Random weighted Sobolev inequalities and application to quantum ergodicity

This paper is a continuation of Poiret-Robert-Thomann (2013) where we studied a randomisation method based on the Laplacian with harmonic potential. Here we extend our previous results to the case of any polynomial and confining potential $V$ on $\mathbb{R}^d$. We construct measures, under concentration type assumptions, on the support of which we prove optimal weighted Sobolev estimates on $\mathbb{R}^d$. This construction relies on accurate estimates on the spectral function in a non-compact configuration space. Then we prove random quantum ergodicity results without specific assumption on the classical dynamics. Finally, we prove that almost all basis of Hermite functions is quantum uniquely ergodic.Comment: Clarifications added in the part concerning QU

Designing optimal- and fast-on-average pattern matching algorithms

Given a pattern $w$ and a text $t$, the speed of a pattern matching algorithm over $t$ with regard to $w$, is the ratio of the length of $t$ to the number of text accesses performed to search $w$ into $t$. We first propose a general method for computing the limit of the expected speed of pattern matching algorithms, with regard to $w$, over iid texts. Next, we show how to determine the greatest speed which can be achieved among a large class of algorithms, altogether with an algorithm running this speed. Since the complexity of this determination make it impossible to deal with patterns of length greater than 4, we propose a polynomial heuristic. Finally, our approaches are compared with 9 pre-existing pattern matching algorithms from both a theoretical and a practical point of view, i.e. both in terms of limit expected speed on iid texts, and in terms of observed average speed on real data. In all cases, the pre-existing algorithms are outperformed

CompiLIG at SemEval-2017 Task 1: Cross-Language Plagiarism Detection Methods for Semantic Textual Similarity

We present our submitted systems for Semantic Textual Similarity (STS) Track 4 at SemEval-2017. Given a pair of Spanish-English sentences, each system must estimate their semantic similarity by a score between 0 and 5. In our submission, we use syntax-based, dictionary-based, context-based, and MT-based methods. We also combine these methods in unsupervised and supervised way. Our best run ranked 1st on track 4a with a correlation of 83.02% with human annotations

Deep Investigation of Cross-Language Plagiarism Detection Methods

This paper is a deep investigation of cross-language plagiarism detection methods on a new recently introduced open dataset, which contains parallel and comparable collections of documents with multiple characteristics (different genres, languages and sizes of texts). We investigate cross-language plagiarism detection methods for 6 language pairs on 2 granularities of text units in order to draw robust conclusions on the best methods while deeply analyzing correlations across document styles and languages.Comment: Accepted to BUCC (10th Workshop on Building and Using Comparable Corpora) colocated with ACL 201

The various manifestations of collisionless dissipation in wave propagation

The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet is Landau damped, so that in the reference frame moving at the group velocity, the wave amplitude decays exponentially with time. In the nonlinear regime, once phase mixing has occurred and when the electron motion is nearly adiabatic, the damping rate is strongly reduced compared to the Landau one, so that the wave amplitude remains nearly constant along the characteristics. Yet, we show here that the electrons are still globally accelerated by the wave packet, and, in one dimension, this leads to a non local amplitude dependence of the group velocity. As a result, a freely propagating wave packet would shrink, and, therefore, so would its total energy. In more than one dimension, not only does the magnitude of the group velocity nonlinearly vary, but also its direction. In the weakly nonlinear regime, when the collisionless damping rate is still significant compared to its linear value, this leads to an effective defocussing effect which we quantify, and which we compare to the self-focussing induced by wave front bowing.Comment: 23 pages, 6 figure