Seminars and Colloquia by Series

Monday, November 5, 2012 - 12:30 , Location: Skiles 005 , Jinyong Ma , School of Mathematics, Georgia Tech , Organizer: Christian Houdre
This work studies two topics in sequence analysis. In the first part, we investigate the large deviations of the shape of the random RSK Young diagrams, associated with a random word of size n whose letters are independently drawn from an alphabet of size m=m(n). When the letters are drawn uniformly and when both n and m converge together to infinity, m not growing too fast with respect to n, the large deviations of the shape of the Young diagrams are shown to be the same as that of the spectrum of the traceless GUE. Since the length of the top row of the Young diagrams is the length of the longest (weakly) increasing subsequence of the random word, the corresponding large deviations follow. When the letters are drawn with non-uniform probability, a control of both highest probabilities will ensure that the length of the top row of the diagrams satisfies a large deviation principle. In either case, speeds and rate functions are identified. To complete this first part, non-asymptotic concentration bounds for the length of the top row of the diagrams are obtained. In the second part, we investigate the order of the r-th, 1\le r < +\infty, central moment of the length of the longest common subsequence of two independent random words of size n whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, the r-th central moment is shown to be of order n^{r/2}. In particular, when r=2, the order of the variance is linear.
Thursday, November 1, 2012 - 13:30 , Location: Skiles 005 , Arash Asadi , Math, GT , Organizer: Robin Thomas
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Tuesday, August 14, 2012 - 13:00 , Location: Skiles 005 , Luke Postle , Math, GT , Organizer: Robin Thomas
Tuesday, June 19, 2012 - 10:00 , Location: Skiles 005 , Marc Sedjro , School of Mathematics, Georgia Tech , Organizer: Wilfrid Gangbo
This work is concerned with the Almost Axisymmetric Flows with Forcing Terms which are derived from the inviscid Boussinesq equations. It is our hope that these flows will be useful in Meteorology to describe tropical cyclones. We show that these flows give rise to a collection of Monge-Ampere equations for which we prove an existence and uniqueness result. What makes these equations unusual is the boundary conditions they are expected to satisfy and the fact that the boundary is part of the unknown. Our study allows us to make inferences in a toy model of the Almost Axisymmetric Flows with Forcing Terms.
Friday, June 15, 2012 - 13:00 , Location: Klaus 3100 , Nathan Chenette , School of Mathematics, Georgia Tech , Organizer:
Thursday, June 7, 2012 - 11:00 , Location: Skiles 005 , Bulent Tosun , School of Mathematics, Georgia Tech , Organizer:
Monday, May 21, 2012 - 14:00 , Location: Skiles 005 , Tianjun Ye , School of Mathematics, Georgia Tech , Organizer:
Classical vertex coloring problems ask for the minimum number of colors needed to color the vertices of a graph, such that adjacent vertices use different colors. Vertex coloring does have quite a few practical applications in communication theory, industry engineering and computer science. Such examples can be found in the book of Hansen and Marcotte. Deciding whether a graph is 3-colorable or not is a well-known NP-complete problem, even for triangle-free graphs. Intutively, large girth may help reduce the chromatic number. However, in 1959, Erdos used the probabilitic method to prove that for any two positive integers g and k, there exist graphs of girth at least g and chromatic number at least k. Thus, restricting girth alone does not help bound the chromatic number. However, if we forbid certain tree structure in addition to girth restriction, then it is possible to bound the chromatic number. Randerath determined several such tree structures, and conjectured that if a graph is fork-free and triangle-free, then it is 3-colorable, where a fork is a star K1,4 with two branches subdivided once. The main result of this thesis is that Randerath's conjecture is true for graphs with odd girth at least 7. We also give an outline of a proof that Randerath's conjecture holds for graphs with maximum degree 4.
Wednesday, May 2, 2012 - 11:00 , Location: Skiles 006 , Huy Huynh , School of Mathematics, Georgia Tech , Organizer:
Tuesday, May 1, 2012 - 15:00 , Location: Skiles 005 , Stanislav Minsker , School of Mathematics, Georgia Tech , Organizer:
This dissertation investigates the statistical learning scenarios where a high-dimensional parameter has to be estimated from a given sample of fixed size, often smaller than the dimension of the problem. The first part answers some open questions for the binary classification problem in the framework of active learning. Given a random couple (X,Y)\in R^d\times {\pm 1} with unknown distribution P, the goal of binary classification is to predict a label Y based on the observation X. The prediction rule is constructed based on the observations (X_i,Y_i)_{i=1}^n sampled from P. The concept of active learning can be informally characterized as follows: on every iteration, the algorithm is allowed to request a label Y for any instance X which it considers to be the most informative. The contribution of this work consists of two parts: first, we provide the minimax lower bounds for performance of the active learning methods under certain assumptions. Second, we propose an active learning algorithm which attains nearly optimal rates over a broad class of underlying distributions and is adaptive with respect to the unknown parameters of the problem. The second part of this work is related to sparse recovery in the framework of dictionary learning. Let (X,Y) be a random couple with unknown distribution P, with X taking its values in some metric space S and Y - in a bounded subset of R. Given a collection of functions H={h_t}_{t\in \mb T} mapping S to R, the goal of dictionary learning is to construct a prediction rule for Y given by a linear (or convex) combination of the elements of H. The problem is sparse if there exists a good prediction rule that depends on a small number of functions from H. We propose an estimator of the unknown optimal prediction rule based on penalized empirical risk minimization algorithm. We show that proposed estimator is able to take advantage of the possible sparse structure of the problem by providing probabilistic bounds for its performance. Finally, we provide similar bounds in the density estimation framework.
Monday, April 30, 2012 - 13:00 , Location: Skiles 006 , Ruoting Gong , School of Mathematics, Georgia Tech , Organizer: