r é s u m é Nous donnons une nouvelle caractérisation de l’inégalité de Sobolev logarithmique. © 2017 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Traditional databases commonly support eecient query and update procedures that operate in time which is sublinear in the size of the database. Our goal in this paper is to take a rst step toward dynamic reasoning in probabilistic databases with comparable eeciency. We propose a dynamic data structure that supports eecient algorithms for updating and querying singly connected Bayesian networks....

Recently J. P. Demailly gave a natural desingularization of the quotient of jet bundles by the full reparametrization group. Using this, he was able to complete an approach by Green and Griiths to construct negatively curved jet pseudometrics on subvarieties of Abelian varieties to prove Bloch's theorem metrically. In the present paper we extend this technique to the logarithmic case, yielding ...

In this paper a novel type of gain-shape vector quantization (GSVQ) is presented, denoted as Logarithmic Cubic Vector Quantization (LCVQ). LCVQ is based on a decomposition of the vector to be quantized into a gain factor and a shape vector which is a normalized version of the input vector. Both components are quantized independently and transmitted to the decoder. Compared to other GSVQ approac...

We define the cotangent complex of a morphism of fine log schemes, prove that it is functorial, and construct under certain restrictions a transitivity triangle. We also discuss its relationship with deformation theory.

A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality. Logarithmic Sobolev inequalities capture the spirit of classical Sobolev inequalities with the logarithm function replacing powers, and they can be considered as limiting cases of...

In a recent work, Girard [1] proposed a new and innovative approach to computational complexity based on the proofs-as-programs correspondence. In a previous paper [2], the authors showed how Girard proposal succeeds in obtaining a new characterization of co-NL languages as a set of operators acting on a Hilbert Space. In this paper, we extend this work by showing that it is also possible to de...

In this paper we propose a method to construct logarithmic signatures which are not amalgamated transversal and further do not even have a periodic block. The latter property was crucial for the successful attack on the system MST 3 by Blackburn et al. [1]. The idea for our construction is based on the theory in Szabó’s book about group factorizations [12].

We present a new class of number systems, called Semi-Logarithmic Number Systems, that constitute a family of various compromises between floating-point and logarithmic number systems. We propose arithmetic algorithms for the Semi-Logarithmic Number Systems, and we compare these number systems to the classical floating-point or logarithmic number systems. performed using tables for the function...

Karp and Lipton [11] introduced the notion of non-uniform complexity classes where a certain amount of additional information, the advice, is given for free. The advice only depends on the length of the input. Karp and Lipton initiated the study of classes with either logarithmic or polynomial advice; however later researchers [24, 19, 2, 14] concentrated on the study of classes of the form C/p...