Noticias en español
Almost sure convergence in evolutionary models with vanishing mutations.
Abstract: We analyze the long-term behavior of evolutionary models where mutations gradually vanish over time. Our focus is on the almost sure convergence of the empirical occupation measure—that is, the time-averaged distribution of states—as the mutation parameter decays in a controlled manner. Under suitable conditions, we prove that this measure converges almost surely to a specific invariant distribution of a limiting Markov chain, while also establishing explicit convergence rates. Our analysis is carried out within a class of time-inhomogeneous Markov chains on a finite state space,...
Read MoreBilevel Hyperparameter Learning for Nonsmooth Regularized Imaging and ML Models.
Abstract: We study a bilevel optimization framework for hyperparameter learning in variational models, focusing on sparse regression and classification. Specifically, we use a weighted elastic-net regularizer, where feature-wise penalties are learned through a bilevel formulation. Our main contribution is a Forward–Backward (FB) reformulation of the nonsmooth lower-level problem that preserves its minimizers. This yields a bilevel objective composed with a locally Lipschitz solution map, enabling the use of generalized subdifferential calculus and efficient subgradient-based methods....
Read MoreCreación de software predictivo para emergencias marítimas: experiencias y proyecciones.
Durante la exposición se presentará el desarrollo de un software de soporte operativo para emergencias marítimas, abordando tanto aspectos técnicos —como la modelación hidrodinámica, la generación de algoritmos de automatización y optimización, y la incorporación de infraestructuras informáticas en la nube— como dimensiones sociales y comerciales del proyecto. El objetivo es compartir las experiencias adquiridas durante el proceso de desarrollo tecnológico y abrir un espacio para el diálogo y la reflexión sobre cómo mejorar los sistemas institucionales, técnicos y de financiamiento que...
Read MoreFully Stochastic Reconstruction for Inverse Radiative Transport.
RESUMEN: The Radiative Transport Equation (RTE) arises in applications in tomography based on photon propagation. Whereas it has a direct solution for non-scattering media it is complicated to solve for cases involving significant scattering. In these cases, Monte Carlo (MC) methods are a widely applicable and accurate class of modelling techniques that converge to the deterministic solution in the limit of an infinite number simulated photons. Classical methods for solving the inverse problem that involve a non-linear optimisation approach can be combined with advances in stochastic...
Read MoreEl borde de Poisson del grupo de Thompson T no es el círculo.
RESUMEN: Dado un grupo numerable G equipado de una medida de probabilidad μ, el borde de Poisson es un G-espacio de probabilidad que parametriza todas las funciones μ-armónicas acotadas sobre G. Dado una acción “natural” de G en un espacio μ-estacionario, uno puede preguntarse si esta acción es un modelo para el borde de Poisson de (G,μ). Cuando G es un grupo actuando proximalmente en el círculo S1, el círculo dotado de su única medida μ-estacionaria es un ejemplo de una tal acción, y para subgrupos discretos de PSL2(R) ésta coincide con el borde de Poisson de (G,μ). Probamos que...
Read MoreFinding (many) prescribed mean curvature surfaces in the presence of a strictly stable minimal surfaces.
Abstract: In the last decades, there has been fascinating progress in the variational theory for the area functional – that is, the codimension 1 volume – using tools from PDEs and Geometric Measure Theory, and in connection with the problem of finding prescribed mean curvature (PMC) hypersurfaces. In this talk, we describe some recent contributions from joint work with Jared Marx-Kuo (Rice University) in which we construct infinitely many PMCs for a large class of prescribing functions in a compact Riemannian manifold containing a strictly stable minimal hypersurface.
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