Noticias en español
Condiciones de grado mínimo para caminos y ciclos monocromáticos en grafos 2-arista-coloreados (segunda parte).
Abstract: Diremos que un grafo $G$ apunta a un grafo $H$ si es que en cada $2$-arista-coloreo de $G$ existe una copia monocromática de $H$. Schelp tenía la idea de que si el grafo completo $K_n$ apunta un grafo pequeño $H$, entonces cada subgrafo denso de $K_n$ también apunta a H.En este seminario, veremos un resultado demostrado por Balogh, Kostochka, Lavrov y Liu en 2021 ( https://arxiv.org/pdf/1906.02854.pdf ) que indica que “para todo $n$ suficientemente grande, si $n = 3t + r$ donde $r\in\{0,1,2\} y $G$ es un grafo en $n$ vértices con $\delta(G) \geq (3n-1)/4$,entonces para todo...
Read MoreThe IID Prophet Inequality with Limited Flexibility.
Abstract: In online sales, sellers usually offer each potential buyer a posted price in a take-it-or-leave fashion. Buyers can sometimes see posted prices faced by other buyers, and changing the price frequently could be considered unfair. The literature on posted price mechanisms and prophet inequality problems has studied the two extremes of pricing policies, the fixed price policy and fully dynamic pricing. The former is suboptimal in revenue but is perceived as fairer than the latter. This work examines the middle situation, where there are at most distinct prices over the selling...
Read MoreCordes-nirenberg type results for nonlocal equations with deforming kernels.
Abstract. We derive Cordes-Nirenberg type results for nonlocal elliptic equations with deforming kernels using a compactness method.Under a natural integrability assumption for the Monge-Ampere solution, we are able to prove a stability lemma that allows the ellipticity class to vary. As a consequence, we get that the limit equation, up to a rotation, behaves like rough fractional Laplacians where the known regularity theory for this class of equation can be applied.
Read MoreThe variational form of mollification: an overview.
Abstract:We shall consider ill-posed linear operator equations in Hilbert spaces, with particular attention to spaces of square integrable functions. We shall introduce the variational form of mollification. The problem of deconvolution of random variable will serve the purpose of illustration. We will also briefly put in perspective the possible extension of mollification to nonlinear inverse problems.
Read MoreMulti-weighted (sample)-prophet and secretary matching problems.
Abstract: A k-graph is a hypergraph whose edges have size k. Consider a k-graph G and a collection of m agents. Agent i has a weight function w_i over all edges. Our task is to assign at most one edge e to each agent i (receiving a profit of w_i(e)) in such a way that no edge is assigned twice, that the set of assigned edges form a matching while maximizing total profit. We tackle online and stochastic variants of this problem and generalizations to other independence systems. In these versions, agents arrive one by one revealing their weight function and the decision maker must assign edges...
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