Noticias en español
Clearing-out of dipoles for minimisers of 2-dimensional discrete energies with topological singularities.
Abstract: A key question in the analysis of discrete models for material defects, such as vortices in spin systems and superconductors or isolated dislocations in metals, is whether information on boundary energy for a domain can be sufficient for controlling the number of defects in the interior. We present a general combinatorial dipole-removal argument for a large class of discrete models including XY systems and screw dislocation models, allowing to prove sharp conditions under which controlled flux and boundary energy guarantee tohave minimizers with zero or one charges in the interior....
Read MoreCaracterización de relaciones regionalmente proximales mediante el semigrupo envolvente.
RESUMEN: El estudio de los sistemas de orden d ha despertado gran interés por sus aplicaciones en sistemas dinámicos, teoría de números y combinatoria. Un aspecto interesante es el estudio de las propiedades algebraicas de sus semigrupos envolventes. En esta charla se abordará la conexión entre el semigrupo envolvente y la relación regionalmente proximal, la cual define a los sistemas de orden d. En particular, se presentará una caracterización algebraica de estas relaciones. Luego mencionaré aplicaciones de estos resultados a la estructura de los cubos dinámicos y al estudio de los...
Read MoreMachine learning-driven COVID-19 early triage and large-scale testing strategies based on the 2021 Costa Rican Actualidades survey.
Resumen: Due to resource limitations, the COVID-19 pandemic presented substantial challenges for large-scale testing. Traditional approaches often fail to balance detection rates with limited reagents and laboratory capacity. In this work we introduced a machine learning–driven triage framework to stratify individuals by contagion risk and deploy adaptive testing protocols accordingly. We adapted the strategies according to the characteristics of RT-PCR tests, which offer high sensitivity, but they require specialized laboratories, and alternative tests, which trade speed for lower accuracy....
Read MoreColumn Generation and the Feature Selection Problem.
Abstract: Column generation is a well-known decomposition method to solve linear and mixed integer problems with a large number of variables. A similar column generation decomposition method can be constructed for conic optimization problems. In this talk we present work that explores whether this can be a competitive solution method for the continuous relaxation of the feature selection problem.
Read MoreComputer-assisted proof of robust transitivity.
RESUMEN: A smooth dynamical system is transitive if it has a dense orbit, loosely meaning that it has some chaos in a topological sense. If this property holds for all diffeomorphisms in a C¹-neighborhood, we say that systems in this neighborhood are robustly transitive. By Bonatti, Diaz and Pujals (2003), robustly transitive diffeomorphisms are volume hyperbolic, and thus they have positive topological entropy, being chaotic in a strict sense and in a robust way. Robust properties are key in classifying smooth dynamical systems, and they are also desirable to model applications. We develop...
Read MoreThe Haagerup property.
Abstract: The Haagerup property is an analytic property of groups that generalises amenability. It originated from the study of C*-algebras, and it has found applications in several areas of mathematics, including harmonic analysis, geometric group theory, topology, and ergodic theory. This talk will consist in an introduction to this property and its connections to group actions on Banach spaces.
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