Bill Sears Colloquia - Spring 2002

Talks will be on Mondays with pizza at 1:00 and the talk at 1:30pm. Other talks will be on Wednesdays again with pizza at 1:00pm and the talk at 1:30pm in 657 Rhodes Hall unless noted otherwise. Pizza is available if ordered before 10 a.m. on the day of the seminar. (To order pizza, send e-mail to dap7@cornell.edu.)

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• February 11 - David Shmoys, ORIE and CS, "Using Linear Programming in the Design and Analysis of Approximation Algorithms"
  Abstract: Most interesting discrete optimization problems are NP-hard, and hence one cannot hope to design polynomial-time algorithms to find optimal solutions. However, it is possible to design such efficient algorithms that are guaranteed to find near-optimal solutions. One important approach to designing such approximation algorithms is to formulate the optimization problem at hand as an integer programming problem, to solve the linear programming relaxation, and then to round the fractional optimal solution to an integer solution that is (hopefully) not too much more expensive. We will discuss a few recent results along these lines.
• February 27 - Warwick Tucker, Math, "Using a Computer to do Rigorous Mathematics"
  Abstract: The general feelings about using computers in science can be divided into two main categories: one group of researchers considers all problems to be solvable, given a sufficiently large and fast computer. The other group claims that computers are inherently inexact, and that virtually no results produced by machines are to be trusted. In this talk, we will show that there is a narrow (but non-empty!) region that fits in between these two schools of thought. The main underlying idea is to NOT try to model the real numbers using a computer's floating point numbers, but rather to enclose entire sets of real numbers in small intervals with well-defined endpoints. As it turns out, computers handle this situation rather well, allowing theorems to be proved with mathematical rigour.
• March 6 - S. Vehrencamp and J. Burt, Neurobiology and Behavioral Ecology, "Modeling vocal interactions in a neighborhood of territorial songbirds"
  Abstract: In many songbird species, males possess a repertoire of song types that they use while singing. Switching events between song types are an important component of communication. In addition, adjacent males often share many of the same song types, and use these shared song types in strategic ways such as type-matching each other. Type matching has been shown to be a signal of aggressive intentions to rival males. The banded wren from Costa Rica is an excellent study species in which males have repertoires of around 20 song types, 75% of which are shared with neighbors on average. During dawn chorus singing, males appear to interact with each other with multi-way exchanges while switching rapidly between song types. Later in the morning, interactions are usually two-way, and involve aggressive interactions. We have been recording whole clusters of males with a microphone array system which provides records of the time and song type of every song sung by 4-5 adjacent males. We would like to develop a null model of type-matching levels given random song-type use, against which to compare our observed data. The next step will then be to model possible "rules", memory periods, and aggression costs that might explain the obviously non-random patterns we observe. This ought to be modeled as a spatially-explicit neighborhood communication network.
• March 11 - David Shalloway, Molecular Biology and Genetics, "Hierarchical Global Optimization and Protein Structure Prediction"
  Abstract: Protein structure prediction methods use both empirical information from large protein databases and biophysical thermodynamic methods. Mathematically they appear as extremely difficult global optimization problems in with tens of thousands of dimensions. I will discuss the use of multiscale hierarchical approaches to solving these types of problems and some of the applied mathematical problems that are raised.
• April 3 - Teresa Gunn, Biomedical Sciences, "Mouse Pigmentation as a Model Genetic System"
  Abstract: Mouse pigmentation provides an amenable system for the study of complex genetic pathways that regulate diverse biological processes throughout the body. For over 100 years, there has been a recognized link between the genetic networks that regulate pigment production and those that regulate feeding behavior due to the identification of an obese mouse mutant with completely yellow fur. In recent years, the study of genes involved in determining whether black or yellow pigment is made has led to a greater understanding of the genes involved in regulating feeding behavior in the brain. I will discuss the identification of novel genes involved in this pigment pathway and what they teach us about other biological processes.