Van Der Hoeven, Joris

In this paper, we present a probabilistic algorithm to multiply two sparse polynomials almost as efficiently as two dense univariate polynomials with a result of approximately the same size. The algorithm depends on unproven heuristics that will be made precise.

Couvreur, Alain Lebacque, Philippe Perret, Marc

We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be "liftable" under finite morphisms, paving the way toward the construction of good codes from towers of surfaces. In the same direction, we establish a crite...

Aubry, Yves Berardini, Elena Herbaut, Fabien Perret, Marc

We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds for surfaces whose arithmetic Picard number equalsone, surfaces without curves with small self-intersection and...

Issartel, Jean-Pierre Busch, X Sharan, Maithili

The elicitation of the background error covariance matrix (becm) is a major difficulty of Bayesian assimilation used in atmospheric and oceanic sciences based on Kalman filter in the form of 3Dvar or 4Dvar. In a preliminary companion paper, the definition of a becm and link to earlier information were seen poorly practicable. Here, more decisive ar...

Lavauzelle, Julien Loidreau, Pierre Pham, Ba-Duc

We present a rank metric code-based encryption scheme with key and ciphertext sizes comparable to that of isogeny-based cryptography for an equivalent security level. The system also benefits from efficient encryption and decryption algorithms, which rely on linear algebra operations over finite fields of moderate sizes. The security only relies on...

Marrelec, Guillaume Giron, Alain

We consider a generalization of information density to a partitioning into N ≥ 2 subvectors. We calculate its cumulant-generating function and its cumulants, showing that these quantities are only a function of all the regression coeﬃcients associated with the partitioning

Van Der Hoeven, Joris

The class of reduction-based algorithms was introduced recently as a new approach towards creative telescoping. Starting with Hermite reduction of rational functions, various reductions have been introduced for increasingly large classes of holonomic functions. In this paper we show how to construct reductions for general holonomic functions, in th...

Couvreur, Alain

Granero-Belinchon, Carlos Roux, Stéphane g. Garnier, Nicolas

We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information and entropy rate can be estimated when only...

Wolff, James Gerard

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about`information compression (IC) via the matching and unication of patterns' (ICMUP). That is itself a novel approach to IC, couched in terms of non-mathematical primitives, as is necessary in any investigation of the foundations ...