Seminars and Colloquia by Series

Risk Sensitivity of Price of Anarchy under Uncertainty

Series
ACO Student Seminar
Time
Friday, March 15, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Georgios Piliouras – ECE, Georgia Tech
In algorithmic game theory, the price of anarchy framework studies efficiency loss in decentralized environments. In optimization and decision theory, the price of robustness framework explores the tradeoffs between optimality and robustness in the case of single agent decision making under uncertainty. We establish a connection between the two that provides a novel analytic framework for proving tight performance guarantees for distributed systems in uncertain environments.We present applications of this framework to novel variants of atomic congestion games with uncertain costs, for which we provide tight performance bounds under a wide range of risk attitudes. Our results establish that the individual's attitude towards uncertainty has a critical effect on system performance and should therefore be a subject of close and systematic investigation.

1-bit compressed sensing, sparse binary regression, and random hyperplane tessellations

Series
Stochastics Seminar
Time
Thursday, March 14, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Yaniv Plan – University of Michigan
1-bit compressed sensing combines the dimension reduction of compressed sensing with extreme quantization -- only the sign of each linear measurement is retained. We discuss recent convex-programming approaches with strong theoretical guarantees. We also discuss connections to related statistical models such as sparse logistic regression. Behind these problems lies a geometric question about random hyperplane tessellations. Picture a subset K of the unit sphere, as in the continents on the planet earth. Now slice the sphere in half with a hyperplane, and then slice it several times more, thus cutting the set K into a number of sections. How many random hyperplanes are needed to ensure that all sections have small diameter? How is the geodesic distance between two points in K related to the number of hyperplanes separating them? We show that a single geometric parameter, the mean width of K, governs the answers to these questions.

A dynamic data structure for counting subgraphs in sparse graphs

Series
Graph Theory Seminar
Time
Thursday, March 14, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Vojtech Tuma – Charles University
We present a dynamic data structure representing a graph G, which allows addition and removal of edges from G and can determine the number of appearances of a graph of a bounded size as an induced subgraph of G. The queries are answered in constant time. When the data structure is used to represent graphs from a class with bounded expansion (which includes planar graphs and more generally all proper classes closed on topological minors, as well as many other natural classes of graphs with bounded average degree), the amortized time complexity of updates is polylogarithmic. This data structure is motivated by improving time complexity of graph coloring algorithms and of random graph generation.

Hamilton-Jacobi Equations and Front Motion in Flows

Series
School of Mathematics Colloquium
Time
Thursday, March 14, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jack Xin – UC Irvine
Front propagation in fluid flows arise in power generation of automobile engines, forest fire spreading, and material interfaces of solidification to name a few. In this talk, we introduce the level set formulation and the resulting Hamilton-Jacobi equation, known as G-equation in turbulent combustion. When the fluid flow has enough intensity, G-equation becomes non-coercive and non-linearity no longer dominates. When front curvature and flow stretching effects are included, the extended G-equation is also non-convex. We discuss recent progress in analysis and computation of homogenization and large time front speeds in cellular flows (two dimensional Hamiltonian flows) from both Lagrangian and Eulerian perspectives, and the recovery of experimental observations from the G-equations.

General Faculty Meeting

Series
Other Talks
Time
Wednesday, March 13, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
William Trotter – School of Mathematics, Georgia Tech

Estimates of the Discrepancy Function in Exponential Orlicz Spaces

Series
Analysis Seminar
Time
Wednesday, March 13, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gagik Amirkhanyan – Georgia Tech
For dimensions n greater than or equal to 3, and integers N greater than 1, there is a distribution of points P in a unit cube [0,1]^{n}, of cardinality N, for which the discrepancy function D_N associated with P has an optimal Exponential Orlicz norm. In particular the same distribution will have optimal L^p norms, for 1 < p < \infty. The collection P is a random digit shift of the examples of W.L. Chen and M. Skriganov.

Teichmuller polynomials for a fibered face of the Thurston norm ball

Series
Geometry Topology Student Seminar
Time
Wednesday, March 13, 2013 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyunshik Shin – Georgia Tech
We will briefly talk about the introduction to Thruston norm and fibered face theory. Then we will discuss polynomial invariants for fibered 3-manifolds, so called Teichmuller polynomials. I will give an example for a Teichmuller polynomial and by using it, determine the stretch factors (dilatations) of a family of pseudo-Anosov homeomorphisms.

On the breakdown mechanisms of Fiberwise Hyperbolic Invariant Tori in skew product systems. Numerical and theoretical results.

Series
CDSNS Colloquium
Time
Tuesday, March 12, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jordi-Lluis Figueras Romero – University of Uppsala –
In this talk we will first present several breakdown mechanisms of Uniformly Hyperbolic Invariant Tori (FHIT) in area-preserving skew product systems by means of numerical examples. Among these breakdowns we will see that there are three types: Hyperbolic to elliptic (smooth bifurcation), the Non-smooth breakdown and the Folding breakdown. Later, we will give a theoretical explanation of the folding breakdown. Joint work with Alex Haro.

Natural and perturbed dynamics about Trojan bodies

Series
CDSNS Colloquium
Time
Tuesday, March 12, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Marta Ceccaroni – University of Rome (Tor Vergata) –
An analysis of the dynamics of a mass-less spacecraft (or point mass) around an in-homogeneousTrojan body in a system composed of three primaries lying at the vertexes of an equilateral triangle, with their mutual positions fixed over the course of the motion is here presented. To this end two suitable models are identified to represent the system, depending on the distance from the primary. The first model, adopted for use close to the asteroid, where the dynamics is dominated by this sole body, is the Restricted Two Body Problem. In this model the in-homogeneities of the asteroid are taken into account as they have a dominant effect on the dynamics of the spacecraft. The second model is the Lagrangian Circular Restricted Four Body Problem (CR4BP), which is adopted far from the asteroid, where the gravitational perturbations of the Sun and Jupiter are dominant while the in-homogeneities of the asteroid are negligible. Low-thrust propulsion perturbations are incorporated into this model. The possibility to determine the range of validity of each model using an application of a Weak Stability Boundary (WSB) theory is investigated and applied. Applications are shown for the main example of Lagrangian configuration in the Solar system, the Sun-Jupiter-Trojan-spacecraft system.

Motion Estimation and Imaging of Complex Scenes with Synthetic Aperture Radar

Series
Job Candidate Talk
Time
Tuesday, March 12, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thomas Callaghan – Rice University
In synthetic aperture radar (SAR) imaging, two important applications are formation of high resolution images and motion estimation of moving targets on the ground. In scenes with both stationary targets and moving targets, two problems arise. Moving targets appear in the computed image as a blurred extended target in the wrong location. Also, the presence of many stationary targets in the vicinity of the moving targets prevents existing algorithms for monostatic SAR from estimating the motion of the moving targets. In this talk I will discuss a data pre-processing strategy I developed to address the challenge of motion estimation in complex scenes. The approach involves decomposing the SAR data into components that correspond to the stationary targets and the moving targets, respectively. Once the decomposition is computed, existing algorithms can be applied to compute images of the stationary targets alone. Similarly, the velocity estimation and imaging of the moving targets can then be carried out separately.The approach for data decomposition adapts a recent development from compressed sensing and convex optimization ideas, namely robust principle component analysis (robust PCA), to the SAR problem. Classicalresults of Szego on the distribution of eigenvalues for Toeplitz matrices and more recent results on g-Toeplitz and g-Hankel matrices are key for the analysis. Numerical simulations will be presented.

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