Noticias en español
Thermodynamics-informed Neural Networks (THINNs).
Abstract: Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that is consistent with the underlying fluctuation structure, as characterized by a large deviations principle. This approach yields a novel formulation of PINNs in which the penalty term is chosen to penalize improbable deviations, rather than being selected heuristically. The resulting...
Read MoreChen-Chvátal Conjecture in Graphs and Hypergraphs.
Abstract: It is well known that a set of n non-collinear points in the Euclidean plane determines at least n distinct lines. In 2008, Chen and Chvátal conjectured that this result extends to arbitrary finite metric spaces with an appropriate definition of line. In this talk, we present a survey of this conjecture, outlining known results in the contexts of metric spaces, hypergraphs, and graphs
Read MoreIdentifying 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...
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