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.
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.
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.
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.
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.
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.
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.
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.