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Internship Experiences
University of Illinois at Urbana-Champaign
Department of Mathematics
Graduate Program
This summer Daniel Carmody worked with Professor Richard Sowers studying traffic in
New York. One of the central goals was to determine the tradeoff between travel time
and safety on various routes through Manhattan. This involved coming up with an
efficient method to solve a bi-objective optimization problem (time and number of
accidents), and writing python code on a computing cluster to perform the optimization.
The project culminated in a paper, "Tradeoffs between Safety and Time: A Scale-Free
Routing Approach", which is currently submitted.
During the summer Mary Angelica Gramcko-Tursi began an internship with the aim of
rigorously quantifying uncertainty in object detection. The first step to this goal was to
create and train an object detector for cars in clear satellite imagery. The point,
however, is not to craft the best detector for all possible environmental circumstances,
but to test and mathematically describe how a well-performing detector trained on clear
images will fail when noise is introduced to the data. The noise could be internal to the
satellite, or some environmental obstruction like clouds or fog. The summer internship
was the start of a year-long project in which she is still involved, but over the summer
she tested multiple approaches to detection and examined how they failed by looking at how they dealt
with before settling on one approach, which I can now use for measuring uncertainty. Since her ultimate
work is more theoretical, he also focused on the mathematics behind the algorithms used to train the
different models.
Lina Li worked as an intern at Ameren innovation center. Her first project aimed to study
demographic data of Ameren customers and determine the likelihood that a given
customer will enroll in the special energy saving programs. This project involved using
multiple approaches to perform feature selection and building predictive model with
random forest classifier. Her second project focused on analyzing accelerometer data of
power poles and proposing an innovative statistical approach to quantify pole health
from existing pole sensor accelerometer data.
William Linz worked as an intern at Sandia National Laboratories. He worked on two
projects related to optimization in optimal power flow problems. His research
investigated linear and convex relaxations of the optimal power flow model. The first
project concerned the scheduling of a power grid; the second project studied
interdiction of a power grid. As part of these projects, he worked on optimal power flow
models using the Pyomo modeling environment. William was also affiliated with the
MARTIANS group at Sandia, where he was able to network with other math and statistics
interns at Sandia, and through which he improved his knowledge of machine learning theory.
Michael Livesay’s internship in summer 2018 was with Sandia National Laboratories. He
worked on two projects one relating to social modeling and the other relating to security
systems and their reliability. For the social modeling project, he applied methods of
measuring the complexity of different aspects of the models, and worked to justify or
improve these measurements. For the reliability of security systems, we confined
ourselves to the problem of the steady state case. Part of what he did was write a
program which calculated conditional events determined by the structure of any
directed graph.
Sarah Mousley Mackay interned at the Naval Research Laboratory in the Center for High
Assurance Computer Systems branch. The goal of the project was to design network
protocols that allow two parties communicate covertly without being detected by a
warden watching their communication channel. She quantified the asymptotic behavior
of a particular detector in network covert channels given the asymptotic behavior of
embedding method. She also studied the maximum size of message that can be sent
while ensuring unlikely detection. She also implemented various embedders and detectors in the
software.
Dileep Menon worked as an Analytics Intern at John Deere World Headquarters in
Moline, IL. He worked on a number of data science projects throughout his internship. In
one project he used clustering algorithms to discover patterns in tractor machine data
which he communicated with engineering and marketing teams. In another, the goal
was to build a live Tableau dashboard that monitors data quality at the enterprise level.
He also had the chance to participate in a company-wide data science competition in
which he placed second. For the competition, he developed a model using XGBoost that predicts the
rejection probability of a warranty claim for tractors and combines.
During this summer, Lan Wang worked as a researcher in the Data Science group at
Open Data Group in Chicago. Her job was to research and develop a recommender
system using machine learning models, intended to provide accurate and value-enabling
recommendations on Mortgage-Backed Securitization (MBS) that their clients may be
interested in. First, she designed, implemented and fine-tuned a Restricted Boltzmann
Machine (RBM) with TensorFlow to realize a proposed collaborative filtering concept,
only to discover that the prediction accuracy of clients’ ratings on the products is
suboptimal. Subsequently, she applied ensemble techniques on a collection of the
Autoencoder model, content-based model and linear regression model, which resulted in a more
sophisticated hybrid recommender system, leveraging three data sources in the computation: clients’
ratings on the products, products’ features and clients’ characteristics. The eventual model accuracy is
higher than 80%. In between Wang’s own project agenda, she has also learned many other interesting
projects from my colleagues such as natural language processing and time series modeling. “All in all, the
experience of this internship was eye-opening and fruitful,” says Wang.
During the summer, Stacey Butler worked with health data at the Champaign-Urbana Public Health District. Specifically, she looked for patterns in sanitary (restaurant) inspections for Champaign area food establishments. Several years of data were analyzed using Pandas in Python, checking for inspector bias regarding different cuisine types using OLS regression and variation among inspectors' average scores, and examining the effects of policy changes on inspection scores.
This summer Sneha Chaubey worked as an intern in the Scientific Content group at Wolfram Research, in Champaign. She continued her work from last year building on the Wolfram function site in Wolfram Alpha, collecting formulas, properties, theorems, etc for both elementary and complex mathematical functions and presenting the information in Mathematica notebooks. Functions include the Riemann zeta function, Dirichlet L-function, gamma function, exponential, logarithmic, sine and cosine integrals, and Jacobi and Elliptic integrals. Another project involved writing programs to construct general differential equations whose solutions in special cases are the Heun functions or Legendre functions.
Yongwoon Escobar worked as an intern at Sandia National Laboratories in the Center for Cybersecurity Defenders program. His first project involved studying cryptographic protocols, gaining experience on implementing a post-quantum public-key protocol on hardware, and establishing a pipeline of tools to process documents of interest relevant to cryptography. His second project implemented additional features and solutions for a graph partitioning algorithm and library in C/C++ for large graphs, on the scale of billions of vertices and trillions of edges, for systems running in parallel. Near the conclusion of his internship, he met and interviewed with various Sandia teams and organizations for potential future employment.
Benjamin Fulan - AbbVie (Research Park)
The internship this summer on the tinnitus project in the Speech and Hearing Science Department (supported by the PI4 grant) continued Mary Angelica Gramcko-Tursi’s work from last year. The overall aim of the project is to find biomarkers for Tinnitus that can be used for diagnosis. The project involves lead matrices, which are used to recover the cyclic order of activity levels in specified regions of interest in the brain, based on fMRI data. Mary Angelica examined differences in lead matrices over each session as well as across different sessions, by projecting them onto subspaces of high variation to determine whether there was any discernible difference between the two subject groups (with and without tinnitus). Her work showed that the data being extracted from lead matrices is in fact meaningful, rather than being a result of noise. These methods may also be useful in other diagnostic settings too.
During this summer, Tigran Hakobyan was a PhD software engineering intern at Facebook. He worked on designing a Traveling Salesman heuristic algorithm for nonlinear path weight and finite traversal duration constraints with arbitrary spatial graph partitioning. His work provided distributional statistics on the number, costs, and values of salesman routes under different constraints.
David Hannasch – Department of Defense
Derek Jung worked at the North Las Vegas facility of National Security Technologies, in an internship arranged through the NSF Mathematical Sciences Graduate Internship program. He worked on deblurring images, by investigating a mathematical model of the blurred image of an opaque edge. That problem serves as a model for understanding how all images are blurred. At a technical level, his work showed a certain integral operator equation is ill-posed while a Tikhonov regularized problem is well-posed, by using techniques from measure theory, functional analysis and harmonic analysis.
William Karr worked at the Caterpillar Data Innovation Lab in the Research Park during the summer of 2017. The Data Innovation Lab hosts a diverse set of projects related to data and technology, proposed by dealers and clients of Caterpillar. Bill worked on developing a mobile web application called vSite for use by workers and supervisors in mining sites. The application would be used to mark problem areas and keep track of work that had been done around the site.
Vaibhav Karve worked with Professor Richard Sowers in the Department of Industrial and Enterprise Systems Engineering this summer. He continued his research into taxi traffic patterns in New York City by helping to develop a new algorithm for Non-negative Matrix Factors, a technique that is gaining traction for finding low-rank structures in large datasets and for predictive estimation of missing data values. Vaibhav is exploring also the underlying topological and geometrical structure of the New York City road network. The insights from this work could find use in the planning and maintenance of large cities.
Cara Monical - Sandia National Labs
Sarah Mousley was an intern at Sandia National Laboratories, funded through the NSF Mathematical Sciences Graduate Internship (MSGI) program. She worked in the Center for Computing Research (CCR), optimizing an energy function used by the meshing community, with the goal of measuring and improving mesh quality. The energy of a mesh measures its fitness for usage in Discrete Exterior Calculus, DEC, a method for numerically solving Partial Differential Equations (PDEs). More specifically, the energy bounds the discretization error of the Hodge-star operator that can be used for numerical formulations of many PDEs. She explored the landscape of the energy function to better understand how to optimize it, using software she developed.
During Joseph Rennie’s summer internship at the Champaign-Urbana Public Health District with funding from the NSF PI4 grant, he examined birth records for Champaign County from 2014. Given hundreds of variables, he searched the literature to create summary variables for whether or not a birth should be considered unusual. Then, grouping by zipcode, he searched for deviations from uniformity in the spatial distribution of unusual births. He found a potentially significant trend, but needs more data before reaching a conclusion with a meaningful degree of certainty.
This summer Vanessa Rivera-Quiñones interned at the lab of Professor Carla Cáceres from the Department of Animal Biology. Her work focused on studying the changes in the phototactic behavior (i.e. movement towards or away from light) of the zooplankter Daphnia Dentifera as a response to infection pressures. As part of her internship, she received lab training and collaborated on the experimental design process, a new experience for her. Vanessa will continue gathering data through the fall semester with the ultimate goal of building a mathematical model that describes this phenomenon.
Nishant Rodrigues worked with the Formal Systems Laboratory in the Computer Science Department to help write an executable semantics for the Ethereum Virtual Machine in the K Framework. The group submitted a paper for review. The K framework has it's foundations in Rewriting and Matching Logic. It allows creating mathematically well-defined and executable specifications for programming languages. With these semantics, K can use Reachability Logic for program verification, that is, to automatically generate proofs of correctness for properties of programs written in these languages. Rewriting Logic, Matching Logic and Reachability have solid mathematical foundations. Many members of the Formal Methods sub-department are interested in working more closely with the Mathematics Department.
Hao Sun’s project at the Ameren Innovation Center in the Research Park aimed to describe the relationship between the temperature and Ameren customers’ usage, and hence to predict future usage based on historical temperature data. Hao combined smart-meter customer data and NOAA’s temperature data in several different mathematical models to predict daily customer usage. Model errors were analyzed using linear regression, multiple linear regression, and modified multiple linear regression. Based on the multiple linear regression model, he used machine learning techniques to construct the modified multiple linear regression model, which was found to give the best predictions.
This summer Albert Tamazyan worked as a software engineering intern with the Communication Products team at Yahoo. His projects in the Android Mail group were about developing machine learning algorithms for categorizing emails in mailboxes and for generating message filters for user accounts. He learned relevant tools and technologies, and gained valuable programming experience.
During the summer of 2017, Corbin Tucker worked as an intern on the Predictive Analytics team at Blue Cross Blue Shield of Tennessee in Chattanooga. His responsibilities included researching possible analysis methods from peer-reviewed articles, assisting in identifying predictive variables, and cleaning text data for a machine learning algorithm. He also had a project of his own predicting patients who are most likely to suffer from a first time heart attack or stroke. As part of the internship, Corbin was introduced to new programming languages, analytics tools, and statistical methods which helped him to build his data analysis skills.
Venkata Sravani Vadali worked at the Ameren Innovation Center (Research Park) for the summer on two separate projects. In one project, her team had to model a new billing scheme for Ameren that analyzes a demand-based charge as opposed to traditional billing. They analyzed terabytes of customers’ data and came up with mathematical equations that related the energy charge to the demand charge to keep Ameren’s revenue unchanged. In her second project, Sravani and the team determined the environmental factors that would affect the movement of utility poles. Various modeling and machine learning techniques were implemented in the project. She will continue working on these projects in the Fall. Her analyses was done in R, Python and SQL / Hive.
During the summer, Lan Wang worked as a researcher in the Data Science group at John Deere, in the Research Park. Her task was to improve the accuracy of position data and smooth out the driving paths using Kalman Filter techniques, and then to analyze the paths using machine learning techniques, visualize the mower stripes, and finally deploy all Python scripts on AWS (Amazon Web Services) Lambda platform. During this work, she had the opportunity to combine her Math knowledge with real industrial problems. When applying the Kalman Filter, she built both linear and non-linear models to make the filter work better. When doing visualization, she took advantage of geometric insights to find efficient and effective methods to clean and parallelize mower paths. Meanwhile, she improved her programming capabilities and learned how to do operations in the cloud, taking advantage of Amazon Web Services, Amazon Turk, and the Google Compute Engine. She really enjoyed working at John Deere!
Xiao Wang’s internship at the Bud Analytics Lab in the Research Park centered on customer data sets from the eCommerce department in China (especially through Tmall.com and Wechat stores). Her job included: analyzing customers’ behavior, especially different promotions and how they affect member conversion rate; training random forests to classify golden/platinum members; clustering customers from their behavior using Kmodes, ROCK (RObust Clustering using linKs) and Correlation Explanation algorithms; applying time series analysis to forecast eCommerce transaction volume. She enjoyed learning how to connect technical results to business insights.
Yingjie Bai - AXIS Capital (Research Park)
During summer 2016, Stacey Butler was supported by the PI4 program to work in the O’Dwyer lab in the Plant Biology Department, on questions from theoretical ecology involving systems of interacting species. The evolutionary dynamics of a network of species containing mutualistic and competitive interactions was modeled using a Lotka-Volterra equation. The first question was an investigation into a pattern noticed in the outcome of an optimization algorithm performed on networks of interacting species. The species interactions were altered to optimize species abundances. It was observed that the number of real eigenvalues of the linearized system at the end of the optimization was significantly increased over the initial situation. An explanation for this pattern and its ecological consequences could be useful for understanding ecological systems in nature. The second question involved searching for patterns in the resistance of a network of interacting species to perturbations in species-intrinsic growth rates. This perturbation can be thought of as representing environmental fluctuations. The structure of the network and the interaction types can impact this resistance to perturbation. These questions were explored with simulations written in Python.
This summer Sneha Chaubey worked as an intern in the Scientific Content group at Wolfram Research, in Champaign. Her main job was to build on the Wolfram function site in Wolfram Alpha. She collected formulas, properties and theorems for both elementary and complex mathematical functions, including the Riemann zeta function, Dirichlet L-function, gamma function, exponential, logarithmic, sine and cosine integrals, and Jacobi and Elliptic integrals. The other project she worked on involved writing programs to construct general differential equations whose solutions in special cases are the Heun functions, Legendre functions and other associated functions.
Jed Chou worked at Ab InBev in the summer of 2016. He developed and integrated an application on Teradata to generate weekly growth forecasts of all Ab InBev craft beer brands. For a second project, he applied machine learning to optimize online auctions hosted by ABI and was able to provide specific recommendations on which auction type to run and which suppliers to invite for different auctions. Jed learned about time series forecasting, auction theory, and machine learning. He also enjoyed many tasty beers.
Erin Compaan worked at CERT, a division of the Software Engineering Institute (SEI) at Carnegie Mellon University. SEI is a federally funded research corporation focused on Internet security. An SEI employee contacted the department in search of mathematics interns, and corresponding with her led to the internship offer. The project was open-ended, and interns were encouraged to find problems to pursue which accorded with their skills and interests. Erin's work centered on analyzing Internet connectivity data, with the object of understanding the growth and vulnerabilities in the network. Day-to-day, this involved a lot of data parsing, programming, and visualization. However, she was also encouraged to spend time learning relevant theory to inform her investigations, such as the mechanics of Internet traffic, statistical concepts, and random network theory.
Lin Cong worked with Wolfram Alpha this summer, for his second summer and the fourth semester internship there. After more then one year's work, he helped finish the Function Space project. His duty there was to summarize properties of function spaces, so that users can access them on the wolframalpha.com website and manipulate the connections between different spaces. He was also participated in the Semantic Math project, which is an on-going and ambitious new development. The first goal is for computers to “understand” pure mathematics theorems, and eventually, to let the computer search for and even give proofs for particular theorems. The group has so far done excellent work towards the first goal by implementing mathematical definitions and structures.
Eliana Duarte - Wolfram Research During the summer internship, Eliana tested algorithms to compute greatest common divisors (GCDs) of multivariate polynomials over finite fields and over algebraic extensions. The main algorithm she tested uses a Gröbner basis to compute GCDs using syzygies, and together with her supervisor, she wrote the paper “Polynomial GCDs by syzygies” which has been accepted for publication at the conference SYNASC 2016. A second project involved writing a function to factorize multivariate polynomials over finite fields. The main ingredient of this algorithm is to reduce to the univariate case and do Hensel lifting to recover multivariate factors.
For his 2016 summer PI4 internship, Matthew Ellis worked with Professors Andrew Ferguson (Materials Science) and Lee DeVille (Mathematics). The project developed from Ferguson’s research into the reconstruction of single molecule free energy surfaces (FES) from experimentally measurable time series. The FES can be conceived of as a low-dimensional manifold in a high-dimensional space of atomic coordinates. However, these coordinates are experimentally unavailable, meaning the FES cannot be recovered precisely. If a coarse-grained time series is accessible (e.g., the molecular size as a function of time), then with Takens’ Theorem from differential geometry coupled with nonlinear manifold learning techniques, a delay map can be used to recover the FES manifold up to diffeomorphism. Matthew worked with these delay maps, deriving bounds for the Jacobian of the diffeomorphism and modeling simple systems with MATLAB to verify the bounds. The implications of this work provide a means to place rigorous bounds on the quality of the reconstructed FES. This project introduced him to new concepts in differential geometry and dynamical systems, and he plans to continue working with Ferguson’s group into the Fall semester.
Ian Ford - Wolfram Research
Benjamin Fulan worked on data analytics projects at the Ameren Innovation Center at the Research Park, during an internship supported by the PI4 grant. He collaborated with other interns on customer usage clustering and detecting anomalies using Ameren’s new cloud-based data. Based on usage patterns, they identified six main clusters containing more than 90% of customers. To detect anomalies, he trained a machine learning model to predict customers’ energy usage patterns for the first three months of 2016, using Ameren data collected by smart meters over the year of 2015. Both projects required a strong knowledge of linear algebra, statistics and programming in Python.
As part of the PI4 program, Vaibhav Karve studied the traffic patterns in New York city taxi data. Under the guidance of Professor Richard Sowers in the Department of Industrial and Systems Engineering, he analyzed the post-processing traffic data of nearly ten thousand taxis running on the 260,000 links in the New York city road grid. This data spanned every hour of the day, every day of the year, for four years. Vaibhav used algorithms of Non-negative Matrix Factorization (NMF) to produce good low-rank approximations to the taxi data, and then isolated patterns in the traffic with the aim of improving our understanding of traffic flow and traffic dynamics. To achieve these goals, he used an algorithm known as Sparse-NMF (a combination of NMF and k- means clustering). Sparse-NMF allowed him to compress data while simultaneously clustering road links based on their traffic patterns. This clustering could be used in the future to understand individual components that contribute in the overall traffic dynamics. For this project, Vaibhav wrote code in Python and ran it on the Illinois Campus Computing Cluster. He will continue the visualization aspects of this project with a larger team as part of the Illinois Geometry Lab in Fall 2016.
Nicholas Kosar spent the summer of 2016 as an intern at Personify, on an internship set up through the PI4 program. Nick worked on two projects: exploring the feasibility of augmented reality with a standard smart phone and using a webcam with a depth sensor to create virtual meetings. Through this internship, Nick gained exposure to current research that is being done in augmented and virtual reality; he also gained experience working in computer vision.
Instagram is a rapidly growing platform with over 400 million users sharing and consuming content everyday. The Instagram Data Products team in the Bay Area, where Shiya Liu worked for the summer, helps users to find content of interest by building search, content discovery and recommendation products on Instagram. The team is focused on using state of the art Machine Learning techniques to understand users' interests and increase the relevance of content shown on Instagram. In particular, Shiya worked in the Media Ranking team. Interesting challenges for the coming year include mapping users' interests to content consumed on Instagram, discovering and identifying events happening on Instagram, and connecting users to the most relevant accounts.
As an intern in the Content Development Division at Wolfram|Alpha Scientific Content, Amita Malik's job was to build data related to number theory and complex analysis, by investigating results equivalent to the Riemann Hypothesis (RH). Since, RH arises in many seemingly different fields of Mathematics, it would be useful to find all this data together, and would save a great deal of time and help mathematicians with their research. The second part of Amita's project was to curate theorems in complex analysis, as a first step towards automatic theorem proving in this area using Mathematica.
During the summer of 2016, Andrew McConvey worked as a summer intern in the Securities division at Goldman Sachs in New York. Andrew rotated between two different "Strats" teams, working first with the Foreign Exchange Electronic Trading desk before moving to the Structured Credit Trading team. His responsibilities included analyzing methods of streaming data to clients, specifically how to balance the need for real time data with the cost of sending new information. He also developed a tool to help evaluate and easily display the cost and risk of a trade. As part of the internship, Andrew was introduced to new programming languages and packages, which helped him to improve his coding and data analysis skills.
Anna Mitchell worked this summer at RLI Insurance Company, a specialty product insurance company headquartered in Peoria. She worked with the reserving team in the risk services department, whose main responsibilities include determining the amount of money to set aside, or “reserve”, for future claims and liabilities. Anna primarily provided assistance with quarterly reserve reviews, and reconciled data for reserve studies, but also had a project of her own analyzing the effectiveness of five methods used by the reserving team to predict future loss development. She had the opportunity to present this information to all the top executives of the firm. This internship experience enhanced Anna’s professional skills and introduced her to several successful practitioners in actuarial science.
During the summer of 2016, Sarka Petrickova worked on data analysis and model fitting in the biological sciences, in an internship arranged through the PI4 program. Under the guidance of David LeBauer (Energy Biosciences Institute) and Yuliy Baryshnikov (Mathematics), she worked together with another intern, Benjamin Wright, on two projects. In the first project they studied light interception in canopies. The second project concerned root systems of canopies like sorghum or maize. Here, the main goal was to compare the precision of various measuring tools that are, or could be, used in the field to estimate important parameters of the root system. Sarka reports that this internship was a great opportunity to learn about crop sciences, improve her programming skills, and get a feel for what it is like to work in an applied setting.
Michael Raftery - Centers for Medicare and Medicaid Services
Sepideh Rezvani worked on data analytics projects at the Ameren Innovation Center at the Research Park. She collaborated with other interns on customer usage clustering, detecting anomalies, and sentiment analysis projects using Ameren’s new cloud-based data. Based on usage patterns, they identified six main clusters containing more than 90% of customers. To detect anomalies, she trained a machine learning model to predict customers’ energy usage patterns for the first three months of 2016, using Ameren data collected by smart meters over the year of 2015. This project helps detect fraud, and the goal for the Fall is to improve the model using neural networks. In the sentiment analysis project, Sepideh analyzed Twitter data in order to alert Ameren if the general sentiment is “very negative” in a specific location, for instance due to an outage. She reports that the internship provided a great opportunity to learn cloud-based tools for cleaning, manipulating, analyzing and visualizing data, and also presentation skills using Tableau dashboards. All the projects required a strong knowledge of linear algebra, statistics and programming in Python.
Bingji Yi - Goldman Sachs (New York; quantitative analyst in their controllers team) During the summer at Goldman Sachs, Bingji worked on price verification in the controllers modeling team. Price verification is an independent modeling process that uses external market data to verify the internal pricing models. The specific project involved price verification of certain exotic interest rate products. Bingji began by learning the Libor Market Model, which is a continuous-time diffusion model, and then developed an approximation method based on linear regression. He ran tests on the method and implemented it into the internal programming environment at Goldman Sachs.
At the Research Park this summer, Shibo Zhu worked at AXIS Reinsurance on selecting and capturing data for professional liability from historical files. Then he used the captured data for pricing analysis.
During her summer 2016 PI4 Internship, Dara Zirlin worked in the Pathobiology Department of the College of Veterinary Medicine with Professor Rebecca Smith. She modeled the spread of bovine tuberculosis in a population of deer in Michigan, with the aim being to study how decreases in hunting will impact its prevalence in the deer population. During this experience she acquired useful programming skills and learned to assess and interpret scientific literature to solve problems.
Nerses Aramyan: During his internship at Wolfram Research in Summer 2015, Nerses Aramyan 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 Wolfram Alpha 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. He reports that “one of the most satisfying theoretical topics I learned in the course of this work was the connection between Lie group theory, representation theory, harmonic analysis, and the theory of special functions.”
Hannah Burson worked with Professor Rebecca Smith in the Pathobiology Department of the College of Veterinary Medicine in the summer of 2015, an internship arranged through the PI program. She worked on models of the spread of Orf, a poxvirus common in sheep, which persists even in closed populations. As little is known about the transmission dynamics of Orf, Hannah used the Python programming language to implement several different possible models. Collaborators have designed a study to collect data that will be compared with the output of the code, in order to better estimate the dynamics Orf transmission.
For the Summer 2015 PI4 internship, Stacey Butler worked on a project in James O'Dwyer’s lab in the Plant Biology Department. The project 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. In particular, the project examined the spectrum of the interaction matrix and of the Jacobian of the system, and the eigenvector associated with the leading eigenvalue, and the models were analyzed via simulations written in Python.
In the summer of 2015, Jed Chou worked in Professor Tandy Warnow’s lab where he and his teammates empirically evaluated a new method, SVDquartets, for inferring evolutionary phylogenies from DNA sequences generated under the Multispecies Coalescent (a statistical model in which gene trees can be topologically different from the overall species tree). A contentious topic in this area is whether so-called "summary methods", which infer tree topologies on individual genes and then combine these gene trees into an overall species trees, should be used to infer species trees. SVDquartets was designed to bypass this issue of gene tree estimation error, but had not yet been compared to other coalescent-based species tree estimation methods. Jed and his team compared it with several other leading methods for phylogenetic inference on simulated datasets with very short gene alignments. One interesting outcome was that leading summary methods can in fact be highly accurate relative to the other methods on some datasets with short sequences. Through this internship, Jed learned about using simulations to understand algorithms, improved his Python and UNIX scripting skills, and he also helped write a paper that will be published in BMC Genomics.
Erin Compaan spent the summer interning at a communications consulting firm in San Diego. She had met the director of the company at a lecture the previous year, and arranged the internship herself. The projects involved using machine learning algorithms to sift through large volumes of data and identify salient characteristics. While programming was a big part of the day-to-day job - mostly in C and Python - the best part of the summer was the opportunity to collaborate with senior research scientists and other interns to make progress on a relevant and challenging problem.
The Ameren Illinois Innovation Center hosted Sushma Kini during Summer 2015, for an internship arranged through the PI4 program in the Department of Mathematics. During her internship period in the customer analytics project, 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 them. The work culture at Innovation Center 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.
Nicholas Kosar spent the summer of 2015 as an intern at the Ameren iCenter in the University of Illinois Research Park, on an internship set up through the PI4 program. 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.
During the Summer of 2015, 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. Throughout the summer, 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. Andrew met representatives from Akuna Capital at the Mathematics Corporate Day last October, and was offered the internship in January.
During her internship at Dow AgroSciences in Summer 2015, which was arranged by the PI program, Tara Negron Santiago worked on the problem of weed resistance resulting from repeated use of a herbicide. Weeds evolve and build up resistance to specific herbicides such as glyphosate (Roundup) through repeated use. Academic herbicide resistance modeling tools have been developed to integrate knowledge about weed biology (species specific), genetics, weed management (herbicide dose response, herbicide rotation), and a variety of other interacting factors such as seed bank density, cropping system, and the initial resistant allele frequency in large weed populations. 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 from an existing but rather complicated weed resistance research tool. Additional functionality included the ability to explore various Best Management Practices to try to avoid future issues analogous to what is observed today with glyphosate resistant weeds.
This summer Wei Qin worked as a Back End Developer intern at Agrible. This data science company at the UI Research Park provides business-critical information to select the agricultural communities. The goal for the internship was to learn the agricultural models and implement them in Python. These models typically involve second order partial differential equations which cannot be solved explicitly, and so numerical methods are essential. Thanks to her prior coursework and research in the Mathematics department, Wei was able to construct 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!”
As part of the PI4 program, Vanessa Rivera-Quiñones interned at the lab of Professor Carla Cáceres in the Department of Animal Biology. Her work focused on the zooplankter Daphnia dentifera, commonly known as the “water flea”, which experiences epidemics of the fungus Metschnikowia bicuspidata. To integrate the three roles of Daphnia as consumers, competitors and hosts, Vanessa studied an ordinary differential equations system and analyzed its dynamics. Specifically, she focused on the case were two strains are present, the wild host and the invader. She used techniques from the theory of adaptive dynamics to describe the long term evolution of the population and determined conditions that allow polymorphisms to occur in the system.
Emily Schlafly spent the summer of 2015 working on tinnitus detection and diagnosis with a team in the Speech and Hearing group on campus. 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 fellow Mathematics student Benjamin Wright 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. Emily enjoyed working with Professor Fatima Husain, and reports that she was enthusiastic about working with the students from Mathematics, clear about what she was looking for, and fantastic at giving feedback.
Sean Shahkarami worked at Argonne National Lab this summer on developing an implementation of the WASH123d watershed model on top of the PETSc framework. The goal of the project was to develop flexible and scalable tools to help other users define interconnected systems of rivers and ponds, as well as groundwater and atmospheric sources, and then simulate their description as a system of interconnected differential-algebraic equations. Most of his time was split between writing tools in Python, doing numerical work in C on top of PETSc, experimenting with numerical methods for hyperbolic partial differential equations and doing some fluid mechanics. Overall, he enjoyed working on a variety of mathematical and physical problems and being put in charge of a project. He even had a chance to contribute a simple network monitoring tool to the PETSc library, which was then used during some of the testing.
The Wolfram Language (Mathematica) includes "Entities”, which carry general types of information. Albert Tamazyan worked at Wolfram Research during the summer of 2015, adding Entities for new families of mathematical functions. The relevant properties include "integral representations”, "functional equations", "asymptotic expansions" and many others. During his internship he collected formulas and theorems from the literature, studying the underlying functions and deriving new formulas. Some of these functions are related to his PhD topic, and so the summer work contributed also to his research. Along with a wonderful work experience in the "Scientific Content" department at Wolfram, Albert enjoyed many valuable conversations with experts on mathematics and Mathematica.
During his internship at the Energy Biosciences Institute (which is funded by BP and housed in the Institute for Genomic Biology), Goran Tomic worked with fellow PI4 intern Elizabeth Fields and investigated various data assimilation packages, under the supervision of Dr. David LeBauer. Data assimilation is one step of a larger process that includes model calibration, validation, and application. The interns worked on the Predictive Ecosystem Analyzer (PEcAn) project, which has two components: a scientific workflow and a Bayesian data assimilation system. They contributed to the second component by implementing a particle filter algorithm to be used in the data assimilation step. The algorithm was implemented based on an academic article using particle filters for parameter estimation in weather forecasting. The algorithm was tested on a real dataset in which biomass observations were used to improve parameter estimates.
