Noticias en español
An SDE perspective on stochastic convex optimization.
Abstract: We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a stochastic differential equation where the drift term is minus the gradient of the objective function and the diffusion term is either bounded or square-integrable. In this context, under Lipschitz continuity of the gradient, our first main result shows almost sure weak convergence of the trajectory process towards a minimizer of the objective...
Read MoreAnalysing necessary optimality conditions for a time optimal control problem in Wasserstein spaces.
Abstract: We are interested in developing necessary optimality conditions in the form of a Pontryagin maximum principle for the minimal time Bolza optimal control problem with constraints in the final time. In this problem, the dynamic is given by a non-local continuity equation in the Wasserstein space of probability measures, the set of controls are taken in open-loop form and the set of constraints is represented by functional inequalities applied to the terminal time. To this end, we relate the main challenges of this problem from which a fair amount is accounted by the fact that...
Read MoreUndestanding the APS boundary condition for the zero modes of the Dirac operator.
Abstract: How many zero modes (states with zero energy) are there of the Dirac operator with magnetic field in two dimensions? This question was answered by Aharonov and Casher in 1979 for the case of plane. They showed that this number is given by the flux of the magnetic field, more precisely the integer part of it. Moreover, the zero modes are chiral, aligning with the direction of the magnetic field. We investigate the same problem for the case of a plane wih holes considering the Atiyah–Patodi–Singer (APS) boundary condition (BC). This BC was introduced by APS in their...
Read MoreDeterminando la fiabilidad de instrumentos de observación para la enseñanza y el aprendizaje mediante la Teoría de la Generalizabilidad
Resumen: En la presentación daré una breve visión general sobre la medición de la calidad de la enseñanza con calificaciones de observadores, que se han utilizado ampliamente en la investigación sobre la eficacia educativa durante la última década. A continuación, presentaré un marco estadístico que ayuda a dar sentido a los datos resultantes de la observación en el aula, denominado Teoría de la Generalizabilidad (TG). Ambas partes de la presentación estarán repletas de ejemplos de datos reales procedentes de proyectos de investigación sobre educación...
Read More“Estimación Del Disconfort Térmico En La Ciudad De Santiago Mediante Modelación Espacio – Temporal De Índices Termales Durante El Periodo Estival De Los Años 2010 – 2020”
Resumen: Debido a la variabilidad en la configuración urbana en la ciudad de Santiago de Chile durante los últimos años, es probable que aumente la población expuesta a mayores niveles de estrés térmico durante los días más calurosos de verano. Para abordar este problema de salud pública, este trabajo propone una metodología para representar la variación espacial y temporal de tres índices de estrés térmico en Santiago. A partir de datos meteorológicos y productos satelitales MODIS se espacializan series de tiempo de variables ambientales para el cálculo de los índices WBGT, DI y ESI....
Read MoreSingular limits arising in mechanical models of tumor growth.
Abstract: The mathematical modelling of cancer has been increasingly applying fluid-dynamics concepts to describe the mechanical properties of tissue growth. The bio-mechanical pressure plays a central role in these models, both as the driving force of cell movement and as an inhibitor of cell proliferation. In this talk, I will present how it is possible to build a bridge between models that have different pressure-velocity or pressure-density relations. In particular, I will focus on the inviscid limit from a visco-elastic model to a Darcy’s law-based model, and the incompressible limit...
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