Seminars and Colloquia by Series

Steady-state $GI/GI/n$ queue in the Halfin-Whitt Regime

Series
Stochastics Seminar
Time
Thursday, September 29, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David Goldberg – ISyE, Georgia Tech
In this talk, we resolve several questions related to a certain heavy traffic scaling regime (Halfin-Whitt) for parallel server queues, a family of stochastic models which arise in the analysis of service systems. In particular, we show that the steady-state queue length scales like $O(\sqrt{n})$, and bound the large deviations behavior of the limiting steady-state queue length. We prove that our bounds are tight for the case of Poisson arrivals. We also derive the first non-trivial bounds for the steady-state probability that an arriving customer has to wait for service under this scaling. Our bounds are of a structural nature, hold for all $n$ and all times $t \geq 0$, and have intuitive closed-form representations as the suprema of certain natural processes. Our upper and lower bounds also exhibit a certain duality relationship, and exemplify a general methodology which may be useful for analyzing a variety of stochastic models. The first part of the talk is joint work with David Gamarnik.

On the Square Dependence Problem

Series
School of Mathematics Colloquium
Time
Thursday, September 29, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ernie Croot – Georgia Tech
In many integer factoring algorithms, one produces a sequence of integers (created in a pseudo-random way), and wishes to rapidly determine a subsequence whose product is a square (which we call a `square product'). In his lecture at the 1994 International Congress of Mathematicians, Pomerance observed that the following problem encapsulates all of the key issues: Select integers a1, a2, ..., at random from the interval [1,x], until some (non-empty) subsequence has product equal to a square. Find good esimates for the expected stopping time of this process. A good solution to this problem should help one to determine the optimal choice of parameters for one's factoring algorithm, and therefore this is a central question. In this talk I will discuss the history of this problem, and its somewhat recent solution due to myself, Andrew Granville, Robin Pemantle, and Prasad Tetali.

New Exciting Approaches to Particle Scattering Amplitudes

Series
Math Physics Seminar
Time
Wednesday, September 28, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Marcus Nanotech Conference
Speaker
Henriette Elvang – Physics Department, University of Michigan

Please Note: Hosted by Predrag Cvitanovic, School of Physics

Particle scattering processes at experiments such as the Large Hadron Collider at CERN are described by scattering amplitudes. In quantum field theory classes, students learn to calculate amplitudes using Feynman diagram methods. This is a wonderful method for a process like electron + positron -> muon^- + muon^+, but it is a highly challenging for a process like gluon+gluon -> 5 gluons, which requires 149 diagrams even at the leading order in perturbation theory. It turns out, however, that the result for such gluon scattering processes is remarkably simple, in some cases it is just a single term! This has lead to new methods for calculating scattering amplitudes, and it has revealed that amplitudes have a surprisingly rich mathematical structure. The applications of these new methods range from calculation of processes relevant for LHC physics to theoretical explorations of quantum gravity. I will give a pedagogical introduction to these new approaches to scattering theory and their applications, not assuming any prior knowledge of quantum field theory or Feynman rules.

Algebraic and geometric aspects of Braid Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, September 28, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Marta Aguilera – Georgia Tech
In this talk I define the braid groups, its Garside structure, and its application to solve the word and conjugacy problems. I present a braid group with $n$ strands as the mapping class group of the disk with $n$ punctures, $\mathbb{D}^2-\{p_1\ldots p_n\}$, and a classification of surface homeomorphisms by the Nielsen Thurston theorem. I will also discuss results that require algebraic and geometric tools.

Wavelet analysis on a metric space

Series
Analysis Seminar
Time
Wednesday, September 28, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tuomas Hytonen – University of Helsinki
Expansion in a wavelet basis provides useful information ona function in different positions and length-scales. The simplest example of wavelets are the Haar functions, which are just linearcombinations of characteristic functions of cubes, but often moresmoothness is preferred. It is well-known that the notion of Haarfunctions carries over to rather general abstract metric spaces. Whatabout more regular wavelets? It turns out that a neat construction canbe given, starting from averages of the indicator functions over arandom selection of the underlying cubes. This is yet anotherapplication of such probabilistic averaging methods in harmonicanalysis. The talk is based on joint work in progress with P. Auscher.

Topology and prediction of RNA pseudoknots

Series
Mathematical Biology Seminar
Time
Wednesday, September 28, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Christian Reidys – Dept. of Mathematics & Computer Science, University of Southern Denmark
In this talk we present the natural topological classification of RNA structures in terms of irreducible components that are embedable in surfaces of fixed genus. We add to the conventional secondary structures four building blocks of genus one in order to construct certain structures of arbitrarilyhigh genus. A corresponding unambiguous multiple context free grammar provides an efficient dynamic programming approach for energy minimization, partition function, and stochastic sampling. It admits a topology-dependent parametrization of pseudoknot penalties that increases the sensitivity and positive predictive value of predicted base pairs by 10-20% compared to earlier approaches.

Electric current in the presence of a Gaussian Thermostat

Series
Regular Seminars
Time
Tuesday, September 27, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Federico Bonetto – SoM, Georgia Tech
I will review numerical and analytic results on a system consistingof one or many particles moving in a chaotic billiard under the influence on an electric field and a Gaussian thermostat.

Numerical Algorithms for Dual Bases of Positive-Dimensional Ideals

Series
Algebra Seminar
Time
Monday, September 26, 2011 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert Krone – Georgia Tech
An ideal of a local polynomial ring can be described by calculating astandard basis with respect to a local monomial ordering. However if we areonly allowed approximate numerical computations, this process is notnumerically stable. On the other hand we can describe the ideal numericallyby finding the space of dual functionals that annihilate it. There areseveral known algorithms for finding the truncated dual up to any specifieddegree, which is useful for zero-dimensional ideals. I present a stoppingcriterion for positive-dimensional cases based on homogenization thatguarantees all generators of the initial monomial ideal are found. This hasapplications for calculating Hilbert functions.

Efficient Numerical Algorithms for Image Reconstruction with Total Variation Regularization and Applications in clinical MRI

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 26, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xiaojing Ye – School of Mathematics, Georgia Tech
 We will discuss the recent developments of fast image reconstrcution with total variation (TV) regularization whose robustness has been justfied by the theory of compressed sensing. However, the solution of TV based reconstruction encounters two main difficulties on the computational aspect of many applications: the inversion matrix can be large, irregular, and severely ill-conditioned, and the objective is nonsmooth. We introduce two algorithms that tackle the problem using variable splitting and optimized step size selection. The algorithms also provide a general framework for solving large and ill-conditioned linear inversion problem with TV regularization. An important and successful application of TV based image reconstruction in magnetic resonance imaging (MRI) known as paratially parallel imaging (PPI) will be discussed. The numerical results demonstrate significantly improved  efficiency and accuracy over the state-of-the-arts. 

Pages