real-world modelling and scientist personality types · 2015. 6. 19. · figure 2a,b and c are...
TRANSCRIPT
Real-world modelling and scientist personality types
Harald Martens drtechn
Prof II Dept Engineering Cybernetics
Norwegian U of Science and Technology Trondheim Norway
CEO IDLETechs AS httpscholargooglecomcitationsuser=60HNWsYAAAAJamphl=da
1 The math gap in biomedical sciences why and what can be done 2 Different science cultures Induction vs Deduction 3 The Beluzov-Zhabotinsky reaction as a reproducable metaphor of life
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 Repeated random sampling of people
Distribution of r(theoretical work creative)
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 Repeated random sampling of people
Distribution of r(theoretical work creative)
r +- 95 conficence limit The true effect may be as strong as -014 or + 01
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others
N=250 norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Non-significant effect estimate does not mean No effect at all
To get non-significant effect just
do bad enough science Low N
Bad sampling Noisy measurements
hellip
Not enough to give p-values
Give 1) The estimated effect
and
2) The uncertainty range
(eg approx 95 confidence region)
From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Tidy orderly
R = 007 p(r=0)=0001 95 range 003-011
May conclude A HIGHLY SIGNIFICANT POSITIVE correlation between Working Theoretically and being Creative But very small effect Only 05 of total variance Irrelevant Better conclusion People working theoretically Both creative and non-creative And some non-theoretical are also very creative
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 Norwegian adults tested
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 Repeated random sampling of people
Distribution of r(theoretical work creative)
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 Repeated random sampling of people
Distribution of r(theoretical work creative)
r +- 95 conficence limit The true effect may be as strong as -014 or + 01
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others
N=250 norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Non-significant effect estimate does not mean No effect at all
To get non-significant effect just
do bad enough science Low N
Bad sampling Noisy measurements
hellip
Not enough to give p-values
Give 1) The estimated effect
and
2) The uncertainty range
(eg approx 95 confidence region)
From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Tidy orderly
R = 007 p(r=0)=0001 95 range 003-011
May conclude A HIGHLY SIGNIFICANT POSITIVE correlation between Working Theoretically and being Creative But very small effect Only 05 of total variance Irrelevant Better conclusion People working theoretically Both creative and non-creative And some non-theoretical are also very creative
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 Norwegian adults tested
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 Repeated random sampling of people
Distribution of r(theoretical work creative)
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 Repeated random sampling of people
Distribution of r(theoretical work creative)
r +- 95 conficence limit The true effect may be as strong as -014 or + 01
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others
N=250 norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Non-significant effect estimate does not mean No effect at all
To get non-significant effect just
do bad enough science Low N
Bad sampling Noisy measurements
hellip
Not enough to give p-values
Give 1) The estimated effect
and
2) The uncertainty range
(eg approx 95 confidence region)
From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Tidy orderly
R = 007 p(r=0)=0001 95 range 003-011
May conclude A HIGHLY SIGNIFICANT POSITIVE correlation between Working Theoretically and being Creative But very small effect Only 05 of total variance Irrelevant Better conclusion People working theoretically Both creative and non-creative And some non-theoretical are also very creative
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 Norwegian adults tested
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 Repeated random sampling of people
Distribution of r(theoretical work creative)
r +- 95 conficence limit The true effect may be as strong as -014 or + 01
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others
N=250 norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Non-significant effect estimate does not mean No effect at all
To get non-significant effect just
do bad enough science Low N
Bad sampling Noisy measurements
hellip
Not enough to give p-values
Give 1) The estimated effect
and
2) The uncertainty range
(eg approx 95 confidence region)
From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Tidy orderly
R = 007 p(r=0)=0001 95 range 003-011
May conclude A HIGHLY SIGNIFICANT POSITIVE correlation between Working Theoretically and being Creative But very small effect Only 05 of total variance Irrelevant Better conclusion People working theoretically Both creative and non-creative And some non-theoretical are also very creative
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 Norwegian adults tested
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Figure 2ab and c
Are Theoretically personality types less creative than others
Hypothesis People who work theoretically are less creative than others
N=250 Norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others
N=250 norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Non-significant effect estimate does not mean No effect at all
To get non-significant effect just
do bad enough science Low N
Bad sampling Noisy measurements
hellip
Not enough to give p-values
Give 1) The estimated effect
and
2) The uncertainty range
(eg approx 95 confidence region)
From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Tidy orderly
R = 007 p(r=0)=0001 95 range 003-011
May conclude A HIGHLY SIGNIFICANT POSITIVE correlation between Working Theoretically and being Creative But very small effect Only 05 of total variance Irrelevant Better conclusion People working theoretically Both creative and non-creative And some non-theoretical are also very creative
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 Norwegian adults tested
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others
N=250 norwegian adults From Helge Brovoldrsquos PhD on personality types and math teaching 2014
r = -002 p=037 min(r )=-014 max(r )=010 1000 random sampling of 250 people
Distribution of r(theoretical work creative) Confirms estimated effect is uncertain even with N=250
Negative correlation r=-002 p(r=0)=037 ie not significant Journalists laquoNo relationship between theoretical work and creativityraquo WRONG
r +- 95 conficence limit standard OLS The true effect may be as strong as -014 or + 01
Non-significant effect estimate does not mean No effect at all
To get non-significant effect just
do bad enough science Low N
Bad sampling Noisy measurements
hellip
Not enough to give p-values
Give 1) The estimated effect
and
2) The uncertainty range
(eg approx 95 confidence region)
From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Tidy orderly
R = 007 p(r=0)=0001 95 range 003-011
May conclude A HIGHLY SIGNIFICANT POSITIVE correlation between Working Theoretically and being Creative But very small effect Only 05 of total variance Irrelevant Better conclusion People working theoretically Both creative and non-creative And some non-theoretical are also very creative
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 Norwegian adults tested
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Tidy orderly
R = 007 p(r=0)=0001 95 range 003-011
May conclude A HIGHLY SIGNIFICANT POSITIVE correlation between Working Theoretically and being Creative But very small effect Only 05 of total variance Irrelevant Better conclusion People working theoretically Both creative and non-creative And some non-theoretical are also very creative
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 Norwegian adults tested
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
R = 007 p(r=0)=0001 95 range 003-011 ie 05 explained variance So Significant not meaningful
Erroneous use of statistics lsquoSignificantrsquo and lsquonot significantrsquo
Hypothesis People who work theoretically are less creative than others N=ALL 2200 norwegian adults tested
Significant effect estimate
does not mean
Meaningful effectst bad measurement
hellip
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Meaningful effect
Meaningful effect
Significant but hardly meaningful effect
[xy]= [x0 y0] + t[pq] + [e f] PC regr
y = a + xb + e OLS regr x = c + yd + f CLS regr
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Relationship between Type of Work and personality
N=ALL 2200 norwegian adults tested From Helge Brovoldrsquos PhD on personality types and math teaching 2014
Creative Tidy orderly
Theoretical work
Abstract work
Technical work
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Personality types and work types are correlated
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Space ( 12 or 3D) eg image
Time
Figure 5
Ontology position and intensity variation in time space and properties
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Time
Space
Measured data X
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Measure Time Space and
Property domains
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
How to deal with Quantitative Big Data
bull More disk storage NOT THE ANSWER
bull Black box modelling with ANN SVM etc NOT THE ANSWER
bull Mechanistic modelling NOT THE ANSWER
bull Cybernetic process model adaptation NOT THE ANSWER
bull Combine prior knowledge and massive amounts of measurements bull Prior knowledge Metamodelling of mechanistic mathematical models
bull Measurements Subspace analysis of data(The Unscrambler etc)
bull Forever learning ndash from on-going processes OnTheFlyCompression
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Prototype of futurersquos highdimensional spatiotemporal instrumentation Hyperspectral NIR video 1-2 GB of datahr
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Time
Space Space
Tim
e
times
times times
Figure 7
Measured data X Yspace
Y Tim
e
Epistemology measure position and intensity variation in time space and properties and extract interpretable essence by data modelling
Combine Time Space and
Property domains
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Figure 4
Define a
hypothesis or
a mechanistic
model
Test the
hypothesis or the
model wrt the data
Measure FEW
properties in FEW
samples
Deduction atomistic confirmatory
THEORI-DRIVEN
Design the
observation
process
Data-modelling
laquoLet the data talkraquo
Measure MANY
properties in
MANY samples
DATA-DRIVEN Induction holistic
exploratory
From questions to answers
Different science cultures Induction vs Deduction
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
The Real System
Hard math model
Idea
Plan
Idea
Plan
Simulation
OBSERVATION
Sensitivity model
Hard stat model
Surrogate model
Limited insight
Insight
Speed
Ad hoc data
Hypothesis
THEORY
Systematic data
Ad hoc critical data
lsquoomics data Semi-soft
stat model
Insight but false discovery
Limited Insight
Computer
TRAD MATH MODELLING
TRAD BIO-MED
TRAD COMPUTATIONAL BIOLOGY
Figure Traditions
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance
b)
c) e)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
100 body parts measured in 1000 children
X = x0 + TPrsquo + E
Bilinear structure model
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
X0
Prsquo
T
i = 1 2 3 1000
k=1234 hellip 100
p1
p2
Height
Weight13
Finger L1 Toe R5
Waist
(AGE)
(BMI)
Name
Toe 9
Shoe size
Diapers
Thigh diam
Run speed
0
t2
t1
i=3t 5t 6t 7F 8t
4n 5n 6n 8n 7n
4f 5f
6f 8f
7f
i=3f
i=3n
8T
4F
0
(Age)
t1
8T
4F
8t 8f
i=3t i=3f
6n
3
0
8
k
p1 (AGE) Height
Waist
(BMI)
Name
Diapers
Toe R5
Run speed Weight
Finger L1
hellip hellip hellip hellip
0 1 2 3 4 hellip of PCs 0
1
Average variance remaining
a)
b)
c) e)
d) g) f)
7F
0 Residual SS after 2 PCs
of children
10
00
ch
ildre
n
100 body measures etc
Hypothetical data
Principal Component Analysis (PCA) of childrenrsquos body parts
X = x0 + TPrsquo + E Bilinear structure model
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
X0 Y0
Prsquo
T U
Qrsquo
Brsquo
Vrsquo
Bilinear model structure for Partial Least Squares Regression
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
X X
X
X
Y
X Y
Z
X X Y
X
hellip
X Y
X
hellip
D
X Y
Z
a) b) c) d) e) f)
j) g) i) h)
X
Figure Table types for soft modelling
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Y(N x 3)
= [dxj N x 1) dt j=123]
Xnominal ( N x 60)
= [Xj j=123] where Xj =[Xj(k) k=12hellip20]
Dark=0
Light=1
B( 60 x 3)
Non-linear data-driven ODE development eg in bilinear Scores
Developing nonlinear ODE models from state variable time series data by nominal-level dynamic PLSR
The Estimated Jacobian B of a dynamic system changing over the state space Low-rank regression coefficients from PLSR of rates Y vs states X (20 nominal 01 state variables for each of 3 quantitative state variables) Martens H Toslashndel K Tafintseva V Kohler A Plahte E Vik JO Gjuvsland AB Omholt SW (2013) PLS-Based Multivariate Metamodeling of Dynamic Systems New Perspectives in Partial Least Squares and Related Methods Springer Proceedings in Mathematics amp Statistics 56 pp 3-30 DOI 101007978-1-4614-8283-3_1
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Multivariate metamodelling
Soft meta-model
Math Model
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Modern computer simulation design 18 parameters 4 levels of each 418 100 000 000 000 possible combinations OMBR design 128 experiments
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Computational compaction of a large biological model via multivariate metamodellering
Application Speeding up a model
Computational times Conventional FEM computation gt 120 minutes (average) Multivariate metamodel (nonlin PLSR) lt 001 minute (average)
FEM of facial muscle groups 18 parameters 4 levels of each OMBR design 128 experiments
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Bruk sansene i naturvitenskap ogsaring 1 Moslashnsterdannelse under celle-differensiering
Datamaskin-simuleringer
Sensorisk deskriptiv profilering paring Matforsk
Fant nye egenskaper i den matematiske modellen
Hvithet
Tykkelse Tohodethet
Fordeling av tetthet og beregnings-tid
Matematisk modell av moslashnsterdannelse ved celle-differensiering
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Bruk sansene i naturvitenskap ogsaring 2 Linje-kurvaturens modellom
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
laquoalleraquo (41) mulige matematiske modeller av linje-kurvatur ble kjoslashrt paring datamaskin hver under laquoalleraquo ulike betingelser
500 av de til sammen 50 000 kurvene
Prinsipal Komponent ndashAnalyse (PCA)
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Soft meta-model
Understand what Model does
Speed-up Model computation
Estimate Model parameters from data
Math Model
Soft meta-model
Math Model
Math Model
Soft meta-model
Measured DATA
Parameters
a) b) c)
Extend hard Model with residual-driven soft model
Soft meta-model
Math Model
Measured DATA
Residuals
Model extension
Compare different Models
Joint Soft meta-
model
Math Model Math
Model Math Model
Model extension
Model extension
Individual metamodels
d)
Figure Metamodel uses
e)
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
The Real System
Hard math model
Idea
Idea
Stat design
Stat design
Soft meta-model
COMPUTER SIMULATIONS
OBSERVATIONS
Hard stat Model
Insight
Speed
Systematic Data
(Hypothesis)
(Hypothesis) Systematic Data
Critical validation
Soft data-model
MODERN INDUCTION DATA-DRIVEN
MODERN DEDUCTIONm THEORY-DRIVEN
Figure Future
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Content
bull Are Theoretically personality types less creative than others
bull Ontology technology data modelling and model modelling
bull Changes in math teaching to non-math students
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Figure 1
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Figure 1
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
Math amp stats teaching RADICAL CHANGES REQUIRED
bull Science and Society gets MUCH MORE REAL-WORLD DATA
bull Crisis in eg biomedical research too much data horrible reproducibility
bull Students must be prepared to interpret huge data tables
bull Students therefore need more MATH MODELLING and DATA MODELLING
bull Crisis in math amp stats teaching students fail math do not learn data analysis
bull Math ability is NOT a reliable measure of intelligence
bull Are math culture(s) still arrogant powerful self-serving and self-recruiting
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to
10
05
-05
-10
0
-10 -05 05 0 10
INTUITIVE
CONTEXTUAL
THEORETICAL
INTROVERT
EXTROVERT
FEELING
DISCRETIZING SENSING
entrepreneur
creative
abstract work courage
critical independent
theoretical work
rational controlled
controller amp revision
humble
techn work
tidy
administrator
proper service-minded
loyal
trusting social work
lighthearted
human-work artistic work impulsive
humour
CENT
DINT CITS
DIST
DISF DETS
CESF DEFN
CENF
CIFN
practical work
DEFS
N=128 groups 23 X 35Y PC1 17X 23 y pc2 15x 17y
Correlation to PC 1
Co
rrel
atio
n t
o P
C 2
Can Introvert Theoreticians teach other personality types
Chemometricians
Math amp statisticans
Engineers
Bio-scientists
Probably YES but only if MAJOR changes in DIDACTICS and CURRICULUM
Do they want to