Noticias en español
Estimación Adaptativa en Modelos de Regresión Funcional Asociado a Proceso de Wiener.
Resumen: En esta charla, estudiaremos métodos de suavizamiento para estimar funciones no-paramétricas. Veremos cómo elegir los parámetros de suavizamiento con el objetivo de tener estimadores óptimos. Más específicamente, introduciremos el método de Goldenshluger-Lepski (2011) que permite obtener estimadores que se adaptan a la regularidad de la función. Mostraremos cómo extender este método en el caso de la regresión funcional donde la variable regresora es un proceso de Wiener. Definiremos una familia de estimadores para la función de regresión basándose en la descomposición de Wiener...
Read MoreDecomposition of Probability Marginals for Security Games in Abstract Networks and Ideal Clutters.
Abstract: Consider a set system on a finite ground set E, where each set P in the system is equipped with a required hitting probability r(P) and each element e of E has a probability marginal p(e). We study the question whether the marginals can be decomposed into a distribution over all subsets of E such that the resulting random set intersects each set P from the system with probability at least r(P). A simple necessary condition is that for every set P in the system, the sum of the marginals of elements in P is at least r(P). Extending a result by Dahan, Amin, and Jaillet (Mathematics of...
Read MoreMean equicontinuity – beyond minimality.
Abstract:: In this talk we present recent developments and new results in the study of mean equicontinuity and weak mean equicontinuity in the context of countable discrete amenable groups, such as a characterization in terms of spectral theory. It is known that the notions of mean eq. and weak mean eq. do not depend on the process of averaging (the Følner sequence), whenever the action is minimal, or the acting group is Abelian. However, we present an example of a (non-minimal, but transitive) action where mean equicontinuity and weak mean equicontinuity do depend on the process of...
Read MoreExistence of quasi-stationary distributions for downward skip-free Markov chains.
Abstract: I talk about existence of a quasi-stationary distribution for downward skip-free continuous-time Markov chains on non-negative integers stopped at zero. The scale function for these processes is introduced and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller’s classification of the boundary for birth-and-death processes.The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.
Read MoreUniform a priori estimates for positive solutions of the Lane-Emden equation and system in the plane.
Abstract A few years ago we proved that positive solutions of the superlinear Lane-Emden equation in a two-dimensional smooth bounded domain are bounded independently of the exponent in the equation. Apart from being interesting in itself, this information plays a pivotal role in the asymptotic study of solutions for large exponents, as well as contributes to the old and hard conjecture of uniqueness of positive solutions in a convex domain. We recently took up a similar study for the Lane-Emden system and discovered that, contrary to initial intuition, the boundedness fails in general. This...
Read MoreCombinatorial Contracts.
Abstract: An emerging frontier in Algorithmic Game Theory is Algorithmic Contract Theory, which studies the classic hidden-action principal-agent problem of contract theory through the computational lens. In this talk, I will present three basic ways in which the problem can be combinatorial and survey both hardness and poly-time (approximation) results. The analysis will uncover some surprising connections (but also fundamental differences) to combinatorial auctions.
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