Multidimensional Apportionment Through Discrepancy Theory. & Determination of functions by the metric slope.

Event Date: Aug 24, 2022 in Optimization and Equilibrium, Seminars

Speaker 1: Víctor Verdugo Title: Multidimensional Apportionment Through Discrepancy Theory. Abstract: Deciding how to allocate the seats of a house of representatives is one of the most fundamental problems in the political organization of societies, and has been widely studied over already two centuries. The idea of proportionality is at the core of most approaches to tackle this problem, and this notion is captured by the divisor methods, such as the Jefferson/D’Hondt method. In a seminal work, Balinski and Demange extended the single-dimensional idea of divisor methods to the...

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On large solutions for fractional Hamilton-Jacobi equations.

Event Date: Aug 25, 2022 in Differential Equations, Seminars

Abstract: In this talk I will report some multiplicity results for large solutions of fractional Hamilton-Jacobi equations posed on a bounded domain, subject to exterior Dirichlet conditions. We construct large solutions using the method of sub and supersolutions, following the classical approach of J.M. Lasry and P.L. Lions for second-order equations with subquadratic gradient growth. We identify two classes of solutions: the one coming from the natural scaling of the problem; and a one-parameter family of solutions, different from the previous, which can be formally described as a...

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A multiple time renewal equation for neural assemblies with elapsed time model.

Event Date: Aug 23, 2022 in Differential Equations, Seminars

Abstract: We introduce and study an extension of the classical elapsed time equation in the context of neuron populations that are described by the elapsed time since last discharge. In this extension we incorporate the elapsed since the penultimate discharge and we obtain a more complex system of integro-differential equations. For this new system we prove convergence to stationary state by means of Doeblin’s theory in the case of weak non-linearities in an appropriate functional setting, inspired by the case of the classical elapsed time equation. Moreover, we present some numerical...

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Árboles generadores en grafos densos I.

Event Date: Aug 18, 2022 in Seminario de Grafos, Seminars

Abstract: Dados dos grafos H y G un problema central en teoría de grafos extremales es determinar condiciones globales en G que garantizan la existencia de una copia de H en G. Un ejemplo de resultado en esa dirección es el Teorema de Dirac, que afirma que si G es un grafo en nvértices con grado mínimo al menos n/2, entonces existe una copia del ciclo en n vértices en G. En este seminario vamos a estudiar la relación entre el grado mínimo de G y la existencia de copias de diferentes árboles generadores de G. Más específicamente, vamos a ver el...

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Event Date: Aug 22, 2022 in Ciclo de Seminarios quincenales de la Alianza Copernicus-Chile, Seminars

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Prophet Inequalities via the Expected Competitive Ratio.

Event Date: Aug 17, 2022 in ACGO, Seminars

Abstract: We consider prophet inequalities under general downward-closed constraints. In a prophet inequality problem, a decision-maker sees a series of online elements and needs to decide immediately and irrevocably whether or not to select each element upon its arrival, subject to an underlying feasibility constraint. Traditionally, the decision-maker’s expected performance has been compared to the expected performance of the prophet, i.e., the expected offline optimum. We refer to this measure as the Ratio of Expectations (or, in short, RoE). However, a major limitation of the RoE measure...

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