NEWSLETTERSolving complex problems with sophisticated mathematical methods

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DEPARTMENT OF APPLIED MATHEMATICS

What Is Algebraic Statistics?By Assistant Professor Sonja Petrović

Basic data-driven scientific discovery rests on our ability to answer the first question one might ask a statisti-cian: What model best fits the observed data? At the

center of this question is a fundamental statistical problem of hypothesis testing. A test consists of proposing a model, calculating some test statistic, and using its theoretical prop-erties to determine whether to reject the model hypothesis or not. Traditional tests assume what are usually referred to as mild conditions: large sample size, model smoothness or regularity. On the other hand, the development of data-ac-quisition technologies has produced many types of data sets, such as social networks or food webs, which may be available only as very sparse, possibly large, single-sample data. In turn, this has motivated the development of new statistical models that can capture the rich structure of such data but

are necessarily more complex and, in fact, non-regular. The regularity and large-sample assumptions are violated.

Data-driven science is then faced with two obvious obstacles. First, if only a single observation (or a small sample) of, say, a network is observed, the well-known hypothesis tests relying on asymptotic methods do not apply. How does a social scientist test how cities grow and evolve as networks if network model-testing tools are not available for her type of data and hypotheses? Second, if genetic mutation models used in biology are extensive and rich enough, there is no theory that justifies their use by estimating parameters by hill-climbing algorithms since it can be shown that parameters are not identifiable in such models, thus leading to incorrect results. How does a researcher in phylogenetics know if she has correctly determined the genetic relationship between species from their

DNA sequences if there is no theory to show that the compu-tational method is reliable? 

My research in algebraic statistics addresses two fun-damental problems: how to extend the hypothesis testing methodology to sparse categorical data and how to bypass parameter estimation issues such as non-identifiability or multimodal likelihood functions. Both translate to alge-braic, geometric, and combinatorial complexity properties of statistical models. My main, broad research objective is the integration of the fields of statistics, algebraic geometry, and combinatorics with focus on providing formalism to an interdisciplinary approach to data analysis and modeling. 

I am currently working on random graphs and network modeling with the goal of understanding what social-net-work-type data are telling us about the world around us. 

For more information, you can read a recent article arxiv.org/pdf/1401.4896v1.pdf or the entry on Algebraic Statis-tics in the International Encyclopedia of Statistical Science, found here: link.springer.com/referenceworkentry/10.1007%2F978-3-642-04898-2_112.

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Dear Friends,

We are excited to have been able to grow the number of faculty in our department in recent years. We now have 15 tenured and tenure-track faculty plus four senior lecturers. Our increased faculty strength has allowed us to better serve the many more students who have joined our department in the past few years.

In addition to our vibrant Ph.D., M.S., and B.S. in applied mathematics and our Master of Mathematical Finance (MMF) program, we launched two new professional master’s programs last year. You will find out more about them in this newsletter. Not only do we appreciate the opportunity to prepare students for careers that crucially depend on modern mathematical methods, but we also find that some excellent Ph.D. students come from our various master’s programs. All told, we now have nearly 70 applied mathematics undergraduate students and more than 100 students enrolled in our graduate programs.

One source that potential students and faculty consult when choosing a program is the U.S. News & World Report rankings. This is the first time in many years that our department was eligible to be ranked because we have recently begun to graduate Ph.D.s at a significant rate. In the recently released 2014 rankings we were ranked 126. While we see ourselves higher than this, it is a big step up from where we were before.

As we endeavor as a department to raise our scholarship and teaching to higher levels, we hope that you can partner with us. If you need to know more about our department, visit or email me. Introduce prospective students to IIT. If they are interested in mathematics, put them in touch with me. Introduce us to companies that might hire applied mathematicians.

Many things that we want to do rely on donations. One of these is the continued success of our F. R. “Buck” McMorris summer stipend to support undergraduate and first-year graduate students doing research. If you can, please give a gift to the department. If you have other ideas for partnering with us, please contact me.

Best regards, Fred J. Hickernell, Professor and Chair Department of Applied Mathematics

Letter from the Chair

The applied mathematics department had a substantial presence at the annual SIAM conference in July in Chicago, organizing several minisymposia highlighting the depart-ment’s recent research.

This research included advances in krylov and extended krylov subspace methods, numerical methods in PDE I, and reliable computational science. Faculty partic-ipants included Fred Hickernell, chair and professor; Greg Fasshauer, assistant chair and professor; Jinqiao Duan and Xiaofan Li, professors; and Shuwang Li, associate profes-sor. Alumni participants included Xingye Kan (Ph.D. ’12), a postdoctoral fellow at the Institute for Mathematics and Its Applications in Minneapolis, and Michael McCourt (AMAT ’07), a visiting assistant professor at Colorado University-Denver.

The conference included presentations of collaborative work done with other scholars and applied math faculty, as well as students.

One of those presentations was the lecture “Growth, Patterning, and Control in Non-Equilibrium System,”

which won the Julian Cole Lectureship Award. The lecture was based on the longtime collaborative work of Professor John Lowengrub at the University of California, Irvine, with Associate Professor Shuwang Li and experimentalists at the Liquid Crystal Institute, together with some recent joint work with Professor Xiaofan Li and alumnus Amlan Barua (AMAT Ph.D. ’12). The Cole Award is presented by SIAM every four years for an outstanding contribution to the solution of challenging problems in science or engineering, or to the development of mathematical methods to solve the problems.

Following the conference, the Department of Applied Mathematics hosted a dinner for SIAM speakers, friends, and students at the Pritzker Club in The McCormick Tribune Campus Center.

For more information on the Department of Applied Mathe-matics presentations, see bit.ly/1o1kq5T.For more information on the SIAM Conference, visit the SIAM website: www.siam.org/meetings/an14.

IIT at the Annual Society for Industrial and Applied Mathematics (SIAM) Conference

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Name: Sonja Petrović joined as an assistant professor.

Education: Ph.D. University of Kentucky

Research Interests: Algebraic statistics, applied and computational algebraic geometry, commutative algebra, and applied discrete mathematics

NEW FACULTY

FACULTY NEWS

Name: Routing Gong joined as an assistant professor.

Education: Ph.D. Georgia Institute of Technology

Research Interests: Mathematical finance, probability, and stochastic finance

Sonja Petrović Routing Gong

Tomasz Bielecki, profes-sor and program director of the Master of Mathematical Finance (MMF) pro-gram, coauthored the book “Counterparty Risk and Funding: A Tale of Two Puzzles” with Stéphane Crépey and Damiano Brigo. Counterparty risk was a key problem in the 2008 global credit crisis and ongoing European sov-ereign debt challenges. The book shows the importance of the proper assessment and management of counterparty risk and explores this particularly challenging issue in portfolio credit modeling.

Jeffrey (Jinqiao) Duan, professor and director for the Laboratory for Stochastics and Dynamics, returned to IIT in fall 2013 after spending two years as associate director of the Institute for Pure and Applied Mathematics. At IPAM, Duan managed part of the ongoing academic programs, identified emerging research areas, and suggested program initiatives to take advan-tage of opportunities that are created by new breakthroughs or new developments in mathe-matics, engineering, and science. He also helped with IPAM’s corpo-rate-partnership program by making connections with Google, Facebook, Microsoft, IBM, Aerospace Corp., and other high-tech companies where mathe-matics and computation play significant roles.

Duan has authored a new book, An Introduction to

Stochastic Dynamics. The book is an introductory text on stochastic dynamics for quantitative finance and laboratory professionals; academic researchers; and graduate science, engineer-ing, and math students. The book, published by Cambridge University Press, is scheduled for publication in April 2015.

Robert Ellis, associate professor, returned from his yearlong sabbatical with the Bioinformatics Group at the University of California in San Diego hosted by Glenn Tesler, associate professor of the Department of Mathematics, UCSD. Ellis also participated in research groups led by Vineet Bafna, professor, Department of Computer Science and Engineering, USCD, and Pavel Pevzner, Ronald R. Taylor Professor of Computer Science and director, NIH Center for Computational Mass Spectrometry, USCD.

While there, he learned about DNA sequencing, microarray experiments, protein form and function, bioinformatic algorithms, metagenomics, and systems biology. Ellis also worked on several projects. One of his projects was on combinato-rial design on the topic of group testing (or pooling) to improve the cost efficiency of microarray experiments for detecting members of a large population having an uncommon biological trait. This project was jointly con-tinued at IIT with Gergely (Greg) Balint (Ph.D. ’14), and has promise for reduc-ing the cost of, for example, blood screening of new-borns for adverse genetic conditions. Ellis looks forward to sharing new ideas from his sabbatical in the classroom and through his research program.

Greg Fasshauer, profes-sor, associate chair, and director of undergraduate studies, took a sabbatical

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The MAS DS program was created by Lulu Kang, assistant professor in the Department of Applied Mathematics and associate director of the MAS DS, and Shlomo Argamon, pro-fessor of computer science and program director of the MAS DS, also with the help of Friedman.

The MAS DS was created to meet the growing demand for data scientists in a variety of fields. Kang says, “The Master of Data Science is designed for

in spring 2014 in order to work on a new book about meshfree methods.

Hemanshu Kaul, associate professor of applied mathematics, took a sabbatical fall 2013. Kaul traveled to Asia and collaborated on research.

Igor Cialenco was promoted from assistant professor to associate professor with tenure (2013). He is taking a sabbatical in spring 2015.

In fall 2013, the Department of Applied Mathematics accepted students into two new professional master’s programs: the Master of Applied Mathematics and the Master of Data Science (MAS DS), a joint program with the Department of Computer Science.

The Master of Applied Mathematics program is designed for students whose immediate goal is to apply mathematics in commerce or industry. Senior Lecturer Charles Tier created this program with the help of Elizabeth Friedman,

director of professional master’s programs for the College of Science.

“The Master of Applied Mathematics program provides a unique opportunity for students to gain advanced applied mathematics training for technology-based jobs in business, industry, or government. The program emphasizes both modeling of real-world problems and using analysis or com-putation to obtain useful results. In addition, there is a capstone project, which is essential for applying learned skills in a business environment,” says Tier.

To learn more about the new applied mathematics program or to apply online, please visit the program website: iit.edu/csl/pro-grams/professional_masters/applied_math.shtml.

John Erickson, an IIT alumnus (Ph.D. ’07), was promoted from lecturer to senior lecturer (2013).

Shuwang Li was promoted from assistant professor to associate professor with tenure (2014). He was also the recipient of the 2014 John W. Rowe Excellence in Teaching Award.

Xiaofan Li was promoted from associate professor to full professor (2013). Li was named associate dean

of academic affairs for the College of Science (2014).

Professor Warren Edelstein retired with 48 years of service in May 2013. His expertise included analysis of linear visco elasticity and nonlinear creep, numerical analysis of flow-induced vibrations in tubes con-veying fluids, numerical solution of boundary value problems arising in the quantum mechanics of semiconductors,

computational mechan-ics, and mathematics of finance.

Two New Professional Master’s Programs

bright, curious students who want to delve deeply into data, not only to extract answers from data but to ask the right questions.” This new interdisciplinary program combines high-level mathematics, statistics, and computer science theory with the business acumen to explore data sets, gather insights, visualize results, and communicate meaningful findings. This program is designed for those who are interested in learning to properly handle data, conduct data analysis, solve real-world problems using data, and effectively communicate the results to business and industry.

To learn about the new MAS DS program or to apply online, please visit the program website: iit.edu/csl/programs/professional_masters/data_science.shtml.Lulu Kang

Charles Tier

Warren Edelstein

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The 2015 Karl Menger Lecture and Awards will be March 30–31 on IIT’s Main Campus. The event celebrates the life of Karl Menger and the accomplishments of the Department of Applied Mathemat-ics at IIT with two days of lectures and presentations.

Andrea Bertozzi, professor of mathematics, Betsy Wood Knapp Chair for Innovation and Creativity, director of applied mathematics at the University of California Los Angeles, will be the guest lecturer. The title of her presentation is “Mathematics of Crime.”

The 2014 Menger Day lecture was cancelled due to illness. The

MENGER DAY

poster contest and presentation of various awards took place on March 31. Lluis Antoni Jimenez Rugama (Ph.D. candidate) and Haocheng Bian (AMAT/CS 4th year) were first-place winners in the 2014 poster competition. The second-place winners were Yiou Li (Ph.D. ’14) and Eda Gjergo (AMAT/PHYS 5th year). Kai Liu (Ph.D. ’14) was the winner of the Menger Student Award. Chris Mitillos (Ph.D. candidate) won the Teaching Assis-tant Award. The Buck McMorris Summer Stipend Award was given to Yuanfang Xiang (AMAT 4th year).

The 2013 Karl Menger Lecturer was Philip Protter, professor of statistics

The Karl Menger Lecture and Awards is made possible by a fund established by the Menger Family, by the

Department of Applied Mathematics, and by contributions from donors.

For the latest information and reserva-tions, please visit the website: www.iit.edu/csl/am/about/menger.

at Columbia University. His presen-tation was titled “Financial Bubbles Through History, Viewed Through Mathematics.”

The event attracted 179 faculty, students, alumni, and guests.

The first-place winners of the 2013 Poster Competition were Lujia Wang (M.S. ’13) and Barrett Leslie (AMAT 5th year). The sec-ond-place winners were Gergely Balint (Ph.D. ’14) and Anita Thomas (B.S. ’13). Yiou Li (AMAT 4th year) was awarded the Menger Student Award and the Department of Applied Mathematics Teaching Assistant Award.

Andrea Bertozzi

Poster contest

Menger Lecture 2013

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The Department of Applied Mathematics established the F. R. “Buck” McMorris Summer Research Stipend in 2008 to support select undergraduates and/or early career graduate students in conducting research for 10 weeks during the summer. The stipend of $3,000 allows them to participate in research work between school terms and to catalyze their scholarly activities and productivity.

Julienne Kabre (Ph.D. candidate) was awarded the 2013 McMorris Summer Stipend for her research with Xiaofan Li, professor and associate dean of academic affairs, in the area of “Energy Conservation in Ion Channels.” “Ion channels are trans-membrane proteins that regulate the balance mechanism in the complex cellular composition of living organisms,” says Kabre. “As an example, potassium channels play critical roles in a wide variety of physiological processes, including heart regulation, muscle contraction, neurotransmitter release, neuronal excitability, insulin secretion, cell volume regulation, and cell proliferation.

Barrett Leslie (AMAT 5th Year)

Research Interests Current: Construction methods and folding algorithms for self-assembly fractals [1]

Past: Vector-Valued Parametric Kernel-Based Interpolation for 2D Facial Animations, 2011 (A list of poster titles, awards, and links may be downloaded here: mypages.iit.edu/~bleslie)

Activities IIT Student Chapter of Society of Industrial and Applied Mathematics: chapter vice president of IIT-SIAM, 2012–present; chapter secretary, 2011

IIT Student Government Association: College of Science student senator, spring 2013

Why did you choose applied mathematics? As a kid I always had an affinity for puzzles and geometry. In my early 20s while working at film school my attention to details and ability to recognize patterns helped me to map out shots, plan shooting schedules, and determine

F. R. “Buck” McMorris Summer Stipend Winner

“We can easily imagine how the understanding of these mechanisms can benefit our society,” she continues. The detection of an impaired-functioning ion channel could lead to the prediction of certain diseases or drug development. The dynamics have nanoscale effects and therefore macroscale mod-eling and accurate computations are necessary in capturing such systems. The Poisson-Nernst-Planck equations describe the diffusion of ions under the effect of an electric field that is itself caused by those same ions,” says Kabre.

McMorris and Kabre

Barrett Leslie

Student Spotlight

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the best allocation of resources. While shooting the final scene for my thesis animation I found myself facing a very technical shot that was beyond my scope. My TA, who did his undergrad in physics at Northwestern, stepped in, measured a few things, gave me instructions, and within minutes had the production up and running again. The incident helped me to see how math, logic, and reasoning could be used to solve real-world problems. I’ve been hooked ever since.

What is the main focus of your math research and why? I became involved in research three years ago when Greg Fasshauer, professor, associate chair, and director of undergraduate studies, invited me to join the Meshfree Seminar summer session. There, he introduced me to meshfree methods by providing me an interpolation problem for applications in the field of animation. This approach worked well because the research relied heavily on the visual skills I gained while at film school. For me, research seemed to be a natural extension of things I was already comfortable with, which gave me the confidence to explore my own ideas and make the transition to fractal geometry research. Professor Fasshauer encouraged this switch and pushed me to enter the fractal research in poster competitions, which led to multiple awards over the past several years.

What are the benefits of the applied mathematics program? The program provides access to a high-caliber institution with a genuine desire to help you succeed in your mathematics education. You have access to applied mathematics professors via office hours, and everyone in the department is very open to communications with their

students. If you have a question you can get a response by email usually within 24 hours, and the department heads are willing to meet with you in person if necessary.

Why is IIT a good fit for you? IIT’s size makes the campus easy to navigate, and the faculty-to-student ratio gives me personal access to my professors. Daily walks to class are an exploration in architecture, and the 15-minute train ride to downtown Chicago offers me access to the great amenities of the city such as the Chicago Symphony Orchestra and Art Institute.

What are your plans after graduation? The field of applied mathematics is constantly growing, and there are many great, emerging job opportunities. Data science has become the next big thing, which makes IIT’s new Master of Data Science program very enticing. The Master of Mathematical Finance program is also top notch. So, there are a lot of opportunities for AMAT majors to say the least. I am currently looking into graduate schools and pursuing research internships and/or short-term jobs. There are few applied topology programs, but I’m holding out for a program that suits my particular research interests.

Do you have any words of advice for incoming applied mathematics students? Get involved, get to know your peers, engage the AMAT faculty, and don’t be afraid to ask questions. People are here to help and really want to see you succeed. One of the greatest decisions I made while at IIT was my choice to become a student officer of IIT-SIAM. This has given me the opportunity to serve my peers, develop collaboration skills, and build a foundation for a professional network.

Applied Mathematics Students Win College of Science Summer Research StipendsEach student received $5,000 to conduct research with a faculty member in the summer. Recipients included three applied mathematics students in 2013 and two applied mathematics students in 2014.

Haocheng Bian (AMAT and CS 4th year) joined forces with Greg Fasshauer, professor, associate chair, and director of undergraduate studies, for the project “Kernel Methods in Computational Mathematics” (2013).

Melanie Dooley (AMAT and PHYS 4th year) teamed up with Carlo Segre, Duchossois Leadership Professor of Physics, for “Fabricating a Rapid Annealing Furnace” (2013).

Martha Razo (AMAT 3rd year) worked with Fred Hickernell, applied mathematics chair and professor, on “Improvements to Quadrature Algorithms” (2013).

Caleb Hamilton (AMAT 3rd year) will work with Shuwang Li, professor of applied mathematics, to test the convergence of the developing algorithms for modeling a vesicle (when a membrane forms a closed structure) in a fluid under various flows (2014).

Weronika Swiechowicz (AMAT 3rd year) will work with Sonja Petrovic, professor of applied mathematics, to analyze the multimodal likelihood arising in statistics and examine a problem for numerical computations of model parameter estimators (2014).

Department of Applied Mathematics Engineering 1 Building, Room 208

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Anita Thomas (AMAT ’13) co-authored the paper “A Rotation Scheme for Accurately Computing Meteoroid Flux” with Martin Ratliff, a scientist in the Reliability Engineering Office at NASA’s Jet Propulsion Laboratory at Caltech, and Shuwang Li, associate professor of applied mathematics at IIT. The paper was published by the Society for Industrial and Applied Mathematics Undergraduate Research Online. The research paper analyzes the risk of collisions with particle-sized meteoroids and spacecrafts flying through interplanetary space. Thomas is currently a graduate student at Ohio State University.

For a copy of the publication visit the SIAM website: www.siam.org/students/siuro/vol7/S01268.pdf.

Applied Mathematics Graduate Gets Published