Noticias en español
Identifying the deviator.
Abstract: Alice and Bob control a random walk: alternately, each of them flips a fair coin, is supposed to report the outcome, and the random work advances according to the report. Suppose that the random walk did not return to the origin infinitely often. We suspect that one of Alice and Bob misreported the outcomes of her or his coin. Can we identify the deviator? More generally, several players are supposed to follow a prescribed profile of strategies (e,g, select each of Right and Left with probability 1/2). If they follow this profile, they will reach a given target (e.g., the...
Read MoreSimultaneous identification of piecewise constant sound speed and initial data for the photoacoustic tomography problem
RESUMEN: Photoacoustic tomography is a biomedical imaging modality whose goal is to reconstruct a map of absorption in biological tissue in order to identify different structures, and in particular to determine whether they are healthy or not. This modality has multiple applications, including tumor detection, breast cancer diagnosis, imaging of blood vessel networks, and measuring blood oxygenation. In this talk, we will focus on acoustic inversion—one of the steps of photoacoustic tomography—in the case where the speed of sound is an unknown piecewise constant function....
Read MoreOptimización del diseño minero considerando la sustentabilidad de la operación
Abstract: El diseño de una operación minera es una decisión estratégica que define la geometría de la explotación, condicionando el acceso al mineral, los costos e inversiones necesarios para esto. El diseño define el método de extracción, el manejo de materiales y por lo tanto los equipos. Más aún, el diseño minero incluye la infraestructura dentro y fuera de la mina, incluyendo plantas tratamiento, botaderos y relaves. Dada esta relevancia, son múltiples los esfuerzos que se han realizado para encontrar un diseño óptimo. Sin embargo, a pesar de los avances en modelos y algoritmos para...
Read MoreSpectral Theory of Substitutions.
RESUMEN: Given a finite alphabet, a substitution is a rule that assigns to each letter a nontrivial word over the same alphabet. Although they are simple combinatorial objects, substitutions arise across a wide range of mathematical disciplines, including combinatorics on words, theoretical computer science (automata theory), number theory (Diophantine approximation, multiplicative functions), mathematical physics (quasicrystals), and ergodic theory (induced systems). In this talk, we will review recent work on the spectral properties of substitution dynamical systems, as well as other...
Read MoreDiameter and mixing time of the giant component in the percolated hypercube.
Resumen: The d-dimensional binary hypercube is the graph whose vertices represent the binary vectors of length d and two vertices are adjacent if they differ in a single coordinate. The percolated hypercube (where every edge is retained independently with probability p) is a classic model in random graph theory. In this talk, we are going to survey some of the history of the model and discuss recent estimates of the mixing time of the lazy simple random walk and the diameter of the giant component in a supercritical percolated hypercube. Based on a joint work with Michael Anastos, Sahar...
Read MoreDrift parameter estimation for a fractional interacting particle system.
Resumen: We consider a system of interacting particles with Lipschitz continuous drift functions, driven by additive fractional Brownian motions with H in [1/2, 1). For this system, we address the drift parameter estimation problem from continuous observations over a fixed time interval, assuming that the drift depends linearly on an unknown parameter vector. We propose estimators inspired by the least squares approach, demonstrate their consistency and asymptotic normality as the number of particles tends to infinity, and present a numerical study illustrating our findings. The proofs rely...
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