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We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive…

Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…

Disentanglement is a difficult property to enforce in neural representations. This might be due, in part, to a formalization of the disentanglement problem that focuses too heavily on separating relevant factors of variation of the data in…

In this paper we study a family of discrete configuration spaces, the so-called protocol complexes, which are of utmost importance in theoretical distributed computing. Specifically, we consider questions of the existance of compliant…

We consider the problem of steering a multi-agent system to multi-consensus, namely a regime where groups of agents agree on a given value which may be different from group to group. We first address the problem by using distributed…

This paper investigates the connections between combinatorial design theory and the creation of new forms of poetry through a specific combinatorial structure called Steiner triple systems. We introduce five original poems constructed using…

Modular composition is the problem of computing the composition of two univariate polynomials modulo a third one. For a long time, the fastest algebraic algorithm for this problem was that of Brent and Kung (1978). Recently, we improved…

Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

The celebrated Birkhoff Ergodic Theorem asserts that, for an ergodic map, orbits of almost every point equidistributes when sampled at integer times. This result was generalized by Bourgain to many natural sparse subsets of the integers. On…

Morphologically rich languages accentuate two properties of distributional vector space models: 1) the difficulty of inducing accurate representations for low-frequency word forms; and 2) insensitivity to distinct lexical relations that…

Variational inequalities are an important tool, which includes minimization, saddles, games, fixed-point problems. Modern large-scale and computationally expensive practical applications make distributed methods for solving these problems…

Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are often subject to constraints, ruling out many candidates for composed rules. Focusing on the case of…

The increasing growth of databases raises an urgent need for more accurate methods to better understand the stored data. In this scope, association rules were extensively used for the analysis and the comprehension of huge amounts of data.…

This work proposes a non-iterative strategy for missing value imputations which is guided by similarity between observations, but instead of explicitly determining distances or nearest neighbors, it assigns observations to overlapping…

These last years, there were many studies on the problem of the conflict coming from information combination, especially in evidence theory. We can summarise the solutions for manage the conflict into three different approaches: first, we…

We simulate a disordered assembly of particles interacting through a repulsive Yukawa potential with a small fraction of the particles coupled to an external drive. Distortions in the arrangement of the nondriven particles produce a…

String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time…

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…

By considering the parity of the degrees and levels of nodes in increasing trees, a new combinatorial interpretation for the coefficients of the Taylor expansions of the Jacobi elliptic functions is found. As one application of this new…