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The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes with a constant drif...
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
From shuffling cards to walking around the building:An Inetroduction to modern markov chain theory
Performance characteristics of Bayes estimates are studied. More exactly, for each subject in a data set, let 5 be a vector of binary covariates and let Y be a normal response variable, with E{YIE...
This paper records the path of a letter that Marty Isaacs wrote to a stranger. The tools in the letter are used to illustrate a di erent way of studying random walk on the Heisenberg group. The author...
Evidence Theory is a branch of mathematics that concerns the combination of empirical evidence in an individual's mind in order to construct a coherent picture of reality. Designed to deal with unex...
In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse B...
In this paper, the first of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs tends to infin...
In this paper, we give a geometrization and a generaliza-tion of a lemma of di erential Galois theory. This geometrization, in addition of giving a nice insight on this result, o ers us the occasion t...
We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been...
It is often the case in mathematical analysis that solving an open problem can be facilitated by finding a new set of coordinates which may illumniate the known difficulties. In this article, we illu...
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribut...
Let $(X,\mathcal{O}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct...
We lift Charles Rezk's complete Segal space model structure on the category of simplicial spaces to a Quillen equivalent one on the category of relative categories.

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