Math Sciences Colloquia - Spring 2007

The Center for Applied Mathematics and the IGERT Nonlinear Systems program are sponsoring the Mathematical Sciences Graduate Student Seminar Series. We hope that this seminar series will become a fixture of Cornell's interdisciplinary programs. As part of these seminars in the mathematical sciences, Cornell graduate students will give informal one-hour talks about their research to fellow graduate students as well as professors.

The idea behind these seminars is twofold: (1) To foster interactions between graduate students in various disciplines for both academic and social purposes. (2) To allow students the opportunity to present and discuss their work with a broad group of their peers in a manner that is not currently available at Cornell. No one is going to demand or expect a polished presentation. The seminar is intended for work in progress. Students should not feel shy about presenting their work, as there are many people who will be interested in hearing about it. It's a chance for graduate students to get to know each other, practice their speaking ability, offer constructive criticism, etc.

This seminar series is a natural extension of the interdiscplinary efforts of CAM and the IGERT program. We hope you'll inform your students and colleagues of this seminar series, and we also invite you to provide suggestions for student speakers. These suggestions or expressions of interest to give a presentation should be e-mailed to Megan Owen (mao29cornell.edu).

All Math Sciences colloquia take place on Thursdays from 12:15 pm to 1pm in 657 Rhodes Hall. Pizza will be served before the talk.

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• Thursday, February 15
  June Andrews, Univ. of California, Berkeley
  Time: 12:15-1pm, with pizza at 12pm.
  Place: 657 Rhodes Hall, conference room
  
  Title: Fast Marching Methods for the continuous Traveling Salesman Problem
  
  Abstract: The Traveling Salesman Problem(TSP) is the problem of finding the shortest tour that visits a set of cities. The algorithms developed for the TSP,
  have their own history books. All have relied on knowing the cost of travel between cities at the outset of the problem. Instead of, at the outset, using a discrete graph to represent the topology of the cities, we can use a speed function to represent the cost of traveling through points in a domain, of which the cities are a subset. With this speed function, the cost of traveling between cities is at the outset, unknown, but can be calculated by the Fast Marching Method. Finally, combining the algorithms developed for the TSP with the shortest path calculations of the Fast Marching Method, yields a faster runtime for solving the continuous Traveling Salesman Problem, in both optimal and heuristic algorithms.
  
• Thursday, March 1
  
  Paul Hurtado, CAM
  Time: 12:00-1pm, with pizza at 12pm.
  Place: 657 Rhodes Hall, conference room
  
  Title: "Conjunctivitis in the Eastern House Finch - Some Mathematical Ramblings on an Infectious Disease in an Introduced North American Song Bird"
  
  Abstract: The House Finch (Carpodacus mexicanus) was introduced into eastern North America via the pet trade in the 1940s and has since spread throughout most of eastern North America. The source population in Southern California is non-migratory, however the introduced eastern population rapidly evolved to be partially migratory. Later, in the early 1990s this introduced population experienced a conjunctivitis epidemic (like "pink-eye" - but lethal!) caused by a bacterial pathogen normally associated with respiratory infections in domestic poultry. This resulted in density dependent declines in the House Finch population, and may also bring about higher mortality rates among birds living in more northerly climates.
  
  For this very informal talk, I will give a brief overview of some of the important biological processes at work in this system. I'll then present some rough "in progress" modeling work I've done in an attempt to answer the question "To what extent can this disease be expected to impact the migratory behavior of eastern House Finches?" Lastly, if time permits I will discuss some of my plans for future work exploring how other susceptible bird species and variation in within-host disease dynamics may impact larger scale dynamics in this wildlife disease system.
  
• Tuesday, March 27
  
  Lauren Childs, CAM
  Time: 12:15 pm, with pizza at 12pm.
  Place: 657 Rhodes Hall, conference room
  
  Title: "The Dynamics of Macrophage Activation"
  
  
• Thursday, April 5
  
  Nico Diener, CAM
  Time: 12:15 pm, with pizza at 12pm.
  Place: 657 Rhodes Hall, conference room
  
  Title: "Multiple Stopping Options and Backward SDEs"
  
  Abstract: This talk is motivated by the study of Swing Options, a contingent claim with multiple exercises of American type. First, I will review the connection between Reflected Backward Stochastic Differential Equations (RBSDE in short), optimal stopping problems and the theory of Snell envelope. I will then prove the existence of a sequence of RBSDE whose solution gives the price and the hedging strategy for a Swing Option. I will conclude by comparing the optimal exercise strategies of two different Swing Options and deduce a nice property of their exercise region.

  
  Comments and suggestions are welcome as this talk is a rehearsal of my A exam.
  
  

• Tuesday, April 24
  
  Deena Schmit, CAM
  Time: 12:15 pm, with pizza at 12pm.
  Place: 657 Rhodes Hall, conference room
  
  Title: "Mathematical models of DNA sequence evolution"
  
  Abstract: We investigate various models of DNA regulatory sequence evolution as they apply to several different organisms. First we develop a model for humans and then extend our study to include organisms with larger effective population sizes such as Drosophila (fruit flies) and yeast. A regulatory sequence is a short sequence of DNA (in vertebrates, many are 6-9 nucleotides long) which is a binding site for transcription factors that promote or inhibit transcription of DNA to make proteins. Changes in regulatory sequences can cause changes in gene expression which in turn can lead to phenotypic evolution. Thus, one possible explanation for the substantial organismal differences between humans and chimpanzees is that there have been changes in gene regulation. Given what is known about transcription factor binding sites, this motivates the following probability question: given a 1000 nucleotide region in our genome, how long does it take for a specified 6-9 letter word to appear in that region in some individual? Previous studies of this problem have only been done using simulation. We give a mathematical analysis of this problem and focus on words of length 6 and 8. We show that the average waiting time is 100,000 years for words of length 6, while for words of length 8, the waiting time has mean 375,000 years when there is a 7 out of 8 letter match in the population consensus sequence (an event of probability roughly 5/16) and has mean 650 million years when there is not. Fortunately, in biological reality, the match to the target word does not have to be perfect for binding to occur. If we model this by saying that a 7 out of 8 letter match is good enough, then the mean reduces to about 60,000 years. These results assume that the human effective population size is 10,000 which is relatively small compared to organisms such as Drosophila and yeast whose effective population sizes are in the millions. In addition, our results show that new regulatory sequences can come from small modifications of existing sequence. Extending our model, we examine the waiting time for a pair of mutations, the first of which inactivates an existing transcription factor binding site and the second which creates a new one. Consistent with recent experimental observations for Drosophila and yeast, we find that a few million years is sufficient in these species, but for humans with a much smaller effective population size, this type of change would take more than 100 million years.
  
• Tuesday, May 8
  
  Sam Arbesman, Computational Biology
  Time: 11:45 am, with pizza at 11:30 am.
  Place: 657 Rhodes Hall, conference room
  
  Title: "Protein Evolution, Function and Interaction. Also, some other things."
  
  Abstract: Have you ever wondered about evolution? Do you think we're descended from dinosaurs? Will we mutate beyond belief in the next twenty years? Find out about these questions and more, as I, Sam Arbesman, demonstrate the excitement of science, perform sleight-of-hand magic tricks, and shoot one lucky volunteer out of a cannon. Marvel at the only accurate scientific calculation of how many angels can dance on the head of a pin! Witness feats of strength as Sam Arbesman lifts an '89 Buick LeSabre above his head, whilst reciting the Gettysburg Address! Be astonished as you see someone drink a gallon of milk in a single hour! Bring your friends, and your sense of wonder, to a noontime presentation that is not to be missed.
  
  The contents of the seminar will more likely be as follows: I will be speaking about evolutionary genetics and present a new analytical tool. Essentially, I will discuss how you can calculate the evolutionary rate of a genetic sequence over time, and how this can be used to gain insight into the interplay between evolutionary rate of change in a protein, its function, and how it interacts with other proteins in the cell. I will focus on yeast. I will also discuss briefly two other projects I am working on. One examines the relationship between the concept of punctuated equilibrium and the progression of world records, in sports and other areas. The second project examines the scaling laws in cities, in analogy to those found in biology. This last project is being done in conjunction with Geoff West from the Santa Fe Institute.
  
  
• Thursday, May 17
  
  Sasha Gutfraind, CAM
  Time: 12:15 , with pizza at noon.
  Place: 657 Rhodes Hall, conference room
  
  Title: "What is LyX"
  
  Abstract: From Lyx.org: What is LyX?
  LyX is the first WYSIWYM (What You See is What You Mean) document processor. Ehhh... please explain. LyX is a document processor that encourages an approach to writing based on the structure of your documents, not their appearance. It is released under a href="http://www.lyx.org/about/license.php"Free Software / Open Source license. LyX is for people that write and want their writing to look great, right out of the box. No more endless tinkering with formatting details, 'finger painting' font attributes or futzing around with page boundaries. You just write. In the background, Prof. Knuth's legendary TeX typesetting engine makes you look good. On screen, LyX looks like any word processor; its printed output -- or richly cross-referenced PDF, just as readily produced -- looks like nothing else. Gone are the days of industrially bland .docs, all looking similarly not-quite-right, yet coming out unpredictably different on different printer drivers. Gone are the crashes 'eating' your dissertation the evening before going to press. LyX is stable and fully featured. It is a multi-platform, fully internationalized application running natively on Unix/Linux and the Macintosh and modern Windows platforms. But where did it come from? LyX is designed for scientists by scientists, and it shows, in world-class support for math and structured document creation. Such staples of scientific authoring as reference list and index creation come standard. But you don't have to be a scientist: with LyX you create just as easily a letter or a novel or a theatre play or film script. A broad array of ready, well designed document layouts and style modification and feature support packages are built in.