Noticias en español
Optimal d-Clique Decompositions for Hypergraphs.
Abstract: We determine the optimal constant for the Erdős-Pyber theorem on hypergraphs. Namely, we prove that every n-vertex d-uniform hypergraph H can be written as the union of a family F of complete d-partite hypergraphs such that every vertex of H belongs to at most (n choose d)/(n lg n) graphs in F. This improves on results of Csirmaz, Ligeti, and Tardos (2014), and answers an old question of Chung, Erdős, and Spencer (1983). Our proofs yield several algorithmic consequences, such as an O(n lg n) algorithm to find large balanced bicliques near the Kővári-Sós-Turán threshold. Moreover,...
Read MoreThe Ramsey Number of Multiple Copies of a Graph
Abstract: Let H be a graph without isolated vertices. The Ramsey Number r(nH) is the minimum N such that every coloring of the edges of the complete graph on N vertices with red and blue contains n pairwise vertex-disjoint monochromatic copies of H of the same color. In 1975, Burr, Erdős and Spencer established that r(nH) is a linear function of n for large enough n. In 1987, Burr proved a superexponential upper bound for when the long-term linear behavior starts. In 2023, Bucic and Sudakov showed that the long-term linear behavior starts already when n is an exponential function of |H|...
Read MoreClearing-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.
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