Seminars and Colloquia by Series

Sparsity in machine learning: recovery in convex hulls of infinite dictionaries

Series
SIAM Student Seminar
Time
Friday, March 12, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Stanislav MinskerSchool of Mathematics, Georgia Tech
We will start with a brief introduction to the broad area of machine learning, with the focus on empirical risk minimization methods and their connection to the theory of empirical processes. Using some results from our recent work with V. Koltchinskii, I will explain how sparsity affects the risk bounds.

The geometry of dissipative evolution equation

Series
SIAM Student Seminar
Time
Friday, March 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yao LiGeorgia Tech
Last semester, I reviewed the relation between dynamical system, Fokker-Planck equation and thermodynamics (free energy and Gibbs distribution). This time let's go further. I will review the geometric properties of a kind of dissipative evolution equations. I will explain why this kind of evolutionary equations (Fokker-Planck equation, nonlinear Fokker-Planck equation, Porous medium equation) are the gradient flow of some energy function on a Riemannian manifold -- 2-Wasserstein metric space.

A Survey of Hardy Inequalities and their Optimization

Series
SIAM Student Seminar
Time
Friday, February 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Craig A. SloaneSchool of Mathematics, Georgia Tech
This will be an introductory talk about Hardy inequalities. These inequalities are solutions to optimization problems, and their results are well-known. I will survey these results, and discuss some of the techniques used to solve these problems. The applications of Hardy inequalities are broad, from PDE's and mathematical physics to brownian motion. This talk will also serve as a lead-in to my talk at the Analysis seminar next Wednesday in which I discuss some current results that Michael Loss and I have obtained.

Introduction to the Latex

Series
SIAM Student Seminar
Time
Friday, February 12, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 156 (undergraduate computer lab)
Speaker
Mitch KellerSchool of Mathematics, Georgia Tech
This is an introductory talk to everyone who wants to learn skills in Latex. We will discuss including and positioning graphics and the beamer document class for presentations. A list of other interesting topics will be covered if time permits.

The existence and uniqueness of one minimization problem

Series
SIAM Student Seminar
Time
Friday, February 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Linwei XinSchool of Mathematics, Georgia Tech
We are dealing with the following minimization problem: inf {I(\mu): \mu is a probability measure on R and \int f(x)=t_{0}}, where I(\mu) = \int (x^2)/2 \mu(dx) + \int\int log|x-y|^{-1} \mu(dx)\mu(dy), f(x) is a bounded continuous function and t is a given real number. Its motivation and its connection to radom matrices theory will be introduced. We will show that the solution is unique and has a compact support. The possible extension of the class of f(x) will be discussed.

The limit distribution the longest significance path(LSP) in point cloud

Series
SIAM Student Seminar
Time
Friday, January 29, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Kai NiSchool of Mathematics, Georgia Tech
In 2006, my coadvisor Xiaoming Huo and his colleague published an annal of statistics paper which designs an asymptotically powerful testing algorithm to detect the potential curvilinear structure in a messy point cloud image. However, such an algorithm involves a membership threshold and a decision threshold which are not well defined in that paper because the distribution of LSP was unknown. Later on, Xiaoming's student Chen, Jihong found some connections between the distribution of LSP and the so-called Erdos-Renyi law. In some sense, the distribution of LSP is just a generalization of the Erdos-Renyi law. However this JASA paper of Chen, Jihong had some restrictions and only partially found out the distribution of LSP. In this talk, I will show the result of the JASA paper is actually very close to the distribution of LSP. However, these is still much potential work to do in order to strengthen this algorithm.

Reducing the Size of a Matrix While Maintaining its Spectrum

Series
SIAM Student Seminar
Time
Friday, January 22, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Benjamin WebbSchool of Mathematics, Georgia Tech
The Fundamental Theorem of Algebra implies that a complex valued nxn matrix has n eigenvalues (including multiplicities). In this talk we introduce a general method for reducing the size of a square matrix while preserving this spectrum. This can then be used to improve on the classic eigenvalue estimates of Gershgorin, Brauer, and Brualdi. As this process has a natural graph theoretic interpretation this talk should be accessible to most anyone with a basic understanding of matrices and graphs. These results are based on joint work with Dr. Bunimovich.

Simulation Study of the Length of Longest Increasing Subsequence of Finite Alphabets

Series
SIAM Student Seminar
Time
Friday, November 20, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Huy HuynhGeorgia Tech
Let X_1, X_2,...,X_n be a sequence of i.i.d random variables with values in a finite alphabet {1,...,m}. Let LI_n be the length of the longest increasing subsequence of X_1,...,X_n. We shall express the limiting distribution of LI_n as functionals of m and (m-1)- dimensional Brownian motions as well as the largest eigenvalue of Gaussian Unitary Ensemble (GUE) matrix. Then I shall illustrate simulation study of these results

From Gibbs free energy to the dynamical system with random perturbation

Series
SIAM Student Seminar
Time
Friday, November 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yao LiSchool of Mathematics, Georgia Tech
Gibbs free energy plays an important role in thermodynamics and has strong connection with PDE, Dynamical system. The results about Gibbsfree energy in 2-Wasserstein metric space are known recently.First I will introduce some basic things, so the background knowledge isnot required. I will begin from the classic definition of Gibbs freeenergy functional and then move to the connection between Gibbs freeenergy and the Fokker-Planck equation, random perturbation of gradientsystems. Second, I will go reversely: from a dynamical system to thegeneralized Gibbs free energy functional. I will also talk about animportant property of the Gibbs free energy functional: TheFokker-Planck equation is the gradient flux of Gibbs free energyfunctional in 2-Wasserstein metric.So it is natural to consider a question: In topological dynamical systemand lattice dynamical system, could we give the similar definition ofGibbs free energy, Fokker-Planck equation and so on? If time allowed, Iwill basicly introduce some of my results in these topics.

Online Algorithms for Graphs and Partially Ordered Sets

Series
SIAM Student Seminar
Time
Friday, November 6, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Mitch KellerSchool of Mathematics, Georgia Tech
Suppose that Amtrak runs a train from Miami, Florida, to Bangor, Maine. The train makes stops at many locations along the way to drop off passengers and pick up new ones. The computer system that sells seats on the train wants to use the smallest number of seats possible to transport the passengers along the route. If the computer knew before it made any seat assignments when all the passengers would get on and off, this would be an easy task. However, passengers must be given seat assignments when they buy their tickets, and tickets are sold over a period of many weeks. The computer system must use an online algorithm to make seat assignments in this case, meaning it can use only the information it knows up to that point and cannot change seat assignments for passengers who purchased tickets earlier. In this situation, the computer cannot guarantee it will use the smallest number of seats possible. However, we are able to bound the number of seats the algorithm will use as a linear function of the minimum number of seats that could be used if assignments were made after all passengers had bought their tickets. In this talk, we'll formulate this problem as a question involving coloring interval graphs and discuss online algorithms for other questions on graphs and posets. We'll introduce or review the needed concepts from graph theory and posets as they arise, minimizing the background knowledge required.

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