2016 - university of illinoisapril 2016. argen west was a student researcher at the john deere...

2016showcasing graduate mathematics interns

department of mathematicscollege of liberal arts and sciences • university of illinois at urbana-champaign

Nerses Aramyan, Lin Cong, and Albert Tamazyan held internships at Wolfram Research in Champaign, Illinois. Nerses investigated and developed identities for classes of special functions such as the Wigner D, Siegel Theta, and Bell Y functions. These identities will now be included on the WolframAlpha website and in the knowledge base of the Mathematica software. Nerses converted abstract mathematical expressions into a machine-readable form, and tested the formulas extensively both symbolically and numerically. Lin worked with WolframAlpha as an intern in the scientific content group. His task there was to summarize properties of function spaces, so that users can access them on the website and manipulate the connections between different spaces. To achieve this goal, Lin consulted academic articles, compared between different authors and references, determined the desired properties, and finally encoded the properties into the Data file. Albert worked at Wolfram Research adding Entities for new families of mathematical functions. The Wolfram Language (Mathematica) includes “Entities,” which carry general types of information. The relevant properties include “integral representations,” “functional equations,” “asymptotic expansions” and many others. During his internship Albert collected formulas and theorems from the literature, studied the underlying functions and derived new formulas.

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Department of Mathematics • University of Illinois at Urbana-Champaign • 1409 W. Green, Urbana, IL 61801 • Tel: (217) 333–3350 • Email: [email protected] • www.math.illinois.edu

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Elizabeth Field and Goran Tomic held internships at the Institute for Genomic Biology, organized through the Program for Interdisciplinary and Industrial Internships at Illinois (PI4) and supervised by Dr. David LeBauer. They joined the Predictive Ecosystem Analyzer (PEcAn) project, which is a toolbox consisting of two main parts: 1) a scientific workflow which manages environmental data and which is compatible with various ecosystem models, and 2) a Bayesian data assimilation system which synthesizes environmental data with the ecological models. Their project was aimed at developing a method of assimilating observations of biomass in order to provide better estimates for initial parameter values for an ecosystem model. To do this, they wrote an R package which implements a particle filter method. The algorithm was implemented based on an academic article using particle filters for parameter estimation in weather forecasting. The algorithm was then tested on a real dataset in which biomass observations were used to improve parameter estimates.

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The internships for Sushma Kini and Nicholas Kosar at the Ameren Illinois Innovation Center in the University of Illinois Research Park were arranged through the PI4 program. Sushma worked on the customer analytics project where she analyzed the customers of Ameren Illinois and their energy usage patterns by means of statistical inferences and Python programming. By the end of the summer, the teams could segment the customers and identify which energy efficiency programs should be offered to different types of customer. The work culture at Ameren iCenter provides a sound technical learning experience along with a focus on opportunities for developing one’s leadership qualities. “Big data” analysts are in high demand in the job market right now, and Sushma highly recommends working as an intern to transition smoothly into a full time career in the field. For Nicholas’ internship at the Ameren iCenter, his two main goals were to segment customers based on electricity and gas consumption patterns and identify customers that could benefit from energy efficiency offerings. In addition, he also helped out on a project that was analyzing the reliability of Ameren’s electrical grid. During this internship, Nicholas gained experience using Python to look at large data sets.

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Argen West was a student researcher at the John Deere Technology and Innovation Center in the University of Illinois Research Park, where he worked on incorporating site data to improve modeling of crop yield, and on evaluating planter performance using statistical methods. While working on these projects, he picked up new software skills (Tableau for data visualization and ArcGIS for geographic and spatial data) and gained experience working with large data sets.

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Tara Negrón Santiago and Xiao Wang completed internships at Dow AgroSciences arranged through the PI4 program.Tara worked on the problem of weed resistance resulting from repeated use of a herbicide. Academic herbicide resistance modeling tools have been developed to integrate knowledge about weed biology, genetics, weed management and a variety of other interacting factors. Tara developed a graphical user interface and post-processing routines in VBA coupled with Matlab, to enable weed scientists and field managers to easily use and interpret results. Xiao worked on a deterministic equivalent modeling method (DEMM), which allows for direct incorporation of uncertainty in model predictions, based explicitly upon uncertainty in inputs. The company’s existing Maple libraries were refined and novel functions (e.g., arbitrary polynomial chaos expansions) were added. The project culminated in the use of DEMM with a model which estimated the evaporation of a water droplet under variable meteorological conditions, and the associated uncertainty in the solution.

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Hannah Burson worked with Rebecca Smith (Pathobiology Department, College of Veterinary Medicine, UI) on models of the spread of Orf, a poxvirus common in sheep, which persists even in closed populations. Byron Heersink worked with Samuel Beshers (Entomology Department, UI) on modeling ant colonies. He designed and wrote a program in Python emulating the behavior of an ant colony, using a stimulus-threshold response model to control how workers perceive and respond to various tasks. Stacey Butler’s project in James O’Dwyer’s lab (Plant Biology Department, UI) explored properties of communities of interacting species, with competitive, mutualistic and trophic interactions. She studied a variety of dynamic evolutionary models, mostly involving ordinary differential equations of Lotka-Volterra type, taken from a variety of ecology papers searching for consistent patterns in the structure of the communities. Vanessa Rivera-Quiñones interned at the lab of Carla Cáceres (Department of Animal Biology, UI). Her work focused on the zooplankter Daphnia dentifera, which experiences epidemics of the fungus Metschnikowia bicuspidata. To integrate the role of Daphnia as consumers, competitors and hosts, Vanessa studied an ODE system and analyzed its dynamics. Using an adaptive dynamics approach, she described the long term evolution of the population and determined conditions that allow polymorphisms to occur in the system. These internships were arranged through the PI4 program.

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Jed Chou worked in Professor Tandy Warnow’s lab at the University of Illinois where he and his teammates empirically evaluated a new method, SVDquartets, for inferring evolutionary phylogenies from DNA sequences generated under the Coalescent, a stochastic model in which gene trees can be topologically different from the overall species tree. Through this internship, he learned about using simulations to understand algorithms, improved his Python and shell scripting skills, and published a paper in BMC Genomics.

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Emily Schlafly and Benjamin Wright did their internships in the Speech and Hearing Science Department at the University of Illinois. Although tinnitus is relatively common, there is no physiological identifier with which to classify and diagnose the condition, which makes treatment difficult. The Speech and Hearing group aims to identify biomarkers associated with tinnitus and hence contribute to the development of a diagnostic tool. Emily and Benjamin worked on developing a method that will establish the activation sequence of given brain regions using functional MRI time series data, so that functional neural connectivity can be compared in sufferers versus non-sufferers. The algorithm was coded in Matlab and its performance analyzed with noisy data to give context to the results.

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Alessandro Gondolo and Wei Qin completed internships, arranged by the PI4 program, at Agrible, a data science company at UI Research Park that provides business-critical information to select agricultural communities. The projects Alessandro worked on bridged the gap between mathematics and computer science—taking his knowledge of numerical analysis and PDEs and implementing physical models in Python. The experience pushed Alessandro to better understand both broad computer science concepts such as object-oriented programming and design patterns and day-to-day coding etiquette such as the data scraping and version control system, Git. He gained experience with code reviews and ticketing systems, JIRA and Trac. Wei worked as a Back-End Developer and learned about agricultural models and how to implement them in Python. She constructed a finite volume method to solve the models, yielding solutions that are stable and consistent. In addition, she employed statistical methods to analyze and calibrate the model results, using the statistical package R to analyze the sensitivity of the model with respect to parameters. Wei says “the ability to learn new things fast will always be important, no matter which jobs we are doing!”

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Andrew McConvey worked at Akuna Capital, a proprietary trading firm based in Chicago. He undertook a month-long crash course in options theory and basic trading strategies, and then got to apply this theory in a simulated environment before trading actual products in the market. Andrew also worked with a small team of other interns to develop a model for the volatility of option markets and identify trading opportunities. This project deepened his knowledge of Python and introduced him to several packages for data analysis. At Deutsche Bank, Bingji Yi found a method to extrapolate the Parametric Implied Volatility (PIV) surface to keep it arbitrage-free and twice differentiable. This surface is a fundamental building block in quantitative finance, for it parameterizes the Black-Scholes implied volatility as a function of strike and expiration; hence modelers can still use Black-Scholes formulas for pricing and hedging efficiently. During this internship, Bingji developed a new method of extrapolation, and proved the method will work for any (arbitrage-free) market data. He also found how to select optimal model parameters, using numerical algorithms.

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Bolor Turmunkh was a Data Science intern at the text analytics startup company Idibon located in San Francisco. Idibon provides cloud-based natural language processing services that enable organizations to efficiently structure and derive business insights from their language data. Bolor worked with millions of twitter data, used a crowd-sourced annotation process to give structure to the data, and built predictive models. Bolor improved her skills in Python and R programming languages, implemented Machine Learning algorithms, and generally learned a great deal about good practices in Data Science.

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Meghan Galiardi held a second summer internship at Sandia National Laboratories in New Mexico. She mainly worked on her thesis research while at Sandia, but took several steps to connect her research with projects at Sandia. First, Meghan worked on a team trying to identify Sandia models in which complex systems features play an integral role. Meghan’s role was to add more mathematical/analytical capabilities to the project. Second, Meghan worked closely with two staff members, explaining to them the details of her thesis and brainstorming possible applications to Sandia projects. Additionally, Meghan learned skills in project development, presentation-giving, and interviewing. During an earlier internship in 2014, Meghan worked with the complex systems group doing population health modeling. The PI4 program provided travel support.

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November 2016

Now more than ever, the Department of Mathematics relies on the generosity of its alumni and friends. Here are some ways you can invest in our future.

Give to our current use funds:

• Mathematics Partnership Fund Unrestricted gifts have the highest impact. They can be applied to our most critical needs, which change from year to year as new opportunities emerge.

• Fund for Altgeld and Illini Halls Support our bold plan to renovate Altgeld Hall and Illini Hall to create a new collaborative environment for mathematics learning and discovery.

• Illinois Mathematics Scholarship Fund Scholarships enable and encourage the most promising admitted undergraduate mathematics students to pursue a superb education at Illinois.

Create an endowment:

• Faculty Endowments Help recruit and develop excellent faculty by supporting their scholarly and educational work.

• Endowed Graduate Fellowships Provide doctoral students with time and resources to pursue innovative ideas.

• If you are interested in creating a new endowment, please contact one of the people listed at right.

Invest in the future by enhancing our existing endowments:

• Gene H. Golub Endowment Fund Support graduate student research.

• Mathematics Research Experience Endowment Fund Support undergraduate student research experiences.

• Please consider giving to the Math Excellence Fund where contributions can be pooled to create endowments.

Join in our future by supporting the Department of Mathematics

in its educational and scholarly missions.

Make your gift today atmath.il l inois.edu/giving/

or contact

Matthew AndoChair, Department of Mathematics

(217) 244-2846 [email protected]

Sheldon KatzDevelopment Committee Chair

Department of Mathematics(217) 265-6258 [email protected]

Evan Tammen Assistant Director of Development

College of Liberal Arts and Sciences(217) 300-5114 [email protected]

This calendar was designed by Tori Corkery for the Department of Mathematics at the University of Illinois at Urbana-Champaign © 2015. Images from iStock.

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2017

Department of MathematicsUniversity of Illinois at Urbana-Champaign

1409 W. Green Street, Urbana, IL 61801

www.math.illinois.edu Tel. (217) 333-3350 Email [email protected]

Ahlgren, Scott Albin, Pierre Allen, Patrick Ando, Matthew Balogh, Jozsef Baryshnikov, Yuliy Bergvelt, Maarten Berndt, Bruce Boca, Florin Bradlow, Steven Bronski, Jared D’Angelo, John DeVille, Lee Dey, Partha Di Francesco, Philippe van den Dries, Lou Dutta, Sankar Dunfield, Nathan

Duursma, Iwan Erdogan, Burak Feng, Runhuan Fernandes, Rui Loja Ford, Kevin Francis, George Fuchs, Elena Gorvett, Rick Haboush, William Heller, Jeremiah Hieronymi, Philipp Hinkkanen, Aimo Hirani, Anil Hur, Vera Mikyoung Ivanov, Sergei Junge, Marius Kapovich, Ilya Katz, Sheldon

Kedem, Rinat Kerman, Ely Kirkpatrick, Kay Kirr, Eduard-Wilhelm Kostochka, Alexandr Laugesen, Richard Leininger, Christopher Lerman, Eugene Li, Shu Li, Xiaochun Luu, Martin McCarthy, Randy Mineyev, Igor Muncaster, Robert Nevins, Thomas Nikolaev, Igor Palmore, Julian Pascaleff, James

Rapti, Zoi Rezk, Charles Reznick, Bruce Ruan, Zhong-Jin Schenck, Hal Solecki, Slawomir Song, Renming Sowers, Richard Stojanoska, Vesna Tolman, Susan Tumanov, Alexander Tserunyan, Anush Tyson, Jeremy Tzirakis, Nikolaos Wu, Jang-Mei Yong, Alexander Zaharescu, Alexandru Zharnitsky, Vadim

Current Faculty

Mathematics touches almost every aspect of modern life, and yet graduate students have traditionally had little opportunity to apply their skills in other fields. That is changing rapidly, as the Department encourages students to take summer internships in BIG fields (Business, Industry and Government) as well as scientific labs on campus. We hope you enjoy the pictures and stories in this year’s calendar, showcasing graduate mathematics interns from 2015! Learn more at www.math.illinois.edu/GraduateProgram/.

2016 - university of illinoisapril 2016. argen west was a student researcher at the john deere...

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