Seminars and Colloquia by Series

Influence of Cellular Substructure on Gene Expression and Regulation

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 12, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Samuel IsaacsonBoston University Mathematics Dept.
We will give an overview of our recent work investigating the influence of incorporating cellular substructure into stochastic reaction-diffusion models of gene regulation and expression. Extensions to the reaction-diffusion master equation that incorporate effects due to the chromatin fiber matrix are introduced. These new mathematical models are then used to study the role of nuclear substructure on the motion of individual proteins and mRNAs within nuclei. We show for certain distributions of binding sites that volume exclusion due to chromatin may reduce the time needed for a regulatory protein to locate a binding site.

Southeast Geometry Seminar

Series
Other Talks
Time
Monday, April 12, 2010 - 08:00 for 8 hours (full day)
Location
Skiles 269
Speaker
Southeast Geometry SeminarSchool of Mathematics, Georgia Tech
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham; The Georgia Institute of Technology; Emory University; The University of Tennessee Knoxville. The presentations will include topics on geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology. See the Schedule for times and abstracts of talks.

Monomer correlations on the square lattice

Series
Combinatorics Seminar
Time
Friday, April 9, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Mihai CiucuProfessor, Indiana University, Bloomington
In 1963 Fisher and Stephenson conjectured that the correlation function of two oppositely colored monomers in a sea of dimers on the square lattice is rotationally invariant in the scaling limit. More precisely, the conjecture states that if one of the monomers is fixed and the other recedes to infinity along a fixed ray, the correlation function is asymptotically $C d^(-1/2)$, where $d$ is the Euclidean distance between the monomers and $C$ is a constant independent of the slope of the ray. Shortly afterward Hartwig rigorously determined $C$ when the ray is in a diagonal direction, and this remains the only direction settled in the literature. We generalize Hartwig's result to any finite collection of monomers along a diagonal direction. This can be regarded as a counterpart of a result of Zuber and Itzykson on n-spin correlations in the Ising model. A special case proves that two same-color monomers interact the way physicists predicted.

CLT for Excursion Sets Volumes of Random Fields

Series
Stochastics Seminar
Time
Thursday, April 8, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alexander BulinskiLomonosov Moscow State University
We consider various dependence concepts for random fields. Special attention is paid to Gaussian and shot-noise fields. The multivariate central limit theorems (CLT) are proved for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$. Formulae for the covariance matrix of the limiting distribution are provided. Statistical versions of the CLT are established as well. They employ three different estimators of the asymptotic covariance matrix. Some numerical results are also discussed.

Critical slowdown for the Ising model on the two-dimensional lattice

Series
Other Talks
Time
Wednesday, April 7, 2010 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Allan SlyMicrosoft Research, Redmond, WA
Intensive study throughout the last three decades has yielded a rigorous understanding of the spectral-gap of the Glauber dynamics for the Ising model on $Z^2$ everywhere except at criticality. While the critical behavior of the Ising model has long been the focus for physicists, mathematicians have only recently developed an understanding of its critical geometry with the advent of SLE, CLE and new tools to study conformally invariant systems. A rich interplay exists between the static and dynamic models. At the static phase-transition for Ising, the dynamics is conjectured to undergo a critical slowdown: At high temperature the inverse-gap is $O(1)$, at the critical $\beta_c$ it is polynomial in the side-length and at low temperature it is exponential in it. A long series of papers verified this on $Z^2$ except at $\beta=\beta_c$ where the behavior remained unknown. In this work we establish the first rigorous polynomial upper bound for the critical mixing, thus confirming the critical slowdown for the Ising model in $Z^2$. Namely, we show that on a finite box with arbitrary (e.g. fixed, free, periodic) boundary conditions, the inverse-gap at $\beta=\beta_c$ is polynomial in the side-length. The proof harnesses recent understanding of the scaling limit of critical Fortuin-Kasteleyn representation of the Ising model together with classical tools from the analysis of Markov chains. Based on joint work with Eyal Lubetzky.

Stochastic molecular modeling and reduction in reacting systems

Series
Mathematical Biology Seminar
Time
Wednesday, April 7, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Martha GroverSchool of Chemical & Biomolecular Engineering, Georgia Tech
Individual chemical reactions between molecules are inherently stochastic, although for a large collection of molecules, the overall system behavior may appear to be deterministic. When deterministic chemical reaction models are sufficient to describe the behavior of interest, they are a compact way to describe chemical reactions. However, in other cases, these mass-action kinetics models are not applicable, such as when the number of molecules of a particular type is small, or when no closed-form expressions exist to describe the dynamic evolution of overall system properties. The former case is common in biological systems, such as intracellular reactions. The latter case may occur in either small or large systems, due to a lack of smoothness in the reaction rates. In both cases, kinetic Monte Carlo simulations are a useful tool to predict the evolution of overall system properties of interest. In this talk, an approach will be presented for generating approximate low-order dynamic models from kinetic Monte Carlo simulations. The low-order model describes the dynamic evolution of several expected properties of the system, and thus is not a stochastic model. The method is demonstrated using a kinetic Monte Carlo simulation of atomic cluster formation on a crystalline surface. The extremely high dimension of the molecular state is reduced using linear and nonlinear principal component analysis, and the state space is discretized using clustering, via a self-organizing map. The transitions between the discrete states are then computed using short simulations of the kinetic Monte Carlo simulations. These transitions may depend on external control inputs―in this application, we use dynamic programming to compute the optimal trajectory of gallium flux to achieve a desired surface structure.

On Landau Damping

Series
PDE Seminar
Time
Tuesday, April 6, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Clement MouhotEcole Normale Superieure
Landau damping is a collisionless stability result of considerable importance in plasma physics, as well as in galactic dynamics. Roughly speaking, it says that spatial waves are damped in time (very rapidly) by purely conservative mechanisms, on a time scale much lower than the effect of collisions. We shall present in this talk a recent work (joint with C. Villani) which provides the first positive mathematical result for this effect in the nonlinear regime, and qualitatively explains its robustness over extremely long time scales. Physical introduction and implications will also be discussed.

Introduction to Numerical Algebraic Geometry

Series
Research Horizons Seminar
Time
Tuesday, April 6, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Anton Leykin School of Math, Georgia Tech

Please Note: Hosted by: Huy Huynh and Yao Li

One of the basic problems arising in many pure and applied areas of mathematics is to solve a system of polynomial equations. Numerical Algebraic Geometry starts with addressing this fundamental problem and develops machinery to describe higher-dimensional solution sets (varieties) with approximate data. I will introduce numerical polynomial homotopy continuation, a technique that is radically different from the classical symbolic approaches as it is powered by (inexact) numerical methods.

Joint ACO/OR Seminar - Semi-algebraic optimization theory

Series
Other Talks
Time
Tuesday, April 6, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
ISyE Executive Classroom
Speaker
Adrian LewisSchool of Operations Research and Information, Cornell University
Concrete optimization problems, while often nonsmooth, are not pathologically so. The class of "semi-algebraic" sets and functions - those arising from polynomial inequalities - nicely exemplifies nonsmoothness in practice. Semi-algebraic sets (and their generalizations) are common, easy to recognize, and richly structured, supporting powerful variational properties. In particular I will discuss a generic property of such sets - partial smoothness - and its relationship with a proximal algorithm for nonsmooth composite minimization, a versatile model for practical optimization.

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