## 2014 Integration Bee

The Fourteenth Annual Pitt Integration Bee organized by Prof. Jon Rubin unfolded in Alumni Hall's 3rd floor Integration Chamber. 26 Pitt undergraduates competed, with 11 making it through two rounds of integration to go head to head in the lightning rounds. These participants were first faced with[ the following monster integrand: [sin(sinx)cos(sinx)(cosx)^3-sinx(cosx)(sin(sinx))^2]; 3 of them successfully tamed it within the allotted time. A fourth place winner was determined by ln(x)(1-ln(x))/x^3, while the overall winner was based on the fastest integration of 1/sqrt(2x-x^2).

And, without further ado: The 2014 INTEGRATION CHAMPION and recipient of the coveted Integration Champ T-shirt is DEREK ORR. In a second place tie were XIAOYUN GU and 2011 champ ARVIND PRASADAN, while in fourth place was repeat prize winner KOSTYA BORISOV. All of these winners shared $200 in book store certificates, generously donated by the Honors College, with Orr as a reward for their integration prowess. Congratulations to all of them, and to all of the competitors, who showed impressive integration talent!

"THANK YOU to everyone who participated in this event in any way! He appreciate the enthusiastic contestants and audience members who added to the atmosphere and, in some cases, walked away with top-notch door prizes. It was great to have several faculty members in the audience, including ALEX BORISOV, who became a lifeline star and even provided us with the a rare father-son lifeline encounter. This event was made possible due to the volunteer efforts of graduate students JEREMY HARRIS, JAY PENA, YANGYANG WANG, and GLENN YOUNG and the recruitment of participants by many of our faculty and TAs. I also thank ANGELA ATHANAS and INNA SYSOEVA once again for their extra recruiting efforts. Finally, thanks to the Honors College and Math Department for funding this competition!" -- Prof. Jon Rubin

## Math Modeling Competition

What is the optimal strategy for evacuating the South Carolina coast before an impending hurricane? What is the best way to have passengers board an airplane? What would be the impact of an asteroid strike at the South Pole? How should gamma radiation be applied to destroy a tumor while sparing surrounding tissue? And just what can be done to avoid grade inflation? These topics sound like fertile ground for semester long projects or seminar courses, and some have confounded experts for years. Yet, as questions in the Mathematical Competition in Modeling (MCM), all have been addressed by talented teams of undergraduate students in 96 hours of intense and exciting intellectual effort.

The MCM is run annually by the Consortium for Mathematics and its Applications, a non-profit organization that aims to improve mathematics education. In the MCM, three-person teams of undergraduate students focus on a broadly interpretable, challenging applied math problem. Each year, there are two problems to choose from, and the competition runs for 96 straight hours after the problems are announced. During that 96 hour period, each team must formulate mathematical models to address one of the contest questions, perform mathematical analysis, calculations, and computer simulations to derive results from the models, and prepare a report on its work. At the end of the 96 hour period, team members submit a report to the COMAP team for judging – and, presumably, collapse into an exhausted sleep!

The number of participating teams has skyrocketed from several hundred to several thousand, from around the world, over the last few years. A handful of winning teams are selected, some of which are recognized at international mathematics meetings. Others who complete the challenge are rated as Meritorious, Honorable Mention, or Successful Participant. University of Pittsburgh teams have competed for most of the last 15 years, and in 2014, for the first time, three Pitt teams entered the contest: Thomas Bednar, Alec Jasen, and Raghu Vaddempudi; Xinyang He, Shiyi Li, and Jingjing Xu; and Robert Cone, Norman Sivi, and Zhen Yuan. Prof. Jon Rubin was thier faculty advisor. All three teams selected the same problem, which asked them to evaluate effectiveness of the “keep-right-except-to-pass” rule of driving at promoting traffic flow and to consider whether alternative rules might do an even better job. This problem posed many challenges, but no doubt our teams overcame them, because, as we all know, Pitt applied math students are driven to succeed!

## Job Seeking Students get Help at Interviewing Seminar

The Pittsburgh Tribune-Review ran an article in the business section of this morning's paper titled "Falling Jobless Figures Mislead" (by Chris Fleisher). The article states that Western Pennsylvania's jobless rate fell from 6.0% in January to 5.8% in February. When one considers that hospitals eliminated more than 2000 full-time jobs this past year (see article for source), one begins to be suspicious that the job market is improving. This is precisely the point of the article: these numbers are misleading as they do not include people that are unemployed but have stopped looking for work.

The point: the current job market is tough. A solution: do everything you can to improve your chances of becoming employed. To help you with this, Prof. Jeff Wheeler organized an "Interviewing Seminar" on Wednesday April 9, 2014.

At this seminar, Mark Burdsall, Senior Consultant Organization Development (Pitt HR), gave a presentation on Interviewing. Mark is an expert in this area and teaches on this subject for the Katz Graduate Business School. Additionally, there was a panel of individuals that make hiring decisions at large, local companies including:

--Jon Coughlin, Technology Audit Director at PNC Bank

--Michael Lowman, eCommerce Site Merchandise Manager for Dick's Sporting Goods.

The seminar was well attended and the students really enjoyed it. The tips were very well received and at least one student suggested the Math Department make the seminar a yearly event.

## Undergraduate Research

**Mentors: Dr. Bard Ermentrout and Dr. David Swigon****Undergraduate Student Researcher: Harini Chandramouli**

Harini Chandramouli is working on a model of in-host immune response to inuenza infection. They have several ODE formulations of the system with various components of the immune response. Harini is using bifurcation analysis to track the attractors of the system and their dependence on virus infectivity. She is also using continuation techniques in conjunction with boundary value problem solving to monitor the dependence of domains of attraction on parameters of the system. The goal of the project is to analyze how immune response controls thevirus dynamics.

**Mentor: Dr. Chris Lennard****Undergraduate Student Research: David Eckman**

David Eckman and Dr. Lennard consider Fibonacci-type sequences in rings and Banach algebras and show that Binet-type formulas can be derived under quite general circumstances. They also show that in certain rings and Banach algebras Binet-type formulas may not exist; e.g., in the Banach algebra L1(R), where the product is convolution. Along the way, they consider the fact that in rings with identity, for every invertible x, and for all positive integers n, xn + 1=xn is a monic polynomial in x + 1=x; and related identities. In particular, we prove two theorems concerning the Banach algebra of all continuous linear operators on a Hilbert space. For example, we show that if x is invertible and x1=x is positive definite, then x_ +(1)_=x_ is positive definite, for all _ 2 N. From the above-mentioned identities, we also recapture some well known results for Fibonacci-type sequences of integers: the Fibonacci, Lucas, Pell and Pell-Lucas sequences; as well as derive less common formulas for some of their subsequences. They have also submitted a paper Fibonacci-type sequences in Banach algebras, Binet-type formulas, and polynomials in x + 1=x for publication.

**Mentor: Dr. Bard Ermentrout**

**Undergraduate Student Research: Mahjub Hammond**

Mahjub Hammond and Dr. Ermentrout have been working with physiologists over in psychiatry. They have a paper submitted where Mahjub did some simulations and are currently working on another paper. Their work first concerns how certain properties of inhibitory neurons affect the synchronization and frequency of gamma rhythms that are associated with cognition and can become disrupted in schizophrenia. They are using both spiking models and a population density model that is derived from the spiking model and has the form of a nonlinear Fokker-Planck equation.

**Mentor: Dr. Bard Ermentrout****Undergraduate Student Researchers: Kruthi Kella and Schweta Ravichandar**

This research team is working with Dr. Ermentrout on a problem similar to Sarah Miller's (below) but on simple trivalent (& tetravalent) graphs that have special symmetries. In these and other graphs, synchronization is always an asymptotically stable solution, but they want to know if all initial data will go to synchrony or whether there are other patterns. They basically simulate thousands of initial conditions and then watch where they end up and are particularly interested in when and why certain graphs do or do not form patterns

**Mentor: Dr. Bard Ermentrout****Undergraduate Student Researcher: Sarah Miller (Neuroscience)**

Sarah is continuing work started with Dr. Ermentrout last semester on simulating and understanding networks of oscillators distributed on three-dimensional graphs that are crude discretizations of a cube. They are searching for simple versions of so-called scroll rings and twisted scrolls that are observed in continuum models of chemical oscillators. They currently have studied networks where each node connects to 6 others (NSEW& Up/down) and are looking at even more sparsely connected systems (4 neighbors) based on a tetrahedral pattern.

**Mentors: Dr. Bard Ermentrout and Dr. David Swigon ****Undergraduate Student Researcher: Joe Molisani**

The research team is continuing to work on modeling the coupling of oscillators when some of the internal parameters in the oscillator are allowed to vary according to what the external stimulus is doing. They have developed some simplified phase models and then can analyze these using standard stability methods. They are able to use some perturbation methods to derive the simple models from a more realistic system and apply this to certain species of fireflies.

#### Research mentored by faculty from other departments

**Undergraduate Student Researcher: Arvand Prasedan**

Arvand Prasedan is working with a professor in the Electrical Engineering department on statistical signal processing applied to speech. He has been working on this a little over a year. In particular, he is working on a method that fits a rational function to the (magnitude squared) Fourier transform of a data vector. It's a lot like a Pade approximant. The problem is that continuous fits capture high frequency components better, whereas discrete methods (on sampled data) handle low frequencies better. He has combined two existing methods for a hybrid method, and they are now working on deriving the Cramer-Rao bound for the new estimator.