on Geometric Design and Computingin Phoenix Arizona in OctoberNovember Dou-glas Bridges and Simona Vıta visited Munich towork with Peter Schuster and Josef Berger andspoke at the Computability amp Complexity in Anal-ysis meeting in Kyoto in August In SeptemberMike Steel gave talks in Canada UC Berkeley andat the Mathematical Biosciences Institute in Ohiowhich hosted a special workshop on Phylogeneticsand Self-Organization in Ecology The 10th an-nual phylogenetics meeting will be held in Kaik-oura from 12ndash17 February 2006 Ben Martin gavea talk at the November Group Theory workshopat the University of Auckland which was held tocelebrate the 65th birthday of Charles Leedham-Green

Professor Dominic Welsh (University of Oxford)is currently visiting as part of the University ofCanterbury and University of Oxford exchange pro-gram The exchange is teaching-based and as aresult Dominic has been lecturing second yeargraph theory as well as a fourth year matroidtheory course Other recent and current visitorsinclude Tanja Gernhard (University of Munich)Dr Granville Tunnicliffe-Wilson (Lancaster Univer-sity) Dr Emily Lane (UCLA) Dr Jon Pitchford(University of York) and Professor Minoru Murata(Tokyo Institute of Technology)

John Hannah organised a sequence of mathemat-ical enrichment talks for schoolpupils during thesecond half of the year The talks covered topicsranging from complexity in computing to algebra topatterns and pictures In a talk on proof in mathe-matics a well-known ldquoproofrdquo was presented of theproposition that Girls are Evil The audience waschallenged to give a proof in a similar spirit that

Boys are Evil Here is the winning entry by JamieMcCloskey and Joan McArdle

BOYS ARE EVIL

Let us start with the singular of the gender ieBOY We find that the inverse of BOY is YOB (iefrom right to left) So we have

BOYminus1 = YOB

We all know that in order to behave in a yobbishfashion the yob must be alive

YOB = LIVE

Now we can invert both sides as follows

YOBminus1 = LIVEminus1

On calculating the inverses of each side we areleft with

BOY = EVIL

So we have proven that BOY = EVIL Let usmultiply both sides by two

2 BOY = 2 EVIL

This can be reduced to

BOYS = 2 EVIL

We feel we ought to be awarded the prize for thisbecause not only have we proven that boys are evilwe have proven they are more evil than evil mdash infact they are too evil

The prize was a $20 book token

Seminars

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoAbstract tubesrdquo

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoUse of gene expressioncomparisons for classification of tissuesamplesrdquo

Dr Christopher Paul Tuffley (University ofCalifornia Davis) ldquoFinite subset spaces ofthe circlerdquo

Dr Stefan Grunewald (University ofCanterbury) ldquoThin quartet setsrdquo

Dr Thomas Forster (University of Cambridge)ldquoDe-linearising Ehrenfeucht-Mostowskirdquo

Professor Ian Stewart (University ofWarwick) ldquoNetwork models of sympatricspeciationrdquo

Dr WP Malcolm (Australian NationalUniversity) ldquoState and mode estimation fordiscrete time-jump Markov systemsrdquo

13

LOCAL NEWS

Dr Granville Tunnicliffe Wilson (LancasterUniversity) ldquoAssessment of empiricalnon-linear time series prediction toolsrdquo

Professor Michael McAleer (University ofWestern Australia) ldquoGeneralizedautoregressive conditional correlation scalarBEKK and indirect DCCrdquo

Liam Wagner (University of Queensland)ldquoRepresentations of finite groups andpre-monoidal categoriesrdquo

Ben Martin

MASSEY UNIVERSITY

Institute of Fundamental Sciences(Palmerston North)

Mathematics

Partir cest mourir a peu

From Dean Halford

ldquoGillian Thornley is retiring after nearly 26 yearsat Massey University having joined the mathemat-ics staff in 1980 when Brian Hayman was Headof Department Following her graduation with aFirst Class Honours MSc from the University ofCanterbury in 1963 Gillian obtained a PhD inmetric differential geometry from the Universityof Toronto in 1965 under the supervision of Pro-fessors Hanno Rund and Ray Vanstone She re-turned to New Zealand where she lectured for twoyears at the University of Canterbury before mar-rying John Thornley and taking up a lectureshipat the Trinidad campus of the University of theWest Indies Then it was back to Nelson whereGillian and Johnrsquos children Louise and Matthewwere born and where Gillian did some part-timeteaching at Nelson Polytechnic In 1973 the familymoved to Wellington where Gillian obtained mostlypart-time positions in Wellington College of Educa-tion Wellington Polytechnic Victoria Universityand held a research position in the Department ofMines

Gillian has had an outstanding career She ishighly respected by staff and students as a top-levelteacher winning three Institute of FundamentalSciencesrsquo Distinguished Teaching Awards Furtherdistinction was the invitation from The Universityof Auckland to deliver the 1996 Aldis Lecture heraddress was entitled From Descartes to Aldis andBeyond A Geometrical History Gillian has givenfine support and encouragement to all of her stu-dents her personal qualities of patience integrity

fairness and professionalism are almost legendaryGillianrsquos research interests lie mainly in differentialgeometry in particular the study of Finsler spacesbut her work on gender issues in mathematics ed-ucation led her to publish and speak at overseasconferences

Gillianrsquos professionalism has been exercised inthe wider community where she has given much tothe development of mathematics and mathematicseducation For 14 years from 1978 to 1992 Gilliancontributed to the activities of the New ZealandMathematical Society in several roles becomingPresident of the Society for two years in 1989 Shewill be remembered for her wise and capable leader-ship during a challenging period and representedthe Society at the IMU meeting in Kobe Japanwhere she was the only woman president presentIndeed Gillian is the only woman President of theNZMS since it was founded in 1974 In 1997 shewas elected a Fellow of the New Zealand Mathe-matical Society and in December 2004 the Societyawarded Gillian Honorary Membership status

In addition to the Mathematics Department andnumerous boards and committees at Massey Uni-versity Gillian has also contributed much to theManawatu Mathematics Teachersrsquo Association Al-ways this was characterized by her superb organi-zational skills her grasp of the mathematics cur-riculum her concern for student welfare and herrepresentation of women in academia

Gillianrsquos professionalism depth of experiencesuperior teaching skills and guidance on studentmatters will be widely missed We wish her a longand happy retirementrdquo

Alas we also had to say farewell to ProfessorAndrew Vince His sunny nature will be missed andalso his excellent contribution towards our teachingprogramme and research

Charles Little has itchy feet again and will be go-ing on an yearrsquos sabbatical to the Federal Univer-sity of Mato Groso do Sul Campo Grande BrazilHe will be visiting Marcelo de Cavallo DesejamosBarbara e Charles um tempo agradavel em Brasil

On a more happy noteCongratulations to

bull Kee Teo and Tammy Smith for securing aMassey University award ldquoFund for Innovationand Excellence in Teachingrdquo for the projectldquoDeveloping MathsFirst A web-based systemto enhance first year mathematics teachingand learningrdquo Last year they were also suc-cessful in obtaining a grant

bull Gillian Thornley and Igor Boglaev who havebeen made Fellows of the New Zealand Math-ematics Society

14

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

LOCAL NEWS

multidisciplinary theme ldquoMoving Towards a Sus-tainable Futurerdquo A paper on ldquoIntercepting thefirst rat ashorerdquo written by James Russell andothers from the Rodent Invasion ProjectResearchGroup (DR Towns SH Anderson amp MN Clout)tells of a rat which was released on Motuhoropapa(one of the uninhabited Noises Islands) which thenswam 400 metres to the island Otata That pa-per was published in NATURE 437(7062) p1107and it has attracted attention around the worldThe story was run by over 100 international newsagencies from the UK Independent to WashingtonNational Public Radio and it also included a fea-ture on NZ TV news

Tim Langlois has gained his PhD for his thesisldquoInfluence of reef-associated predators on adjacentsoft-sediment communitiesrdquo He has been based atthe Leigh Marine Laboratory Yuichi Hirose hascompleted his PhD

An NZIMA Postgraduate Scholarship has beenawarded to Adam Smith for a Masters thesisproject at The University of Auckland (from July2005) on the statistical validation of the NZ MarineEnvironment Classification under the supervisionof Drs Marti Anderson and Clinton Duffy MikeManning who is studying for his MSc while work-ing for NIWA in Wellington appeared on ldquo60 Min-utesrdquo in April in a piece about the satellite taggingof white sharks

IASS 55 was organised and run by this Depart-ment and held at the Maritime Museum in Auck-land New Zealand Alastair Scott chaired some ofthe sessions CR Rao spoke to a packed room inthis Department In his talk he covered a historyof statistics

From June 2 to 7 the SRTL-4 conference washeld at Grafton Hall It was organised largely byRoss Parsonage and Maxine Pfannkuch along withinput from Dani Ben-Zvi Joan Garfield and oth-ers Rachel Cunliffe Ross Ihaka Chris Wild MikeForster and Ilze Ziedins attended ISI 55 in SydneyAustralia

Seminars

Dr Beatrix Jones (Massey University(Albany)) ldquoFitting and interpreting sparseGaussian graphical models forhigh-dimensional datardquo

Associate Professor David Whittaker (TheUniversity of Waikato) ldquoThe state of the artin the generation of efficient statisticaldesignsrdquo

Associate Professor Russell Millar ldquoLocalsensitivity of Bayesian inference to priors anddatardquo

Dr W Paul Malcolm (ANU) ldquoNew Gaussianmixture techniques for filtering andsmoothing of discrete-time Gauss-Markovjump Markov systemsrdquo

Dr Stephane Guindon (BioinformaticsInstitute) ldquoStatistical modelling of thenatural selection processes acting on proteinsequencesrdquo

Dr Ross Ihaka ldquoColour me carefullyrdquo

Dr Roger Marshall (School of PopulationHealth Epidemiology and Biostatistics)ldquoUse of scaled rectangle diagrams to visualizecategorical data with particular reference toclinical and epidemiological datardquo

Professor Goeran Kauermann (University ofBielefeldUNSW) ldquoPenalized splinesmoothing and generalized linear mixedmodelsmdashsome theory and applicationsrdquo

Garry J Tee

UNIVERSITY OF CANTERBURY

Department of Mathematics and Statistics

Dr Mike Plank will be taking up a position as Lec-turer from 2006 Mike does mathematical mod-elling especially of problems arising from biologyIn current joint work with David Wall and TimDavid (Engineering) he is studying the early stagesof cardiovascular disease by modelling blood flow inthe human body He finished his PhD at the Uni-versity of Leeds in 2003 then began a postdoctoraljob here in February 2004 Mike has already beenmaking himself useful around the place and he is awelcome addition to the department

Another current Postdoctoral Fellow Dr Si-mona Vıta will be staying here for a further yearHer new position is supported by the FoRSTNZScience amp Technology ldquoBridge to Employmentrdquoscheme

Dr Paul Mullowney is a recent arrival He starteda two-year university-funded postdoctoral fellow-ship in June 2005 Paul is working with Alex Jameson stochasticity in biological processes He com-pleted his PhD on dynamical systems and fluid me-chanics at the University of Colorado at Boulder in2004

Professor Ian Stewart who is well knownas a mathematician and an expositor visited

12

NZMS Newsletter No 95

Christchurch in September He delivered a keynotespeech at the New Zealand Association of Mathe-matics Teachers Biennial Conference as well as giv-ing a departmental colloquium

Douglas Bridges was awarded a standard Mars-den grant for his project ldquoConstructive reversemathematicsrdquo The project has two main aimsto classify constructive theorems according tothe proof principles that are necessary to estab-lish them and to classify essentially nonconstruc-tive theorems according to the nonconstructiveproof principles that they require for their proofBen Martin and Gerhard Rohrle (Southampton)were awarded a standard Marsden grant for theirproject ldquoA geometric approach to reductive alge-braic groupsrdquo They will use geometric techniquesto study reductive algebraic groups and their sub-groups and the way in which they act on theirassociated buildings

Rick Beatson was an invited speaker at the SIAMconference on Geometric Design and Computingin Phoenix Arizona in OctoberNovember Dou-glas Bridges and Simona Vıta visited Munich towork with Peter Schuster and Josef Berger andspoke at the Computability amp Complexity in Anal-ysis meeting in Kyoto in August In SeptemberMike Steel gave talks in Canada UC Berkeley andat the Mathematical Biosciences Institute in Ohiowhich hosted a special workshop on Phylogeneticsand Self-Organization in Ecology The 10th an-nual phylogenetics meeting will be held in Kaik-oura from 12ndash17 February 2006 Ben Martin gavea talk at the November Group Theory workshopat the University of Auckland which was held tocelebrate the 65th birthday of Charles Leedham-Green

Professor Dominic Welsh (University of Oxford)is currently visiting as part of the University ofCanterbury and University of Oxford exchange pro-gram The exchange is teaching-based and as aresult Dominic has been lecturing second yeargraph theory as well as a fourth year matroidtheory course Other recent and current visitorsinclude Tanja Gernhard (University of Munich)Dr Granville Tunnicliffe-Wilson (Lancaster Univer-sity) Dr Emily Lane (UCLA) Dr Jon Pitchford(University of York) and Professor Minoru Murata(Tokyo Institute of Technology)

John Hannah organised a sequence of mathemat-ical enrichment talks for schoolpupils during thesecond half of the year The talks covered topicsranging from complexity in computing to algebra topatterns and pictures In a talk on proof in mathe-matics a well-known ldquoproofrdquo was presented of theproposition that Girls are Evil The audience waschallenged to give a proof in a similar spirit that

Boys are Evil Here is the winning entry by JamieMcCloskey and Joan McArdle

BOYS ARE EVIL

Let us start with the singular of the gender ieBOY We find that the inverse of BOY is YOB (iefrom right to left) So we have

BOYminus1 = YOB

We all know that in order to behave in a yobbishfashion the yob must be alive

YOB = LIVE

Now we can invert both sides as follows

YOBminus1 = LIVEminus1

On calculating the inverses of each side we areleft with

BOY = EVIL

So we have proven that BOY = EVIL Let usmultiply both sides by two

2 BOY = 2 EVIL

This can be reduced to

BOYS = 2 EVIL

We feel we ought to be awarded the prize for thisbecause not only have we proven that boys are evilwe have proven they are more evil than evil mdash infact they are too evil

The prize was a $20 book token

Seminars

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoAbstract tubesrdquo

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoUse of gene expressioncomparisons for classification of tissuesamplesrdquo

Dr Christopher Paul Tuffley (University ofCalifornia Davis) ldquoFinite subset spaces ofthe circlerdquo

Dr Stefan Grunewald (University ofCanterbury) ldquoThin quartet setsrdquo

Dr Thomas Forster (University of Cambridge)ldquoDe-linearising Ehrenfeucht-Mostowskirdquo

Professor Ian Stewart (University ofWarwick) ldquoNetwork models of sympatricspeciationrdquo

Dr WP Malcolm (Australian NationalUniversity) ldquoState and mode estimation fordiscrete time-jump Markov systemsrdquo

13

LOCAL NEWS

Dr Granville Tunnicliffe Wilson (LancasterUniversity) ldquoAssessment of empiricalnon-linear time series prediction toolsrdquo

Professor Michael McAleer (University ofWestern Australia) ldquoGeneralizedautoregressive conditional correlation scalarBEKK and indirect DCCrdquo

Liam Wagner (University of Queensland)ldquoRepresentations of finite groups andpre-monoidal categoriesrdquo

Ben Martin

MASSEY UNIVERSITY

Institute of Fundamental Sciences(Palmerston North)

Mathematics

Partir cest mourir a peu

From Dean Halford

ldquoGillian Thornley is retiring after nearly 26 yearsat Massey University having joined the mathemat-ics staff in 1980 when Brian Hayman was Headof Department Following her graduation with aFirst Class Honours MSc from the University ofCanterbury in 1963 Gillian obtained a PhD inmetric differential geometry from the Universityof Toronto in 1965 under the supervision of Pro-fessors Hanno Rund and Ray Vanstone She re-turned to New Zealand where she lectured for twoyears at the University of Canterbury before mar-rying John Thornley and taking up a lectureshipat the Trinidad campus of the University of theWest Indies Then it was back to Nelson whereGillian and Johnrsquos children Louise and Matthewwere born and where Gillian did some part-timeteaching at Nelson Polytechnic In 1973 the familymoved to Wellington where Gillian obtained mostlypart-time positions in Wellington College of Educa-tion Wellington Polytechnic Victoria Universityand held a research position in the Department ofMines

Gillian has had an outstanding career She ishighly respected by staff and students as a top-levelteacher winning three Institute of FundamentalSciencesrsquo Distinguished Teaching Awards Furtherdistinction was the invitation from The Universityof Auckland to deliver the 1996 Aldis Lecture heraddress was entitled From Descartes to Aldis andBeyond A Geometrical History Gillian has givenfine support and encouragement to all of her stu-dents her personal qualities of patience integrity

fairness and professionalism are almost legendaryGillianrsquos research interests lie mainly in differentialgeometry in particular the study of Finsler spacesbut her work on gender issues in mathematics ed-ucation led her to publish and speak at overseasconferences

Gillianrsquos professionalism has been exercised inthe wider community where she has given much tothe development of mathematics and mathematicseducation For 14 years from 1978 to 1992 Gilliancontributed to the activities of the New ZealandMathematical Society in several roles becomingPresident of the Society for two years in 1989 Shewill be remembered for her wise and capable leader-ship during a challenging period and representedthe Society at the IMU meeting in Kobe Japanwhere she was the only woman president presentIndeed Gillian is the only woman President of theNZMS since it was founded in 1974 In 1997 shewas elected a Fellow of the New Zealand Mathe-matical Society and in December 2004 the Societyawarded Gillian Honorary Membership status

In addition to the Mathematics Department andnumerous boards and committees at Massey Uni-versity Gillian has also contributed much to theManawatu Mathematics Teachersrsquo Association Al-ways this was characterized by her superb organi-zational skills her grasp of the mathematics cur-riculum her concern for student welfare and herrepresentation of women in academia

Gillianrsquos professionalism depth of experiencesuperior teaching skills and guidance on studentmatters will be widely missed We wish her a longand happy retirementrdquo

Alas we also had to say farewell to ProfessorAndrew Vince His sunny nature will be missed andalso his excellent contribution towards our teachingprogramme and research

Charles Little has itchy feet again and will be go-ing on an yearrsquos sabbatical to the Federal Univer-sity of Mato Groso do Sul Campo Grande BrazilHe will be visiting Marcelo de Cavallo DesejamosBarbara e Charles um tempo agradavel em Brasil

On a more happy noteCongratulations to

bull Kee Teo and Tammy Smith for securing aMassey University award ldquoFund for Innovationand Excellence in Teachingrdquo for the projectldquoDeveloping MathsFirst A web-based systemto enhance first year mathematics teachingand learningrdquo Last year they were also suc-cessful in obtaining a grant

bull Gillian Thornley and Igor Boglaev who havebeen made Fellows of the New Zealand Math-ematics Society

14

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

NZMS Newsletter No 95

Christchurch in September He delivered a keynotespeech at the New Zealand Association of Mathe-matics Teachers Biennial Conference as well as giv-ing a departmental colloquium

Douglas Bridges was awarded a standard Mars-den grant for his project ldquoConstructive reversemathematicsrdquo The project has two main aimsto classify constructive theorems according tothe proof principles that are necessary to estab-lish them and to classify essentially nonconstruc-tive theorems according to the nonconstructiveproof principles that they require for their proofBen Martin and Gerhard Rohrle (Southampton)were awarded a standard Marsden grant for theirproject ldquoA geometric approach to reductive alge-braic groupsrdquo They will use geometric techniquesto study reductive algebraic groups and their sub-groups and the way in which they act on theirassociated buildings

Rick Beatson was an invited speaker at the SIAMconference on Geometric Design and Computingin Phoenix Arizona in OctoberNovember Dou-glas Bridges and Simona Vıta visited Munich towork with Peter Schuster and Josef Berger andspoke at the Computability amp Complexity in Anal-ysis meeting in Kyoto in August In SeptemberMike Steel gave talks in Canada UC Berkeley andat the Mathematical Biosciences Institute in Ohiowhich hosted a special workshop on Phylogeneticsand Self-Organization in Ecology The 10th an-nual phylogenetics meeting will be held in Kaik-oura from 12ndash17 February 2006 Ben Martin gavea talk at the November Group Theory workshopat the University of Auckland which was held tocelebrate the 65th birthday of Charles Leedham-Green

Professor Dominic Welsh (University of Oxford)is currently visiting as part of the University ofCanterbury and University of Oxford exchange pro-gram The exchange is teaching-based and as aresult Dominic has been lecturing second yeargraph theory as well as a fourth year matroidtheory course Other recent and current visitorsinclude Tanja Gernhard (University of Munich)Dr Granville Tunnicliffe-Wilson (Lancaster Univer-sity) Dr Emily Lane (UCLA) Dr Jon Pitchford(University of York) and Professor Minoru Murata(Tokyo Institute of Technology)

John Hannah organised a sequence of mathemat-ical enrichment talks for schoolpupils during thesecond half of the year The talks covered topicsranging from complexity in computing to algebra topatterns and pictures In a talk on proof in mathe-matics a well-known ldquoproofrdquo was presented of theproposition that Girls are Evil The audience waschallenged to give a proof in a similar spirit that

Boys are Evil Here is the winning entry by JamieMcCloskey and Joan McArdle

BOYS ARE EVIL

Let us start with the singular of the gender ieBOY We find that the inverse of BOY is YOB (iefrom right to left) So we have

BOYminus1 = YOB

We all know that in order to behave in a yobbishfashion the yob must be alive

YOB = LIVE

Now we can invert both sides as follows

YOBminus1 = LIVEminus1

On calculating the inverses of each side we areleft with

BOY = EVIL

So we have proven that BOY = EVIL Let usmultiply both sides by two

2 BOY = 2 EVIL

This can be reduced to

BOYS = 2 EVIL

We feel we ought to be awarded the prize for thisbecause not only have we proven that boys are evilwe have proven they are more evil than evil mdash infact they are too evil

The prize was a $20 book token

Seminars

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoAbstract tubesrdquo

Professor Daniel Naiman (Johns HopkinsUniversity) ldquoUse of gene expressioncomparisons for classification of tissuesamplesrdquo

Dr Christopher Paul Tuffley (University ofCalifornia Davis) ldquoFinite subset spaces ofthe circlerdquo

Dr Stefan Grunewald (University ofCanterbury) ldquoThin quartet setsrdquo

Dr Thomas Forster (University of Cambridge)ldquoDe-linearising Ehrenfeucht-Mostowskirdquo

Professor Ian Stewart (University ofWarwick) ldquoNetwork models of sympatricspeciationrdquo

Dr WP Malcolm (Australian NationalUniversity) ldquoState and mode estimation fordiscrete time-jump Markov systemsrdquo

13

LOCAL NEWS

Dr Granville Tunnicliffe Wilson (LancasterUniversity) ldquoAssessment of empiricalnon-linear time series prediction toolsrdquo

Professor Michael McAleer (University ofWestern Australia) ldquoGeneralizedautoregressive conditional correlation scalarBEKK and indirect DCCrdquo

Liam Wagner (University of Queensland)ldquoRepresentations of finite groups andpre-monoidal categoriesrdquo

Ben Martin

MASSEY UNIVERSITY

Institute of Fundamental Sciences(Palmerston North)

Mathematics

Partir cest mourir a peu

From Dean Halford

ldquoGillian Thornley is retiring after nearly 26 yearsat Massey University having joined the mathemat-ics staff in 1980 when Brian Hayman was Headof Department Following her graduation with aFirst Class Honours MSc from the University ofCanterbury in 1963 Gillian obtained a PhD inmetric differential geometry from the Universityof Toronto in 1965 under the supervision of Pro-fessors Hanno Rund and Ray Vanstone She re-turned to New Zealand where she lectured for twoyears at the University of Canterbury before mar-rying John Thornley and taking up a lectureshipat the Trinidad campus of the University of theWest Indies Then it was back to Nelson whereGillian and Johnrsquos children Louise and Matthewwere born and where Gillian did some part-timeteaching at Nelson Polytechnic In 1973 the familymoved to Wellington where Gillian obtained mostlypart-time positions in Wellington College of Educa-tion Wellington Polytechnic Victoria Universityand held a research position in the Department ofMines

Gillian has had an outstanding career She ishighly respected by staff and students as a top-levelteacher winning three Institute of FundamentalSciencesrsquo Distinguished Teaching Awards Furtherdistinction was the invitation from The Universityof Auckland to deliver the 1996 Aldis Lecture heraddress was entitled From Descartes to Aldis andBeyond A Geometrical History Gillian has givenfine support and encouragement to all of her stu-dents her personal qualities of patience integrity

fairness and professionalism are almost legendaryGillianrsquos research interests lie mainly in differentialgeometry in particular the study of Finsler spacesbut her work on gender issues in mathematics ed-ucation led her to publish and speak at overseasconferences

Gillianrsquos professionalism has been exercised inthe wider community where she has given much tothe development of mathematics and mathematicseducation For 14 years from 1978 to 1992 Gilliancontributed to the activities of the New ZealandMathematical Society in several roles becomingPresident of the Society for two years in 1989 Shewill be remembered for her wise and capable leader-ship during a challenging period and representedthe Society at the IMU meeting in Kobe Japanwhere she was the only woman president presentIndeed Gillian is the only woman President of theNZMS since it was founded in 1974 In 1997 shewas elected a Fellow of the New Zealand Mathe-matical Society and in December 2004 the Societyawarded Gillian Honorary Membership status

In addition to the Mathematics Department andnumerous boards and committees at Massey Uni-versity Gillian has also contributed much to theManawatu Mathematics Teachersrsquo Association Al-ways this was characterized by her superb organi-zational skills her grasp of the mathematics cur-riculum her concern for student welfare and herrepresentation of women in academia

Gillianrsquos professionalism depth of experiencesuperior teaching skills and guidance on studentmatters will be widely missed We wish her a longand happy retirementrdquo

Alas we also had to say farewell to ProfessorAndrew Vince His sunny nature will be missed andalso his excellent contribution towards our teachingprogramme and research

Charles Little has itchy feet again and will be go-ing on an yearrsquos sabbatical to the Federal Univer-sity of Mato Groso do Sul Campo Grande BrazilHe will be visiting Marcelo de Cavallo DesejamosBarbara e Charles um tempo agradavel em Brasil

On a more happy noteCongratulations to

bull Kee Teo and Tammy Smith for securing aMassey University award ldquoFund for Innovationand Excellence in Teachingrdquo for the projectldquoDeveloping MathsFirst A web-based systemto enhance first year mathematics teachingand learningrdquo Last year they were also suc-cessful in obtaining a grant

bull Gillian Thornley and Igor Boglaev who havebeen made Fellows of the New Zealand Math-ematics Society

14

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

LOCAL NEWS

Dr Granville Tunnicliffe Wilson (LancasterUniversity) ldquoAssessment of empiricalnon-linear time series prediction toolsrdquo

Professor Michael McAleer (University ofWestern Australia) ldquoGeneralizedautoregressive conditional correlation scalarBEKK and indirect DCCrdquo

Liam Wagner (University of Queensland)ldquoRepresentations of finite groups andpre-monoidal categoriesrdquo

Ben Martin

MASSEY UNIVERSITY

Institute of Fundamental Sciences(Palmerston North)

Mathematics

Partir cest mourir a peu

From Dean Halford

ldquoGillian Thornley is retiring after nearly 26 yearsat Massey University having joined the mathemat-ics staff in 1980 when Brian Hayman was Headof Department Following her graduation with aFirst Class Honours MSc from the University ofCanterbury in 1963 Gillian obtained a PhD inmetric differential geometry from the Universityof Toronto in 1965 under the supervision of Pro-fessors Hanno Rund and Ray Vanstone She re-turned to New Zealand where she lectured for twoyears at the University of Canterbury before mar-rying John Thornley and taking up a lectureshipat the Trinidad campus of the University of theWest Indies Then it was back to Nelson whereGillian and Johnrsquos children Louise and Matthewwere born and where Gillian did some part-timeteaching at Nelson Polytechnic In 1973 the familymoved to Wellington where Gillian obtained mostlypart-time positions in Wellington College of Educa-tion Wellington Polytechnic Victoria Universityand held a research position in the Department ofMines

Gillian has had an outstanding career She ishighly respected by staff and students as a top-levelteacher winning three Institute of FundamentalSciencesrsquo Distinguished Teaching Awards Furtherdistinction was the invitation from The Universityof Auckland to deliver the 1996 Aldis Lecture heraddress was entitled From Descartes to Aldis andBeyond A Geometrical History Gillian has givenfine support and encouragement to all of her stu-dents her personal qualities of patience integrity

fairness and professionalism are almost legendaryGillianrsquos research interests lie mainly in differentialgeometry in particular the study of Finsler spacesbut her work on gender issues in mathematics ed-ucation led her to publish and speak at overseasconferences

Gillianrsquos professionalism has been exercised inthe wider community where she has given much tothe development of mathematics and mathematicseducation For 14 years from 1978 to 1992 Gilliancontributed to the activities of the New ZealandMathematical Society in several roles becomingPresident of the Society for two years in 1989 Shewill be remembered for her wise and capable leader-ship during a challenging period and representedthe Society at the IMU meeting in Kobe Japanwhere she was the only woman president presentIndeed Gillian is the only woman President of theNZMS since it was founded in 1974 In 1997 shewas elected a Fellow of the New Zealand Mathe-matical Society and in December 2004 the Societyawarded Gillian Honorary Membership status

In addition to the Mathematics Department andnumerous boards and committees at Massey Uni-versity Gillian has also contributed much to theManawatu Mathematics Teachersrsquo Association Al-ways this was characterized by her superb organi-zational skills her grasp of the mathematics cur-riculum her concern for student welfare and herrepresentation of women in academia

Gillianrsquos professionalism depth of experiencesuperior teaching skills and guidance on studentmatters will be widely missed We wish her a longand happy retirementrdquo

Alas we also had to say farewell to ProfessorAndrew Vince His sunny nature will be missed andalso his excellent contribution towards our teachingprogramme and research

Charles Little has itchy feet again and will be go-ing on an yearrsquos sabbatical to the Federal Univer-sity of Mato Groso do Sul Campo Grande BrazilHe will be visiting Marcelo de Cavallo DesejamosBarbara e Charles um tempo agradavel em Brasil

On a more happy noteCongratulations to

bull Kee Teo and Tammy Smith for securing aMassey University award ldquoFund for Innovationand Excellence in Teachingrdquo for the projectldquoDeveloping MathsFirst A web-based systemto enhance first year mathematics teachingand learningrdquo Last year they were also suc-cessful in obtaining a grant

bull Gillian Thornley and Igor Boglaev who havebeen made Fellows of the New Zealand Math-ematics Society

14

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

NZMS Newsletter No 95

bull Robert McLachlan who was awarded a MasseyUniversity Research Medal and also won theNew Zealand Maths Society Research Awardfor 2005

bull Jonathan Marshall who successfully defendedhis PhD thesis ldquoHolomorphic Solutions toFunctional Differential Equationsrdquo

To take note of the above events the mathematicsmob and associates went to a Thai Restaurant forlunch Normally this restaurant does not open till1700 but they specially opened for us again (forthe 4th time)

Igor Boglaev spent two weeks (140805ndash280805) working with Assoc Prof S Wang (Schoolof Mathematics and Statistics the University ofWestern Australia Perth) on the joint researchproject ldquoNovel Numerical Methods for ModellingSemiconductor Devicesrdquo His visit was supportedin part by the University of Western Australia

Bruce van Brunt visited KAIST in South Koreafor two months He came as part of an appliedmathematics visiting professor team and lecturedon the calculus of variations among other topicsMissing the hot humid summer he enjoyed twomonths of autumn weather and the hospitality ofthe Koreans Rumour has it that he spent manyweekends tramping around various local nationalparks

Allan Wilson Centre newsmdashMike Hendy re-ports

ldquoOur congratulations to Barbara Holland on win-ning the trifecta Barbara completes her NZSampTpost-doctoral Fellowship with the Centre in Febru-ary but will be rehired as a Research Fellow withinthe Centre with the assistance of a FRST ldquoBridgeto Employmentrdquo grant which will meet 50 of hersalary for the first year This is on top of her re-cent successes in winning a FULL Marsden grantin the 2005 round as sole PI and her success inbeing awarded the 2005 Hamilton Memorial Prizeby the RSNZ Academy for her ldquopioneering mathe-matical research in evolutionary biology includingthe development of new instruments for phyloge-netic network representation The prize recognizesher achievements in the conception and applica-tion of sophisticated mathematical and statisticaltechniques to evolutionary biology especially in therepresentation of phylogenetic networks and trees(A phylogenetic tree is a graphical means to de-pict the evolutionary relationships of a group oforganisms) With her solid background in oper-ations research Dr Holland has developed noveltools for representing the conflicting information

that arises in many studies of evolutionary rela-tionships where a large collection of phylogenetictrees occurs as opposed to a single treerdquo Congrat-ulations Barbara

The AWC has hosted six German 4th year ex-change students from the Biomathematics pro-gramme at Greifswald for this semester Theyeach did a paper in Computational Biology andin Bioinformatics as well as some advanced math-ematics papers The project reports from theirComputational Biology papers were all excellentand we expect most will be incorporated in researchpublications currently under preparation This isthe third group to come form Greifswald we areexpecting a larger number next year

Bernard Beckett our RSNZ Teaching Fellow for2005 is just completing his year with us before hereturns to Onslow College (Wellington) where heteaches maths economics and drama This hasbeen an excellent placement for us and we hopeto have a report from Bernard in the next newslet-ter During this year Bernard was awarded theNZPost and NZ Booksellerrsquos prizes for his teenagenovel ldquoMalcolm and Julietrdquo Bhalchandra Thattehas recently returned from Spain (via India) Hereports

ldquoI visited Centre de Recerca Matematica Bel-laterra (near Barcelona) for a month in Septem-ber and October There were two courses on Ran-dom Graphs (by Bela Bollobas) and Graph Ho-momorphisms (by Jaroslav Nesetril) The courseswere followed by two more conferencesmdashone onGraph Morphisms and Applications and another onTutte Polynomials and Applications The coursesand conferences were exciting and have given meenough food for thought The conference on Tuttepolynomials had several presentations on prob-lems related to statistical mechanics The Spanishweather during that time was also not bad On theway to Spain I visited my home in Pune India Myniece Vaidehee recently represented India at the In-ternational Mathematics Olympiad in Mexico Al-though she didnrsquot win a medal she did win a prizefor the best solution of the most difficult problemShe is now pursuing BMath Honours at the In-dian Statistical Institute in Bangalore In Indianow there is a lot of encouragement and scholar-ships for students who participate in the Olympiador are selected for the ldquobase camprdquo The state levelOlympiads are now attracting increasing numberof students many of whom want to do research inmathematics or theoretical computer science Itis good to see mathematics successfully competingwith professional courses for the best students Iam sure we will see more Olympiad medals andmore mathematicians from India in futurerdquo

15

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

LOCAL NEWS

Seminars

Professor Mike Steel (University ofCanterbury) ldquoHungarian chickenscratchingsmdasha new weapon in the war onerrorrdquo

Professor Robert McLachlan ldquoBoundarylayer separation in high-speed flowrdquo

Tilak Ratnanather (Centre for ImagingScience The John Hopkins University)ldquoComputational anatomy shape analysis ofbrain cortical cardiac and dendriticstructuresrdquo

Professor Andrew Vince ldquoTiling Euclideanspacerdquo and ldquoRep-tiling Euclidean spacerdquo

Graduate Seminars Series

Dion OrsquoNeale ldquoSplit-step methods for highlyoscillatory non-linear problemsrdquo

Philip Zhang ldquoThree lectures on partialdifferential equationsrdquo and ldquoApplications ofsemigroup theory to PDErsquosrdquo

Marijcke Vlieg-Hulstman

Institute of Information andMathematical Sciences (Albany)

Beatrix Jones Alona Ben-Tal and Winston Sweat-man were all successful in the latest MarsdenFund round Beatrix has received a Fast StartGrant ldquoDesign of parentage analysis experimentsa case study for understanding uncertainty inmodels with latent (unobserved) variablesrdquo Alonaalso received a Fast Start Grant ldquoA new mech-anism for Cheyne-Stokes respirationrdquo Winstonis an associate investigator on the Astronomyproject ldquoMicrolensing a new way to explorethe Galaxyrdquo which is led by Ian Bond (also fromIIMS) Both Beatrix and Alona have positionsavailable for MSc students (httpiimsmasseyacnzscholarshipsjones MastershtmhttpiimsmasseyacnzscholarshipsAdv MasterStudentpdf) and PhD positionsare available with Ian and Winston (httpwwwmasseyacnzsimiabondprojectshtm)

The third (and last) ANZIAM Mathematics-in-Industry Study Group to be hosted in New Zealandis coming up fast It is being held in Massey Uni-versity Albany Auckland the week Monday 30thJanuaryndashFriday 3 February 2006 The Minister ofResearch Science and Technology Steve Maharey

will open MISG2006 on the Monday Registra-tions are free with student-grants available thanksmostly to CSIRO (Aus) and FRST (NZ) So weinvite you all to come for a packed week of brain-storming FRST have indicated support for on-going contracts is likely to be available This yearthe problems look the best ever Seven are definiteone from Western Australasiamdasha real beautymdashandthree of the seven are biological problems Reg-ular companies like NZ Steel Transpower andFisher and Paykel are coming back with some in-teresting new contributors Dr Peter Howell fromOCIAM Oxford is coming at our invitation to pro-vide overview support Director Graeme Wake andhis team are really keen to make this the best everThe Proceedings of the MISG2004 are publishedand the 2005 version will appear soon For more de-tails see httpmisg2006masseyacnz〈httpmisg2006masseyacnz〉 and you can registeron this site

Carlo Laing Leng Leng Lim Robert McKibbinGalkadowite Senaratne Ratnesh Suri and GraemeWake all participated in the Auckland-Waikato Ap-plied Mathematics Day at The University of Auck-land in September Graeme presented ldquoA modelof transient cell-growthrdquo Sena ldquoMicrowave signalprocessing for breast cancer detectionrdquo and LengLeng ldquoModelling of volcanic ashfallrdquo

Mick Roberts is back in Europe again He firstvisited the Netherlands and is currently at OxfordUniversity as a Visiting Fellow at St CatherinersquosCollege Jo Mann is at the present time (mid-November) visiting Mick for a week

All the postgraduates were involved in presenta-tions at the IIMS Postgraduate Conference at theend of October The careful planning and prepara-tion led to a fine day Jo Mann was again on theconference committee The Proceedings volumedesigned by Jo and compiled by the postgraduateson the Committee will be a lasting testament toan excellent set of papers talks and posters

In November Senaratne Galkowite will be partic-ipating in the International Conference on SensingTechnology (ICST 2005) in Palmerston North Hewill present ldquoA New Approach to Breast TumourDetection Using Microwave Frequencies A Two-dimensional Modelrdquo a joint paper with his PhDsupervisors Graeme Wake Winston Sweatman andRick Keam (Keam Holden Associates)

Mathematics was as usual well represented at theAuckland MarathonHalf Marathon event on Sun-day 30th October with aches and pains to show forit and some good times Jo Mann and Martyn Smitcompleted the half marathon It was Jorsquos first halfmarathon while Martyn sped to a personal besttime for the distance Shaun Cooper and Winston

16

NZMS Newsletter No 95

Sweatman both completed the full marathon alsoposting personal best times improving by severalminutes on their times from last year

Jo Mann who is a member of the Mint DanceClub on campus also performed display dances forthe ASA Ball (This was a few weeks before herhalf marathon performance)

Visitors

Heng Huat Chan from the National Universityof Singapore

Wen-Chin Liaw from the National ChungCheng University Taiwan

Michael Hirschhorn from the University ofNew South Wales

Bruce Berndt from the University of Illinois

Mark Nelson (joint with School of EngineeringUA) from University of Wollongong

Seminars

Boris Pavlov (The University of Auckland)ldquoSolvable models of quantum networksquantum switch and spin filterrdquo

Winfried Kohnen (Universitaat HeidelbergGermany) ldquoRepresentation numbers ofintegers by positive definite quadratic formsrdquo

Samuel Nosal ldquoAround a stochastic model forepidemicsrdquo

Robert McKibbin ldquo3 animalcoursesmdashquantitatively of courserdquo

Claire Jordan ldquoReliability of the PBRF datardquo

Wen-Chin Liaw (National Chung ChengUniversity Taiwan) ldquoEvaluations ofalternating Euler sumsrdquo

Wolfgang Willems(Otto-von-Guericke-Universitat Germany)ldquoA survey of problems in coding theoryrdquo

Robert McKibbin ldquoA Model for dispersal oferuption ejectardquo

Joanne Mann ldquoModelling Measles Nearlyrdquo

Nicolas Smith (The University of Auckland)ldquoVirtual heart diseaserdquo

Douglas S Bridges (University of Canterbury)ldquoApartness on latticesrdquo

Ratneesh Suri ldquoStochastic differentialequations (SDEs)rdquo

Michael Hirschhorn (University of New SouthWales) ldquoPartitions into four squaresrdquo

Sharleen Harper ldquoTransport of individualdroplets in spraysrdquo

Frederick Lam ldquoThe number of solutions ofa2 + 2b2 + 2c2 + 4d2 = n in integersrdquo

Gaven Martin ldquoAspects of modernmathematics or what the hell does a puremathematician dordquo

Ulrich Zuelicke (IFS Massey University atPalmerston North) ldquoElectronics with spinrdquo

Bruce Berndt (University of Illinois)ldquoRamanujanrsquos life and notebooksrdquo

Winston Sweatman

Institute of Information Sciencesand Technology (Palmerston North)

Statistics

Steve Haslett has again been travelling extensivelyoverseas with recent visits to Minneapolis as aninvited speaker at the Joint Statistical Meetingsand Helsinki to speak at a conference in small areaestimation but also taking in Washington Dublinand Newcastle to visit research colleagues

Steve and Geoff Jones are completing anotherpoverty-mapping project for the UN World FoodProgramme producing small-area estimates ofpoverty and malnutrition for Nepal for use in aidtargeting They have each spent several weeks inKathmandu working with staff at the Nepal Cen-tral Bureau of Statistics and the local WFP officeThe Himalayas did become visible one evening butthe rest of the time were hidden by the monsoonclouds No signs of Maoist activity in the Kath-mandu Valley but there were a few student demon-strations and road closures to contend with

Doug Stirling is currently on sabbatical at theUniversity of Reading developing his CAST (Com-puter Assisted Statistics Teaching) software inparticular adding chapters about multiple regres-sion and multivariate analysis In September heis running a Workshop in Slovenia at the AppliedStatistics 2005 conference

A large (but not random) sample of Massey PNstatisticians attended and presented at the NZSAconference in Otago Many of us even managed to

17

LOCAL NEWS

return from it eventually although we suspect afew may still be lost in the fog

Congratulations to Jonathan Godfrey who hasbeen appointed to a permanent position as Lec-turer in Statistics Sadly Jonathan will no longerbe eligible for the Best Student Presentation prizeat the NZSA (or any other) conference so his longwinning streak has finally come to an end

Mark Bebbington signed himself out of hospi-tal to attend the first Hidden Markov Models andComplex Systems workshop in Wanaka Appar-ently the scientific programme just edged the foodfor accolades although the fusion cuisine was a lit-tle rough on his tender stomach For his pains (lit-erally) he now finds himself in charge of the pro-gramme for the second workshop scheduled for theless distracting surrounds of downtown WellingtonMark is also eagerly anticipating the arrival of thenew professor to take over his administrative du-ties although it is not true that that he is crossingoff the days on his calendar

Chin Diew Lai presented a talk at an invitedsession ldquoVariance issues in the design of controlchartsrdquo at the Fourth International Symposiumon Business and Industrial Statistics Palm CoveQueensland 13ndash16 April 2005 Jonathan Godfreyalso attended this symposium

Dr Ganes S Ganesalingam and Dr Alasdair Nobleorganised a Palmy Statisticianrsquos Forum on Friday28 October The Statistics Forum was held in theRussell Room at Wharerata and included 42 par-ticipants from IVABS EpiCentre The Allan WilsonCentre IFNHH AgResearch Grasslands AgRe-search Ruakura HortResearch Fonterra Land-care the Ministry of Social Development Welling-ton the IIST Statistics Group and several post-graduate students from the Massey University cam-pus Professors Richard Harris (acting HoI IIST)Jeff Hunter (IIMS Albany) and Steve Haslett(IIST) opened the forum welcoming the opportu-nity to hear and discuss current research amongstscientists and statisticians on the local scene Thekeynote speaker Dr Harold Henderson from AgRe-search Ruakura suggested a dynamic approach tosolving statistical problems which gave all the par-ticipants lsquofood for thoughtrsquo Twelve presentationswere given in total and provided much to discussin the short breaks throughout the day New linkswere formed amongst all the participants and theground set for research collaborations in the futureThe prospect of holding this event on an annual ba-sis was also mooted and may provide more positiveinteraction in future years for the benefit of all

Geoff Jones

UNIVERSITY OF OTAGO

Department of Mathematics and Statistics

Boris Baeumer received a University of Otago EarlyCareer Award for Distinction in Research Theseawards were introduced for the first time in 2004 torecognise the universityrsquos most talented early careerresearchers There were five successful nomineesthis year who each received $2000 to help supporttheir respective research programmes Boris hasdeveloped models to describe flow and transportin pourous media The novel and interdisciplinarynature of his work was recognised in 2003 when hewon a Marsden Fast-Start grant which led to a fullMarsden proposal

We welcomed Dr Mihaly Kovacs to the Depart-ment in September Misi is a Postdoctoral Fellowworking with Mark Meerschaert for one year

The NZSA Annual Conference was held atSalmond Hall from 4ndash6 July and was a great suc-cess Since the conference and the accommodationwere in one place no one was compelled to get outinto the Dunedin mid-winter (which is a beauti-ful thing) The number of students who enteredtalks and posters was gratifying Some partici-pants (nominally the Young Statisticians) spentan evening playing Laser Strike and having din-ner Tiri Sullivan of Statistics New Zealand wonthe SPSS Graduate Package At the conferencedinner the next night music was provided by a lo-cal Dunedin Band Student prizes were awarded byRay Hoare of HRS It seemed that everyone had apretty good time

David Fletcher left for Europe immediately af-ter the NZSA conference on conference and studyleave He attended the 25th European Meeting ofStatisticians in Oslo where he bumped into Mur-ray Jorgensen Murray and David both enjoyedthe conference dinner held at a grand hotel highabove the city that was the venue for the talks thateventually lead to the Oslo Peace Accord in theMiddle East David presented a poster on ldquoModel-Averaging in Factorial Experimentsrdquo David ar-rived in London en route to the conference the dayafter the first bombings in London and was notsure what to expect on his arrival All went wellfor the first half hour before his laptop bag con-taining a computer passports tickets camera andcellphone were whisked away by a modern-day Art-ful Dodger quite a welcome in many ways anda world away from Dunedin Several days laterthings had calmed down and Oslo was a most en-joyable location for a conference There was talkof many things including ldquoSparsityrdquo which seemsto be a fruitful area of research for those withminds clever enough to deal with these things such

18

NZMS Newsletter No 95

as David Donoho of Stanford one of the invitedspeakers

Richard Barker has been in the US on sabbaticalfor three months working with Bill Link at thePatuxent Wildlife Research Center on a book aboutBayesian inference in statistical ecology

Jonni Bidwell John Curran and Dennis Mc-Caughan attended a two-day Group Theory work-shop held in Auckland on 1ndash2 November as afestschrift for Charles Leedham-Green The threerepresentatives from the deep South very much en-joyed the proceedings which were organised by Ea-monn OrsquoBrien in his own inimitable style Lots ofstimulating talks on group theory amusing remi-niscences from the guest of honour and a memo-rable closing dinner what more could an algebraistwant

The following people are currently visiting orhave visited the Department since the last Newslet-ter

Linda Hutchison Department HeadAssociateProfessor of Secondary Education University ofWyoming from July 2005ndashJune 2006 Her researchinterest is Maths Education

Robert Aldred hosted visits from Professor AkiraSaito (Nihon Unversity) looking at forbidden sub-graph characterizations for 2-factors and ProfessorWal Wallis (Southern Illinois University) looking atsome interesting labelling problems for graphs

David Guichard Professor of Mathematics atWhitman College Washington USA is visitingthe Department from mid-October to DecemberHis areas of interest are Graph Theory and Com-binatorics

Estate Khmaladze Professor of Statistics at theSchool of Mathematics Statistics and ComputerScience Victoria University of Wellington visitedon November 11 and 12 and gave two talks

Seminars

Professor Richard Porter (University ofBristol) ldquoWave scattering by ice sheets ofvarying thicknessrdquo

Professor Martin Bridson (Imperial CollegeLondon 2005 Forder Lecturer) ldquoThelanguage of symmetry and the grammar ofspacerdquo

Gareth Vaughan ldquoSimulating Breaking WavesUsing Smoothed Particle Hydrodynamicsrdquo

Bill Jackson (Queen Mary University ofLondon) ldquoRigidity of Frameworksrdquo

Jeff Miller (Department of Psychology)ldquoReactive Time Measurements in CognitivePsychology Inferences from ProbabilityDistribution Analysisrdquo

Professor James Sneyd (The University ofAuckland) ldquoCalcium Oscillations UsingMaths to do Physiologyrdquo

Chris Linsell (Dunedin College of Education)ldquoThe Role of Activities in Teaching EarlyAlgebrardquo

Michael Albert (Department of ComputerScience) ldquoPlaying at Cross Purposesrdquo

Richard Barker ldquoAdvances in Statisticalthinking in the late 20th Centuryrdquo

Coralie Daniel ldquoHaving Blossoms with theLeavesrdquo

Colin Cheyne (Department of Philosophy) ldquoDoNumbers Exist An Introduction to thePhilosophy of Mathematicsrdquo

Fourth Year COMO and MATHS ProjectPresentations

Vivien Challis ldquoModelling Flow in the Ross IceShelfrdquo

John Irving ldquoIntroduction to RelativisticQuantum Theoryrdquo

Scott McCracken ldquoSylow Theoryrdquo

Mike Paulin (Department of Zoology andCentre for Neuroscience) ldquoSymmetry inmotion mathematical models of agilityrdquo

Paul Mullowney (University of Canterbury)ldquoThe role of variance in capped-ratestochastic growth modelsrdquo

Estate Khmaladze (Victoria University ofWellington) ldquoTowards statistical theory ofdiversity statistical analysis of large numberof rare events (LNRE)rdquo

Estate Khmaladze (Victoria University ofWellington) ldquoMartingale transform goodnessof fit tests for general parametric regressionrdquo

Lenette Grant

19

LOCAL NEWS

THE UNIVERSITY OF WAIKATO

Department of Mathematics

Now that examination marking is all over and donewith a number of members of the departmentwill be doing some travelling Kevin BroughanIan Hawthorn Ernie Kalnins Rua Murray TimStokes and Stephen Joe will be attending theMathematics Colloquium in Palmerston North Af-ter the Colloquium Tim will be flying to Australiato work with his collaborators Also crossing theTasman is Ian Craig who will be visiting the Uni-versity of Sydney for a week towards the end ofNovember Meanwhile Sean Oughton and GabrielFruit will be attending conferences in the US inearly December

Kevin is still on study leave as is Alfred SneydAlfred is expected back in the country in early De-cember

At the end of September Ian H and Tim at-tended the 49th Annual Meeting of the AustralianMathematical Society held at the University ofWestern Australia in Perth Tim gave a talk titledldquoIdempotent semiheaps I restrictive semiheapsrdquowhile in a similar vein Ian presented a talk titledldquoIdempotent semiheaps IIrdquo Before this conferenceTim attended the Twenty Third Victorian AlgebraConference (in Perth) where he presented a talkon ldquoEnriching Scheinrsquos algebra of partial mapsrdquo

One of our post-docs David Pontin left in earlyOctober to take up a position at the University ofNew Hampshire

In the first week of October Stephen had FrancesKuo from the University of New South Wales andDirk Nuyens from Katholieke Universiteit Leuvenas visitors

Seminars

G Tee (The University of Auckland) ldquoSirWilliam Rowan Hamilton (1805ndash1865 RoyalAstronomer of Irelandrdquo

D Nuyens (Katholieke Universiteit LeuvenBelgium) ldquoOn the construction of rank-1lattice rulesrdquo

T Stokes and I Hawthorn ldquoIdempotentsemiheapsrdquo

Stephen Joe

Department of Statistics

2005 has seen some quite dramatic changes tothe constitution of the Statistics Department atWaikato University At the end of the first semesterwe farewelled James Curren who left us to take up aposition as Senior Lecturer at Auckland UniversityHis contributions to the departmental teaching andadministration particularly his vast knowledge onthe latest happenings in the computer world aregreatly missed Our loss is definitely their gainWe have also seen the departure of Professor NyeJohn Nye announced his retirement at the endof June 2006 In his honour Ken Russell of theUniversity of Wollongong NSW organised a work-shop on ldquoExperimental Designrdquo which was held atthe end of November 2005 Nye and Ken have col-laborated on many projects over the years Nyeand his wife Alison have ldquoretiredrdquo to the sunnyMarlborough to run a vineyard We wish themboth a very happy retirement We have also hadto farewell our long time departmental assistantKaren Devoy In October Karen left to take up aposition as PA to Professor Ian Graham who wasoriginally in the Computer Science Department andthen long time Dean of the School of Computingand Mathematical Sciences here at the UniversityHe now heads up his own very successful comput-ing company Endace Technology Karen has beenreplaced by Rhonda Robertson who is doing a mar-vellous job filling the ldquobig shoesrdquo that Karen left

More than 75 participants from as far away asHelsinki took part in our one day workshop en-titled ldquoData Scrutiny and Data Miningrdquo held inMarch 2005 We were very privileged to have asthe presenter the NZSA Visiting Lecturer Profes-sor C R Rao from Penn State University USA Asmost people are aware Professor Rao is one of themost eminent statisticians in the world with a bi-ography that lists two pages of medals high levelappointments awards publications and qualifica-tions spanning six decades Anyone who has stud-ied statistics will have come across his name Tech-nical terms such as Cramer-Rao inequality RaorsquosScore Test the Fisher-Rao Theorem and Rao dis-tance appear in all standard books on statistics

Now for a little on the ldquocomings and goingsrdquo ofmembers of our department Dave Whitaker re-turned from leave at the beginning of the secondsemester and resumed his role of Chairperson ofthe department While he was away he visitedDave Johnson at Loughborough England Duringhis time there they put in the final touches for thesecond edition of their book ldquoStatistical Think-ing for Managersrdquo which is co-authored with NyeJohn

Local News Section continued on page 22

20

NZMS Newsletter No 95

GEORGE SZEKERES

29 May 1911ndash28 August 2005

The month of August 2005 has been a sad one for mathematics in Australia with thepassing of Ren Potts1 (on 9 August) and George Szekeres Both mathematicians wereclosely associated with Adelaide and many New Zealand mathematicians have had thepleasure of meeting these remarkably creative individuals Of special note is that bothmay perhaps be best known for work performed outside their specialist areas with thePotts model applying to statistical physics (not in Operational Research) and the Kruskal-Szekeres coordinates applying in general relativity (not in combinatorics)

Figure George and Esther at the Investiture Ceremony for Australian Honours heldat Government House George Szekeres received his award of Member of the Order of

Australia September 2002 at the age of 90

The following notes on George draw heavily from an article for the annual newsletter ofthe National Mathematics Summer School in 2001 by David Harvey now studying for aPhD in Harvard George inspired admiration and optimism from those fortunate to havemet him

George Szekeres was born in Budapest Hungary in 1911 and his gifts in science andmathematics were soon apparent An important influence during his high school careerwas the journal Kzpiskolai Matematikai s Fizikai Lapok which provided mathematicalproblems and enrichment (George was much later instrumental in establishing a similarhigh school mathematics journal Parabola in Australia) George went on to study chemi-cal engineering at the Technological University of Budapest to contribute to the familyrsquosleather business During his time at university he often met with a small group of enthusi-astic students drawn from the ranks of the Lapok problem-solvers to pose mathematicalproblems and discuss solutions The group was simmering with talent including PaulErdos and Paul Turan both outstanding mathematicians of this century Also attendingwas Esther Klein who has lectured on geometry at NMSS on two occasions and whomGeorge would marry in 1937

1see the article (and accompanying photos) by Earnie Tuck on Ren Potts atwwwmathsadelaideeduauappliedrecentRenPotts

21

LOCAL NEWS

return from it eventually although we suspect afew may still be lost in the fog

Congratulations to Jonathan Godfrey who hasbeen appointed to a permanent position as Lec-turer in Statistics Sadly Jonathan will no longerbe eligible for the Best Student Presentation prizeat the NZSA (or any other) conference so his longwinning streak has finally come to an end

Mark Bebbington signed himself out of hospi-tal to attend the first Hidden Markov Models andComplex Systems workshop in Wanaka Appar-ently the scientific programme just edged the foodfor accolades although the fusion cuisine was a lit-tle rough on his tender stomach For his pains (lit-erally) he now finds himself in charge of the pro-gramme for the second workshop scheduled for theless distracting surrounds of downtown WellingtonMark is also eagerly anticipating the arrival of thenew professor to take over his administrative du-ties although it is not true that that he is crossingoff the days on his calendar

Chin Diew Lai presented a talk at an invitedsession ldquoVariance issues in the design of controlchartsrdquo at the Fourth International Symposiumon Business and Industrial Statistics Palm CoveQueensland 13ndash16 April 2005 Jonathan Godfreyalso attended this symposium

Dr Ganes S Ganesalingam and Dr Alasdair Nobleorganised a Palmy Statisticianrsquos Forum on Friday28 October The Statistics Forum was held in theRussell Room at Wharerata and included 42 par-ticipants from IVABS EpiCentre The Allan WilsonCentre IFNHH AgResearch Grasslands AgRe-search Ruakura HortResearch Fonterra Land-care the Ministry of Social Development Welling-ton the IIST Statistics Group and several post-graduate students from the Massey University cam-pus Professors Richard Harris (acting HoI IIST)Jeff Hunter (IIMS Albany) and Steve Haslett(IIST) opened the forum welcoming the opportu-nity to hear and discuss current research amongstscientists and statisticians on the local scene Thekeynote speaker Dr Harold Henderson from AgRe-search Ruakura suggested a dynamic approach tosolving statistical problems which gave all the par-ticipants lsquofood for thoughtrsquo Twelve presentationswere given in total and provided much to discussin the short breaks throughout the day New linkswere formed amongst all the participants and theground set for research collaborations in the futureThe prospect of holding this event on an annual ba-sis was also mooted and may provide more positiveinteraction in future years for the benefit of all

Geoff Jones

UNIVERSITY OF OTAGO

Department of Mathematics and Statistics

Boris Baeumer received a University of Otago EarlyCareer Award for Distinction in Research Theseawards were introduced for the first time in 2004 torecognise the universityrsquos most talented early careerresearchers There were five successful nomineesthis year who each received $2000 to help supporttheir respective research programmes Boris hasdeveloped models to describe flow and transportin pourous media The novel and interdisciplinarynature of his work was recognised in 2003 when hewon a Marsden Fast-Start grant which led to a fullMarsden proposal

We welcomed Dr Mihaly Kovacs to the Depart-ment in September Misi is a Postdoctoral Fellowworking with Mark Meerschaert for one year

The NZSA Annual Conference was held atSalmond Hall from 4ndash6 July and was a great suc-cess Since the conference and the accommodationwere in one place no one was compelled to get outinto the Dunedin mid-winter (which is a beauti-ful thing) The number of students who enteredtalks and posters was gratifying Some partici-pants (nominally the Young Statisticians) spentan evening playing Laser Strike and having din-ner Tiri Sullivan of Statistics New Zealand wonthe SPSS Graduate Package At the conferencedinner the next night music was provided by a lo-cal Dunedin Band Student prizes were awarded byRay Hoare of HRS It seemed that everyone had apretty good time

David Fletcher left for Europe immediately af-ter the NZSA conference on conference and studyleave He attended the 25th European Meeting ofStatisticians in Oslo where he bumped into Mur-ray Jorgensen Murray and David both enjoyedthe conference dinner held at a grand hotel highabove the city that was the venue for the talks thateventually lead to the Oslo Peace Accord in theMiddle East David presented a poster on ldquoModel-Averaging in Factorial Experimentsrdquo David ar-rived in London en route to the conference the dayafter the first bombings in London and was notsure what to expect on his arrival All went wellfor the first half hour before his laptop bag con-taining a computer passports tickets camera andcellphone were whisked away by a modern-day Art-ful Dodger quite a welcome in many ways anda world away from Dunedin Several days laterthings had calmed down and Oslo was a most en-joyable location for a conference There was talkof many things including ldquoSparsityrdquo which seemsto be a fruitful area of research for those withminds clever enough to deal with these things such

18

NZMS Newsletter No 95

as David Donoho of Stanford one of the invitedspeakers

Richard Barker has been in the US on sabbaticalfor three months working with Bill Link at thePatuxent Wildlife Research Center on a book aboutBayesian inference in statistical ecology

Jonni Bidwell John Curran and Dennis Mc-Caughan attended a two-day Group Theory work-shop held in Auckland on 1ndash2 November as afestschrift for Charles Leedham-Green The threerepresentatives from the deep South very much en-joyed the proceedings which were organised by Ea-monn OrsquoBrien in his own inimitable style Lots ofstimulating talks on group theory amusing remi-niscences from the guest of honour and a memo-rable closing dinner what more could an algebraistwant

The following people are currently visiting orhave visited the Department since the last Newslet-ter

Linda Hutchison Department HeadAssociateProfessor of Secondary Education University ofWyoming from July 2005ndashJune 2006 Her researchinterest is Maths Education

Robert Aldred hosted visits from Professor AkiraSaito (Nihon Unversity) looking at forbidden sub-graph characterizations for 2-factors and ProfessorWal Wallis (Southern Illinois University) looking atsome interesting labelling problems for graphs

David Guichard Professor of Mathematics atWhitman College Washington USA is visitingthe Department from mid-October to DecemberHis areas of interest are Graph Theory and Com-binatorics

Estate Khmaladze Professor of Statistics at theSchool of Mathematics Statistics and ComputerScience Victoria University of Wellington visitedon November 11 and 12 and gave two talks

Seminars

Professor Richard Porter (University ofBristol) ldquoWave scattering by ice sheets ofvarying thicknessrdquo

Professor Martin Bridson (Imperial CollegeLondon 2005 Forder Lecturer) ldquoThelanguage of symmetry and the grammar ofspacerdquo

Gareth Vaughan ldquoSimulating Breaking WavesUsing Smoothed Particle Hydrodynamicsrdquo

Bill Jackson (Queen Mary University ofLondon) ldquoRigidity of Frameworksrdquo

Jeff Miller (Department of Psychology)ldquoReactive Time Measurements in CognitivePsychology Inferences from ProbabilityDistribution Analysisrdquo

Professor James Sneyd (The University ofAuckland) ldquoCalcium Oscillations UsingMaths to do Physiologyrdquo

Chris Linsell (Dunedin College of Education)ldquoThe Role of Activities in Teaching EarlyAlgebrardquo

Michael Albert (Department of ComputerScience) ldquoPlaying at Cross Purposesrdquo

Richard Barker ldquoAdvances in Statisticalthinking in the late 20th Centuryrdquo

Coralie Daniel ldquoHaving Blossoms with theLeavesrdquo

Colin Cheyne (Department of Philosophy) ldquoDoNumbers Exist An Introduction to thePhilosophy of Mathematicsrdquo

Fourth Year COMO and MATHS ProjectPresentations

Vivien Challis ldquoModelling Flow in the Ross IceShelfrdquo

John Irving ldquoIntroduction to RelativisticQuantum Theoryrdquo

Scott McCracken ldquoSylow Theoryrdquo

Mike Paulin (Department of Zoology andCentre for Neuroscience) ldquoSymmetry inmotion mathematical models of agilityrdquo

Paul Mullowney (University of Canterbury)ldquoThe role of variance in capped-ratestochastic growth modelsrdquo

Estate Khmaladze (Victoria University ofWellington) ldquoTowards statistical theory ofdiversity statistical analysis of large numberof rare events (LNRE)rdquo

Estate Khmaladze (Victoria University ofWellington) ldquoMartingale transform goodnessof fit tests for general parametric regressionrdquo

Lenette Grant

19

LOCAL NEWS

THE UNIVERSITY OF WAIKATO

Department of Mathematics

Now that examination marking is all over and donewith a number of members of the departmentwill be doing some travelling Kevin BroughanIan Hawthorn Ernie Kalnins Rua Murray TimStokes and Stephen Joe will be attending theMathematics Colloquium in Palmerston North Af-ter the Colloquium Tim will be flying to Australiato work with his collaborators Also crossing theTasman is Ian Craig who will be visiting the Uni-versity of Sydney for a week towards the end ofNovember Meanwhile Sean Oughton and GabrielFruit will be attending conferences in the US inearly December

Kevin is still on study leave as is Alfred SneydAlfred is expected back in the country in early De-cember

At the end of September Ian H and Tim at-tended the 49th Annual Meeting of the AustralianMathematical Society held at the University ofWestern Australia in Perth Tim gave a talk titledldquoIdempotent semiheaps I restrictive semiheapsrdquowhile in a similar vein Ian presented a talk titledldquoIdempotent semiheaps IIrdquo Before this conferenceTim attended the Twenty Third Victorian AlgebraConference (in Perth) where he presented a talkon ldquoEnriching Scheinrsquos algebra of partial mapsrdquo

One of our post-docs David Pontin left in earlyOctober to take up a position at the University ofNew Hampshire

In the first week of October Stephen had FrancesKuo from the University of New South Wales andDirk Nuyens from Katholieke Universiteit Leuvenas visitors

Seminars

G Tee (The University of Auckland) ldquoSirWilliam Rowan Hamilton (1805ndash1865 RoyalAstronomer of Irelandrdquo

D Nuyens (Katholieke Universiteit LeuvenBelgium) ldquoOn the construction of rank-1lattice rulesrdquo

T Stokes and I Hawthorn ldquoIdempotentsemiheapsrdquo

Stephen Joe

Department of Statistics

2005 has seen some quite dramatic changes tothe constitution of the Statistics Department atWaikato University At the end of the first semesterwe farewelled James Curren who left us to take up aposition as Senior Lecturer at Auckland UniversityHis contributions to the departmental teaching andadministration particularly his vast knowledge onthe latest happenings in the computer world aregreatly missed Our loss is definitely their gainWe have also seen the departure of Professor NyeJohn Nye announced his retirement at the endof June 2006 In his honour Ken Russell of theUniversity of Wollongong NSW organised a work-shop on ldquoExperimental Designrdquo which was held atthe end of November 2005 Nye and Ken have col-laborated on many projects over the years Nyeand his wife Alison have ldquoretiredrdquo to the sunnyMarlborough to run a vineyard We wish themboth a very happy retirement We have also hadto farewell our long time departmental assistantKaren Devoy In October Karen left to take up aposition as PA to Professor Ian Graham who wasoriginally in the Computer Science Department andthen long time Dean of the School of Computingand Mathematical Sciences here at the UniversityHe now heads up his own very successful comput-ing company Endace Technology Karen has beenreplaced by Rhonda Robertson who is doing a mar-vellous job filling the ldquobig shoesrdquo that Karen left

More than 75 participants from as far away asHelsinki took part in our one day workshop en-titled ldquoData Scrutiny and Data Miningrdquo held inMarch 2005 We were very privileged to have asthe presenter the NZSA Visiting Lecturer Profes-sor C R Rao from Penn State University USA Asmost people are aware Professor Rao is one of themost eminent statisticians in the world with a bi-ography that lists two pages of medals high levelappointments awards publications and qualifica-tions spanning six decades Anyone who has stud-ied statistics will have come across his name Tech-nical terms such as Cramer-Rao inequality RaorsquosScore Test the Fisher-Rao Theorem and Rao dis-tance appear in all standard books on statistics

Now for a little on the ldquocomings and goingsrdquo ofmembers of our department Dave Whitaker re-turned from leave at the beginning of the secondsemester and resumed his role of Chairperson ofthe department While he was away he visitedDave Johnson at Loughborough England Duringhis time there they put in the final touches for thesecond edition of their book ldquoStatistical Think-ing for Managersrdquo which is co-authored with NyeJohn

Local News Section continued on page 22

20

NZMS Newsletter No 95

GEORGE SZEKERES

29 May 1911ndash28 August 2005

The month of August 2005 has been a sad one for mathematics in Australia with thepassing of Ren Potts1 (on 9 August) and George Szekeres Both mathematicians wereclosely associated with Adelaide and many New Zealand mathematicians have had thepleasure of meeting these remarkably creative individuals Of special note is that bothmay perhaps be best known for work performed outside their specialist areas with thePotts model applying to statistical physics (not in Operational Research) and the Kruskal-Szekeres coordinates applying in general relativity (not in combinatorics)

Figure George and Esther at the Investiture Ceremony for Australian Honours heldat Government House George Szekeres received his award of Member of the Order of

Australia September 2002 at the age of 90

The following notes on George draw heavily from an article for the annual newsletter ofthe National Mathematics Summer School in 2001 by David Harvey now studying for aPhD in Harvard George inspired admiration and optimism from those fortunate to havemet him

George Szekeres was born in Budapest Hungary in 1911 and his gifts in science andmathematics were soon apparent An important influence during his high school careerwas the journal Kzpiskolai Matematikai s Fizikai Lapok which provided mathematicalproblems and enrichment (George was much later instrumental in establishing a similarhigh school mathematics journal Parabola in Australia) George went on to study chemi-cal engineering at the Technological University of Budapest to contribute to the familyrsquosleather business During his time at university he often met with a small group of enthusi-astic students drawn from the ranks of the Lapok problem-solvers to pose mathematicalproblems and discuss solutions The group was simmering with talent including PaulErdos and Paul Turan both outstanding mathematicians of this century Also attendingwas Esther Klein who has lectured on geometry at NMSS on two occasions and whomGeorge would marry in 1937

1see the article (and accompanying photos) by Earnie Tuck on Ren Potts atwwwmathsadelaideeduauappliedrecentRenPotts

21

NZMS Newsletter No 95

as David Donoho of Stanford one of the invitedspeakers

Richard Barker has been in the US on sabbaticalfor three months working with Bill Link at thePatuxent Wildlife Research Center on a book aboutBayesian inference in statistical ecology

Jonni Bidwell John Curran and Dennis Mc-Caughan attended a two-day Group Theory work-shop held in Auckland on 1ndash2 November as afestschrift for Charles Leedham-Green The threerepresentatives from the deep South very much en-joyed the proceedings which were organised by Ea-monn OrsquoBrien in his own inimitable style Lots ofstimulating talks on group theory amusing remi-niscences from the guest of honour and a memo-rable closing dinner what more could an algebraistwant

The following people are currently visiting orhave visited the Department since the last Newslet-ter

Linda Hutchison Department HeadAssociateProfessor of Secondary Education University ofWyoming from July 2005ndashJune 2006 Her researchinterest is Maths Education

Robert Aldred hosted visits from Professor AkiraSaito (Nihon Unversity) looking at forbidden sub-graph characterizations for 2-factors and ProfessorWal Wallis (Southern Illinois University) looking atsome interesting labelling problems for graphs

David Guichard Professor of Mathematics atWhitman College Washington USA is visitingthe Department from mid-October to DecemberHis areas of interest are Graph Theory and Com-binatorics

Estate Khmaladze Professor of Statistics at theSchool of Mathematics Statistics and ComputerScience Victoria University of Wellington visitedon November 11 and 12 and gave two talks

Seminars

Professor Richard Porter (University ofBristol) ldquoWave scattering by ice sheets ofvarying thicknessrdquo

Professor Martin Bridson (Imperial CollegeLondon 2005 Forder Lecturer) ldquoThelanguage of symmetry and the grammar ofspacerdquo

Gareth Vaughan ldquoSimulating Breaking WavesUsing Smoothed Particle Hydrodynamicsrdquo

Bill Jackson (Queen Mary University ofLondon) ldquoRigidity of Frameworksrdquo

Jeff Miller (Department of Psychology)ldquoReactive Time Measurements in CognitivePsychology Inferences from ProbabilityDistribution Analysisrdquo

Professor James Sneyd (The University ofAuckland) ldquoCalcium Oscillations UsingMaths to do Physiologyrdquo

Chris Linsell (Dunedin College of Education)ldquoThe Role of Activities in Teaching EarlyAlgebrardquo

Michael Albert (Department of ComputerScience) ldquoPlaying at Cross Purposesrdquo

Richard Barker ldquoAdvances in Statisticalthinking in the late 20th Centuryrdquo

Coralie Daniel ldquoHaving Blossoms with theLeavesrdquo

Colin Cheyne (Department of Philosophy) ldquoDoNumbers Exist An Introduction to thePhilosophy of Mathematicsrdquo

Fourth Year COMO and MATHS ProjectPresentations

Vivien Challis ldquoModelling Flow in the Ross IceShelfrdquo

John Irving ldquoIntroduction to RelativisticQuantum Theoryrdquo

Scott McCracken ldquoSylow Theoryrdquo

Mike Paulin (Department of Zoology andCentre for Neuroscience) ldquoSymmetry inmotion mathematical models of agilityrdquo

Paul Mullowney (University of Canterbury)ldquoThe role of variance in capped-ratestochastic growth modelsrdquo

Estate Khmaladze (Victoria University ofWellington) ldquoTowards statistical theory ofdiversity statistical analysis of large numberof rare events (LNRE)rdquo

Estate Khmaladze (Victoria University ofWellington) ldquoMartingale transform goodnessof fit tests for general parametric regressionrdquo

Lenette Grant

19

LOCAL NEWS

THE UNIVERSITY OF WAIKATO

Department of Mathematics

Now that examination marking is all over and donewith a number of members of the departmentwill be doing some travelling Kevin BroughanIan Hawthorn Ernie Kalnins Rua Murray TimStokes and Stephen Joe will be attending theMathematics Colloquium in Palmerston North Af-ter the Colloquium Tim will be flying to Australiato work with his collaborators Also crossing theTasman is Ian Craig who will be visiting the Uni-versity of Sydney for a week towards the end ofNovember Meanwhile Sean Oughton and GabrielFruit will be attending conferences in the US inearly December

Kevin is still on study leave as is Alfred SneydAlfred is expected back in the country in early De-cember

At the end of September Ian H and Tim at-tended the 49th Annual Meeting of the AustralianMathematical Society held at the University ofWestern Australia in Perth Tim gave a talk titledldquoIdempotent semiheaps I restrictive semiheapsrdquowhile in a similar vein Ian presented a talk titledldquoIdempotent semiheaps IIrdquo Before this conferenceTim attended the Twenty Third Victorian AlgebraConference (in Perth) where he presented a talkon ldquoEnriching Scheinrsquos algebra of partial mapsrdquo

One of our post-docs David Pontin left in earlyOctober to take up a position at the University ofNew Hampshire

In the first week of October Stephen had FrancesKuo from the University of New South Wales andDirk Nuyens from Katholieke Universiteit Leuvenas visitors

Seminars

G Tee (The University of Auckland) ldquoSirWilliam Rowan Hamilton (1805ndash1865 RoyalAstronomer of Irelandrdquo

D Nuyens (Katholieke Universiteit LeuvenBelgium) ldquoOn the construction of rank-1lattice rulesrdquo

T Stokes and I Hawthorn ldquoIdempotentsemiheapsrdquo

Stephen Joe

Department of Statistics

2005 has seen some quite dramatic changes tothe constitution of the Statistics Department atWaikato University At the end of the first semesterwe farewelled James Curren who left us to take up aposition as Senior Lecturer at Auckland UniversityHis contributions to the departmental teaching andadministration particularly his vast knowledge onthe latest happenings in the computer world aregreatly missed Our loss is definitely their gainWe have also seen the departure of Professor NyeJohn Nye announced his retirement at the endof June 2006 In his honour Ken Russell of theUniversity of Wollongong NSW organised a work-shop on ldquoExperimental Designrdquo which was held atthe end of November 2005 Nye and Ken have col-laborated on many projects over the years Nyeand his wife Alison have ldquoretiredrdquo to the sunnyMarlborough to run a vineyard We wish themboth a very happy retirement We have also hadto farewell our long time departmental assistantKaren Devoy In October Karen left to take up aposition as PA to Professor Ian Graham who wasoriginally in the Computer Science Department andthen long time Dean of the School of Computingand Mathematical Sciences here at the UniversityHe now heads up his own very successful comput-ing company Endace Technology Karen has beenreplaced by Rhonda Robertson who is doing a mar-vellous job filling the ldquobig shoesrdquo that Karen left

More than 75 participants from as far away asHelsinki took part in our one day workshop en-titled ldquoData Scrutiny and Data Miningrdquo held inMarch 2005 We were very privileged to have asthe presenter the NZSA Visiting Lecturer Profes-sor C R Rao from Penn State University USA Asmost people are aware Professor Rao is one of themost eminent statisticians in the world with a bi-ography that lists two pages of medals high levelappointments awards publications and qualifica-tions spanning six decades Anyone who has stud-ied statistics will have come across his name Tech-nical terms such as Cramer-Rao inequality RaorsquosScore Test the Fisher-Rao Theorem and Rao dis-tance appear in all standard books on statistics

Now for a little on the ldquocomings and goingsrdquo ofmembers of our department Dave Whitaker re-turned from leave at the beginning of the secondsemester and resumed his role of Chairperson ofthe department While he was away he visitedDave Johnson at Loughborough England Duringhis time there they put in the final touches for thesecond edition of their book ldquoStatistical Think-ing for Managersrdquo which is co-authored with NyeJohn

Local News Section continued on page 22

20

NZMS Newsletter No 95

GEORGE SZEKERES

29 May 1911ndash28 August 2005

The month of August 2005 has been a sad one for mathematics in Australia with thepassing of Ren Potts1 (on 9 August) and George Szekeres Both mathematicians wereclosely associated with Adelaide and many New Zealand mathematicians have had thepleasure of meeting these remarkably creative individuals Of special note is that bothmay perhaps be best known for work performed outside their specialist areas with thePotts model applying to statistical physics (not in Operational Research) and the Kruskal-Szekeres coordinates applying in general relativity (not in combinatorics)

Figure George and Esther at the Investiture Ceremony for Australian Honours heldat Government House George Szekeres received his award of Member of the Order of

Australia September 2002 at the age of 90

The following notes on George draw heavily from an article for the annual newsletter ofthe National Mathematics Summer School in 2001 by David Harvey now studying for aPhD in Harvard George inspired admiration and optimism from those fortunate to havemet him

George Szekeres was born in Budapest Hungary in 1911 and his gifts in science andmathematics were soon apparent An important influence during his high school careerwas the journal Kzpiskolai Matematikai s Fizikai Lapok which provided mathematicalproblems and enrichment (George was much later instrumental in establishing a similarhigh school mathematics journal Parabola in Australia) George went on to study chemi-cal engineering at the Technological University of Budapest to contribute to the familyrsquosleather business During his time at university he often met with a small group of enthusi-astic students drawn from the ranks of the Lapok problem-solvers to pose mathematicalproblems and discuss solutions The group was simmering with talent including PaulErdos and Paul Turan both outstanding mathematicians of this century Also attendingwas Esther Klein who has lectured on geometry at NMSS on two occasions and whomGeorge would marry in 1937

1see the article (and accompanying photos) by Earnie Tuck on Ren Potts atwwwmathsadelaideeduauappliedrecentRenPotts

21

LOCAL NEWS

THE UNIVERSITY OF WAIKATO

Department of Mathematics

Now that examination marking is all over and donewith a number of members of the departmentwill be doing some travelling Kevin BroughanIan Hawthorn Ernie Kalnins Rua Murray TimStokes and Stephen Joe will be attending theMathematics Colloquium in Palmerston North Af-ter the Colloquium Tim will be flying to Australiato work with his collaborators Also crossing theTasman is Ian Craig who will be visiting the Uni-versity of Sydney for a week towards the end ofNovember Meanwhile Sean Oughton and GabrielFruit will be attending conferences in the US inearly December

Kevin is still on study leave as is Alfred SneydAlfred is expected back in the country in early De-cember

At the end of September Ian H and Tim at-tended the 49th Annual Meeting of the AustralianMathematical Society held at the University ofWestern Australia in Perth Tim gave a talk titledldquoIdempotent semiheaps I restrictive semiheapsrdquowhile in a similar vein Ian presented a talk titledldquoIdempotent semiheaps IIrdquo Before this conferenceTim attended the Twenty Third Victorian AlgebraConference (in Perth) where he presented a talkon ldquoEnriching Scheinrsquos algebra of partial mapsrdquo

One of our post-docs David Pontin left in earlyOctober to take up a position at the University ofNew Hampshire

In the first week of October Stephen had FrancesKuo from the University of New South Wales andDirk Nuyens from Katholieke Universiteit Leuvenas visitors

Seminars

G Tee (The University of Auckland) ldquoSirWilliam Rowan Hamilton (1805ndash1865 RoyalAstronomer of Irelandrdquo

D Nuyens (Katholieke Universiteit LeuvenBelgium) ldquoOn the construction of rank-1lattice rulesrdquo

T Stokes and I Hawthorn ldquoIdempotentsemiheapsrdquo

Stephen Joe

Department of Statistics

2005 has seen some quite dramatic changes tothe constitution of the Statistics Department atWaikato University At the end of the first semesterwe farewelled James Curren who left us to take up aposition as Senior Lecturer at Auckland UniversityHis contributions to the departmental teaching andadministration particularly his vast knowledge onthe latest happenings in the computer world aregreatly missed Our loss is definitely their gainWe have also seen the departure of Professor NyeJohn Nye announced his retirement at the endof June 2006 In his honour Ken Russell of theUniversity of Wollongong NSW organised a work-shop on ldquoExperimental Designrdquo which was held atthe end of November 2005 Nye and Ken have col-laborated on many projects over the years Nyeand his wife Alison have ldquoretiredrdquo to the sunnyMarlborough to run a vineyard We wish themboth a very happy retirement We have also hadto farewell our long time departmental assistantKaren Devoy In October Karen left to take up aposition as PA to Professor Ian Graham who wasoriginally in the Computer Science Department andthen long time Dean of the School of Computingand Mathematical Sciences here at the UniversityHe now heads up his own very successful comput-ing company Endace Technology Karen has beenreplaced by Rhonda Robertson who is doing a mar-vellous job filling the ldquobig shoesrdquo that Karen left

More than 75 participants from as far away asHelsinki took part in our one day workshop en-titled ldquoData Scrutiny and Data Miningrdquo held inMarch 2005 We were very privileged to have asthe presenter the NZSA Visiting Lecturer Profes-sor C R Rao from Penn State University USA Asmost people are aware Professor Rao is one of themost eminent statisticians in the world with a bi-ography that lists two pages of medals high levelappointments awards publications and qualifica-tions spanning six decades Anyone who has stud-ied statistics will have come across his name Tech-nical terms such as Cramer-Rao inequality RaorsquosScore Test the Fisher-Rao Theorem and Rao dis-tance appear in all standard books on statistics

Now for a little on the ldquocomings and goingsrdquo ofmembers of our department Dave Whitaker re-turned from leave at the beginning of the secondsemester and resumed his role of Chairperson ofthe department While he was away he visitedDave Johnson at Loughborough England Duringhis time there they put in the final touches for thesecond edition of their book ldquoStatistical Think-ing for Managersrdquo which is co-authored with NyeJohn

Local News Section continued on page 22

20

NZMS Newsletter No 95

GEORGE SZEKERES

29 May 1911ndash28 August 2005

The month of August 2005 has been a sad one for mathematics in Australia with thepassing of Ren Potts1 (on 9 August) and George Szekeres Both mathematicians wereclosely associated with Adelaide and many New Zealand mathematicians have had thepleasure of meeting these remarkably creative individuals Of special note is that bothmay perhaps be best known for work performed outside their specialist areas with thePotts model applying to statistical physics (not in Operational Research) and the Kruskal-Szekeres coordinates applying in general relativity (not in combinatorics)

Figure George and Esther at the Investiture Ceremony for Australian Honours heldat Government House George Szekeres received his award of Member of the Order of

Australia September 2002 at the age of 90

The following notes on George draw heavily from an article for the annual newsletter ofthe National Mathematics Summer School in 2001 by David Harvey now studying for aPhD in Harvard George inspired admiration and optimism from those fortunate to havemet him

George Szekeres was born in Budapest Hungary in 1911 and his gifts in science andmathematics were soon apparent An important influence during his high school careerwas the journal Kzpiskolai Matematikai s Fizikai Lapok which provided mathematicalproblems and enrichment (George was much later instrumental in establishing a similarhigh school mathematics journal Parabola in Australia) George went on to study chemi-cal engineering at the Technological University of Budapest to contribute to the familyrsquosleather business During his time at university he often met with a small group of enthusi-astic students drawn from the ranks of the Lapok problem-solvers to pose mathematicalproblems and discuss solutions The group was simmering with talent including PaulErdos and Paul Turan both outstanding mathematicians of this century Also attendingwas Esther Klein who has lectured on geometry at NMSS on two occasions and whomGeorge would marry in 1937

1see the article (and accompanying photos) by Earnie Tuck on Ren Potts atwwwmathsadelaideeduauappliedrecentRenPotts

21

NZMS Newsletter No 95

GEORGE SZEKERES

29 May 1911ndash28 August 2005

The month of August 2005 has been a sad one for mathematics in Australia with thepassing of Ren Potts1 (on 9 August) and George Szekeres Both mathematicians wereclosely associated with Adelaide and many New Zealand mathematicians have had thepleasure of meeting these remarkably creative individuals Of special note is that bothmay perhaps be best known for work performed outside their specialist areas with thePotts model applying to statistical physics (not in Operational Research) and the Kruskal-Szekeres coordinates applying in general relativity (not in combinatorics)

Figure George and Esther at the Investiture Ceremony for Australian Honours heldat Government House George Szekeres received his award of Member of the Order of

Australia September 2002 at the age of 90

The following notes on George draw heavily from an article for the annual newsletter ofthe National Mathematics Summer School in 2001 by David Harvey now studying for aPhD in Harvard George inspired admiration and optimism from those fortunate to havemet him

George Szekeres was born in Budapest Hungary in 1911 and his gifts in science andmathematics were soon apparent An important influence during his high school careerwas the journal Kzpiskolai Matematikai s Fizikai Lapok which provided mathematicalproblems and enrichment (George was much later instrumental in establishing a similarhigh school mathematics journal Parabola in Australia) George went on to study chemi-cal engineering at the Technological University of Budapest to contribute to the familyrsquosleather business During his time at university he often met with a small group of enthusi-astic students drawn from the ranks of the Lapok problem-solvers to pose mathematicalproblems and discuss solutions The group was simmering with talent including PaulErdos and Paul Turan both outstanding mathematicians of this century Also attendingwas Esther Klein who has lectured on geometry at NMSS on two occasions and whomGeorge would marry in 1937

1see the article (and accompanying photos) by Earnie Tuck on Ren Potts atwwwmathsadelaideeduauappliedrecentRenPotts

21

CENTREFOLD

Towards the end of the 1930s life was becoming increasingly difficult for Jews in Hun-gary George and Esther eventually found it necessary to leave and moved to Shanghaiwhere their son Peter was born in 1940 George worked as a leather chemist there andlater as a clerk in an American air force base In 1948 George accepted an offer of alectureship at the University of Adelaide He remained there for fifteen years duringwhich time their daughter Judith was born in 1954 In 1963 the family moved to Sydney(except for Peter who was studying physics in London) where George had accepted aposition at the University of New South Wales as the Chair of Pure Mathematics on thecondition that he would not have to be an administrator Also in 1963 he was electedto the Australian Academy of Science and awarded the Academyrsquos Lyle Medal in 1968George retired in 1976 but continued to work several days a week as Emeritus Professorin the mathematics department at UNSW In Sydney George was also a valued mem-ber of the amateur classical musical scene playing violin and viola in the North SydneySymphony Orchestra and the Ku-ring-gai Philharmonic Orchestra

Georgersquos original mathematical output continued through most of his adult life be-ginning even during his undergraduate days His mathematical interests were incrediblydiverse but there are several recurring themes One prominent topic is combinatoricsand there is at least one combinatorial problem which has been a thread running throughGeorgersquos whole life It was first posed by Esther in the early 1930s and was the subjectof a collaborative paper with Paul Erdos (A combinatorial problem in geometry 1935)Erdos referred to this problem as the lsquoHappy Ending Problemrsquo because it had a happyendingmdashnamely George and Estherrsquos marriage The problem has yet to be fully solvedand George continued working on a computer search that would test a particular specialcase Besides combinatorial geometry he also made contributions in the theory of par-titions graph theory and other areas of combinatorics He embraced the computer agewith enthusiasm making early contributions to techniques of numerical analysis espe-cially in the theory of computing high dimensional integrals His later research interestsincluded combinatorial geometry Hadamard determinants and chaos theory

Despite these wide areas of activity many applied mathematicians in New Zealand willassociate George with yet another areamdashbecause of his ground breaking work in generalrelativity in 1960 when he studied the passage of (hypothetical) observers through theevent horizon of a black hole in his paper ldquoOn the singularities of a Riemannian man-ifoldrdquo This original work was also published almost simultaneously and independentlyby Kruskal who originally received the credit However over time the contribution ofGeorge was recognised so that today the Kruskal-Szekeres coordinates are widely known

These coordinates do not follow the passage of an observer but rather follow the pathsof light as it moves into the black hole The light cone then looks as it does in specialrelativity which can greatly facilitate some calculations A remarkable aspect of thesecoordinates is that the coordinate singularity in the Schwarzschild metric at the eventhorizon is now missing in the new line element but the real singularity at the ldquooriginrdquoof the Schwarzschild metric now splits into two singular surfaces revealing the presenceof two exterior regions This had been found by Synge in 1950 but the Kruskal-Szekerescoordinates are probably the easiest way to observe this The classic text Gravitationby Misner Thorne and Wheeler advises students ldquoOne good way for the reader to be-come conversant with the basic features of the Schwarzschild geometry is to carefullyreinterpret everything in terms of the Kruskal-Szekeres diagramrdquo It seems likely thenthat Georgersquos influence will extend far into the future

Graham Weir

22

NZMS Newsletter No 95

Local News Section continued

In April Dave and also Nye John presented pa-pers at the 4th International Symposium on Busi-ness and Industrial Statistics held in QueenslandAfter that conference Nye attended the 55th Ses-sion of ISI held in Sydney Nye was also an invitedspeaker at the 24th International Workshop on Ma-trices and Statistics held in Auckland at the endof March

Before James left us he went to Tempe Ari-zona where he was an invited speaker at the 6thInternational Conference on Forensic Statistics InJune he went to Sitges Spain where he had beeninvited to give a day long workshop on the sta-tistical evaluation of multivariate trace evidenceBill Bolstad attended the American Statistical As-sociation meeting held in Minneapolis Minnesotawhere he gave a paper Murray Jorgensen alsoattended 55th Session of ISI held in Sydney inMarch and in July he was an invited contributorat the Satellite meeting on Hidden Markov Mod-els held in Wanaka prior to attending the NZSA2005 meeting in Dunedin Judi McWhirter alsoattended this conference At the AGM held atthe conference Murray was re-elected as Presidentof the Society and Judi was re-elected SecretaryCurrently Murray is on sabbatical Since goingon leave Murray has given a contributed paperat the European Meeting of Statisticians held inOslo visiting Bill Reed at the University of Victo-ria in British Columbia en route He has also vis-ited Queensland where he was working with GeoffMcLaughlin

Seminars

Lyn Hunt ldquoUsing multiple choice questions asan assessment device for statistical thinkingrdquo

David Whitaker ldquoThe state of the art in thegeneration of efficient statistical designsrdquo

Rosemary Bailey (Queen Mary University ofLondon) ldquoHasse diagrams to describe thestructure of designed experimentsrdquo

Nye John ldquoDesign GenStat and CycDesigNrdquo

Peter Mullins (Sage Consultants Ltd) ldquoUsingExcel for inspecting segments of a time seriesof reasonable lengthrdquo

Beatix Jones (Institute of Information andMathematical Sciences Massey UniversityAlbany Campus Auckland) ldquoFitting andinterpreting sparse Gaussian graphicalmodels for high dimensional datardquo

Chris Triggs (Department of Statistics TheUniversity of Auckland) ldquoEstablishingIdentityrdquo

Michael Stuart (Trinity College Dublin)ldquoMathematical thinking versus statisticalthinking redressing the balance in statisticalteachingrdquo

Claire Jordan (Institute of Information andMathematical Sciences Massey UniversityAlbany Campus Auckland) ldquoCART PPMrsquosand PBRFrdquo

George Styan (McGill University Montreal)ldquoIssai Schur (1875-1941) and the earlydevelopment of the Schur complementS-RP-1Q photographs documents andbiographical remarksrdquo

Daniel Walsh (Institute of Information andMathematical Sciences Massey UniversityAlbany Campus Auckland) ldquoTheImportance Sampling Hough Transformrdquo

Judi McWhirter

VICTORIA UNIVERSITY OFWELLINGTON

School of Mathematics Statistics andComputing Sciences Te Kura Tatau

Enrolments in Mathematics are levelling out after a30 drop over the past three years Our academicnumbers are now down to just nine tenured posi-tions in Mathematics with currently just over 1 po-sition of contracted semi-retired academics Manyyears ago we had fourteen tenured positions

Our studentstaff ratio is about 181 at presentWe will possibly appoint one new tenured mathe-matician next year but the finances do not lookgood for any more appointments to replace the sig-nificant recent drop in tenured mathematicians atVic

Mathematics Statistics and Operations Re-search were reviewed in August this year aspart of Vics routine academic programme reviewtimetable We were commended for a very thor-ough and searching self-review and Mathematicsat Vic was praised for the excellence of its researchprogramme The review was more directed at ourteaching programmes however and made somesuggestions for how to improve the number of stu-dents enrolling in Mathematics at Vic This wasa response to our expressed concerns about falling

23

LOCAL NEWS

numbers of tenured academics and how the finan-cial system in place at Vic seems to mediate againstmaking the new appointments we feel are needed

The review also noted that our workloads seemedinordinately high (averaging over 9 contact hoursper week during term time) and suggested we re-view our tutorial and assessment practices with aview to reducing staff workload Overall it was avery positive review with many nice things to sayabout the teaching of mathematics at Vic

Ken Pledger retired early this year and was soonre-hired on contract to teach geometry and alge-bra Philip Rhodes-Robinson has also retired thisyear and is now back on contract teaching cal-culus and mathematical modelling Lindsay John-ston continues on contract teaching calculus andmathematical modelling and our summer courseIntroductory Algebra Geoff Whittle will take upa McLaurin Fellowship in July next year releasinghim from teaching duties for a full year YinhuoZhang takes Research and Study Leave next yeartoo

Peter Donelan is currently on Research andStudy leave (and trying to get used to a Frenchkeyboard) After attending the Australian Math-ematical Society Annual Conference he have vis-ited Jon Selig at London South Bank UniversityCurrently he is with Jean-Pierre Merlet at INRIASophia Antipolis in France before also visitingClement Gosselin at University of Laval Quebec

We had visits from several statisticians

bull Professor Albert Shiryaev (this is a fact histrue name not a rumour) one of the bestcontemporary specialists in stochastic analysisand financial mathematics (and this is rumourbut very widely spread) visited in July-Augustand gave a public lecture and a sequence offour seminar talks

bull Professor Robert Liptser form Jerusalem Tech-nical University visited for a week in June

bull Professor VS Mandrekar from Michigan StateUniversity paid us a short visit at the begin-ning of August

Yu Laing has left us for a one year postdoc inthe National University of Singapore and then to apermamant position at Nanjing University in 2006Guohua Wu has a tenure track position at NanyangTechnological University

Rod Downey delivered 5 tutorial lectures for theInstitute of Mathematics National University ofSingapore as part of their thematic program Com-putational Prospects of Infinity He also organizedand attended the Dagstuhl meeting on parameter-ized complexity and is invited to give a 45 minutetalk at the next ICM in Madrid

Rebecca Weber is visiting Rod from Dartmouthfor a short term postdoc and Noam Greenbergfrom Cornell and Notre dame arrives for a yearlong postdoc in August

Rob Goldblatt gave the opening plenary addressat the conference Algebraic and Topological Meth-ods in Non-Classical Logics in Barcelona in June

Mark McGuinness visited Oxford again this yearfor a couple of weeks to work on cardiac controlmodels with Andrew Fowler He also spent twomonths at the Korea Advanced Institute for Scienceand Technology in Taejon South Korea towardsthe end of the year teaching and researching inapplied maths

Seminars

Carl Bender (Washington University in SaintLouis) ldquoGhost bustingmdashmaking sense ofnon-Hermitian Hamiltoniansrdquo

Faith Fich (Univeristy of Toronto) ldquoHow hardis it to take a snapshotrdquo

Mark Moir (Sun Microsystems)ldquoObstruction-free algorithms can bepractically wait-freerdquo

Antonija Mitrovic (Canterbury University)ldquoConstraint-based tutors theoreticalfoundations developmentrdquo

Xiaogu Zheng (NIWA) ldquoA mixture model forsimulation of precipitation in the upperWaitaki catchment New Zealand and itsrelation with interdecadal pacific sscillationrdquo

Carl Wieman (2001 Nobel Prize for PhysicsJILA and University of Boulder Colorado)ldquoTeaching physicsrdquo

Zbigniew Michalewicz (Adelaide) ldquoAdaptivebusiness intelligencerdquo

Paul Mullowney (Christchurch) ldquoThe role ofvariance in capped-rate stochastic growthmodelsrdquo

Paul Malcolm (Canberra) ldquoParameterestimation for asset-price evolution dynamicsvia M-ary detectionrdquo

Mike Paulin (University of Otago) ldquoThe neuralparticle filter a model of neuralcomputations for dynamical state estimationin the brainrdquo

Hans van Ditmarsch (University of Otago)ldquoBelief change and dynamic logicrdquo

24

NZMS Newsletter No 95

Dr Antonija Mitrovic (Canterbury University)ldquoConstraint-based tutors theoreticalfoundations and developmentrdquo

David Bryant (Department of MathematicsNZInstitute of Bioinformatics The University ofAuckland) ldquoContinuous and (mostly) tractablemodels for the variation of evolutionary ratesrdquo

Malcolm Longair (Cavendish LaboratoryCambridge University) ldquoAstrophysics andcosmology of the 21st centuryrdquo

Jin Seo Cho ldquoTesting for unobservedheterogeneity in Weibull and exponentialduration modelsrdquo

Philippe Kruchten (University of BritishColombia) ldquoSoftware architecture knowledgeand design decisionrdquo

Mark McGuinness

THE CRAWLER

At Massey we talk of nothing but PBRF Publishing in good journals is good for PBRF Annals ofMathematics is supposed to be a good journal It has the highest 20-year impact of any maths journal andits editors although limited to a one mile radius of Fine Hall are no slouches As far as I can determine(Math Reviews only began listing institutions in 1982) the only New Zealand-based mathematician tohave published in the Annals is Peter Fenton whose first paper Some results of WimanndashValiron type forintegral functions of finite lower order (Ann Math 103 (1976) 237ndash252) appeared there in the sameyear he joined Otago All in all I think I can say that this is not a good effort How about it fellowmathematicians

Fortunately expats are busy keeping up our name One in particular A quick search on Web ofScience (not properly a subject for the Crawler since it is far from free but Massey has just extendedits sub back to 1945) reveals that Vaughan Jonesrsquos 1987 Annals paper Hecke algebra representations ofbraid-groups and link polynomials (Ann Math 126 (1987) 335ndash388) is the most-cited Annals papersince 1968 It has 413 citations (In 1968 itrsquos eclipsed by Atiyah and Singerrsquos Index of elliptic operatorsIII 620 citations) Vaughan comments

I think the reasons for the success are twofold One is that the subject underwent a spectacularburst of popularity at the time of the paper which was sustained for several years The workalso made connections with several areas like quantum field theory and statistical mechanicsand my paper contained several of the basic results A whole new direction has been developedin the last five years called Khovanov homology which interprets the polynomial invariants asEuler characteristics of complexes whose homology groups are themselves invariants So perhapsI can catch up to Atiyah and Singer eventually

The other reason for the success of this particular paper is that I dared to write a comprehensiblearticle in the Annals There is really only one really technical part so itrsquos a paper people couldactually read and learn something from

Robert McLachlan

25

FEATURES

FEATURES

NEW ZEALAND INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS(NZIMA)

This is an update on the NZIMA for the NZMS Newsletter We hope that members of the NZMShave benefitted and will continue to benefit from the NZIMArsquos activities following its establishment asone of the first five CoREs in 2002

NZIMA programmes

Three programmes have commenced in 2005

bull Mathematical Models for Optimizing Transportation ServicesDirectors Matthias Ehrgott Andy Philpott David Ryan (The University of Auckland)

bull Hidden Markov Models and Complex SystemsDirector David Vere-Jones (Victoria University of Wellington and Statistics Research Associates)

bull Geometric Methods in the Topology of 3-Dimensional ManifoldsDirectors David Gauld (The University of Auckland) Roger Fenn (University of Sussex) andVaughan Jones (The University of Auckland and University of California Berkeley)

Two new programmes will commence in 200607 as follows

bull Modelling Invasive Species and Weed ImpactDirectors Jennifer Brown Alex James and David Wall (University of Canterbury) proposed tostart late 2006 or early 2007

bull Partial Differential Equations Applications Analysis and Inverse ProblemsDirectors Colin Fox Mike Meylan Boris Pavlov (The University of Auckland) proposed to startin the second half of 2006

Maclaurin Fellows

This yearrsquos Maclaurin Fellow has been Professor Robert McLachlan (Massey University) pursuing hisresearch on geometric integration

Next yearrsquos Maclaurin Fellow will be Professor Geoff Whittle (Victoria University of Wellington) whowill use his Fellowship to spend time tackling Rotarsquos conjecture and the well-quasi-ordering conjecturefor matroids

Visiting Maclaurin Fellows for 2005 include Professors Hyman Bass (Michigan) Jonathan Borwein(Dalhousie) John Conway (Princeton) and Martin Liebeck (London)

Renewal of CoRE Funding

In early September we were very pleased to learn that the NZIMArsquos Centres of Research Excellence(CoRE) funding has been renewed through to 2008 following a positive review by the Tertiary EducationCommission (TEC) At the same time the New Zealand government announced that all seven CoREswould be reviewed again in 2006 with the aim of extending CoRE funding for successful centres throughto 201415 (and offering three years of lsquophase-downrsquo funding for any that are unsuccessful)

This yearrsquos review complimented the NZIMA on its achievements to date especially the highquality of our research programmes and record the strength of our international linkages gover-nance and management and encouragement of students Also it recommended that we take further

26

NZMS Newsletter No 95

steps to build up the profile of the NZIMA and develop a longer term vision and identity in order toenhance the NZIMArsquos sustainability We will be taking up these recommendations in the coming months

Establishment of Pacific Rim Mathematical Association

Marston Conder took part in a Pacific Rim Mathematical Forum at the Banff International ResearchStation (BIRS) in October 2005 at the invitation of the directors of the MSRI (Berkeley) and PIMS(Canada) There he gave a short presentation on the NZIMA and also had helpful discussions withrepresentatives of AIM (the American Institute of Mathematics) AMSI (the Australian MathematicalSciences Institute) IMS (the Institute of Mathematical Sciences in Singapore) and PIMS

A principal outcome of the meeting was a decision to establish a Pacific Rim Mathematical Association(otherwise known as lsquoPRIMArsquo) with the aim of promoting and facilitating the development of themathematical sciences throughout the Pacific Rim region It is intended that this will involve improvednetworking coordination of activities training (eg summer schools) infrastructural assistance sharingof expertise pooling of resources etc The NZIMA will be joining this association and Marston Conderhas been invited to join the Liaison Committee

Further details of the NZIMArsquos activities and opportunities for the future can be found on the NZIMArsquoswebsite

httpwwwnzimaaucklandacnz

Marston ConderVaughan Jones

27

NZMS Newsletter No 95

Local News Section continued

In April Dave and also Nye John presented pa-pers at the 4th International Symposium on Busi-ness and Industrial Statistics held in QueenslandAfter that conference Nye attended the 55th Ses-sion of ISI held in Sydney Nye was also an invitedspeaker at the 24th International Workshop on Ma-trices and Statistics held in Auckland at the endof March

Before James left us he went to Tempe Ari-zona where he was an invited speaker at the 6thInternational Conference on Forensic Statistics InJune he went to Sitges Spain where he had beeninvited to give a day long workshop on the sta-tistical evaluation of multivariate trace evidenceBill Bolstad attended the American Statistical As-sociation meeting held in Minneapolis Minnesotawhere he gave a paper Murray Jorgensen alsoattended 55th Session of ISI held in Sydney inMarch and in July he was an invited contributorat the Satellite meeting on Hidden Markov Mod-els held in Wanaka prior to attending the NZSA2005 meeting in Dunedin Judi McWhirter alsoattended this conference At the AGM held atthe conference Murray was re-elected as Presidentof the Society and Judi was re-elected SecretaryCurrently Murray is on sabbatical Since goingon leave Murray has given a contributed paperat the European Meeting of Statisticians held inOslo visiting Bill Reed at the University of Victo-ria in British Columbia en route He has also vis-ited Queensland where he was working with GeoffMcLaughlin

Seminars

Lyn Hunt ldquoUsing multiple choice questions asan assessment device for statistical thinkingrdquo

David Whitaker ldquoThe state of the art in thegeneration of efficient statistical designsrdquo

Rosemary Bailey (Queen Mary University ofLondon) ldquoHasse diagrams to describe thestructure of designed experimentsrdquo

Nye John ldquoDesign GenStat and CycDesigNrdquo

Peter Mullins (Sage Consultants Ltd) ldquoUsingExcel for inspecting segments of a time seriesof reasonable lengthrdquo

Beatix Jones (Institute of Information andMathematical Sciences Massey UniversityAlbany Campus Auckland) ldquoFitting andinterpreting sparse Gaussian graphicalmodels for high dimensional datardquo

Chris Triggs (Department of Statistics TheUniversity of Auckland) ldquoEstablishingIdentityrdquo

Michael Stuart (Trinity College Dublin)ldquoMathematical thinking versus statisticalthinking redressing the balance in statisticalteachingrdquo

Claire Jordan (Institute of Information andMathematical Sciences Massey UniversityAlbany Campus Auckland) ldquoCART PPMrsquosand PBRFrdquo

George Styan (McGill University Montreal)ldquoIssai Schur (1875-1941) and the earlydevelopment of the Schur complementS-RP-1Q photographs documents andbiographical remarksrdquo

Daniel Walsh (Institute of Information andMathematical Sciences Massey UniversityAlbany Campus Auckland) ldquoTheImportance Sampling Hough Transformrdquo

Judi McWhirter

VICTORIA UNIVERSITY OFWELLINGTON

School of Mathematics Statistics andComputing Sciences Te Kura Tatau

Enrolments in Mathematics are levelling out after a30 drop over the past three years Our academicnumbers are now down to just nine tenured posi-tions in Mathematics with currently just over 1 po-sition of contracted semi-retired academics Manyyears ago we had fourteen tenured positions

Our studentstaff ratio is about 181 at presentWe will possibly appoint one new tenured mathe-matician next year but the finances do not lookgood for any more appointments to replace the sig-nificant recent drop in tenured mathematicians atVic

Mathematics Statistics and Operations Re-search were reviewed in August this year aspart of Vics routine academic programme reviewtimetable We were commended for a very thor-ough and searching self-review and Mathematicsat Vic was praised for the excellence of its researchprogramme The review was more directed at ourteaching programmes however and made somesuggestions for how to improve the number of stu-dents enrolling in Mathematics at Vic This wasa response to our expressed concerns about falling

23

LOCAL NEWS

numbers of tenured academics and how the finan-cial system in place at Vic seems to mediate againstmaking the new appointments we feel are needed

The review also noted that our workloads seemedinordinately high (averaging over 9 contact hoursper week during term time) and suggested we re-view our tutorial and assessment practices with aview to reducing staff workload Overall it was avery positive review with many nice things to sayabout the teaching of mathematics at Vic

Ken Pledger retired early this year and was soonre-hired on contract to teach geometry and alge-bra Philip Rhodes-Robinson has also retired thisyear and is now back on contract teaching cal-culus and mathematical modelling Lindsay John-ston continues on contract teaching calculus andmathematical modelling and our summer courseIntroductory Algebra Geoff Whittle will take upa McLaurin Fellowship in July next year releasinghim from teaching duties for a full year YinhuoZhang takes Research and Study Leave next yeartoo

Peter Donelan is currently on Research andStudy leave (and trying to get used to a Frenchkeyboard) After attending the Australian Math-ematical Society Annual Conference he have vis-ited Jon Selig at London South Bank UniversityCurrently he is with Jean-Pierre Merlet at INRIASophia Antipolis in France before also visitingClement Gosselin at University of Laval Quebec

We had visits from several statisticians

bull Professor Albert Shiryaev (this is a fact histrue name not a rumour) one of the bestcontemporary specialists in stochastic analysisand financial mathematics (and this is rumourbut very widely spread) visited in July-Augustand gave a public lecture and a sequence offour seminar talks

bull Professor Robert Liptser form Jerusalem Tech-nical University visited for a week in June

bull Professor VS Mandrekar from Michigan StateUniversity paid us a short visit at the begin-ning of August

Yu Laing has left us for a one year postdoc inthe National University of Singapore and then to apermamant position at Nanjing University in 2006Guohua Wu has a tenure track position at NanyangTechnological University

Rod Downey delivered 5 tutorial lectures for theInstitute of Mathematics National University ofSingapore as part of their thematic program Com-putational Prospects of Infinity He also organizedand attended the Dagstuhl meeting on parameter-ized complexity and is invited to give a 45 minutetalk at the next ICM in Madrid

Rebecca Weber is visiting Rod from Dartmouthfor a short term postdoc and Noam Greenbergfrom Cornell and Notre dame arrives for a yearlong postdoc in August

Rob Goldblatt gave the opening plenary addressat the conference Algebraic and Topological Meth-ods in Non-Classical Logics in Barcelona in June

Mark McGuinness visited Oxford again this yearfor a couple of weeks to work on cardiac controlmodels with Andrew Fowler He also spent twomonths at the Korea Advanced Institute for Scienceand Technology in Taejon South Korea towardsthe end of the year teaching and researching inapplied maths

Seminars

Carl Bender (Washington University in SaintLouis) ldquoGhost bustingmdashmaking sense ofnon-Hermitian Hamiltoniansrdquo

Faith Fich (Univeristy of Toronto) ldquoHow hardis it to take a snapshotrdquo

Mark Moir (Sun Microsystems)ldquoObstruction-free algorithms can bepractically wait-freerdquo

Antonija Mitrovic (Canterbury University)ldquoConstraint-based tutors theoreticalfoundations developmentrdquo

Xiaogu Zheng (NIWA) ldquoA mixture model forsimulation of precipitation in the upperWaitaki catchment New Zealand and itsrelation with interdecadal pacific sscillationrdquo

Carl Wieman (2001 Nobel Prize for PhysicsJILA and University of Boulder Colorado)ldquoTeaching physicsrdquo

Zbigniew Michalewicz (Adelaide) ldquoAdaptivebusiness intelligencerdquo

Paul Mullowney (Christchurch) ldquoThe role ofvariance in capped-rate stochastic growthmodelsrdquo

Paul Malcolm (Canberra) ldquoParameterestimation for asset-price evolution dynamicsvia M-ary detectionrdquo

Mike Paulin (University of Otago) ldquoThe neuralparticle filter a model of neuralcomputations for dynamical state estimationin the brainrdquo

Hans van Ditmarsch (University of Otago)ldquoBelief change and dynamic logicrdquo

24

NZMS Newsletter No 95

Dr Antonija Mitrovic (Canterbury University)ldquoConstraint-based tutors theoreticalfoundations and developmentrdquo

David Bryant (Department of MathematicsNZInstitute of Bioinformatics The University ofAuckland) ldquoContinuous and (mostly) tractablemodels for the variation of evolutionary ratesrdquo

Malcolm Longair (Cavendish LaboratoryCambridge University) ldquoAstrophysics andcosmology of the 21st centuryrdquo

Jin Seo Cho ldquoTesting for unobservedheterogeneity in Weibull and exponentialduration modelsrdquo

Philippe Kruchten (University of BritishColombia) ldquoSoftware architecture knowledgeand design decisionrdquo

Mark McGuinness

THE CRAWLER

At Massey we talk of nothing but PBRF Publishing in good journals is good for PBRF Annals ofMathematics is supposed to be a good journal It has the highest 20-year impact of any maths journal andits editors although limited to a one mile radius of Fine Hall are no slouches As far as I can determine(Math Reviews only began listing institutions in 1982) the only New Zealand-based mathematician tohave published in the Annals is Peter Fenton whose first paper Some results of WimanndashValiron type forintegral functions of finite lower order (Ann Math 103 (1976) 237ndash252) appeared there in the sameyear he joined Otago All in all I think I can say that this is not a good effort How about it fellowmathematicians

Fortunately expats are busy keeping up our name One in particular A quick search on Web ofScience (not properly a subject for the Crawler since it is far from free but Massey has just extendedits sub back to 1945) reveals that Vaughan Jonesrsquos 1987 Annals paper Hecke algebra representations ofbraid-groups and link polynomials (Ann Math 126 (1987) 335ndash388) is the most-cited Annals papersince 1968 It has 413 citations (In 1968 itrsquos eclipsed by Atiyah and Singerrsquos Index of elliptic operatorsIII 620 citations) Vaughan comments

I think the reasons for the success are twofold One is that the subject underwent a spectacularburst of popularity at the time of the paper which was sustained for several years The workalso made connections with several areas like quantum field theory and statistical mechanicsand my paper contained several of the basic results A whole new direction has been developedin the last five years called Khovanov homology which interprets the polynomial invariants asEuler characteristics of complexes whose homology groups are themselves invariants So perhapsI can catch up to Atiyah and Singer eventually

The other reason for the success of this particular paper is that I dared to write a comprehensiblearticle in the Annals There is really only one really technical part so itrsquos a paper people couldactually read and learn something from

Robert McLachlan

25

FEATURES

FEATURES

NEW ZEALAND INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS(NZIMA)

This is an update on the NZIMA for the NZMS Newsletter We hope that members of the NZMShave benefitted and will continue to benefit from the NZIMArsquos activities following its establishment asone of the first five CoREs in 2002

NZIMA programmes

Three programmes have commenced in 2005

bull Mathematical Models for Optimizing Transportation ServicesDirectors Matthias Ehrgott Andy Philpott David Ryan (The University of Auckland)

bull Hidden Markov Models and Complex SystemsDirector David Vere-Jones (Victoria University of Wellington and Statistics Research Associates)

bull Geometric Methods in the Topology of 3-Dimensional ManifoldsDirectors David Gauld (The University of Auckland) Roger Fenn (University of Sussex) andVaughan Jones (The University of Auckland and University of California Berkeley)

Two new programmes will commence in 200607 as follows

bull Modelling Invasive Species and Weed ImpactDirectors Jennifer Brown Alex James and David Wall (University of Canterbury) proposed tostart late 2006 or early 2007

bull Partial Differential Equations Applications Analysis and Inverse ProblemsDirectors Colin Fox Mike Meylan Boris Pavlov (The University of Auckland) proposed to startin the second half of 2006

Maclaurin Fellows

This yearrsquos Maclaurin Fellow has been Professor Robert McLachlan (Massey University) pursuing hisresearch on geometric integration

Next yearrsquos Maclaurin Fellow will be Professor Geoff Whittle (Victoria University of Wellington) whowill use his Fellowship to spend time tackling Rotarsquos conjecture and the well-quasi-ordering conjecturefor matroids

Visiting Maclaurin Fellows for 2005 include Professors Hyman Bass (Michigan) Jonathan Borwein(Dalhousie) John Conway (Princeton) and Martin Liebeck (London)

Renewal of CoRE Funding

In early September we were very pleased to learn that the NZIMArsquos Centres of Research Excellence(CoRE) funding has been renewed through to 2008 following a positive review by the Tertiary EducationCommission (TEC) At the same time the New Zealand government announced that all seven CoREswould be reviewed again in 2006 with the aim of extending CoRE funding for successful centres throughto 201415 (and offering three years of lsquophase-downrsquo funding for any that are unsuccessful)

This yearrsquos review complimented the NZIMA on its achievements to date especially the highquality of our research programmes and record the strength of our international linkages gover-nance and management and encouragement of students Also it recommended that we take further

26

NZMS Newsletter No 95

steps to build up the profile of the NZIMA and develop a longer term vision and identity in order toenhance the NZIMArsquos sustainability We will be taking up these recommendations in the coming months

Establishment of Pacific Rim Mathematical Association

Marston Conder took part in a Pacific Rim Mathematical Forum at the Banff International ResearchStation (BIRS) in October 2005 at the invitation of the directors of the MSRI (Berkeley) and PIMS(Canada) There he gave a short presentation on the NZIMA and also had helpful discussions withrepresentatives of AIM (the American Institute of Mathematics) AMSI (the Australian MathematicalSciences Institute) IMS (the Institute of Mathematical Sciences in Singapore) and PIMS

A principal outcome of the meeting was a decision to establish a Pacific Rim Mathematical Association(otherwise known as lsquoPRIMArsquo) with the aim of promoting and facilitating the development of themathematical sciences throughout the Pacific Rim region It is intended that this will involve improvednetworking coordination of activities training (eg summer schools) infrastructural assistance sharingof expertise pooling of resources etc The NZIMA will be joining this association and Marston Conderhas been invited to join the Liaison Committee

Further details of the NZIMArsquos activities and opportunities for the future can be found on the NZIMArsquoswebsite

httpwwwnzimaaucklandacnz

Marston ConderVaughan Jones

27

LOCAL NEWS

numbers of tenured academics and how the finan-cial system in place at Vic seems to mediate againstmaking the new appointments we feel are needed

The review also noted that our workloads seemedinordinately high (averaging over 9 contact hoursper week during term time) and suggested we re-view our tutorial and assessment practices with aview to reducing staff workload Overall it was avery positive review with many nice things to sayabout the teaching of mathematics at Vic

Ken Pledger retired early this year and was soonre-hired on contract to teach geometry and alge-bra Philip Rhodes-Robinson has also retired thisyear and is now back on contract teaching cal-culus and mathematical modelling Lindsay John-ston continues on contract teaching calculus andmathematical modelling and our summer courseIntroductory Algebra Geoff Whittle will take upa McLaurin Fellowship in July next year releasinghim from teaching duties for a full year YinhuoZhang takes Research and Study Leave next yeartoo

Peter Donelan is currently on Research andStudy leave (and trying to get used to a Frenchkeyboard) After attending the Australian Math-ematical Society Annual Conference he have vis-ited Jon Selig at London South Bank UniversityCurrently he is with Jean-Pierre Merlet at INRIASophia Antipolis in France before also visitingClement Gosselin at University of Laval Quebec

We had visits from several statisticians

bull Professor Albert Shiryaev (this is a fact histrue name not a rumour) one of the bestcontemporary specialists in stochastic analysisand financial mathematics (and this is rumourbut very widely spread) visited in July-Augustand gave a public lecture and a sequence offour seminar talks

bull Professor Robert Liptser form Jerusalem Tech-nical University visited for a week in June

bull Professor VS Mandrekar from Michigan StateUniversity paid us a short visit at the begin-ning of August

Yu Laing has left us for a one year postdoc inthe National University of Singapore and then to apermamant position at Nanjing University in 2006Guohua Wu has a tenure track position at NanyangTechnological University

Rod Downey delivered 5 tutorial lectures for theInstitute of Mathematics National University ofSingapore as part of their thematic program Com-putational Prospects of Infinity He also organizedand attended the Dagstuhl meeting on parameter-ized complexity and is invited to give a 45 minutetalk at the next ICM in Madrid

Rebecca Weber is visiting Rod from Dartmouthfor a short term postdoc and Noam Greenbergfrom Cornell and Notre dame arrives for a yearlong postdoc in August

Rob Goldblatt gave the opening plenary addressat the conference Algebraic and Topological Meth-ods in Non-Classical Logics in Barcelona in June

Mark McGuinness visited Oxford again this yearfor a couple of weeks to work on cardiac controlmodels with Andrew Fowler He also spent twomonths at the Korea Advanced Institute for Scienceand Technology in Taejon South Korea towardsthe end of the year teaching and researching inapplied maths

Seminars

Carl Bender (Washington University in SaintLouis) ldquoGhost bustingmdashmaking sense ofnon-Hermitian Hamiltoniansrdquo

Faith Fich (Univeristy of Toronto) ldquoHow hardis it to take a snapshotrdquo

Mark Moir (Sun Microsystems)ldquoObstruction-free algorithms can bepractically wait-freerdquo

Antonija Mitrovic (Canterbury University)ldquoConstraint-based tutors theoreticalfoundations developmentrdquo

Xiaogu Zheng (NIWA) ldquoA mixture model forsimulation of precipitation in the upperWaitaki catchment New Zealand and itsrelation with interdecadal pacific sscillationrdquo

Carl Wieman (2001 Nobel Prize for PhysicsJILA and University of Boulder Colorado)ldquoTeaching physicsrdquo

Zbigniew Michalewicz (Adelaide) ldquoAdaptivebusiness intelligencerdquo

Paul Mullowney (Christchurch) ldquoThe role ofvariance in capped-rate stochastic growthmodelsrdquo

Paul Malcolm (Canberra) ldquoParameterestimation for asset-price evolution dynamicsvia M-ary detectionrdquo

Mike Paulin (University of Otago) ldquoThe neuralparticle filter a model of neuralcomputations for dynamical state estimationin the brainrdquo

Hans van Ditmarsch (University of Otago)ldquoBelief change and dynamic logicrdquo

24

NZMS Newsletter No 95

Dr Antonija Mitrovic (Canterbury University)ldquoConstraint-based tutors theoreticalfoundations and developmentrdquo

David Bryant (Department of MathematicsNZInstitute of Bioinformatics The University ofAuckland) ldquoContinuous and (mostly) tractablemodels for the variation of evolutionary ratesrdquo

Malcolm Longair (Cavendish LaboratoryCambridge University) ldquoAstrophysics andcosmology of the 21st centuryrdquo

Jin Seo Cho ldquoTesting for unobservedheterogeneity in Weibull and exponentialduration modelsrdquo

Philippe Kruchten (University of BritishColombia) ldquoSoftware architecture knowledgeand design decisionrdquo

Mark McGuinness

THE CRAWLER

At Massey we talk of nothing but PBRF Publishing in good journals is good for PBRF Annals ofMathematics is supposed to be a good journal It has the highest 20-year impact of any maths journal andits editors although limited to a one mile radius of Fine Hall are no slouches As far as I can determine(Math Reviews only began listing institutions in 1982) the only New Zealand-based mathematician tohave published in the Annals is Peter Fenton whose first paper Some results of WimanndashValiron type forintegral functions of finite lower order (Ann Math 103 (1976) 237ndash252) appeared there in the sameyear he joined Otago All in all I think I can say that this is not a good effort How about it fellowmathematicians

Fortunately expats are busy keeping up our name One in particular A quick search on Web ofScience (not properly a subject for the Crawler since it is far from free but Massey has just extendedits sub back to 1945) reveals that Vaughan Jonesrsquos 1987 Annals paper Hecke algebra representations ofbraid-groups and link polynomials (Ann Math 126 (1987) 335ndash388) is the most-cited Annals papersince 1968 It has 413 citations (In 1968 itrsquos eclipsed by Atiyah and Singerrsquos Index of elliptic operatorsIII 620 citations) Vaughan comments

I think the reasons for the success are twofold One is that the subject underwent a spectacularburst of popularity at the time of the paper which was sustained for several years The workalso made connections with several areas like quantum field theory and statistical mechanicsand my paper contained several of the basic results A whole new direction has been developedin the last five years called Khovanov homology which interprets the polynomial invariants asEuler characteristics of complexes whose homology groups are themselves invariants So perhapsI can catch up to Atiyah and Singer eventually

The other reason for the success of this particular paper is that I dared to write a comprehensiblearticle in the Annals There is really only one really technical part so itrsquos a paper people couldactually read and learn something from

Robert McLachlan

25

FEATURES

FEATURES

NEW ZEALAND INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS(NZIMA)

This is an update on the NZIMA for the NZMS Newsletter We hope that members of the NZMShave benefitted and will continue to benefit from the NZIMArsquos activities following its establishment asone of the first five CoREs in 2002

NZIMA programmes

Three programmes have commenced in 2005

bull Mathematical Models for Optimizing Transportation ServicesDirectors Matthias Ehrgott Andy Philpott David Ryan (The University of Auckland)

bull Hidden Markov Models and Complex SystemsDirector David Vere-Jones (Victoria University of Wellington and Statistics Research Associates)

bull Geometric Methods in the Topology of 3-Dimensional ManifoldsDirectors David Gauld (The University of Auckland) Roger Fenn (University of Sussex) andVaughan Jones (The University of Auckland and University of California Berkeley)

Two new programmes will commence in 200607 as follows

bull Modelling Invasive Species and Weed ImpactDirectors Jennifer Brown Alex James and David Wall (University of Canterbury) proposed tostart late 2006 or early 2007

bull Partial Differential Equations Applications Analysis and Inverse ProblemsDirectors Colin Fox Mike Meylan Boris Pavlov (The University of Auckland) proposed to startin the second half of 2006

Maclaurin Fellows

This yearrsquos Maclaurin Fellow has been Professor Robert McLachlan (Massey University) pursuing hisresearch on geometric integration

Next yearrsquos Maclaurin Fellow will be Professor Geoff Whittle (Victoria University of Wellington) whowill use his Fellowship to spend time tackling Rotarsquos conjecture and the well-quasi-ordering conjecturefor matroids

Visiting Maclaurin Fellows for 2005 include Professors Hyman Bass (Michigan) Jonathan Borwein(Dalhousie) John Conway (Princeton) and Martin Liebeck (London)

Renewal of CoRE Funding

In early September we were very pleased to learn that the NZIMArsquos Centres of Research Excellence(CoRE) funding has been renewed through to 2008 following a positive review by the Tertiary EducationCommission (TEC) At the same time the New Zealand government announced that all seven CoREswould be reviewed again in 2006 with the aim of extending CoRE funding for successful centres throughto 201415 (and offering three years of lsquophase-downrsquo funding for any that are unsuccessful)

This yearrsquos review complimented the NZIMA on its achievements to date especially the highquality of our research programmes and record the strength of our international linkages gover-nance and management and encouragement of students Also it recommended that we take further

26

NZMS Newsletter No 95

steps to build up the profile of the NZIMA and develop a longer term vision and identity in order toenhance the NZIMArsquos sustainability We will be taking up these recommendations in the coming months

Establishment of Pacific Rim Mathematical Association

Marston Conder took part in a Pacific Rim Mathematical Forum at the Banff International ResearchStation (BIRS) in October 2005 at the invitation of the directors of the MSRI (Berkeley) and PIMS(Canada) There he gave a short presentation on the NZIMA and also had helpful discussions withrepresentatives of AIM (the American Institute of Mathematics) AMSI (the Australian MathematicalSciences Institute) IMS (the Institute of Mathematical Sciences in Singapore) and PIMS

A principal outcome of the meeting was a decision to establish a Pacific Rim Mathematical Association(otherwise known as lsquoPRIMArsquo) with the aim of promoting and facilitating the development of themathematical sciences throughout the Pacific Rim region It is intended that this will involve improvednetworking coordination of activities training (eg summer schools) infrastructural assistance sharingof expertise pooling of resources etc The NZIMA will be joining this association and Marston Conderhas been invited to join the Liaison Committee

Further details of the NZIMArsquos activities and opportunities for the future can be found on the NZIMArsquoswebsite

httpwwwnzimaaucklandacnz

Marston ConderVaughan Jones

27

NZMS Newsletter No 95

Dr Antonija Mitrovic (Canterbury University)ldquoConstraint-based tutors theoreticalfoundations and developmentrdquo

David Bryant (Department of MathematicsNZInstitute of Bioinformatics The University ofAuckland) ldquoContinuous and (mostly) tractablemodels for the variation of evolutionary ratesrdquo

Malcolm Longair (Cavendish LaboratoryCambridge University) ldquoAstrophysics andcosmology of the 21st centuryrdquo

Jin Seo Cho ldquoTesting for unobservedheterogeneity in Weibull and exponentialduration modelsrdquo

Philippe Kruchten (University of BritishColombia) ldquoSoftware architecture knowledgeand design decisionrdquo

Mark McGuinness

THE CRAWLER

At Massey we talk of nothing but PBRF Publishing in good journals is good for PBRF Annals ofMathematics is supposed to be a good journal It has the highest 20-year impact of any maths journal andits editors although limited to a one mile radius of Fine Hall are no slouches As far as I can determine(Math Reviews only began listing institutions in 1982) the only New Zealand-based mathematician tohave published in the Annals is Peter Fenton whose first paper Some results of WimanndashValiron type forintegral functions of finite lower order (Ann Math 103 (1976) 237ndash252) appeared there in the sameyear he joined Otago All in all I think I can say that this is not a good effort How about it fellowmathematicians

Fortunately expats are busy keeping up our name One in particular A quick search on Web ofScience (not properly a subject for the Crawler since it is far from free but Massey has just extendedits sub back to 1945) reveals that Vaughan Jonesrsquos 1987 Annals paper Hecke algebra representations ofbraid-groups and link polynomials (Ann Math 126 (1987) 335ndash388) is the most-cited Annals papersince 1968 It has 413 citations (In 1968 itrsquos eclipsed by Atiyah and Singerrsquos Index of elliptic operatorsIII 620 citations) Vaughan comments

I think the reasons for the success are twofold One is that the subject underwent a spectacularburst of popularity at the time of the paper which was sustained for several years The workalso made connections with several areas like quantum field theory and statistical mechanicsand my paper contained several of the basic results A whole new direction has been developedin the last five years called Khovanov homology which interprets the polynomial invariants asEuler characteristics of complexes whose homology groups are themselves invariants So perhapsI can catch up to Atiyah and Singer eventually

The other reason for the success of this particular paper is that I dared to write a comprehensiblearticle in the Annals There is really only one really technical part so itrsquos a paper people couldactually read and learn something from

Robert McLachlan

25

FEATURES

FEATURES

NEW ZEALAND INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS(NZIMA)

This is an update on the NZIMA for the NZMS Newsletter We hope that members of the NZMShave benefitted and will continue to benefit from the NZIMArsquos activities following its establishment asone of the first five CoREs in 2002

NZIMA programmes

Three programmes have commenced in 2005

bull Mathematical Models for Optimizing Transportation ServicesDirectors Matthias Ehrgott Andy Philpott David Ryan (The University of Auckland)

bull Hidden Markov Models and Complex SystemsDirector David Vere-Jones (Victoria University of Wellington and Statistics Research Associates)

bull Geometric Methods in the Topology of 3-Dimensional ManifoldsDirectors David Gauld (The University of Auckland) Roger Fenn (University of Sussex) andVaughan Jones (The University of Auckland and University of California Berkeley)

Two new programmes will commence in 200607 as follows

bull Modelling Invasive Species and Weed ImpactDirectors Jennifer Brown Alex James and David Wall (University of Canterbury) proposed tostart late 2006 or early 2007

bull Partial Differential Equations Applications Analysis and Inverse ProblemsDirectors Colin Fox Mike Meylan Boris Pavlov (The University of Auckland) proposed to startin the second half of 2006

Maclaurin Fellows

This yearrsquos Maclaurin Fellow has been Professor Robert McLachlan (Massey University) pursuing hisresearch on geometric integration

Next yearrsquos Maclaurin Fellow will be Professor Geoff Whittle (Victoria University of Wellington) whowill use his Fellowship to spend time tackling Rotarsquos conjecture and the well-quasi-ordering conjecturefor matroids

Visiting Maclaurin Fellows for 2005 include Professors Hyman Bass (Michigan) Jonathan Borwein(Dalhousie) John Conway (Princeton) and Martin Liebeck (London)

Renewal of CoRE Funding

In early September we were very pleased to learn that the NZIMArsquos Centres of Research Excellence(CoRE) funding has been renewed through to 2008 following a positive review by the Tertiary EducationCommission (TEC) At the same time the New Zealand government announced that all seven CoREswould be reviewed again in 2006 with the aim of extending CoRE funding for successful centres throughto 201415 (and offering three years of lsquophase-downrsquo funding for any that are unsuccessful)

This yearrsquos review complimented the NZIMA on its achievements to date especially the highquality of our research programmes and record the strength of our international linkages gover-nance and management and encouragement of students Also it recommended that we take further

26

NZMS Newsletter No 95

steps to build up the profile of the NZIMA and develop a longer term vision and identity in order toenhance the NZIMArsquos sustainability We will be taking up these recommendations in the coming months

Establishment of Pacific Rim Mathematical Association

Marston Conder took part in a Pacific Rim Mathematical Forum at the Banff International ResearchStation (BIRS) in October 2005 at the invitation of the directors of the MSRI (Berkeley) and PIMS(Canada) There he gave a short presentation on the NZIMA and also had helpful discussions withrepresentatives of AIM (the American Institute of Mathematics) AMSI (the Australian MathematicalSciences Institute) IMS (the Institute of Mathematical Sciences in Singapore) and PIMS

A principal outcome of the meeting was a decision to establish a Pacific Rim Mathematical Association(otherwise known as lsquoPRIMArsquo) with the aim of promoting and facilitating the development of themathematical sciences throughout the Pacific Rim region It is intended that this will involve improvednetworking coordination of activities training (eg summer schools) infrastructural assistance sharingof expertise pooling of resources etc The NZIMA will be joining this association and Marston Conderhas been invited to join the Liaison Committee

Further details of the NZIMArsquos activities and opportunities for the future can be found on the NZIMArsquoswebsite

httpwwwnzimaaucklandacnz

Marston ConderVaughan Jones

27

FEATURES

FEATURES

NEW ZEALAND INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS(NZIMA)

This is an update on the NZIMA for the NZMS Newsletter We hope that members of the NZMShave benefitted and will continue to benefit from the NZIMArsquos activities following its establishment asone of the first five CoREs in 2002

NZIMA programmes

Three programmes have commenced in 2005

bull Mathematical Models for Optimizing Transportation ServicesDirectors Matthias Ehrgott Andy Philpott David Ryan (The University of Auckland)

bull Hidden Markov Models and Complex SystemsDirector David Vere-Jones (Victoria University of Wellington and Statistics Research Associates)

bull Geometric Methods in the Topology of 3-Dimensional ManifoldsDirectors David Gauld (The University of Auckland) Roger Fenn (University of Sussex) andVaughan Jones (The University of Auckland and University of California Berkeley)

Two new programmes will commence in 200607 as follows

bull Modelling Invasive Species and Weed ImpactDirectors Jennifer Brown Alex James and David Wall (University of Canterbury) proposed tostart late 2006 or early 2007

bull Partial Differential Equations Applications Analysis and Inverse ProblemsDirectors Colin Fox Mike Meylan Boris Pavlov (The University of Auckland) proposed to startin the second half of 2006

Maclaurin Fellows

This yearrsquos Maclaurin Fellow has been Professor Robert McLachlan (Massey University) pursuing hisresearch on geometric integration

Next yearrsquos Maclaurin Fellow will be Professor Geoff Whittle (Victoria University of Wellington) whowill use his Fellowship to spend time tackling Rotarsquos conjecture and the well-quasi-ordering conjecturefor matroids

Visiting Maclaurin Fellows for 2005 include Professors Hyman Bass (Michigan) Jonathan Borwein(Dalhousie) John Conway (Princeton) and Martin Liebeck (London)

Renewal of CoRE Funding

In early September we were very pleased to learn that the NZIMArsquos Centres of Research Excellence(CoRE) funding has been renewed through to 2008 following a positive review by the Tertiary EducationCommission (TEC) At the same time the New Zealand government announced that all seven CoREswould be reviewed again in 2006 with the aim of extending CoRE funding for successful centres throughto 201415 (and offering three years of lsquophase-downrsquo funding for any that are unsuccessful)

This yearrsquos review complimented the NZIMA on its achievements to date especially the highquality of our research programmes and record the strength of our international linkages gover-nance and management and encouragement of students Also it recommended that we take further

26

NZMS Newsletter No 95

steps to build up the profile of the NZIMA and develop a longer term vision and identity in order toenhance the NZIMArsquos sustainability We will be taking up these recommendations in the coming months

Establishment of Pacific Rim Mathematical Association

Marston Conder took part in a Pacific Rim Mathematical Forum at the Banff International ResearchStation (BIRS) in October 2005 at the invitation of the directors of the MSRI (Berkeley) and PIMS(Canada) There he gave a short presentation on the NZIMA and also had helpful discussions withrepresentatives of AIM (the American Institute of Mathematics) AMSI (the Australian MathematicalSciences Institute) IMS (the Institute of Mathematical Sciences in Singapore) and PIMS

A principal outcome of the meeting was a decision to establish a Pacific Rim Mathematical Association(otherwise known as lsquoPRIMArsquo) with the aim of promoting and facilitating the development of themathematical sciences throughout the Pacific Rim region It is intended that this will involve improvednetworking coordination of activities training (eg summer schools) infrastructural assistance sharingof expertise pooling of resources etc The NZIMA will be joining this association and Marston Conderhas been invited to join the Liaison Committee

Further details of the NZIMArsquos activities and opportunities for the future can be found on the NZIMArsquoswebsite

httpwwwnzimaaucklandacnz

Marston ConderVaughan Jones

27

NZMS Newsletter No 95

steps to build up the profile of the NZIMA and develop a longer term vision and identity in order toenhance the NZIMArsquos sustainability We will be taking up these recommendations in the coming months

Establishment of Pacific Rim Mathematical Association

Marston Conder took part in a Pacific Rim Mathematical Forum at the Banff International ResearchStation (BIRS) in October 2005 at the invitation of the directors of the MSRI (Berkeley) and PIMS(Canada) There he gave a short presentation on the NZIMA and also had helpful discussions withrepresentatives of AIM (the American Institute of Mathematics) AMSI (the Australian MathematicalSciences Institute) IMS (the Institute of Mathematical Sciences in Singapore) and PIMS

A principal outcome of the meeting was a decision to establish a Pacific Rim Mathematical Association(otherwise known as lsquoPRIMArsquo) with the aim of promoting and facilitating the development of themathematical sciences throughout the Pacific Rim region It is intended that this will involve improvednetworking coordination of activities training (eg summer schools) infrastructural assistance sharingof expertise pooling of resources etc The NZIMA will be joining this association and Marston Conderhas been invited to join the Liaison Committee

Further details of the NZIMArsquos activities and opportunities for the future can be found on the NZIMArsquoswebsite

httpwwwnzimaaucklandacnz

Marston ConderVaughan Jones

27

MINUTES

MINUTES

Provisional Minutes of the 31st Annual General Meeting of theNew Zealand Mathematical Society

1230 pm Wednesday 7 December 2005AH2 Massey University Palmerston North

Present Graeme Wake (Chair) Winston Sweatman Shaun Hendy Tammy Smith Aroon ParshotamKee Teo Stephen Joe Peter Kelly Kevin Broughan Graham Weir David Wall Eamonn OrsquoBrien KenPledger David Gauld Charles Little Robert McLachlan Garry Tee Alona Ben-Tal Igor Boglaev CarloLaing Gillian Thornley

Winston Sweatman opened the meeting It was moved (Hendy and Thornley) that in the absenceof the President and Vice-President Graeme Wake as former President would chair the meeting Themotion was carried

1 Apologies

Apologies were received from Mick Roberts Gaven Martin Charles Semple Warren Moors MichaelAlbert Robert McKibbin Marston Conder and John Butcher

2 Minutes of 30th Annual General Meeting

It was moved (Wake Smith) that the minutes of the 30th Annual General Meeting of the NZMS beaccepted The motion was carried

3 Matters arising from the minutes (numbers refer to items of the 30th Annual General Meeting)

8 The issue of long waiting time for publication in the NZJM was again raised This is addressedin item [9]

11 It was reported that Council had investigated the cost and possible form of a research medalCouncil supports the idea and has approached the NZIMA for possible funding It has beenindicated that the NZIMA is eager to support the medal in some way For example they mayhelp fund a New Zealand tour by the medal winner Further discussions are to be held betweenthe Council and the NZIMA It is hoped that something will be in place for next year

4 Presidents report

(a) The report was delivered to the meeting and will appear in the NZMS newsletter

(b) It was moved (Wake Smith) the report be accepted The motion was carried

5 Treasurerrsquos report

(a) The Treasurerrsquos report was delivered to the meeting and the financial statements and auditorrsquosreport were distributed to the members

(b) The Treasurer noted a problem with unpaid subscriptions She also asked members present toactively promote new members Subscriptions cover the operating costs of the Society while thetravel fund is being used to build up an endownment In response to a question the Treasurerconfirmed that grants and awards are funded from interest generated from the Societyrsquos fundsIt was noted that the total balance of net assets of $ 184 900 had increased by about $ 60 000over the last 10 yearsIt was suggested that one way to build up funds was by small bequests and perhaps a draftcodicil could be included in the newsletter These ideas were refered to the Council for consid-eration

(c) It was moved (Smith Hendy) that the statements be accepted The motion was carried

28

NZMS Newsletter No 95

6 Membership Secretaryrsquos report and annual subscriptions

A report from the Membership Secretary John Shanks was presented It was noted that membershipwas slightly down It was moved (Wake Smith) that the report be accepted The motion was carried

The drop in membership was considered It was felt that further encouragement was needed It wassuggested that Heads of Departments could ask for nominations for new society members (staff andstudents) at the beginning of the year

Council had recommended that subscriptions be fixed at current levels ($36 ordinary member $18reciprocal $18 overseas student and $760 student) It was moved that subscriptions be fixed atcurrent levels (Smith Hendy) The meeting approved

It was suggested that Council could consider the possibility of larger discounts for early payment ofsubscriptions

The Treasurer also informed the meeting that the Membership Secretary was investigating otherways in which subscriptions could be paid

7 Election of Coucillors

Gaven Martin takes over as NZMS President with the outgoing President Mick Roberts remainingon Council as Vice-President for a year The terms of office of Tammy Smith and Charles Semplehave ended Tammy Smith has been renominated for a second term and Rick Beatson (Universityof Canterbury) has also been nominated Both were elected unopposed

8 Appointment of auditors

It was moved (Wake Thornley) that the current auditors McKenzie McPhail (4th floor FarmersMutual House 68 The Square Palmerston North) be reappointed for another year The motionwas carried

9 New Zealand Journal of Mathematics

David Gauld reported to the meeting that he had taken over mid-year from David Alcorn as chairof the NZJM Committee He said that the Committee was currently reviewing the membership ofthe Editorial Board They were aiming to increase the speed and quality of publication Electronicpublication was also being considered

The meeting encouraged the NZJM committee and editor in their consideration of processes leadingto faster publication It was suggested that perhaps the process beyond acceptance could be fast-tracked for NZMS members

It was noted that Gaven Martin is the NZJM Editor as well as incoming NZMS President and so iswell-placed for these issues

David Gauld was thanked for his report

10 NZMS Visiting Lecturer 2006

This is still being arranged The meeting was informed that Mike Steel had been approached andthat he had also suggested his visitor Daniel Huson It may be possible to combine these two

11 General Business

(a) Robert McLachlan was thanked for his service as Editor of the NZMS Newsletter MarkMcGuinness has been appointed as new Editor

(b) The meeting congratulated Mick Roberts on his personal chair at Massey University

(c) The meeting thanked Charles Semple for his two terms on council and Mick Roberts for histwo years as President

The meeting closed at 1pm

29

BOOK REVIEWS

BOOK REVIEWS

PUBLICATIONS

Information has been received about the following publications Anyone interested in reviewing any ofthese books should contact

Bruce van BruntInstitute of Fundamental SciencesMassey University(email BvanBruntmasseyacnz)

SPRINGER-VERLAG PUBLICATIONS

Back K A Course in Derivative Securities ndash Introduction to Theory and Computation (SpringerFinance) 355pp

Crandall R Prime Numbers ndash A Computational Perspective 600pp

Crossley MD Essential Topology (Springer Undergraduate Mathematics Series) 224pp

Cull P Difference Equations ndash From Rabbits to Chaos (Undergraduate Texts in Mathematics) 394pp

Manin Yu I Introduction to Modern Number Theory ndash Fundamental Problems Ideas and Theories(Encyclopaedia of Mathematical Sciences) 514pp

Miller E Combinatorial Commutative Algebra 426pp

Runde V A Taste of Topology (Universitext) 182pp

Shreve SE Stochastic Calculus for Finance I ndash The Binomial Asset Pricing Model 192pp

Stroock DW An Introduction to Markov Processes 171pp

Zhu K Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) 268pp

30

NZMS Newsletter No 95

Partial Differential EquationsModelingAnalysis ComputationR M M Mattheij SW Rienstra J H M ten Thije BoonkkampMathematical Modeling and Computation 10

While most existing texts on PDEs deal with either analytical ornumerical aspects of PDEs this innovative and comprehensivetextbook features a unique approach that integrates analysis andnumerical solution methods and includes a third componentmdashmodelingmdashto address real-life problems It includes a separate

chapter containing 16 user-friendly case studies of elliptic parabolic and hyperbolicequations plus numerous exercises are included in all other chapters 2005 middot xxxiv + 665 pages middot Softcover middot ISBN 0-89871-594-6List Price $12700 middot SIAM Member Price $8890 middot Order Code MM10

Variational Analysis in Sobolev and BV SpacesApplications to PDEs and OptimizationHedy Attouch Giuseppe Buttazzo and Geacuterard MichailleMPS-SIAM Series on Optimization 6

This self-contained book is excellent for graduate-level coursesdevoted to variational analysis optimization and partial differentialequations (PDEs) It provides readers with a complete guide toproblems in these fields as well as a detailed presentation of themost important tools and methods of variational analysis Newtrends in variational analysis are also presented along with recentdevelopments and applications in this area Variational Analysis inSobolev and BV Spaces Applications to PDEs and Optimization is not just for studentshowever it is a comprehensive guide for anyone who wants to approach the field ofvariational analysis in a systematic way starting from the most classical examples andworking up to a research level It also contains several applications to problems in geometrymechanics elasticity and computer vision along with a complete list of references2005 middot xii + 634 pages middot Softcover middot ISBN 0-89871-600-4List Price $14000 middot MPS-SIAM Member Price $9800 middot Order Code MP06

Computational Methods for Option PricingYves Achdou and Olivier PironneauFrontiers in Applied Mathematics 30

Here is a book for anyone who would like to become betteracquainted with the modern tools of numerical analysis for severalsignificant computational problems arising in finance The authorsreview some important aspects of finance modeling involvingpartial differential equations and focus on numerical algorithms forthe fast and accurate pricing of financial derivatives and for thecalibration of parameters Option pricing has become a technical

topic that requires sophisticated numerical methods for robust and fast numericalsolutions This book explores the best numerical algorithms and discusses them in depthfrom their mathematical analysis up to their implementation in C++ with efficientnumerical libraries Much of this information is not available elsewhere 2005 middot xviii + 297 pages middot Softcover middot ISBN 0-89871-573-3List Price $8000 middot SIAM Member Price $5600 middot Order Code FR30

TO ORDERUse your credit card (AMEX MC and VISA) Go to wwwsiamorgcatalog bull Call toll-free in USACanada800-447-SIAM middot Worldwide call +1-215-382-9800 bull Fax +1-215-386-7999 bull E-mail servicesiamorg Send check or money order to SIAM Dept BKNZ05 3600 University City Science Center Philadelphia PA 19104-2688 USA

Applied Math Titleswwww wwww wwww ssss iiii aaaa mmmm oooo rrrr gggg cccc aaaa tttt aaaa llll oooo gggg

Society for Industr ia l and Appl ied Mathemat ics

Solving PDEs in C++Yair ShapiraComputational Science and Engineering 1

This comprehensive book not onlyintroduces the C and C++programming languages but also showshow to use them in the numericalsolution of partial differentialequations (PDEs) It leads the readerthrough the entire solution processfrom the original PDE through thediscretization stage to the numericalsolution of the resulting algebraicsystem The well-debugged and testedcode segments implement thenumerical methods efficiently andtransparently Basic and advancednumerical methods are introduced andimplemented easily and efficiently in aunified object-oriented approach

The high level of abstraction availablein C++ is particularly useful in theimplementation of complexmathematical objects such asunstructured mesh sparse matrix andmultigrid hierarchy often used innumerical modeling This bookintroduces a unified approach for theimplementation of these objects Thecode segments and their detailedexplanations clearly show how easy itis to implement advanced algorithmsin C++

Solving PDEs in C++ contains all therequired background in programmingPDEs and numerical methods onlyan elementary background in linearalgebra and calculus is required Usefulexercises and solutions conclude eachchapter January 2006 middot xxiv + 500 pages middot SoftcoverISBN 0-89871-601-2 middot List Price $12500SIAM Member Price $8750 middot Order Code CS01

fromnew

31

CONFERENCES

CONFERENCES

Conferences in 2006

9ndash13 January 2006 International Symposium on Fractional Calculus (20 international speakers)website httpwwwmathsotagoacnzsimbbaeumersymposiumhtm

8ndash15 January 2006 at Taipa Northland NZMRI Workshop on Geometric Methods in theTopology of 3-Dimensional Manifoldswebsite httpwwwmathaucklandacnzEvents2006SummerWorkshop

30 Januaryndash3 February 2006 at Albany Auckland Mathematics in Industry Study Group(MISG 2006)website httpmisg2006masseyacnz

5ndash9 February 2006 at the Alzburg Inn Resort Mansfield Victoria Australia Annual conferenceof Australian and New Zealand Industrial and Applied Mathematics (ANZIAM 2006)website httpwwwmathsmonasheduauanziam06

12ndash16 February 2006 in Auckland Third International Conference on Ethnomathematicswebsite httpwwwmathaucklandacnzEvents2006ICEM-3

5ndash8 June 2006 University of Brunei Darussalam Brunei (Borneo) International Conference onMathematical Modelling and Computationemail Seminar Secretariat Dr Malcolm Andersonmmc06fosubdedubnwebsite httpwwwubdedubnnewsconferencesfosmmc06

3ndash7 July 2006 at Sky City Auckland ASCNZSA 2006mdashAustralian Statistical Confer-enceNew Zealand Statistical Association Conferencewebsite httpwwwstatsnz2006com

REPORT ON THE 2005 NEW ZEALAND MATHEMATICS COLLOQUIUMPALMERSTON NORTH

5ndash7 December 2005

The Colloquia began in 1966 making this yearrsquos event (counting five years in which instead an Aus-tralasian Mathematics Convention was held in Australia or New Zealand) number 40 Some participantshave been present at nearly every one Despite some debate at last yearrsquos meeting about the continuedrole of the Colloquium another successful event has been run attracting 111 delegates It was particularlygood to see 6 people from Otago which must be a modern day record for a North Island Colloquium(Victoriamdashbest not mentioned)

The NZMC invited speakers were

Professor Peter Kuchment Texas AampM University Circular Radon transform nodal lines ther-mal acoustic tomography and all that

Tatiana Marquez Lago University of New Mexico Butcher Prizewinner Stochastic variationestimates of progesterone transcriptional activity in the EGFR pathway

Professor Mark Meerschaert Otago University ANZIAM Speaker Vector fractional calculus

Associate Professor Eamonn OrsquoBrien University of Auckland NZMS Speaker and 2004 NZMSResearch Award winner Algorithmic approaches to the study of linear groups

Associate Professor Bruce van-Brunt Massey University Complex functional differential equa-tions

32

NZMS Newsletter No 95

6 Membership Secretaryrsquos report and annual subscriptions

A report from the Membership Secretary John Shanks was presented It was noted that membershipwas slightly down It was moved (Wake Smith) that the report be accepted The motion was carried

The drop in membership was considered It was felt that further encouragement was needed It wassuggested that Heads of Departments could ask for nominations for new society members (staff andstudents) at the beginning of the year

Council had recommended that subscriptions be fixed at current levels ($36 ordinary member $18reciprocal $18 overseas student and $760 student) It was moved that subscriptions be fixed atcurrent levels (Smith Hendy) The meeting approved

It was suggested that Council could consider the possibility of larger discounts for early payment ofsubscriptions

The Treasurer also informed the meeting that the Membership Secretary was investigating otherways in which subscriptions could be paid

7 Election of Coucillors

Gaven Martin takes over as NZMS President with the outgoing President Mick Roberts remainingon Council as Vice-President for a year The terms of office of Tammy Smith and Charles Semplehave ended Tammy Smith has been renominated for a second term and Rick Beatson (Universityof Canterbury) has also been nominated Both were elected unopposed

8 Appointment of auditors

It was moved (Wake Thornley) that the current auditors McKenzie McPhail (4th floor FarmersMutual House 68 The Square Palmerston North) be reappointed for another year The motionwas carried

9 New Zealand Journal of Mathematics

David Gauld reported to the meeting that he had taken over mid-year from David Alcorn as chairof the NZJM Committee He said that the Committee was currently reviewing the membership ofthe Editorial Board They were aiming to increase the speed and quality of publication Electronicpublication was also being considered

The meeting encouraged the NZJM committee and editor in their consideration of processes leadingto faster publication It was suggested that perhaps the process beyond acceptance could be fast-tracked for NZMS members

It was noted that Gaven Martin is the NZJM Editor as well as incoming NZMS President and so iswell-placed for these issues

David Gauld was thanked for his report

10 NZMS Visiting Lecturer 2006

This is still being arranged The meeting was informed that Mike Steel had been approached andthat he had also suggested his visitor Daniel Huson It may be possible to combine these two

11 General Business

(a) Robert McLachlan was thanked for his service as Editor of the NZMS Newsletter MarkMcGuinness has been appointed as new Editor

(b) The meeting congratulated Mick Roberts on his personal chair at Massey University

(c) The meeting thanked Charles Semple for his two terms on council and Mick Roberts for histwo years as President

The meeting closed at 1pm

29

BOOK REVIEWS

BOOK REVIEWS

PUBLICATIONS

Information has been received about the following publications Anyone interested in reviewing any ofthese books should contact

Bruce van BruntInstitute of Fundamental SciencesMassey University(email BvanBruntmasseyacnz)

SPRINGER-VERLAG PUBLICATIONS

Back K A Course in Derivative Securities ndash Introduction to Theory and Computation (SpringerFinance) 355pp

Crandall R Prime Numbers ndash A Computational Perspective 600pp

Crossley MD Essential Topology (Springer Undergraduate Mathematics Series) 224pp

Cull P Difference Equations ndash From Rabbits to Chaos (Undergraduate Texts in Mathematics) 394pp

Manin Yu I Introduction to Modern Number Theory ndash Fundamental Problems Ideas and Theories(Encyclopaedia of Mathematical Sciences) 514pp

Miller E Combinatorial Commutative Algebra 426pp

Runde V A Taste of Topology (Universitext) 182pp

Shreve SE Stochastic Calculus for Finance I ndash The Binomial Asset Pricing Model 192pp

Stroock DW An Introduction to Markov Processes 171pp

Zhu K Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) 268pp

30

NZMS Newsletter No 95

Partial Differential EquationsModelingAnalysis ComputationR M M Mattheij SW Rienstra J H M ten Thije BoonkkampMathematical Modeling and Computation 10

While most existing texts on PDEs deal with either analytical ornumerical aspects of PDEs this innovative and comprehensivetextbook features a unique approach that integrates analysis andnumerical solution methods and includes a third componentmdashmodelingmdashto address real-life problems It includes a separate

chapter containing 16 user-friendly case studies of elliptic parabolic and hyperbolicequations plus numerous exercises are included in all other chapters 2005 middot xxxiv + 665 pages middot Softcover middot ISBN 0-89871-594-6List Price $12700 middot SIAM Member Price $8890 middot Order Code MM10

Variational Analysis in Sobolev and BV SpacesApplications to PDEs and OptimizationHedy Attouch Giuseppe Buttazzo and Geacuterard MichailleMPS-SIAM Series on Optimization 6

This self-contained book is excellent for graduate-level coursesdevoted to variational analysis optimization and partial differentialequations (PDEs) It provides readers with a complete guide toproblems in these fields as well as a detailed presentation of themost important tools and methods of variational analysis Newtrends in variational analysis are also presented along with recentdevelopments and applications in this area Variational Analysis inSobolev and BV Spaces Applications to PDEs and Optimization is not just for studentshowever it is a comprehensive guide for anyone who wants to approach the field ofvariational analysis in a systematic way starting from the most classical examples andworking up to a research level It also contains several applications to problems in geometrymechanics elasticity and computer vision along with a complete list of references2005 middot xii + 634 pages middot Softcover middot ISBN 0-89871-600-4List Price $14000 middot MPS-SIAM Member Price $9800 middot Order Code MP06

Computational Methods for Option PricingYves Achdou and Olivier PironneauFrontiers in Applied Mathematics 30

Here is a book for anyone who would like to become betteracquainted with the modern tools of numerical analysis for severalsignificant computational problems arising in finance The authorsreview some important aspects of finance modeling involvingpartial differential equations and focus on numerical algorithms forthe fast and accurate pricing of financial derivatives and for thecalibration of parameters Option pricing has become a technical

topic that requires sophisticated numerical methods for robust and fast numericalsolutions This book explores the best numerical algorithms and discusses them in depthfrom their mathematical analysis up to their implementation in C++ with efficientnumerical libraries Much of this information is not available elsewhere 2005 middot xviii + 297 pages middot Softcover middot ISBN 0-89871-573-3List Price $8000 middot SIAM Member Price $5600 middot Order Code FR30

TO ORDERUse your credit card (AMEX MC and VISA) Go to wwwsiamorgcatalog bull Call toll-free in USACanada800-447-SIAM middot Worldwide call +1-215-382-9800 bull Fax +1-215-386-7999 bull E-mail servicesiamorg Send check or money order to SIAM Dept BKNZ05 3600 University City Science Center Philadelphia PA 19104-2688 USA

Applied Math Titleswwww wwww wwww ssss iiii aaaa mmmm oooo rrrr gggg cccc aaaa tttt aaaa llll oooo gggg

Society for Industr ia l and Appl ied Mathemat ics

Solving PDEs in C++Yair ShapiraComputational Science and Engineering 1

This comprehensive book not onlyintroduces the C and C++programming languages but also showshow to use them in the numericalsolution of partial differentialequations (PDEs) It leads the readerthrough the entire solution processfrom the original PDE through thediscretization stage to the numericalsolution of the resulting algebraicsystem The well-debugged and testedcode segments implement thenumerical methods efficiently andtransparently Basic and advancednumerical methods are introduced andimplemented easily and efficiently in aunified object-oriented approach

The high level of abstraction availablein C++ is particularly useful in theimplementation of complexmathematical objects such asunstructured mesh sparse matrix andmultigrid hierarchy often used innumerical modeling This bookintroduces a unified approach for theimplementation of these objects Thecode segments and their detailedexplanations clearly show how easy itis to implement advanced algorithmsin C++

Solving PDEs in C++ contains all therequired background in programmingPDEs and numerical methods onlyan elementary background in linearalgebra and calculus is required Usefulexercises and solutions conclude eachchapter January 2006 middot xxiv + 500 pages middot SoftcoverISBN 0-89871-601-2 middot List Price $12500SIAM Member Price $8750 middot Order Code CS01

fromnew

31

CONFERENCES

CONFERENCES

Conferences in 2006

9ndash13 January 2006 International Symposium on Fractional Calculus (20 international speakers)website httpwwwmathsotagoacnzsimbbaeumersymposiumhtm

8ndash15 January 2006 at Taipa Northland NZMRI Workshop on Geometric Methods in theTopology of 3-Dimensional Manifoldswebsite httpwwwmathaucklandacnzEvents2006SummerWorkshop

30 Januaryndash3 February 2006 at Albany Auckland Mathematics in Industry Study Group(MISG 2006)website httpmisg2006masseyacnz

5ndash9 February 2006 at the Alzburg Inn Resort Mansfield Victoria Australia Annual conferenceof Australian and New Zealand Industrial and Applied Mathematics (ANZIAM 2006)website httpwwwmathsmonasheduauanziam06

12ndash16 February 2006 in Auckland Third International Conference on Ethnomathematicswebsite httpwwwmathaucklandacnzEvents2006ICEM-3

5ndash8 June 2006 University of Brunei Darussalam Brunei (Borneo) International Conference onMathematical Modelling and Computationemail Seminar Secretariat Dr Malcolm Andersonmmc06fosubdedubnwebsite httpwwwubdedubnnewsconferencesfosmmc06

3ndash7 July 2006 at Sky City Auckland ASCNZSA 2006mdashAustralian Statistical Confer-enceNew Zealand Statistical Association Conferencewebsite httpwwwstatsnz2006com

REPORT ON THE 2005 NEW ZEALAND MATHEMATICS COLLOQUIUMPALMERSTON NORTH

5ndash7 December 2005

The Colloquia began in 1966 making this yearrsquos event (counting five years in which instead an Aus-tralasian Mathematics Convention was held in Australia or New Zealand) number 40 Some participantshave been present at nearly every one Despite some debate at last yearrsquos meeting about the continuedrole of the Colloquium another successful event has been run attracting 111 delegates It was particularlygood to see 6 people from Otago which must be a modern day record for a North Island Colloquium(Victoriamdashbest not mentioned)

The NZMC invited speakers were

Professor Peter Kuchment Texas AampM University Circular Radon transform nodal lines ther-mal acoustic tomography and all that

Tatiana Marquez Lago University of New Mexico Butcher Prizewinner Stochastic variationestimates of progesterone transcriptional activity in the EGFR pathway

Professor Mark Meerschaert Otago University ANZIAM Speaker Vector fractional calculus

Associate Professor Eamonn OrsquoBrien University of Auckland NZMS Speaker and 2004 NZMSResearch Award winner Algorithmic approaches to the study of linear groups

Associate Professor Bruce van-Brunt Massey University Complex functional differential equa-tions

32

BOOK REVIEWS

BOOK REVIEWS

PUBLICATIONS

Information has been received about the following publications Anyone interested in reviewing any ofthese books should contact

Bruce van BruntInstitute of Fundamental SciencesMassey University(email BvanBruntmasseyacnz)

SPRINGER-VERLAG PUBLICATIONS

Back K A Course in Derivative Securities ndash Introduction to Theory and Computation (SpringerFinance) 355pp

Crandall R Prime Numbers ndash A Computational Perspective 600pp

Crossley MD Essential Topology (Springer Undergraduate Mathematics Series) 224pp

Cull P Difference Equations ndash From Rabbits to Chaos (Undergraduate Texts in Mathematics) 394pp

Manin Yu I Introduction to Modern Number Theory ndash Fundamental Problems Ideas and Theories(Encyclopaedia of Mathematical Sciences) 514pp

Miller E Combinatorial Commutative Algebra 426pp

Runde V A Taste of Topology (Universitext) 182pp

Shreve SE Stochastic Calculus for Finance I ndash The Binomial Asset Pricing Model 192pp

Stroock DW An Introduction to Markov Processes 171pp

Zhu K Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) 268pp

30

NZMS Newsletter No 95

Partial Differential EquationsModelingAnalysis ComputationR M M Mattheij SW Rienstra J H M ten Thije BoonkkampMathematical Modeling and Computation 10

While most existing texts on PDEs deal with either analytical ornumerical aspects of PDEs this innovative and comprehensivetextbook features a unique approach that integrates analysis andnumerical solution methods and includes a third componentmdashmodelingmdashto address real-life problems It includes a separate

chapter containing 16 user-friendly case studies of elliptic parabolic and hyperbolicequations plus numerous exercises are included in all other chapters 2005 middot xxxiv + 665 pages middot Softcover middot ISBN 0-89871-594-6List Price $12700 middot SIAM Member Price $8890 middot Order Code MM10

Variational Analysis in Sobolev and BV SpacesApplications to PDEs and OptimizationHedy Attouch Giuseppe Buttazzo and Geacuterard MichailleMPS-SIAM Series on Optimization 6

This self-contained book is excellent for graduate-level coursesdevoted to variational analysis optimization and partial differentialequations (PDEs) It provides readers with a complete guide toproblems in these fields as well as a detailed presentation of themost important tools and methods of variational analysis Newtrends in variational analysis are also presented along with recentdevelopments and applications in this area Variational Analysis inSobolev and BV Spaces Applications to PDEs and Optimization is not just for studentshowever it is a comprehensive guide for anyone who wants to approach the field ofvariational analysis in a systematic way starting from the most classical examples andworking up to a research level It also contains several applications to problems in geometrymechanics elasticity and computer vision along with a complete list of references2005 middot xii + 634 pages middot Softcover middot ISBN 0-89871-600-4List Price $14000 middot MPS-SIAM Member Price $9800 middot Order Code MP06

Computational Methods for Option PricingYves Achdou and Olivier PironneauFrontiers in Applied Mathematics 30

Here is a book for anyone who would like to become betteracquainted with the modern tools of numerical analysis for severalsignificant computational problems arising in finance The authorsreview some important aspects of finance modeling involvingpartial differential equations and focus on numerical algorithms forthe fast and accurate pricing of financial derivatives and for thecalibration of parameters Option pricing has become a technical

topic that requires sophisticated numerical methods for robust and fast numericalsolutions This book explores the best numerical algorithms and discusses them in depthfrom their mathematical analysis up to their implementation in C++ with efficientnumerical libraries Much of this information is not available elsewhere 2005 middot xviii + 297 pages middot Softcover middot ISBN 0-89871-573-3List Price $8000 middot SIAM Member Price $5600 middot Order Code FR30

TO ORDERUse your credit card (AMEX MC and VISA) Go to wwwsiamorgcatalog bull Call toll-free in USACanada800-447-SIAM middot Worldwide call +1-215-382-9800 bull Fax +1-215-386-7999 bull E-mail servicesiamorg Send check or money order to SIAM Dept BKNZ05 3600 University City Science Center Philadelphia PA 19104-2688 USA

Applied Math Titleswwww wwww wwww ssss iiii aaaa mmmm oooo rrrr gggg cccc aaaa tttt aaaa llll oooo gggg

Society for Industr ia l and Appl ied Mathemat ics

Solving PDEs in C++Yair ShapiraComputational Science and Engineering 1

This comprehensive book not onlyintroduces the C and C++programming languages but also showshow to use them in the numericalsolution of partial differentialequations (PDEs) It leads the readerthrough the entire solution processfrom the original PDE through thediscretization stage to the numericalsolution of the resulting algebraicsystem The well-debugged and testedcode segments implement thenumerical methods efficiently andtransparently Basic and advancednumerical methods are introduced andimplemented easily and efficiently in aunified object-oriented approach

The high level of abstraction availablein C++ is particularly useful in theimplementation of complexmathematical objects such asunstructured mesh sparse matrix andmultigrid hierarchy often used innumerical modeling This bookintroduces a unified approach for theimplementation of these objects Thecode segments and their detailedexplanations clearly show how easy itis to implement advanced algorithmsin C++

Solving PDEs in C++ contains all therequired background in programmingPDEs and numerical methods onlyan elementary background in linearalgebra and calculus is required Usefulexercises and solutions conclude eachchapter January 2006 middot xxiv + 500 pages middot SoftcoverISBN 0-89871-601-2 middot List Price $12500SIAM Member Price $8750 middot Order Code CS01

fromnew

31

CONFERENCES

CONFERENCES

Conferences in 2006

9ndash13 January 2006 International Symposium on Fractional Calculus (20 international speakers)website httpwwwmathsotagoacnzsimbbaeumersymposiumhtm

8ndash15 January 2006 at Taipa Northland NZMRI Workshop on Geometric Methods in theTopology of 3-Dimensional Manifoldswebsite httpwwwmathaucklandacnzEvents2006SummerWorkshop

30 Januaryndash3 February 2006 at Albany Auckland Mathematics in Industry Study Group(MISG 2006)website httpmisg2006masseyacnz

5ndash9 February 2006 at the Alzburg Inn Resort Mansfield Victoria Australia Annual conferenceof Australian and New Zealand Industrial and Applied Mathematics (ANZIAM 2006)website httpwwwmathsmonasheduauanziam06

12ndash16 February 2006 in Auckland Third International Conference on Ethnomathematicswebsite httpwwwmathaucklandacnzEvents2006ICEM-3

5ndash8 June 2006 University of Brunei Darussalam Brunei (Borneo) International Conference onMathematical Modelling and Computationemail Seminar Secretariat Dr Malcolm Andersonmmc06fosubdedubnwebsite httpwwwubdedubnnewsconferencesfosmmc06

3ndash7 July 2006 at Sky City Auckland ASCNZSA 2006mdashAustralian Statistical Confer-enceNew Zealand Statistical Association Conferencewebsite httpwwwstatsnz2006com

REPORT ON THE 2005 NEW ZEALAND MATHEMATICS COLLOQUIUMPALMERSTON NORTH

5ndash7 December 2005

The Colloquia began in 1966 making this yearrsquos event (counting five years in which instead an Aus-tralasian Mathematics Convention was held in Australia or New Zealand) number 40 Some participantshave been present at nearly every one Despite some debate at last yearrsquos meeting about the continuedrole of the Colloquium another successful event has been run attracting 111 delegates It was particularlygood to see 6 people from Otago which must be a modern day record for a North Island Colloquium(Victoriamdashbest not mentioned)

The NZMC invited speakers were

Professor Peter Kuchment Texas AampM University Circular Radon transform nodal lines ther-mal acoustic tomography and all that

Tatiana Marquez Lago University of New Mexico Butcher Prizewinner Stochastic variationestimates of progesterone transcriptional activity in the EGFR pathway

Professor Mark Meerschaert Otago University ANZIAM Speaker Vector fractional calculus

Associate Professor Eamonn OrsquoBrien University of Auckland NZMS Speaker and 2004 NZMSResearch Award winner Algorithmic approaches to the study of linear groups

Associate Professor Bruce van-Brunt Massey University Complex functional differential equa-tions

32

NZMS Newsletter No 95

Partial Differential EquationsModelingAnalysis ComputationR M M Mattheij SW Rienstra J H M ten Thije BoonkkampMathematical Modeling and Computation 10

While most existing texts on PDEs deal with either analytical ornumerical aspects of PDEs this innovative and comprehensivetextbook features a unique approach that integrates analysis andnumerical solution methods and includes a third componentmdashmodelingmdashto address real-life problems It includes a separate

chapter containing 16 user-friendly case studies of elliptic parabolic and hyperbolicequations plus numerous exercises are included in all other chapters 2005 middot xxxiv + 665 pages middot Softcover middot ISBN 0-89871-594-6List Price $12700 middot SIAM Member Price $8890 middot Order Code MM10

Variational Analysis in Sobolev and BV SpacesApplications to PDEs and OptimizationHedy Attouch Giuseppe Buttazzo and Geacuterard MichailleMPS-SIAM Series on Optimization 6

This self-contained book is excellent for graduate-level coursesdevoted to variational analysis optimization and partial differentialequations (PDEs) It provides readers with a complete guide toproblems in these fields as well as a detailed presentation of themost important tools and methods of variational analysis Newtrends in variational analysis are also presented along with recentdevelopments and applications in this area Variational Analysis inSobolev and BV Spaces Applications to PDEs and Optimization is not just for studentshowever it is a comprehensive guide for anyone who wants to approach the field ofvariational analysis in a systematic way starting from the most classical examples andworking up to a research level It also contains several applications to problems in geometrymechanics elasticity and computer vision along with a complete list of references2005 middot xii + 634 pages middot Softcover middot ISBN 0-89871-600-4List Price $14000 middot MPS-SIAM Member Price $9800 middot Order Code MP06

Computational Methods for Option PricingYves Achdou and Olivier PironneauFrontiers in Applied Mathematics 30

Here is a book for anyone who would like to become betteracquainted with the modern tools of numerical analysis for severalsignificant computational problems arising in finance The authorsreview some important aspects of finance modeling involvingpartial differential equations and focus on numerical algorithms forthe fast and accurate pricing of financial derivatives and for thecalibration of parameters Option pricing has become a technical

topic that requires sophisticated numerical methods for robust and fast numericalsolutions This book explores the best numerical algorithms and discusses them in depthfrom their mathematical analysis up to their implementation in C++ with efficientnumerical libraries Much of this information is not available elsewhere 2005 middot xviii + 297 pages middot Softcover middot ISBN 0-89871-573-3List Price $8000 middot SIAM Member Price $5600 middot Order Code FR30

TO ORDERUse your credit card (AMEX MC and VISA) Go to wwwsiamorgcatalog bull Call toll-free in USACanada800-447-SIAM middot Worldwide call +1-215-382-9800 bull Fax +1-215-386-7999 bull E-mail servicesiamorg Send check or money order to SIAM Dept BKNZ05 3600 University City Science Center Philadelphia PA 19104-2688 USA

Applied Math Titleswwww wwww wwww ssss iiii aaaa mmmm oooo rrrr gggg cccc aaaa tttt aaaa llll oooo gggg

Society for Industr ia l and Appl ied Mathemat ics

Solving PDEs in C++Yair ShapiraComputational Science and Engineering 1

This comprehensive book not onlyintroduces the C and C++programming languages but also showshow to use them in the numericalsolution of partial differentialequations (PDEs) It leads the readerthrough the entire solution processfrom the original PDE through thediscretization stage to the numericalsolution of the resulting algebraicsystem The well-debugged and testedcode segments implement thenumerical methods efficiently andtransparently Basic and advancednumerical methods are introduced andimplemented easily and efficiently in aunified object-oriented approach

The high level of abstraction availablein C++ is particularly useful in theimplementation of complexmathematical objects such asunstructured mesh sparse matrix andmultigrid hierarchy often used innumerical modeling This bookintroduces a unified approach for theimplementation of these objects Thecode segments and their detailedexplanations clearly show how easy itis to implement advanced algorithmsin C++

Solving PDEs in C++ contains all therequired background in programmingPDEs and numerical methods onlyan elementary background in linearalgebra and calculus is required Usefulexercises and solutions conclude eachchapter January 2006 middot xxiv + 500 pages middot SoftcoverISBN 0-89871-601-2 middot List Price $12500SIAM Member Price $8750 middot Order Code CS01

fromnew

31

CONFERENCES

CONFERENCES

Conferences in 2006

9ndash13 January 2006 International Symposium on Fractional Calculus (20 international speakers)website httpwwwmathsotagoacnzsimbbaeumersymposiumhtm

8ndash15 January 2006 at Taipa Northland NZMRI Workshop on Geometric Methods in theTopology of 3-Dimensional Manifoldswebsite httpwwwmathaucklandacnzEvents2006SummerWorkshop

30 Januaryndash3 February 2006 at Albany Auckland Mathematics in Industry Study Group(MISG 2006)website httpmisg2006masseyacnz

5ndash9 February 2006 at the Alzburg Inn Resort Mansfield Victoria Australia Annual conferenceof Australian and New Zealand Industrial and Applied Mathematics (ANZIAM 2006)website httpwwwmathsmonasheduauanziam06

12ndash16 February 2006 in Auckland Third International Conference on Ethnomathematicswebsite httpwwwmathaucklandacnzEvents2006ICEM-3

5ndash8 June 2006 University of Brunei Darussalam Brunei (Borneo) International Conference onMathematical Modelling and Computationemail Seminar Secretariat Dr Malcolm Andersonmmc06fosubdedubnwebsite httpwwwubdedubnnewsconferencesfosmmc06

3ndash7 July 2006 at Sky City Auckland ASCNZSA 2006mdashAustralian Statistical Confer-enceNew Zealand Statistical Association Conferencewebsite httpwwwstatsnz2006com

REPORT ON THE 2005 NEW ZEALAND MATHEMATICS COLLOQUIUMPALMERSTON NORTH

5ndash7 December 2005

The Colloquia began in 1966 making this yearrsquos event (counting five years in which instead an Aus-tralasian Mathematics Convention was held in Australia or New Zealand) number 40 Some participantshave been present at nearly every one Despite some debate at last yearrsquos meeting about the continuedrole of the Colloquium another successful event has been run attracting 111 delegates It was particularlygood to see 6 people from Otago which must be a modern day record for a North Island Colloquium(Victoriamdashbest not mentioned)

The NZMC invited speakers were

Professor Peter Kuchment Texas AampM University Circular Radon transform nodal lines ther-mal acoustic tomography and all that

Tatiana Marquez Lago University of New Mexico Butcher Prizewinner Stochastic variationestimates of progesterone transcriptional activity in the EGFR pathway

Professor Mark Meerschaert Otago University ANZIAM Speaker Vector fractional calculus

Associate Professor Eamonn OrsquoBrien University of Auckland NZMS Speaker and 2004 NZMSResearch Award winner Algorithmic approaches to the study of linear groups

Associate Professor Bruce van-Brunt Massey University Complex functional differential equa-tions

32

CONFERENCES

CONFERENCES

Conferences in 2006

9ndash13 January 2006 International Symposium on Fractional Calculus (20 international speakers)website httpwwwmathsotagoacnzsimbbaeumersymposiumhtm

8ndash15 January 2006 at Taipa Northland NZMRI Workshop on Geometric Methods in theTopology of 3-Dimensional Manifoldswebsite httpwwwmathaucklandacnzEvents2006SummerWorkshop

30 Januaryndash3 February 2006 at Albany Auckland Mathematics in Industry Study Group(MISG 2006)website httpmisg2006masseyacnz

5ndash9 February 2006 at the Alzburg Inn Resort Mansfield Victoria Australia Annual conferenceof Australian and New Zealand Industrial and Applied Mathematics (ANZIAM 2006)website httpwwwmathsmonasheduauanziam06

12ndash16 February 2006 in Auckland Third International Conference on Ethnomathematicswebsite httpwwwmathaucklandacnzEvents2006ICEM-3

5ndash8 June 2006 University of Brunei Darussalam Brunei (Borneo) International Conference onMathematical Modelling and Computationemail Seminar Secretariat Dr Malcolm Andersonmmc06fosubdedubnwebsite httpwwwubdedubnnewsconferencesfosmmc06

3ndash7 July 2006 at Sky City Auckland ASCNZSA 2006mdashAustralian Statistical Confer-enceNew Zealand Statistical Association Conferencewebsite httpwwwstatsnz2006com

REPORT ON THE 2005 NEW ZEALAND MATHEMATICS COLLOQUIUMPALMERSTON NORTH

5ndash7 December 2005

The Colloquia began in 1966 making this yearrsquos event (counting five years in which instead an Aus-tralasian Mathematics Convention was held in Australia or New Zealand) number 40 Some participantshave been present at nearly every one Despite some debate at last yearrsquos meeting about the continuedrole of the Colloquium another successful event has been run attracting 111 delegates It was particularlygood to see 6 people from Otago which must be a modern day record for a North Island Colloquium(Victoriamdashbest not mentioned)

The NZMC invited speakers were

Professor Peter Kuchment Texas AampM University Circular Radon transform nodal lines ther-mal acoustic tomography and all that

Tatiana Marquez Lago University of New Mexico Butcher Prizewinner Stochastic variationestimates of progesterone transcriptional activity in the EGFR pathway

Professor Mark Meerschaert Otago University ANZIAM Speaker Vector fractional calculus

Associate Professor Eamonn OrsquoBrien University of Auckland NZMS Speaker and 2004 NZMSResearch Award winner Algorithmic approaches to the study of linear groups

Associate Professor Bruce van-Brunt Massey University Complex functional differential equa-tions

32

NZMS Newsletter No 95

An innovation this year was the talk by Tatiana Marquez Lago the inaugural winner of the JohnButcher Award in Numerical Analysis After completing undergraduate degrees in Mexico Tatianagained an MSc in Mathematics at Simon Fraser University She began her PhD at McGill Universityin the Department of Mathematics in conjunction with the Centre for Nonlinear Dynamics in Physiologyand Medicine and then transferred to the University of New Mexico where she is working under thesupervision of Dr Stanly Steinberg The John Butcher Award in Numerical Analysis was establishedto recognise Johnrsquos long and productive career in numerical analysis and in particular in the numericalsolution of ordinary differential equations In keeping with Johnrsquos consistent encouragement of studentsthe award is for the best student talk at SciCADE considering both the academic merit of the contentand the presentation itself This year thanks to a grant from the NZIMA the winner was able to visitNew Zealand to speak at the Colloquium

In addition to the 5 invited speakers there were 54 contributed talks There were also two specialstreams a Mathematics Education stream on Monday afternoon and a Dynamical Systems stream onMonday The latter included an invited lecture by Dr Lennaert van Veen La Trobe University onldquoPeriodic motion vs turbulent motion scaling laws bursting and Lyapunov spectra In fact this streamproved so popular that the talks had to be spread over all three days and several sessions Powerpointcontinued its inexorable rise with only a few diehards holding out on the OHP For the first time I didnrsquotsee a single chalk talk Sic transit gloria

A well catered and enjoyable dinner was held at the Institute of Rugby building on Tuesday night Herethe Aitken Prize was awarded The judges remarked on the high standard of this yearrsquos student talks andalthough I know judges say that sort of thing every year in this case I concur Sharlene Harper (MasseyUniversity) was awarded Honourable Mention for her talk Transport of individual droplets sprayed froma line or point source Dion OrsquoNeale (Massey University) was awarded Honourable Mention for histalk Geometric integration for a two spin system and the Aitken Prize was awarded jointly to ElanGin (University of Auckland) for her talk Calcium waves and buffers and to Amanda Elvin (MasseyUniversity) for her talk The role of gap junctions in a neural field model Congratulations to all

Enjoyable excursions were made on Tuesday afternoon to Cross Hills Gardens to see the rhododendronsand to walk the Manawatu Gorge Since 25mm of rain fell on Monday and another 13mm between 9and 12 on Tuesday morning there was some concern about the conditions but in the event the rain heldoff and David Gauldrsquos feet obtained excellent traction in the mud

Irsquod like to thank the chairs of the organizing committee Dean Halford and Charles Little for doingsuch a thorough job Next yearrsquos colloquium will be 4ndash6 December at the University of Waikato

Robert McLachlan

33

NOTICES

NOTICES

NEW ZEALAND MATHEMATICAL SOCIETYPresidentrsquos Report 2005

This report covers the period from the AGM in December 2004 in Dunedin to December 2005

At the colloquium dinner in Dunedin in 2004 the society awarded honorary memberships of the NZMSto Marston Conder Rob Goldblatt Gillian Thornley and Graeme Wake in recognition of theirservice to the society over many years In addition the NZMS council has made John Shanks ourlong-serving membership secretary an honorary member My congratulations to all five and my thanksfor their contribution to NZMS

The Forder Lecturer for 2005 was Professor Martin Bridson of Imperial College London His talkswere well-received with excellent reports from all who attended Professor Bridson is to be congratulatedon his achievement His visit was coordinated by Gaven Martin who also went to considerable lengthsto make Martin and his family welcome in New Zealand Thank you Gaven

Two NZMS Research Awards for 2005 were presented at the RSNZ Science Honours Dinner inWellington to Robert McLachlan of Massey University ldquofor creative pioneering work leading todeep advances in the theory of geometric numerical integration and its application in the study ofdynamical systemsrdquo and to James Sneyd of The University of Auckland ldquofor extensive and celebratedcontributions in mathematical biology demonstrating approaches that combine originality with biologicalrealismrdquo My thanks go to the committee Mike Steel Geoff Whittle and Graham Weir The winnerof the Research Award for 2004 Eamonn OrsquoBrien of The University of Auckland is to be the NZMSspeaker at the 2005 colloquium

I would like to welcome two new Fellows of the NZMS Igor Boglaev and Kee Teo both of MasseyUniversity in Palmerson North My thanks to the selection committee who were Derek Holton RobGoldblatt and Graeme Wake

The Aitken Prize for the best student talk at the 2004 colloquium was awarded to Joanne Manna graduate student at Massey University (Albany) working under the supervision of Mick Roberts forher talk lsquoTo vaccinate or not to vaccinatersquo

The NZMS supported a speaker at the International Workshop on Matrices in Statistics2005 held at Albany The keynote address on lsquoCoefficients of ergodicity in a matrix settingrsquo waspresented by Professor Eugene Seneta of the School of Mathematics and Statistics at the Universityof Sydney Another meeting supported by the NZMS was the 2005 Mathematics in Industry StudyGroup organized by Graeme Wake at Albany The society contributed towards the participation ofstudents at the meeting

Congratulations to our members

bull James Sneyd on being elected a Fellow of the Royal Society of New Zealand

bull Robert McLachlan for being awarded the Individual Researcher Award from Massey University

bull Jeff Hunter on being awarded a DSc by Massey University

My thanks go to Charles Semple who is stepping down from council and to Tammy Smith who is dueto step down as treasurer but has indicated her willingness to be reappointed Thank you too to RobertMcLachlan for editing the newsletter from 2000 to 2005 Many thanks also to the other council memberswho have supported me in my second year as president and the numerous others who have providedhelp and information My term has now come to an end and I wish my successor Gaven Martin the bestfor his term as president

Mick RobertsPresident New Zealand Mathematical Society

Institute of Information and Mathematical SciencesMassey University Albany

34

NZMS Newsletter No 95

ELECTION OF THREE MATHEMATICAL SCIENTISTS AS FELLOWSOF THE ROYAL SOCIETY OF NEW ZEALAND

Dr John S Buckleton Principal Scientist Environment and Scientific Research (ESR) has anoutstanding international reputation in the analysis and interpretation of forensic evidence He is anauthor of more than 100 significant publications or patents largely in the forensic field (shoeprintsfirearms DNA blood grouping tool marks fire debris analysis glass and paint) His monograph Theforensic interpretation of glass evidence (2000) has been adopted as the standard text by many countries

John Buckleton has been a key scientist in establishing New Zealandrsquos reputation at the forefrontinternationally of the application of DNA-based methods for the matching of forensic samples to archivedrecords in databases In collaboration with statistician Professor C M Triggs and others he developedapplied and refined analytical methods for DNA profiling used in New Zealand from the 1980s to thepresent His co-authored monograph Forensic DNA evidence interpretation was published this year(2005)

John Buckleton is regularly called upon to appear as an expert witness in New Zealand courts and hasappeared as an expert witness in several courts overseas He is a research consultant to advisory bodiesin several countries and is in wide demand as a leader of training workshops on evidence interpretationin New Zealand Australia England Europe Asia and the USA

Professor Bakhadyr M Khoussainov Department of Computer Science The University of Auck-land is a leading expert in the area of logic and theoretical computer science His work involves deepand exceptionally broad studies into computability and complexity theory Computability theory is con-cerned with the extent to which mathematics can be implemented on a machine and complexity theoryis concerned with delineating the resources (running time memory etc) needed for processes that canbe implemented He works with world leaders in logic in the USA Russia and New Zealand and hasreceived international acclaim for his ideas ingenuity and exceptional technical brilliance particularly inthe area of ldquoautomatic structuresrdquomdashmathematical structures where the basic operations are implementedby finite state automata

Bakhadyr Khoussainovrsquos research has been supported by Fellowships from the von Humboldt Foun-dation the Japan Society for Promotion of Science and the Marsden Fund His research publicationsinclude one book and more than 90 papers Since his arrival in New Zealand in 1996 he has givenmore than 75 seminars and invited talks at prestigious international gatherings including the EuropeanLogic Colloquium (2002) and Asian Logic Symposium (2002) His excellence in teaching and researchhas been recognised by a University of Auckland Distinguished Teaching Award and the New ZealandMathematical Societyrsquos Research Award (2002)

Professor A James Sneyd Professor of Applied Mathematics The University of Auckland is oneof the worldrsquos leading mathematical biologists His substantial international reputation rests on hisbasic research into pattern formation and self-organisation in biological systems and a study of the sub-cellular calcium dynamics involved in cell signalling in a variety of cell types With over 50 researchpublications many in top-ranked journals in mathematical biology he has established himself as a worldleader in these fields For example in elegant mathematical models he has shown how the formation ofthe complex patterns in honey and pollen observed in honeycomb can be explained by some very simplerules his research has also led the development of control strategies for the tropical disease leishmaniasisHowever he is probably most widely known for his influential research-based textbooks Self-organisationin Biological Systems (2001) and Mathematical Physiology (1998) both of which have won Best Bookawards from the American Association of Publishers

James Sneyd is one of the very few mathematicians to have won research grants from the AmericanNational Institute of Health His modelling is characterised by ingenuity technical prowess and a clearunderstanding of biological phenomena at an appropriate level of detail

35

NOTICES

A SCHOLARSHIP FOR A MASTERS STUDENTat the Institute of Information and Mathematical Sciences Massey University Auckland

A Masters student is sought to study a puzzling phenomenon called Cheyne-Stokes Respiration (CSR)CSR is a weird type of breathing where a person experiences cycles of increasing followed by decreasingventilation followed by periods of breath-holding It is usually seen during sleep in healthy people athigh altitude in people with heart failure in people with neurological disorders and in infants The aimof the project is to explain the mechanism that leads to the appearance of Cheyne-Stokes Respirationby studying nonlinear differential equations This is truly a multi-disciplinary project that involvesmathematical modelling mathematical analysis and computer simulations

Applicants should have strong undergraduate training in applied mathematics and a good backgroundin computing A good knowledge in nonlinear dynamics and a background in physiology will be anadvantage

Salary $16000 pa scholarship (tax free) for two years + domestic fees Other scholarships can be heldconcurrently

For more information contact Dr Alona Ben-Tal Institute of Information and Mathematical SciencesMassey University Auckland E-mail aben-talmasseyacnz Phone 09-4140800 ext 41050 Fax09-4418136

DOCTOR OF SCIENCE AWARDED TO JEFF HUNTER

Professor Jeff Hunter received the highest of science degrees when he became a Doctor of Science atMassey Universitys recent graduation ceremonies in Auckland

Professor Hunter is the Professor of Statistics within the Institute of Information and MathematicalSciences (IIMS) His specialisation is in applied probability a branch of mathematics that involves theuse of probability concepts and methods to model random phenomena The Doctor of Science degreehas been conferred for his work in this area in which he has published more than 40 sole-authoredscientific papers in international journals He is author of the two-volume book Mathematical Techniquesof Applied Probability published by Academic Press in 1983 In 2003 he was awarded a New ZealandScience and Technology Bronze Medal for his contributions to the mathematical and information sciences

Professor Hunter was awarded his Master of Science degree with first class honours in Mathematicsfrom the University of Auckland in 1963 and his Doctor of Philosophy in Statistics from the Universityof North Carolina at Chapel Hill in 1968 Professor Hunter was at the University of Auckland until hecame to Massey in 1990 He was the foundation Head of the Department of Statistics and foundationHead of IIMS at the Albany campusProfessor Hunter retires in June He will continue working at theUniversity on a part time basis

36

NZMS Newsletter No 95

HONORARY DOCTOR OF SCIENCE AWARDED TO SHAYLE SEARLE

Few people could envisage making a career out of proving that applied mathematical statistics is notan oxymoron but a valuable area of statistics Professor Shayle Searle managed this feat through anearly and continued interest in translating applied problems into solvable mathematical formulations

In 1950 he completed a Master of Arts with First Class Honours in Mathematics at Victoria UniversityCollege followed in 1953 by a postgraduate diploma in mathematical statistics at Cambridge UniversityHe returned to New Zealand to work as a research statistician at the New Zealand Dairy Board duringwhich time he was awarded a Fulbright Travel Award which enabled him to enrol in a PhD in AnimalBreeding at Cornell University

After completing his PhD he continued working at the New Zealand Dairy Board until 1962 when hewas invited back to Cornell as a statistical consultant for the universityrsquos computer centre By 1970 hehad attained the rank of professor and remained at Cornell University until his retirement in 1995 whenhe was appointed Professor Emeritus of Biological Statistics

One of Professor Searlersquos earliest contributions to his field was to bring the power of matrix algebra tobear on the multivariate statistical analysis developed in the 1950s to analyse the inheritance of animalcharacteristics At the time these calculations were well beyond the power of computers He providedproof of a formula that enabled direct computation of the huge number of genetic variations underlyingobservable differences of animal characteristics

He developed formulae so that estimates based on field data rather than data from controlled experi-ments were not biased by different sizes of data sets These formulae have been implemented in one ofthe most widely used commercial statistical software packages SAS

During his academic career Professor Searle wrote eight textbooks that are widely regarded for theirclarity and comprehensiveness He also served as an associate editor for Biometrics on the EditorialBoard of the Biometric Society (International) and as a member of the International Biometric Society(ENAR) In 1985 he was awarded the US Senior Scientist Award by the Alexander von HumboldtFoundation

Professor Searle has a long-standing association with Victoria University In 2003 he established aVisiting Fellowship in Statistics to enable leading international statisticians to visit research and presentseminars An active member of the US Friends of Victoria he endowed a prize in first-year appliedstatistics which has been awarded since 1999

HAMILTON MEMORIAL PRIZE

The 2005 Hamilton Memorial Prize has been awarded to Dr Barbara Holland Allan Wilson Cen-tre at Massey University for her pioneering mathematical research in evolutionary biology includingthe development of new instruments for phylogenetic network representation The prize recognizes herachievements in the conception and application of sophisticated mathematical and statistical techniquesto evolutionary biology especially in the representation of phylogenetic networks and trees (A phyloge-netic tree is a graphical means to depict the evolutionary relationships of a group of organisms) Withher solid background in operations research Dr Holland has developed novel tools for representing theconflicting information that arises in many studies of evolutionary relationships where a large collectionof phylogenetic trees occurs as opposed to a single tree

37

NOTICES

Stop-Press PRIZE offered below

Inviting all Problem SeekersSolversStudents Here is an opportunity you CANNOT afford to miss

Mathematics-in-Industry Study Group 2006

Study Centre Massey University Auckland New Zealand

30th January ndash 3rd February 2006

Registrations are open and now welcome via website httpmisg2006masseyacnz

(Click on registration) bull $250 ldquogrants-in-aidrdquo for each of the fifth tenth fifteenth etc

registrants who mention this advertisement (NZMS Newsletter Dec 2005)

bull Offer closes 22nd December 2005 bull Applicants should mention ANZIAM after their name

eg Ms Nikki Luke (ANZIAM)

bull 7 fascinating industrial problems from biology medicine engineering and logistics hellipnow available to view on website

bull Free registration (via website)

bull Student grants available upwards of $500 each

bull Supported by the Foundation for Research Science and

Technology under their lsquoSmartstartrsquo program bull All enquiries to Nikki Luke Administrator

+ 64 9 414 0800 ext 41066 or nlukemasseyacnz

38

NZMS Newsletter No 95

Please complete below and mail to John Shanks NZMS Membership Secretary Department of Mathematics and Statisticsor Fax +64 (3) 479 8427 University of Otago PO Box 56 Dunedin NZ

E-mail jshanksmathsotagoacnz

Name Title

Address

E-mail

Membership category Ordinary Reciprocal Student Overseas student

If Reciprocal then complete this I am a fully-paid up member of

I wish to receive the NZ Journal of Mathematics at special rate

Signed Date

Please send no money now You will be invoiced once your application is accepted

Application for membership of the NZMS

The New Zealand Mathematical Society (Inc) is the representative body of professional mathematicians in New Zealand and was founded in 1974 Its aims include promotion of research in the mathematical sciences the development application and dissemination of mathematical knowledge within New Zealand and effective cooperation and collaboration between mathematicians and their colleagues in New Zealand and in other countries

Membership categories

Ordinary $36 pa Reciprocal $18 pa For overseas residents who are fully paid-up members of societies with which the NZMS maintains a reciprocity agreement (including the American Mathematical Society the Australian Mathematical Society the Canadian Mathematical Society the London Mathematical Society and the Mathematical Society of Japan)

Student $760 pa For currently enrolled students in NZ

Overseas student $18 pa For currently enrolled students in overseas

(GST is added to rates for NZ residents)

Members can subscribe to the New Zealand Journal of Mathematics (httpwwwmathaucklandacnzNZJMindexhtml) at a reduced rate

Members can also elect to make a donation when paying their subs to the NZMS Endowment for Student Support

The Society offers NZ students and new staff a special free one-year membership

NZ

MS A

pp

licatio

n F

orm

Aninstitutional

addressis

preferred

(Full details at wwwmathwaikatoacnzNZMSNZMShtml)

39

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf

NOTICES

NOTICES

NEW ZEALAND MATHEMATICAL SOCIETYPresidentrsquos Report 2005

This report covers the period from the AGM in December 2004 in Dunedin to December 2005

At the colloquium dinner in Dunedin in 2004 the society awarded honorary memberships of the NZMSto Marston Conder Rob Goldblatt Gillian Thornley and Graeme Wake in recognition of theirservice to the society over many years In addition the NZMS council has made John Shanks ourlong-serving membership secretary an honorary member My congratulations to all five and my thanksfor their contribution to NZMS

The Forder Lecturer for 2005 was Professor Martin Bridson of Imperial College London His talkswere well-received with excellent reports from all who attended Professor Bridson is to be congratulatedon his achievement His visit was coordinated by Gaven Martin who also went to considerable lengthsto make Martin and his family welcome in New Zealand Thank you Gaven

Two NZMS Research Awards for 2005 were presented at the RSNZ Science Honours Dinner inWellington to Robert McLachlan of Massey University ldquofor creative pioneering work leading todeep advances in the theory of geometric numerical integration and its application in the study ofdynamical systemsrdquo and to James Sneyd of The University of Auckland ldquofor extensive and celebratedcontributions in mathematical biology demonstrating approaches that combine originality with biologicalrealismrdquo My thanks go to the committee Mike Steel Geoff Whittle and Graham Weir The winnerof the Research Award for 2004 Eamonn OrsquoBrien of The University of Auckland is to be the NZMSspeaker at the 2005 colloquium

I would like to welcome two new Fellows of the NZMS Igor Boglaev and Kee Teo both of MasseyUniversity in Palmerson North My thanks to the selection committee who were Derek Holton RobGoldblatt and Graeme Wake

The Aitken Prize for the best student talk at the 2004 colloquium was awarded to Joanne Manna graduate student at Massey University (Albany) working under the supervision of Mick Roberts forher talk lsquoTo vaccinate or not to vaccinatersquo

The NZMS supported a speaker at the International Workshop on Matrices in Statistics2005 held at Albany The keynote address on lsquoCoefficients of ergodicity in a matrix settingrsquo waspresented by Professor Eugene Seneta of the School of Mathematics and Statistics at the Universityof Sydney Another meeting supported by the NZMS was the 2005 Mathematics in Industry StudyGroup organized by Graeme Wake at Albany The society contributed towards the participation ofstudents at the meeting

Congratulations to our members

bull James Sneyd on being elected a Fellow of the Royal Society of New Zealand

bull Robert McLachlan for being awarded the Individual Researcher Award from Massey University

bull Jeff Hunter on being awarded a DSc by Massey University

My thanks go to Charles Semple who is stepping down from council and to Tammy Smith who is dueto step down as treasurer but has indicated her willingness to be reappointed Thank you too to RobertMcLachlan for editing the newsletter from 2000 to 2005 Many thanks also to the other council memberswho have supported me in my second year as president and the numerous others who have providedhelp and information My term has now come to an end and I wish my successor Gaven Martin the bestfor his term as president

Mick RobertsPresident New Zealand Mathematical Society

Institute of Information and Mathematical SciencesMassey University Albany

34

NZMS Newsletter No 95

ELECTION OF THREE MATHEMATICAL SCIENTISTS AS FELLOWSOF THE ROYAL SOCIETY OF NEW ZEALAND

Dr John S Buckleton Principal Scientist Environment and Scientific Research (ESR) has anoutstanding international reputation in the analysis and interpretation of forensic evidence He is anauthor of more than 100 significant publications or patents largely in the forensic field (shoeprintsfirearms DNA blood grouping tool marks fire debris analysis glass and paint) His monograph Theforensic interpretation of glass evidence (2000) has been adopted as the standard text by many countries

John Buckleton has been a key scientist in establishing New Zealandrsquos reputation at the forefrontinternationally of the application of DNA-based methods for the matching of forensic samples to archivedrecords in databases In collaboration with statistician Professor C M Triggs and others he developedapplied and refined analytical methods for DNA profiling used in New Zealand from the 1980s to thepresent His co-authored monograph Forensic DNA evidence interpretation was published this year(2005)

John Buckleton is regularly called upon to appear as an expert witness in New Zealand courts and hasappeared as an expert witness in several courts overseas He is a research consultant to advisory bodiesin several countries and is in wide demand as a leader of training workshops on evidence interpretationin New Zealand Australia England Europe Asia and the USA

Professor Bakhadyr M Khoussainov Department of Computer Science The University of Auck-land is a leading expert in the area of logic and theoretical computer science His work involves deepand exceptionally broad studies into computability and complexity theory Computability theory is con-cerned with the extent to which mathematics can be implemented on a machine and complexity theoryis concerned with delineating the resources (running time memory etc) needed for processes that canbe implemented He works with world leaders in logic in the USA Russia and New Zealand and hasreceived international acclaim for his ideas ingenuity and exceptional technical brilliance particularly inthe area of ldquoautomatic structuresrdquomdashmathematical structures where the basic operations are implementedby finite state automata

Bakhadyr Khoussainovrsquos research has been supported by Fellowships from the von Humboldt Foun-dation the Japan Society for Promotion of Science and the Marsden Fund His research publicationsinclude one book and more than 90 papers Since his arrival in New Zealand in 1996 he has givenmore than 75 seminars and invited talks at prestigious international gatherings including the EuropeanLogic Colloquium (2002) and Asian Logic Symposium (2002) His excellence in teaching and researchhas been recognised by a University of Auckland Distinguished Teaching Award and the New ZealandMathematical Societyrsquos Research Award (2002)

Professor A James Sneyd Professor of Applied Mathematics The University of Auckland is oneof the worldrsquos leading mathematical biologists His substantial international reputation rests on hisbasic research into pattern formation and self-organisation in biological systems and a study of the sub-cellular calcium dynamics involved in cell signalling in a variety of cell types With over 50 researchpublications many in top-ranked journals in mathematical biology he has established himself as a worldleader in these fields For example in elegant mathematical models he has shown how the formation ofthe complex patterns in honey and pollen observed in honeycomb can be explained by some very simplerules his research has also led the development of control strategies for the tropical disease leishmaniasisHowever he is probably most widely known for his influential research-based textbooks Self-organisationin Biological Systems (2001) and Mathematical Physiology (1998) both of which have won Best Bookawards from the American Association of Publishers

James Sneyd is one of the very few mathematicians to have won research grants from the AmericanNational Institute of Health His modelling is characterised by ingenuity technical prowess and a clearunderstanding of biological phenomena at an appropriate level of detail

35

NOTICES

A SCHOLARSHIP FOR A MASTERS STUDENTat the Institute of Information and Mathematical Sciences Massey University Auckland

A Masters student is sought to study a puzzling phenomenon called Cheyne-Stokes Respiration (CSR)CSR is a weird type of breathing where a person experiences cycles of increasing followed by decreasingventilation followed by periods of breath-holding It is usually seen during sleep in healthy people athigh altitude in people with heart failure in people with neurological disorders and in infants The aimof the project is to explain the mechanism that leads to the appearance of Cheyne-Stokes Respirationby studying nonlinear differential equations This is truly a multi-disciplinary project that involvesmathematical modelling mathematical analysis and computer simulations

Applicants should have strong undergraduate training in applied mathematics and a good backgroundin computing A good knowledge in nonlinear dynamics and a background in physiology will be anadvantage

Salary $16000 pa scholarship (tax free) for two years + domestic fees Other scholarships can be heldconcurrently

For more information contact Dr Alona Ben-Tal Institute of Information and Mathematical SciencesMassey University Auckland E-mail aben-talmasseyacnz Phone 09-4140800 ext 41050 Fax09-4418136

DOCTOR OF SCIENCE AWARDED TO JEFF HUNTER

Professor Jeff Hunter received the highest of science degrees when he became a Doctor of Science atMassey Universitys recent graduation ceremonies in Auckland

Professor Hunter is the Professor of Statistics within the Institute of Information and MathematicalSciences (IIMS) His specialisation is in applied probability a branch of mathematics that involves theuse of probability concepts and methods to model random phenomena The Doctor of Science degreehas been conferred for his work in this area in which he has published more than 40 sole-authoredscientific papers in international journals He is author of the two-volume book Mathematical Techniquesof Applied Probability published by Academic Press in 1983 In 2003 he was awarded a New ZealandScience and Technology Bronze Medal for his contributions to the mathematical and information sciences

Professor Hunter was awarded his Master of Science degree with first class honours in Mathematicsfrom the University of Auckland in 1963 and his Doctor of Philosophy in Statistics from the Universityof North Carolina at Chapel Hill in 1968 Professor Hunter was at the University of Auckland until hecame to Massey in 1990 He was the foundation Head of the Department of Statistics and foundationHead of IIMS at the Albany campusProfessor Hunter retires in June He will continue working at theUniversity on a part time basis

36

NZMS Newsletter No 95

HONORARY DOCTOR OF SCIENCE AWARDED TO SHAYLE SEARLE

Few people could envisage making a career out of proving that applied mathematical statistics is notan oxymoron but a valuable area of statistics Professor Shayle Searle managed this feat through anearly and continued interest in translating applied problems into solvable mathematical formulations

In 1950 he completed a Master of Arts with First Class Honours in Mathematics at Victoria UniversityCollege followed in 1953 by a postgraduate diploma in mathematical statistics at Cambridge UniversityHe returned to New Zealand to work as a research statistician at the New Zealand Dairy Board duringwhich time he was awarded a Fulbright Travel Award which enabled him to enrol in a PhD in AnimalBreeding at Cornell University

After completing his PhD he continued working at the New Zealand Dairy Board until 1962 when hewas invited back to Cornell as a statistical consultant for the universityrsquos computer centre By 1970 hehad attained the rank of professor and remained at Cornell University until his retirement in 1995 whenhe was appointed Professor Emeritus of Biological Statistics

One of Professor Searlersquos earliest contributions to his field was to bring the power of matrix algebra tobear on the multivariate statistical analysis developed in the 1950s to analyse the inheritance of animalcharacteristics At the time these calculations were well beyond the power of computers He providedproof of a formula that enabled direct computation of the huge number of genetic variations underlyingobservable differences of animal characteristics

He developed formulae so that estimates based on field data rather than data from controlled experi-ments were not biased by different sizes of data sets These formulae have been implemented in one ofthe most widely used commercial statistical software packages SAS

During his academic career Professor Searle wrote eight textbooks that are widely regarded for theirclarity and comprehensiveness He also served as an associate editor for Biometrics on the EditorialBoard of the Biometric Society (International) and as a member of the International Biometric Society(ENAR) In 1985 he was awarded the US Senior Scientist Award by the Alexander von HumboldtFoundation

Professor Searle has a long-standing association with Victoria University In 2003 he established aVisiting Fellowship in Statistics to enable leading international statisticians to visit research and presentseminars An active member of the US Friends of Victoria he endowed a prize in first-year appliedstatistics which has been awarded since 1999

HAMILTON MEMORIAL PRIZE

The 2005 Hamilton Memorial Prize has been awarded to Dr Barbara Holland Allan Wilson Cen-tre at Massey University for her pioneering mathematical research in evolutionary biology includingthe development of new instruments for phylogenetic network representation The prize recognizes herachievements in the conception and application of sophisticated mathematical and statistical techniquesto evolutionary biology especially in the representation of phylogenetic networks and trees (A phyloge-netic tree is a graphical means to depict the evolutionary relationships of a group of organisms) Withher solid background in operations research Dr Holland has developed novel tools for representing theconflicting information that arises in many studies of evolutionary relationships where a large collectionof phylogenetic trees occurs as opposed to a single tree

37

NOTICES

Stop-Press PRIZE offered below

Inviting all Problem SeekersSolversStudents Here is an opportunity you CANNOT afford to miss

Mathematics-in-Industry Study Group 2006

Study Centre Massey University Auckland New Zealand

30th January ndash 3rd February 2006

Registrations are open and now welcome via website httpmisg2006masseyacnz

(Click on registration) bull $250 ldquogrants-in-aidrdquo for each of the fifth tenth fifteenth etc

registrants who mention this advertisement (NZMS Newsletter Dec 2005)

bull Offer closes 22nd December 2005 bull Applicants should mention ANZIAM after their name

eg Ms Nikki Luke (ANZIAM)

bull 7 fascinating industrial problems from biology medicine engineering and logistics hellipnow available to view on website

bull Free registration (via website)

bull Student grants available upwards of $500 each

bull Supported by the Foundation for Research Science and

Technology under their lsquoSmartstartrsquo program bull All enquiries to Nikki Luke Administrator

+ 64 9 414 0800 ext 41066 or nlukemasseyacnz

38

NZMS Newsletter No 95

Please complete below and mail to John Shanks NZMS Membership Secretary Department of Mathematics and Statisticsor Fax +64 (3) 479 8427 University of Otago PO Box 56 Dunedin NZ

E-mail jshanksmathsotagoacnz

Name Title

Address

E-mail

Membership category Ordinary Reciprocal Student Overseas student

If Reciprocal then complete this I am a fully-paid up member of

I wish to receive the NZ Journal of Mathematics at special rate

Signed Date

Please send no money now You will be invoiced once your application is accepted

Application for membership of the NZMS

The New Zealand Mathematical Society (Inc) is the representative body of professional mathematicians in New Zealand and was founded in 1974 Its aims include promotion of research in the mathematical sciences the development application and dissemination of mathematical knowledge within New Zealand and effective cooperation and collaboration between mathematicians and their colleagues in New Zealand and in other countries

Membership categories

Ordinary $36 pa Reciprocal $18 pa For overseas residents who are fully paid-up members of societies with which the NZMS maintains a reciprocity agreement (including the American Mathematical Society the Australian Mathematical Society the Canadian Mathematical Society the London Mathematical Society and the Mathematical Society of Japan)

Student $760 pa For currently enrolled students in NZ

Overseas student $18 pa For currently enrolled students in overseas

(GST is added to rates for NZ residents)

Members can subscribe to the New Zealand Journal of Mathematics (httpwwwmathaucklandacnzNZJMindexhtml) at a reduced rate

Members can also elect to make a donation when paying their subs to the NZMS Endowment for Student Support

The Society offers NZ students and new staff a special free one-year membership

NZ

MS A

pp

licatio

n F

orm

Aninstitutional

addressis

preferred

(Full details at wwwmathwaikatoacnzNZMSNZMShtml)

39

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf

NZMS Newsletter No 95

ELECTION OF THREE MATHEMATICAL SCIENTISTS AS FELLOWSOF THE ROYAL SOCIETY OF NEW ZEALAND

Dr John S Buckleton Principal Scientist Environment and Scientific Research (ESR) has anoutstanding international reputation in the analysis and interpretation of forensic evidence He is anauthor of more than 100 significant publications or patents largely in the forensic field (shoeprintsfirearms DNA blood grouping tool marks fire debris analysis glass and paint) His monograph Theforensic interpretation of glass evidence (2000) has been adopted as the standard text by many countries

John Buckleton has been a key scientist in establishing New Zealandrsquos reputation at the forefrontinternationally of the application of DNA-based methods for the matching of forensic samples to archivedrecords in databases In collaboration with statistician Professor C M Triggs and others he developedapplied and refined analytical methods for DNA profiling used in New Zealand from the 1980s to thepresent His co-authored monograph Forensic DNA evidence interpretation was published this year(2005)

John Buckleton is regularly called upon to appear as an expert witness in New Zealand courts and hasappeared as an expert witness in several courts overseas He is a research consultant to advisory bodiesin several countries and is in wide demand as a leader of training workshops on evidence interpretationin New Zealand Australia England Europe Asia and the USA

Professor Bakhadyr M Khoussainov Department of Computer Science The University of Auck-land is a leading expert in the area of logic and theoretical computer science His work involves deepand exceptionally broad studies into computability and complexity theory Computability theory is con-cerned with the extent to which mathematics can be implemented on a machine and complexity theoryis concerned with delineating the resources (running time memory etc) needed for processes that canbe implemented He works with world leaders in logic in the USA Russia and New Zealand and hasreceived international acclaim for his ideas ingenuity and exceptional technical brilliance particularly inthe area of ldquoautomatic structuresrdquomdashmathematical structures where the basic operations are implementedby finite state automata

Bakhadyr Khoussainovrsquos research has been supported by Fellowships from the von Humboldt Foun-dation the Japan Society for Promotion of Science and the Marsden Fund His research publicationsinclude one book and more than 90 papers Since his arrival in New Zealand in 1996 he has givenmore than 75 seminars and invited talks at prestigious international gatherings including the EuropeanLogic Colloquium (2002) and Asian Logic Symposium (2002) His excellence in teaching and researchhas been recognised by a University of Auckland Distinguished Teaching Award and the New ZealandMathematical Societyrsquos Research Award (2002)

Professor A James Sneyd Professor of Applied Mathematics The University of Auckland is oneof the worldrsquos leading mathematical biologists His substantial international reputation rests on hisbasic research into pattern formation and self-organisation in biological systems and a study of the sub-cellular calcium dynamics involved in cell signalling in a variety of cell types With over 50 researchpublications many in top-ranked journals in mathematical biology he has established himself as a worldleader in these fields For example in elegant mathematical models he has shown how the formation ofthe complex patterns in honey and pollen observed in honeycomb can be explained by some very simplerules his research has also led the development of control strategies for the tropical disease leishmaniasisHowever he is probably most widely known for his influential research-based textbooks Self-organisationin Biological Systems (2001) and Mathematical Physiology (1998) both of which have won Best Bookawards from the American Association of Publishers

James Sneyd is one of the very few mathematicians to have won research grants from the AmericanNational Institute of Health His modelling is characterised by ingenuity technical prowess and a clearunderstanding of biological phenomena at an appropriate level of detail

35

NOTICES

A SCHOLARSHIP FOR A MASTERS STUDENTat the Institute of Information and Mathematical Sciences Massey University Auckland

A Masters student is sought to study a puzzling phenomenon called Cheyne-Stokes Respiration (CSR)CSR is a weird type of breathing where a person experiences cycles of increasing followed by decreasingventilation followed by periods of breath-holding It is usually seen during sleep in healthy people athigh altitude in people with heart failure in people with neurological disorders and in infants The aimof the project is to explain the mechanism that leads to the appearance of Cheyne-Stokes Respirationby studying nonlinear differential equations This is truly a multi-disciplinary project that involvesmathematical modelling mathematical analysis and computer simulations

Applicants should have strong undergraduate training in applied mathematics and a good backgroundin computing A good knowledge in nonlinear dynamics and a background in physiology will be anadvantage

Salary $16000 pa scholarship (tax free) for two years + domestic fees Other scholarships can be heldconcurrently

For more information contact Dr Alona Ben-Tal Institute of Information and Mathematical SciencesMassey University Auckland E-mail aben-talmasseyacnz Phone 09-4140800 ext 41050 Fax09-4418136

DOCTOR OF SCIENCE AWARDED TO JEFF HUNTER

Professor Jeff Hunter received the highest of science degrees when he became a Doctor of Science atMassey Universitys recent graduation ceremonies in Auckland

Professor Hunter is the Professor of Statistics within the Institute of Information and MathematicalSciences (IIMS) His specialisation is in applied probability a branch of mathematics that involves theuse of probability concepts and methods to model random phenomena The Doctor of Science degreehas been conferred for his work in this area in which he has published more than 40 sole-authoredscientific papers in international journals He is author of the two-volume book Mathematical Techniquesof Applied Probability published by Academic Press in 1983 In 2003 he was awarded a New ZealandScience and Technology Bronze Medal for his contributions to the mathematical and information sciences

Professor Hunter was awarded his Master of Science degree with first class honours in Mathematicsfrom the University of Auckland in 1963 and his Doctor of Philosophy in Statistics from the Universityof North Carolina at Chapel Hill in 1968 Professor Hunter was at the University of Auckland until hecame to Massey in 1990 He was the foundation Head of the Department of Statistics and foundationHead of IIMS at the Albany campusProfessor Hunter retires in June He will continue working at theUniversity on a part time basis

36

NZMS Newsletter No 95

HONORARY DOCTOR OF SCIENCE AWARDED TO SHAYLE SEARLE

Few people could envisage making a career out of proving that applied mathematical statistics is notan oxymoron but a valuable area of statistics Professor Shayle Searle managed this feat through anearly and continued interest in translating applied problems into solvable mathematical formulations

In 1950 he completed a Master of Arts with First Class Honours in Mathematics at Victoria UniversityCollege followed in 1953 by a postgraduate diploma in mathematical statistics at Cambridge UniversityHe returned to New Zealand to work as a research statistician at the New Zealand Dairy Board duringwhich time he was awarded a Fulbright Travel Award which enabled him to enrol in a PhD in AnimalBreeding at Cornell University

After completing his PhD he continued working at the New Zealand Dairy Board until 1962 when hewas invited back to Cornell as a statistical consultant for the universityrsquos computer centre By 1970 hehad attained the rank of professor and remained at Cornell University until his retirement in 1995 whenhe was appointed Professor Emeritus of Biological Statistics

One of Professor Searlersquos earliest contributions to his field was to bring the power of matrix algebra tobear on the multivariate statistical analysis developed in the 1950s to analyse the inheritance of animalcharacteristics At the time these calculations were well beyond the power of computers He providedproof of a formula that enabled direct computation of the huge number of genetic variations underlyingobservable differences of animal characteristics

He developed formulae so that estimates based on field data rather than data from controlled experi-ments were not biased by different sizes of data sets These formulae have been implemented in one ofthe most widely used commercial statistical software packages SAS

During his academic career Professor Searle wrote eight textbooks that are widely regarded for theirclarity and comprehensiveness He also served as an associate editor for Biometrics on the EditorialBoard of the Biometric Society (International) and as a member of the International Biometric Society(ENAR) In 1985 he was awarded the US Senior Scientist Award by the Alexander von HumboldtFoundation

Professor Searle has a long-standing association with Victoria University In 2003 he established aVisiting Fellowship in Statistics to enable leading international statisticians to visit research and presentseminars An active member of the US Friends of Victoria he endowed a prize in first-year appliedstatistics which has been awarded since 1999

HAMILTON MEMORIAL PRIZE

The 2005 Hamilton Memorial Prize has been awarded to Dr Barbara Holland Allan Wilson Cen-tre at Massey University for her pioneering mathematical research in evolutionary biology includingthe development of new instruments for phylogenetic network representation The prize recognizes herachievements in the conception and application of sophisticated mathematical and statistical techniquesto evolutionary biology especially in the representation of phylogenetic networks and trees (A phyloge-netic tree is a graphical means to depict the evolutionary relationships of a group of organisms) Withher solid background in operations research Dr Holland has developed novel tools for representing theconflicting information that arises in many studies of evolutionary relationships where a large collectionof phylogenetic trees occurs as opposed to a single tree

37

NOTICES

Stop-Press PRIZE offered below

Inviting all Problem SeekersSolversStudents Here is an opportunity you CANNOT afford to miss

Mathematics-in-Industry Study Group 2006

Study Centre Massey University Auckland New Zealand

30th January ndash 3rd February 2006

Registrations are open and now welcome via website httpmisg2006masseyacnz

(Click on registration) bull $250 ldquogrants-in-aidrdquo for each of the fifth tenth fifteenth etc

registrants who mention this advertisement (NZMS Newsletter Dec 2005)

bull Offer closes 22nd December 2005 bull Applicants should mention ANZIAM after their name

eg Ms Nikki Luke (ANZIAM)

bull 7 fascinating industrial problems from biology medicine engineering and logistics hellipnow available to view on website

bull Free registration (via website)

bull Student grants available upwards of $500 each

bull Supported by the Foundation for Research Science and

Technology under their lsquoSmartstartrsquo program bull All enquiries to Nikki Luke Administrator

+ 64 9 414 0800 ext 41066 or nlukemasseyacnz

38

NZMS Newsletter No 95

Please complete below and mail to John Shanks NZMS Membership Secretary Department of Mathematics and Statisticsor Fax +64 (3) 479 8427 University of Otago PO Box 56 Dunedin NZ

E-mail jshanksmathsotagoacnz

Name Title

Address

E-mail

Membership category Ordinary Reciprocal Student Overseas student

If Reciprocal then complete this I am a fully-paid up member of

I wish to receive the NZ Journal of Mathematics at special rate

Signed Date

Please send no money now You will be invoiced once your application is accepted

Application for membership of the NZMS

The New Zealand Mathematical Society (Inc) is the representative body of professional mathematicians in New Zealand and was founded in 1974 Its aims include promotion of research in the mathematical sciences the development application and dissemination of mathematical knowledge within New Zealand and effective cooperation and collaboration between mathematicians and their colleagues in New Zealand and in other countries

Membership categories

Ordinary $36 pa Reciprocal $18 pa For overseas residents who are fully paid-up members of societies with which the NZMS maintains a reciprocity agreement (including the American Mathematical Society the Australian Mathematical Society the Canadian Mathematical Society the London Mathematical Society and the Mathematical Society of Japan)

Student $760 pa For currently enrolled students in NZ

Overseas student $18 pa For currently enrolled students in overseas

(GST is added to rates for NZ residents)

Members can subscribe to the New Zealand Journal of Mathematics (httpwwwmathaucklandacnzNZJMindexhtml) at a reduced rate

Members can also elect to make a donation when paying their subs to the NZMS Endowment for Student Support

The Society offers NZ students and new staff a special free one-year membership

NZ

MS A

pp

licatio

n F

orm

Aninstitutional

addressis

preferred

(Full details at wwwmathwaikatoacnzNZMSNZMShtml)

39

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf

NOTICES

A SCHOLARSHIP FOR A MASTERS STUDENTat the Institute of Information and Mathematical Sciences Massey University Auckland

A Masters student is sought to study a puzzling phenomenon called Cheyne-Stokes Respiration (CSR)CSR is a weird type of breathing where a person experiences cycles of increasing followed by decreasingventilation followed by periods of breath-holding It is usually seen during sleep in healthy people athigh altitude in people with heart failure in people with neurological disorders and in infants The aimof the project is to explain the mechanism that leads to the appearance of Cheyne-Stokes Respirationby studying nonlinear differential equations This is truly a multi-disciplinary project that involvesmathematical modelling mathematical analysis and computer simulations

Applicants should have strong undergraduate training in applied mathematics and a good backgroundin computing A good knowledge in nonlinear dynamics and a background in physiology will be anadvantage

Salary $16000 pa scholarship (tax free) for two years + domestic fees Other scholarships can be heldconcurrently

For more information contact Dr Alona Ben-Tal Institute of Information and Mathematical SciencesMassey University Auckland E-mail aben-talmasseyacnz Phone 09-4140800 ext 41050 Fax09-4418136

DOCTOR OF SCIENCE AWARDED TO JEFF HUNTER

Professor Jeff Hunter received the highest of science degrees when he became a Doctor of Science atMassey Universitys recent graduation ceremonies in Auckland

Professor Hunter is the Professor of Statistics within the Institute of Information and MathematicalSciences (IIMS) His specialisation is in applied probability a branch of mathematics that involves theuse of probability concepts and methods to model random phenomena The Doctor of Science degreehas been conferred for his work in this area in which he has published more than 40 sole-authoredscientific papers in international journals He is author of the two-volume book Mathematical Techniquesof Applied Probability published by Academic Press in 1983 In 2003 he was awarded a New ZealandScience and Technology Bronze Medal for his contributions to the mathematical and information sciences

Professor Hunter was awarded his Master of Science degree with first class honours in Mathematicsfrom the University of Auckland in 1963 and his Doctor of Philosophy in Statistics from the Universityof North Carolina at Chapel Hill in 1968 Professor Hunter was at the University of Auckland until hecame to Massey in 1990 He was the foundation Head of the Department of Statistics and foundationHead of IIMS at the Albany campusProfessor Hunter retires in June He will continue working at theUniversity on a part time basis

36

NZMS Newsletter No 95

HONORARY DOCTOR OF SCIENCE AWARDED TO SHAYLE SEARLE

Few people could envisage making a career out of proving that applied mathematical statistics is notan oxymoron but a valuable area of statistics Professor Shayle Searle managed this feat through anearly and continued interest in translating applied problems into solvable mathematical formulations

In 1950 he completed a Master of Arts with First Class Honours in Mathematics at Victoria UniversityCollege followed in 1953 by a postgraduate diploma in mathematical statistics at Cambridge UniversityHe returned to New Zealand to work as a research statistician at the New Zealand Dairy Board duringwhich time he was awarded a Fulbright Travel Award which enabled him to enrol in a PhD in AnimalBreeding at Cornell University

After completing his PhD he continued working at the New Zealand Dairy Board until 1962 when hewas invited back to Cornell as a statistical consultant for the universityrsquos computer centre By 1970 hehad attained the rank of professor and remained at Cornell University until his retirement in 1995 whenhe was appointed Professor Emeritus of Biological Statistics

One of Professor Searlersquos earliest contributions to his field was to bring the power of matrix algebra tobear on the multivariate statistical analysis developed in the 1950s to analyse the inheritance of animalcharacteristics At the time these calculations were well beyond the power of computers He providedproof of a formula that enabled direct computation of the huge number of genetic variations underlyingobservable differences of animal characteristics

He developed formulae so that estimates based on field data rather than data from controlled experi-ments were not biased by different sizes of data sets These formulae have been implemented in one ofthe most widely used commercial statistical software packages SAS

During his academic career Professor Searle wrote eight textbooks that are widely regarded for theirclarity and comprehensiveness He also served as an associate editor for Biometrics on the EditorialBoard of the Biometric Society (International) and as a member of the International Biometric Society(ENAR) In 1985 he was awarded the US Senior Scientist Award by the Alexander von HumboldtFoundation

Professor Searle has a long-standing association with Victoria University In 2003 he established aVisiting Fellowship in Statistics to enable leading international statisticians to visit research and presentseminars An active member of the US Friends of Victoria he endowed a prize in first-year appliedstatistics which has been awarded since 1999

HAMILTON MEMORIAL PRIZE

The 2005 Hamilton Memorial Prize has been awarded to Dr Barbara Holland Allan Wilson Cen-tre at Massey University for her pioneering mathematical research in evolutionary biology includingthe development of new instruments for phylogenetic network representation The prize recognizes herachievements in the conception and application of sophisticated mathematical and statistical techniquesto evolutionary biology especially in the representation of phylogenetic networks and trees (A phyloge-netic tree is a graphical means to depict the evolutionary relationships of a group of organisms) Withher solid background in operations research Dr Holland has developed novel tools for representing theconflicting information that arises in many studies of evolutionary relationships where a large collectionof phylogenetic trees occurs as opposed to a single tree

37

NOTICES

Stop-Press PRIZE offered below

Inviting all Problem SeekersSolversStudents Here is an opportunity you CANNOT afford to miss

Mathematics-in-Industry Study Group 2006

Study Centre Massey University Auckland New Zealand

30th January ndash 3rd February 2006

Registrations are open and now welcome via website httpmisg2006masseyacnz

(Click on registration) bull $250 ldquogrants-in-aidrdquo for each of the fifth tenth fifteenth etc

registrants who mention this advertisement (NZMS Newsletter Dec 2005)

bull Offer closes 22nd December 2005 bull Applicants should mention ANZIAM after their name

eg Ms Nikki Luke (ANZIAM)

bull 7 fascinating industrial problems from biology medicine engineering and logistics hellipnow available to view on website

bull Free registration (via website)

bull Student grants available upwards of $500 each

bull Supported by the Foundation for Research Science and

Technology under their lsquoSmartstartrsquo program bull All enquiries to Nikki Luke Administrator

+ 64 9 414 0800 ext 41066 or nlukemasseyacnz

38

NZMS Newsletter No 95

Please complete below and mail to John Shanks NZMS Membership Secretary Department of Mathematics and Statisticsor Fax +64 (3) 479 8427 University of Otago PO Box 56 Dunedin NZ

E-mail jshanksmathsotagoacnz

Name Title

Address

E-mail

Membership category Ordinary Reciprocal Student Overseas student

If Reciprocal then complete this I am a fully-paid up member of

I wish to receive the NZ Journal of Mathematics at special rate

Signed Date

Please send no money now You will be invoiced once your application is accepted

Application for membership of the NZMS

The New Zealand Mathematical Society (Inc) is the representative body of professional mathematicians in New Zealand and was founded in 1974 Its aims include promotion of research in the mathematical sciences the development application and dissemination of mathematical knowledge within New Zealand and effective cooperation and collaboration between mathematicians and their colleagues in New Zealand and in other countries

Membership categories

Ordinary $36 pa Reciprocal $18 pa For overseas residents who are fully paid-up members of societies with which the NZMS maintains a reciprocity agreement (including the American Mathematical Society the Australian Mathematical Society the Canadian Mathematical Society the London Mathematical Society and the Mathematical Society of Japan)

Student $760 pa For currently enrolled students in NZ

Overseas student $18 pa For currently enrolled students in overseas

(GST is added to rates for NZ residents)

Members can subscribe to the New Zealand Journal of Mathematics (httpwwwmathaucklandacnzNZJMindexhtml) at a reduced rate

Members can also elect to make a donation when paying their subs to the NZMS Endowment for Student Support

The Society offers NZ students and new staff a special free one-year membership

NZ

MS A

pp

licatio

n F

orm

Aninstitutional

addressis

preferred

(Full details at wwwmathwaikatoacnzNZMSNZMShtml)

39

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf

NZMS Newsletter No 95

HONORARY DOCTOR OF SCIENCE AWARDED TO SHAYLE SEARLE

Few people could envisage making a career out of proving that applied mathematical statistics is notan oxymoron but a valuable area of statistics Professor Shayle Searle managed this feat through anearly and continued interest in translating applied problems into solvable mathematical formulations

In 1950 he completed a Master of Arts with First Class Honours in Mathematics at Victoria UniversityCollege followed in 1953 by a postgraduate diploma in mathematical statistics at Cambridge UniversityHe returned to New Zealand to work as a research statistician at the New Zealand Dairy Board duringwhich time he was awarded a Fulbright Travel Award which enabled him to enrol in a PhD in AnimalBreeding at Cornell University

After completing his PhD he continued working at the New Zealand Dairy Board until 1962 when hewas invited back to Cornell as a statistical consultant for the universityrsquos computer centre By 1970 hehad attained the rank of professor and remained at Cornell University until his retirement in 1995 whenhe was appointed Professor Emeritus of Biological Statistics

One of Professor Searlersquos earliest contributions to his field was to bring the power of matrix algebra tobear on the multivariate statistical analysis developed in the 1950s to analyse the inheritance of animalcharacteristics At the time these calculations were well beyond the power of computers He providedproof of a formula that enabled direct computation of the huge number of genetic variations underlyingobservable differences of animal characteristics

He developed formulae so that estimates based on field data rather than data from controlled experi-ments were not biased by different sizes of data sets These formulae have been implemented in one ofthe most widely used commercial statistical software packages SAS

During his academic career Professor Searle wrote eight textbooks that are widely regarded for theirclarity and comprehensiveness He also served as an associate editor for Biometrics on the EditorialBoard of the Biometric Society (International) and as a member of the International Biometric Society(ENAR) In 1985 he was awarded the US Senior Scientist Award by the Alexander von HumboldtFoundation

Professor Searle has a long-standing association with Victoria University In 2003 he established aVisiting Fellowship in Statistics to enable leading international statisticians to visit research and presentseminars An active member of the US Friends of Victoria he endowed a prize in first-year appliedstatistics which has been awarded since 1999

HAMILTON MEMORIAL PRIZE

The 2005 Hamilton Memorial Prize has been awarded to Dr Barbara Holland Allan Wilson Cen-tre at Massey University for her pioneering mathematical research in evolutionary biology includingthe development of new instruments for phylogenetic network representation The prize recognizes herachievements in the conception and application of sophisticated mathematical and statistical techniquesto evolutionary biology especially in the representation of phylogenetic networks and trees (A phyloge-netic tree is a graphical means to depict the evolutionary relationships of a group of organisms) Withher solid background in operations research Dr Holland has developed novel tools for representing theconflicting information that arises in many studies of evolutionary relationships where a large collectionof phylogenetic trees occurs as opposed to a single tree

37

NOTICES

Stop-Press PRIZE offered below

Inviting all Problem SeekersSolversStudents Here is an opportunity you CANNOT afford to miss

Mathematics-in-Industry Study Group 2006

Study Centre Massey University Auckland New Zealand

30th January ndash 3rd February 2006

Registrations are open and now welcome via website httpmisg2006masseyacnz

(Click on registration) bull $250 ldquogrants-in-aidrdquo for each of the fifth tenth fifteenth etc

registrants who mention this advertisement (NZMS Newsletter Dec 2005)

bull Offer closes 22nd December 2005 bull Applicants should mention ANZIAM after their name

eg Ms Nikki Luke (ANZIAM)

bull 7 fascinating industrial problems from biology medicine engineering and logistics hellipnow available to view on website

bull Free registration (via website)

bull Student grants available upwards of $500 each

bull Supported by the Foundation for Research Science and

Technology under their lsquoSmartstartrsquo program bull All enquiries to Nikki Luke Administrator

+ 64 9 414 0800 ext 41066 or nlukemasseyacnz

38

NZMS Newsletter No 95

Please complete below and mail to John Shanks NZMS Membership Secretary Department of Mathematics and Statisticsor Fax +64 (3) 479 8427 University of Otago PO Box 56 Dunedin NZ

E-mail jshanksmathsotagoacnz

Name Title

Address

E-mail

Membership category Ordinary Reciprocal Student Overseas student

If Reciprocal then complete this I am a fully-paid up member of

I wish to receive the NZ Journal of Mathematics at special rate

Signed Date

Please send no money now You will be invoiced once your application is accepted

Application for membership of the NZMS

The New Zealand Mathematical Society (Inc) is the representative body of professional mathematicians in New Zealand and was founded in 1974 Its aims include promotion of research in the mathematical sciences the development application and dissemination of mathematical knowledge within New Zealand and effective cooperation and collaboration between mathematicians and their colleagues in New Zealand and in other countries

Membership categories

Ordinary $36 pa Reciprocal $18 pa For overseas residents who are fully paid-up members of societies with which the NZMS maintains a reciprocity agreement (including the American Mathematical Society the Australian Mathematical Society the Canadian Mathematical Society the London Mathematical Society and the Mathematical Society of Japan)

Student $760 pa For currently enrolled students in NZ

Overseas student $18 pa For currently enrolled students in overseas

(GST is added to rates for NZ residents)

Members can subscribe to the New Zealand Journal of Mathematics (httpwwwmathaucklandacnzNZJMindexhtml) at a reduced rate

Members can also elect to make a donation when paying their subs to the NZMS Endowment for Student Support

The Society offers NZ students and new staff a special free one-year membership

NZ

MS A

pp

licatio

n F

orm

Aninstitutional

addressis

preferred

(Full details at wwwmathwaikatoacnzNZMSNZMShtml)

39

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf

NOTICES

Stop-Press PRIZE offered below

Inviting all Problem SeekersSolversStudents Here is an opportunity you CANNOT afford to miss

Mathematics-in-Industry Study Group 2006

Study Centre Massey University Auckland New Zealand

30th January ndash 3rd February 2006

Registrations are open and now welcome via website httpmisg2006masseyacnz

(Click on registration) bull $250 ldquogrants-in-aidrdquo for each of the fifth tenth fifteenth etc

registrants who mention this advertisement (NZMS Newsletter Dec 2005)

bull Offer closes 22nd December 2005 bull Applicants should mention ANZIAM after their name

eg Ms Nikki Luke (ANZIAM)

bull 7 fascinating industrial problems from biology medicine engineering and logistics hellipnow available to view on website

bull Free registration (via website)

bull Student grants available upwards of $500 each

bull Supported by the Foundation for Research Science and

Technology under their lsquoSmartstartrsquo program bull All enquiries to Nikki Luke Administrator

+ 64 9 414 0800 ext 41066 or nlukemasseyacnz

38

NZMS Newsletter No 95

Please complete below and mail to John Shanks NZMS Membership Secretary Department of Mathematics and Statisticsor Fax +64 (3) 479 8427 University of Otago PO Box 56 Dunedin NZ

E-mail jshanksmathsotagoacnz

Name Title

Address

E-mail

Membership category Ordinary Reciprocal Student Overseas student

If Reciprocal then complete this I am a fully-paid up member of

I wish to receive the NZ Journal of Mathematics at special rate

Signed Date

Please send no money now You will be invoiced once your application is accepted

Application for membership of the NZMS

The New Zealand Mathematical Society (Inc) is the representative body of professional mathematicians in New Zealand and was founded in 1974 Its aims include promotion of research in the mathematical sciences the development application and dissemination of mathematical knowledge within New Zealand and effective cooperation and collaboration between mathematicians and their colleagues in New Zealand and in other countries

Membership categories

Ordinary $36 pa Reciprocal $18 pa For overseas residents who are fully paid-up members of societies with which the NZMS maintains a reciprocity agreement (including the American Mathematical Society the Australian Mathematical Society the Canadian Mathematical Society the London Mathematical Society and the Mathematical Society of Japan)

Student $760 pa For currently enrolled students in NZ

Overseas student $18 pa For currently enrolled students in overseas

(GST is added to rates for NZ residents)

Members can subscribe to the New Zealand Journal of Mathematics (httpwwwmathaucklandacnzNZJMindexhtml) at a reduced rate

Members can also elect to make a donation when paying their subs to the NZMS Endowment for Student Support

The Society offers NZ students and new staff a special free one-year membership

NZ

MS A

pp

licatio

n F

orm

Aninstitutional

addressis

preferred

(Full details at wwwmathwaikatoacnzNZMSNZMShtml)

39

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf

NZMS Newsletter No 95

Please complete below and mail to John Shanks NZMS Membership Secretary Department of Mathematics and Statisticsor Fax +64 (3) 479 8427 University of Otago PO Box 56 Dunedin NZ

E-mail jshanksmathsotagoacnz

Name Title

Address

E-mail

Membership category Ordinary Reciprocal Student Overseas student

If Reciprocal then complete this I am a fully-paid up member of

I wish to receive the NZ Journal of Mathematics at special rate

Signed Date

Please send no money now You will be invoiced once your application is accepted

Application for membership of the NZMS

The New Zealand Mathematical Society (Inc) is the representative body of professional mathematicians in New Zealand and was founded in 1974 Its aims include promotion of research in the mathematical sciences the development application and dissemination of mathematical knowledge within New Zealand and effective cooperation and collaboration between mathematicians and their colleagues in New Zealand and in other countries

Membership categories

Ordinary $36 pa Reciprocal $18 pa For overseas residents who are fully paid-up members of societies with which the NZMS maintains a reciprocity agreement (including the American Mathematical Society the Australian Mathematical Society the Canadian Mathematical Society the London Mathematical Society and the Mathematical Society of Japan)

Student $760 pa For currently enrolled students in NZ

Overseas student $18 pa For currently enrolled students in overseas

(GST is added to rates for NZ residents)

Members can subscribe to the New Zealand Journal of Mathematics (httpwwwmathaucklandacnzNZJMindexhtml) at a reduced rate

Members can also elect to make a donation when paying their subs to the NZMS Endowment for Student Support

The Society offers NZ students and new staff a special free one-year membership

NZ

MS A

pp

licatio

n F

orm

Aninstitutional

addressis

preferred

(Full details at wwwmathwaikatoacnzNZMSNZMShtml)

39

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf

MATHEMATICAL MINIATURE 29

A 2005 puzzle a skew matrix and a mathematical musician

Sometimes it seems a nice thing to do to propose a problem with the number of the current year built intoit I believe this often happens with Mathematics Olympiad questions and the puzzle I am proposing today isat a level a little below this

Many years ago when I was teaching myself how to do simulation calculations I thought it might be agood idea to base pseudo random number sequences on difference equations over finite fields Because in thosedays there was no choice but to work in machine arithmetic with numbers in the set minus239minus239 +1 239minus2 239 minus 1 I thought I should consider GF(p) where p is as close as possible to 239 and generate my randomnumber sequence using a simple difference equation modulo p The value of p was chosen as 239 minus 7 and thedifference equation was the famous Fibonacci equation xn = xnminus1 + xnminus2 or written another way[

xn

xnminus1

]= M

[xnminus1

xnminus2

]where M =

[1 11 0

]

In congruential sequences it is possible to do some basic analyses of their statistical properties to see if theyare likely to pass muster as pretend uniformly distributed random numbers However my only interest was tosee how long the number sequence was before it started all over again In other words the order of the groupgenerated by M A first step is to see if M is diagonalizable mod p Because the characteristic polynomialof M is reducible if and only if 5 is a quadratic residue of p we need to determine if this is the case Bythe quadratic reciprocity theorem this will be true iff p is a quadratic residue of 5 which it is in the casep = 239 minus 7 equiv 1 mod 5 Because M can be diagonalized Mpminus1 equiv I mod p and the order is therefore a divisorof pminus1 = 23 middot33 middot5 middot7 middot13 middot19 middot37 middot73 middot109 A systematic exploration of the possible divisors shows that the orderis (pminus 1)15 = 36650387592 In the days of my first computer it would have taken more than a millisecond togenerate each pseudo random number so that more than a year would have passed before there was a repetitionWith likely computer failures every hour or two this was well beyond practical needs

My little 2005 problem is just the same except that arithmetic is performed modulo 2005 This means solvingtwo problems as above but with p = 5 and p = 401 In the field of integers modulo 5 the minimal polynomialof M is λ2 minus λminus 1 equiv (λminus 3)2 and the order of M turns out to be 20 As for 401 5 is a quadratic residue andthe order is found to be 200 (which is also the period of the Fibonacci sequence modulo 5times 401 = 2005)

In a problem a colleague and I are working on we wanted to search for something over the set of matrices Xin n dimensions such that the spectral radius is ρ(X) = 0 Let T be a transformation to Jordan canonical formso that Tminus1XT is zero except for the diagonal immediately to the right of the main diagonal For the numericalsearch we are performing we want to avoid the possibility that T will degenerate in some way One way ofavoiding this is to write T = QR using the QR factorization (that is the product of an orthogonal matrix andan upper triangular matrix) The condition on X now becomes that the lower triangular part of QT XQ is zeroThis can be generalized slightly by allowing the possibility that Q is post-multiplied by a diagonal matrix ofplusmn1 diagonals Hence we might as well assume that det(Q) = 1 To characterize Q as the search proceeds wedecided to write Q in terms of a skew matrix S such that S = (Q + I)(Q minus I)minus1 There is still a danger thatthat the absolute values of some of the elements of S will drift upwards as perhaps Q drifts towards I To avoidthis we tried applying a diagonal post-multiplication to make sure that the computation of S is always possibleand that the elements of S are reasonably small Extensive computations have led us to believe the followingmight be true

Given an n times n orthogonal matrix Q there exists a matrix D = diag(d11 d22 d33 dnn) with eachdii isin minus1 1 such that QD + I is non-singular and such that if

S = (QD minus I)(QD + I)minus1

then the skew matrix S has every element in [minus1 1] Hints on finding a proof or a rebuttal of this assertion arewelcomed

I keep writing these little pieces always looking forward to someone letting me know that he or she has readone of them This week my patience was rewarded with a message from a person I have never met saying shedisagreed with something I wrote more than two years ago In Miniature number 20 (April 2003) I gave myopinion that although many mathematicians take an interest in music it is less common for musicians to beinterested in mathematics I should have listened to my parents who passed on to me a culture which did notvalue personally held opinions What I have learned from a short correspondence with this interesting ladyis that she is a musician with a passionate interest in mathematics Of particular significance to her was thecontention that spirals are a common feature in music and mathematics I will read the notes she gave me morecarefully to see if I can understand the connection she is referring to However I have already had considerableenjoyment from looking at a website she told me about httpmathematische-basteleiende

Now it is time for me to retire from the pleasant task of composing these Miniatures

John Butcher butchermathaucklandacnz

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

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• titlepagepdf
• Newsletter95pdf
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  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
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  • • MathMin28pdf

Introducing 64-bit amp multicore technical computing

New in Mathematica 52 mdash All-platform support for 64-bit addressing Multicore support on major platforms Multithreaded numerical linear algebra 64-bit-enhanced arbitrary-precision numerics Vector-based performance enhancements Bundled notebook indexing for desktop search SSH support for secure remote kernels

New in Mathematica 51 and 50 mdash Optimized numerical linear algebra Industrial-strength string manipulation Event handling in di erential equations Fully integrated piecewise functions Integrated support for assumptions Support for quanti ers and quanti er elimination Large-scale linear programming Advanced methods for solving di erential equations Solvers for di erential algebraic equations Built-in universal database connectivity Integrated web services support Graphical user interface development tool Support for more than 60 importexport formats Highly optimized binary data IO

A Selection of Mathematica FeaturesmdashNumeric computation full support for arbitrary and machine precision hundreds of mathematical functions fully implemented for all parameters fast

sparse and dense matrix operations solvers for equations and di erential equations nite and in nite sums and products integral transforms global optimization linear programming automatic or manual algorithm selection precision control

Symbolic computation expanding simpli cation factoring solvers for equations di erential equations di erence equations and inequalities sums products di erentiation integration limits power series integral

transforms algebraic and semi-algebraic domains

Statistics and data analysis descriptive statistics of uni- and multivariate data generalized linear and nonlinear tting multidimensional interpolation convolution correlation regression ANOVA con dence intervals distributions

hypothesis testing statistical plots

Programming multiparadigm symbolic programming language support for procedural functional list-based rule-based and object-oriented programming advanced pattern matching just-in-time compilation platform-independent implementation

Discrete mathematics combinatorics graph theory computational geometry number theory Diophantine equations

Graphics over 50 2D and 3D plot types graphics language animations sound generation

Connectivity NET Java and CC++ APIs import and export lters for over 40 data and image formats

XML support symbolic language XML

Publishing full technical document system for presentation print and the web interactive typesetting and graphics sound outlining one-step export to TeX LaTeX XML MathML HTML and XHTML

Platforms Windows Macintosh Linux other Unix platforms web and grid versions available

User interface WYSIWYG notebook interface programmable buttons and palettes presentation

environment with slide show fully interactive help

copy 2005 Wolfram Research Inc Mathematica is a registered trademark of Wolfram Research Inc All other trademarks are the property of their respective owners Mathematica is not associated with Mathematica Policy Research Inc or MathTech Inc

Contact Details

Name___________________________________________Position__________________________________________Department______________________________________Organisation______________________________________Address 1_________________________________________Address 2_________________________________________City_____________________________________________Phone___________________Fax_____________________E-mail___________________________________________Your industry______________________________________Your particular interest_______________________________

1704

Five Ways of obtaining your FREE Mathematica Info Pack1 Call 0800 477 776 or 07 839 9102 2 Email 1704hrsconz 3 Fax the form below to 07 839 9103 4 Mail a copy of this form completed to HRS PO Box 4153 Hamilton East5 Visit wwwhrsconz1704aspx to request your info pack or download a trial versionNote Please ask for the Mathematica 52 information pack and quote lead reference 1704 when contacting us

Contact us today to get your

FREE Info Pack

New Zealandrsquos Technical Software Source

Please tick the appropriate boxes below

I already use Mathematica but I want to upgrade to 52 from version________

Please send me my Mathematica 52 info pack

Please include the HRS Software Guide in the pack

• titlepagepdf
• Newsletter95pdf
• • PUBLISHERS NOTICE
  • EDITORIAL
  • PRESIDENTS COLUMN
  • LOCAL NEWS
  • FEATURES
  • MINUTES
  • BOOK REVIEWS
  • CONFERENCES
  • NOTICES
  • • MathMin28pdf