Seminars

Uniquely ergodic subshifts over compactifications of the naturals

Event Date: Jan 08, 2024 in Dynamical Systems, Seminars

RESUMEN: In this talk, we will discuss one-dimensional substitution subshifts over (infinite) compact alphabets and their dynamical properties. As a motivating class, we will focus on shifts generated by a parametrised family of substitutions on certain compactifications of the natural numbers. We will provide a general checkable condition for unique ergodicity that relies on compactness properties of the substitution operator, which the analogue of the substitution matrix for infinite alphabets.

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An SDE perspective on stochastic convex optimization.

Event Date: Dec 20, 2023 in Optimization and Equilibrium, Seminars

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...

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Analysing necessary optimality conditions for a time optimal control problem in Wasserstein spaces.

Event Date: Dec 20, 2023 in Optimization and Equilibrium, Seminars

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...

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Undestanding the APS boundary condition for the zero modes of the Dirac operator.

Event Date: Dec 11, 2023 in Differential Equations, Seminars

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...

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Determinando la fiabilidad de instrumentos de observación para la enseñanza y el aprendizaje mediante la Teoría de la Generalizabilidad

Event Date: Dec 12, 2023 in Education, Seminars

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...

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“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”

Event Date: Dec 01, 2023 in Ciclo de Seminarios conjuntos CopLAC-Chile, Seminars

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....

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