Noticias en español
Construcción lookdown a un modelo Moran con Banco de semillas.
Abstract: En esta plática abordaremos un trabajo en conjunto con M.C. Fittipaldi (FC,UNAM) y A. Gonzáles Casanova (IMATE, UNAM, UC, Berkeley) en el cual estudiamos una representación alterna al modelo de Moran con Banco de semillas. Se mostrará que bajo la misma distribución inicial intercambiable ambos modelos son iguales en ley. Dicha construcción nos permitirá profundizar en el estudio del tiempo hasta el ancestro en común de una muestra de individuos (TMRCA). Adicionalmente traduciremos este resultado en el tiempo de fijación de un mutante en la población.
Read MoreEnergy-Efficient Distributed Algorithms for Synchronous Networks.
Abstract: We study the design of energy-efficient algorithms for well known distributed models of computation: the LOCAL and CONGEST models. Specifically, as a measure of complexity, we consider the maximum, taken over all the edges, or over all the nodes, of the number of rounds at which an edge, or a node, is activein the algorithm. We first show that every Turing-computable problem has a CONGEST algorithm with constant node-activation complexity, and therefore constant edge-activation complexity as well. That is, every node (resp., edge) is active in sending (resp., transmitting) messages...
Read MoreIn this apportionment lottery, the House always wins.
Abstract Apportionment is the problem of distributing h indivisible seats across states in proportion to the states’ populations. In the context of the US House of Representatives, this problem has a rich history and is a prime example of interactions between mathematical analysis and political practice. Grimmett suggested to apportion seats in a randomized way such that each state receives exactly their proportional share qᵢ of seats in expectation (ex ante proportionality) and receives either ⌊qᵢ⌋ or ⌈qᵢ⌉ many seats ex post (quota). However, there is a vast space of randomized...
Read MoreOn the collapse of the local Rayleigh condition for the hydrostatic Euler equations.
Abstract: The hydrostatic Euler equations are derived from the incompressible Euler equations by means of the hydrostatic approximation. Among the different stability criteria that arise in the study of linear stability for the incompressible Euler equations, we can mention Rayeligh’s stability criterion, which gives rise to the local Rayleigh condition. Linear and nonlinear instability of the hydrostatic Euler equations around certain shear flows is well-known, as well as the finite time blow-up of certain solutions that do not satisfy the local Rayleigh condition. On the other hand,...
Read MoreJoint ergodicity beyond polynomials
RESUMEN: In this talk we will present recent joint ergodicity results for various non-polynomial functions of polynomial growth. We will mention the historical context of the question, and the techniques we use, which combine recent works of Frantzikinakis and Tsinas with the machinery of seminorms for multiple averages for polynomial iterates that we have developed in a previous work with A. Ferre-Moragues, A. Koutsogiannis, and W. Sun. If time permits, we will provide comments on open questions and current ongoing work. This is joint work with A. Koutsogiannis and W. Sun.
Read MoreMarchas aleatorias activadas críticas.
Resumen: El modelo de marchas aleatorias activadas (Activated Random Walks, ARW) es un sistema de partículas introducido con el fin de estudiar la criticalidad auto-organizada. Este consiste en una familia de partículas que se mueven aleatoriamente y que pueden dormirse espontáneamente, lo que detiene el movimiento. La interacción ocurre cuando una partícula activa visita a una durmiendo, lo que gatilla que la partícula dormida se active y continúe su movimiento. Este modelo presenta una transición de fase en términos de la densidad de partículas. Si hay muchas partículas la actividad en el...
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