Noticias en español
Algunas soluciones bi y tridimensionales de mapas armónicos inspirados en la biología y la astrofísica.
Resumen: Presentamos algunas soluciones exactas y aproximadas de mapas armónicos débiles de las ecuaciones no lineales de Frank-Oseen provenientes de la teoría de cristales líquidos y sus posibles aplicaciones en el marco de la identificación no invasiva de la dirección de fibras musculares en el corazón humano, así como la sorprendente similitud que tienen con ciertas estructuras en en campo de la astrofísica.
Read MoreThe multi-type bisexual Galton-Watson branching process.
Resumen: The bisexual Galton-Watson process [Daley, ’68] is an extension of the classical Galton-Watson process, but taking into account the mating of females and males, which form couples that can accomplish reproduction. Properties such as extinction conditions and asymptotic behaviour have been studied in the past years, but multi-type versions have only been treated in some particular cases. In this work we deal with a general multi-dimensional version of Daley’s model, where we consider different types of females and males, which mate according to a “mating function”....
Read MoreSelection and Ordering Policies for Hiring Pipelines via Linear Programming.
Abstract: Motivated by hiring pipelines, we study three selection and ordering problems in which applicants for a finite set of positions must be interviewed or made offers to. There is a finite time budget for interviewing or making offers, and a stochastic realization after each decision, leading to computationally-challenging problems. In the first problem, we study sequential interviewing and show that a computationally-tractable, non-adaptive policy that must make offers immediately after interviewing is near-optimal, assuming offerees always accept their offers. In the second problem,...
Read MoreReversal in the Stationary Prandtl Equations.
Abstract: We investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by spatio-temporal regions in which $u > 0$ and $u < 0$. The classical point of view of regarding the Prandtl equations as an evolution $x$ completely breaks down. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. Joint work with Nader Masmoudi.
Read MoreWeak Ergodicity Approach to POMDPs.
Abstract: This seminar introduces Partially Observable Markov Decision Processes (POMDPs), emphasizing their relationship with decision problems and decidability. We then explore a novel theoretical class of POMDPs based on a weak ergodicity property. The seminar concludes by identifying necessary conditions for POMDPs to exhibit this characteristic, bridging the gap between this theoretical result and its potential practical implementation.
Read MoreZero-sum random games on graphs.
Resumen: We consider two adversary players that move in turn a token along the edges of some graph. Player 1 has to pay a random cost to Player 2 for each edge that is crossed by the token. We study the value of the game with average cost, when the duration goes to infinity, and establish a connection with oriented percolation.
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