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Series: CDSNS Colloquium

Despite advances in treatment of chronic hepatitis B virus (HBV) infection,
liver transplantation remains the only hope for many patients with end-stage
liver disease due to HBV. A complication with liver transplantation,
however, is that the new liver is eventually reinfected in chronic HBV
patients by infection in other compartments of the body. We have formulated
a model to describe the dynamics of HBV after liver transplant, considering
the liver and the blood of areas of infection. Analyzing the model, we
observe that the system shows either a transcritical or a backward
bifurcation. Explicit conditions on the model parameters are given for the
backward bifurcation to be present, to be reduced, or disappear.
Consequently, we investigate possible factors that are responsible for
HBV/HCV infection and assess control strategies to reduce HBV/HCV
reinfection and improve graft survival after liver transplantation.

Series: Combinatorics Seminar

There has been substantial work on approximation algorithms for clustering
data under distance-based objective functions such as k-median, k-means, and
min-sum objectives. This work is fueled in part by the hope that
approximating these objectives well will indeed yield more accurate
solutions. That is, for problems such as clustering proteins by function, or
clustering images by subject, there is some unknown correct "target"
clustering and the implicit assumption is that clusterings that are
approximately optimal in terms of these distance-based measures are also
approximately correct in terms of error with respect to the target. In this
work we show that if we make this implicit assumption explicit -- that is, if
we assume that any c-approximation to the given clustering objective Phi is
epsilon-close to the target -- then we can produce clusterings that are
O(epsilon)-close to the target, even for values c for which obtaining a
c-approximation is NP-hard. In particular, for the k-median, k-means, and
min-sum objectives, we show that we can achieve this guarantee for any
constant c > 1.
Our results show how by explicitly considering the alignment between the
objective function used and the true underlying clustering goals, one can
bypass computational barriers and perform as if these objectives were
computationally substantially easier.
This talk is based on joint work with Avrim Blum and Anupam Gupta (SODA
2009), Mark Braverman (COLT 2009), and Heiko Roeglin and Shang-Hua Teng (ALT 2009).

Friday, October 16, 2009 - 15:00 ,
Location: Skiles 169 ,
Amey Kaloti ,
Georgia Tech ,
Organizer:

This is a 2-hour talk.

Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter
Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with
connections to contact topology. In these talks we will try to define the Heegaard Floer
homology without assuming much background in low dimensional topology. One more goal is
to present the combinatorial description for this theory.

Series: SIAM Student Seminar

This talk considers the following sequence shufling problem: Given a biological sequence (either DNA or protein) s, generate a random instance among all the permutations of s that exhibit the same frequencies of k-lets (e.g. dinucleotides, doublets of amino acids, triplets, etc.). Since certain biases in the usage of k-lets are fundamental to biological sequences, effective generation of such sequences is essential for the evaluation of the results of many sequence analysis tools. This talk introduces two sequence shuffling algorithms: A simple swapping-based algorithm is shown to generate a near-random instance and appears to work well, although its efficiency is unproven; a generation algorithm based on Euler tours is proven to produce a precisely uniforminstance, and hence solve the sequence shuffling problem, in time not much more than linear in the sequence length.

Series: Analysis Seminar

In this talk, I will discuss some results obtained in my Ph.D. thesis.
First, the point mass formula will be introduced. Using the formula, we
shall see how the asymptotics of orthogonal polynomials relate to the
perturbed Verblunsky coefficients. Then I will discuss two classes of
measures on the unit circle -- one with Verblunsky coefficients \alpha_n -->
0 and the other one with \alpha_n --> L (non-zero) -- and explain the
methods I used to tackle the point mass problem involving these measures.
Finally, I will discuss the point mass problem on the real line. For a long
time it was believed that point mass perturbation will generate
exponentially small perturbation on the recursion coefficients. I will
demonstrate that indeed there is a large class of measures such that that
proposition is false.

Series: Analysis Seminar

Given an "infinite symmetric matrix" W we give a simple condition, related
to the shift operator being expansive on a certain sequence space, under
which W is positive. We apply this result to AAK-type theorems for
generalized Hankel operators, providing new insights related to previous
work by S. Treil and A. Volberg. We also discuss applications and open
problems.

Wednesday, October 14, 2009 - 13:00 ,
Location: Skiles 269 ,
Edson Denis Leonel ,
Universidade Estadual Paulista, Rio Claro, Brazil ,
Organizer:

Fermi acceleration is a phenomenon where a classical particle canacquires unlimited energy upon collisions with a heavy moving wall. Inthis talk, I will make a short review for the one-dimensional Fermiaccelerator models and discuss some scaling properties for them. Inparticular, when inelastic collisions of the particle with the boundaryare taken into account, suppression of Fermi acceleration is observed.I will give an example of a two dimensional time-dependent billiardwhere such a suppression also happens.

Series: Other Talks

We will briefly review the definition of the Cech cohomology groups of a sheaf (so if you missed last weeks talk, you should still be able to follow this weeks), discuss some basic properties of the Cech construction and give some computations that shows how the theory connects to other things (like ordinary cohomology and line bundles).

Series: Research Horizons Seminar

Image segmentation has been widely studied, specially since Mumford-Shah
functional was been proposed. Many theoretical works as well as numerous
extensions have been studied rough out the years. This talk will focus on
introduction to these image segmentation functionals. I will start with
the review of Mumford-Shah functional and discuss Chan-Vese model. Some
new extensions will be presented at the end.

Wednesday, October 14, 2009 - 11:00 ,
Location: Skiles 269 ,
Bart Haegeman ,
INRIA, Montpellier, France ,
Organizer:

Hubbell's neutral model provides a rich theoretical framework to study
ecological communities. By coupling ecological and evolutionary time
scales, it allows investigating how communities are shaped by speciation
processes. The speciation model in the basic neutral model is particularly
simple, describing speciation as a point mutation event in a birth of a
single individual. The stationary species abundance distribution of the
basic model, which can be solved exactly, fits empirical data of
distributions of species abundances surprisingly well. More realistic
speciation models have been proposed such as the random fission model in
which new species appear by splitting up existing species. However, no
analytical solution is available for these models, impeding quantitative
comparison with data. Here we present a self-consistent approximation
method for the neutral community model with random fission speciation. We
derive explicit formulas for the stationary species abundance
distribution, which agree very well with simulations. However, fitting the
model to tropical tree data sets, we find that it performs worse than the
original neutral model with point mutation speciation.