Noticias en español
“On the non-local Lazer-McKenna conjecture with superlinear potential under a partial symmetry condition on the domain: Critical and supercritical cases”
Abstract: “In 1983 A. Lazer and P.J. McKenna conjectured that the Ambrosetti-Prodi type problems have an unbounded number of solutions as a defined parameter grows to infinity. There were not results on this conjecture, other than the one dimensional case, until 2003 by Breuer . In this talk we will see the existence of a family of solutions indexed by a real number for the non-local problem with superlinear potential under a partial symmetry condition on the domain”
Read MoreUnderstanding physical mixing processes via transfer operator approach
ABSTRACT: Industrial and chemical mixing processes of various kinds occur throughout nature and are vital in many technological applications.In the context of discrete dynamical systems, the transfer operator approach has been shown as a powerful tools from both theoretic and numerical viewpoint. In this talk, I will use a toy model (i.e., the one dimensional stretch and fold map) as an example to provide a brief introductionon the relationships between the spectral properties of the associated transfer operator and the estimations of the optimal mixing rate of the mixing process. Moreover,...
Read MoreMaximizing Covered Area in a Euclidean Plane with Connectivity Constraint
Abstract: Given a set of unit disks in the plane and an integer K, the maximum area connected subset problem asks for a subset of K disks covering the maximum area, under the constraint that the area covered by the K disks is connected. This problem is motivated by wireless router deployment and is a special case of maximizing a submodular function under a connectivity constraint.
Read MoreFast Rates for Unbounded Losses: from ERM to Generalized Bayes
Abstract: I will present new excess risk bounds for randomized and deterministic estimators, discarding boundedness assumptions to handle general unbounded loss functions like log loss and squared loss under heavy tails. These bounds have a PAC-Bayesian flavor in both derivation and form, and their expression in terms of the information complexity forms a natural connection to generalized Bayesian estimators. The bounds hold with high probability and a fast $\tilde{O}(1/n)$ rate in parametric settings, under the recently introduced central’ condition (or various weakenings of this condition...
Read MoreProphet Secretary Through Blind Strategies
Abstract: In the classic prophet inequality, a problem in optimal stopping theory, samples from independent random variables arrive online. A gambler that knows the distributions, but cannot see the future, must decide at each point in time whether to stop and pick the current sample or to continue and lose that sample forever. The goal of the gambler is to maximize the expected value of what she picks and the performance measure is the worst case ratio between the expected value the gambler gets and what a prophet, that sees all the realizations in advance, gets. We study when the samples...
Read MoreA Linear Programming Based Approach to the Steiner Tree Problem with a Fixed Number of Terminals
Abstract: We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our main result is that the linear programming (LP) relaxation of each IP is integral so that it can be solved as a linear program. However, the number of IPs grows exponentially with the number of terminals in the Steiner tree. As a consequence, we are able to solve the Steiner tree problem by solving a polynomial number of LPs, when the number of...
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