On Disjoint hypercubes in Fibonacci cubes

The {\em Fibonacci cube} of dimension $n$, denoted as $\Gamma\_n$, is the subgraph of $n$-cube $Q\_n$ induced by vertices with no consecutive 1's. We study the maximum number of disjoint subgraphs in $\Gamma\_n$ isomorphic to $Q\_k$, and denote this number by $q\_k(n)$. We prove several recursive results for $q\_k(n)$, in particular we prove that $q\_{k}(n) = q\_{k-1}(n-2) + q\_{k}(n-3)$. We also prove a closed formula in which $q\_k(n)$ is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence $\{q\_{k}(n)\}\_{n=0}^{ \infty}$

A New Game Invariant of Graphs: the Game Distinguishing Number

The distinguishing number of a graph $G$ is a symmetry related graph invariant whose study started two decades ago. The distinguishing number $D(G)$ is the least integer $d$ such that $G$ has a $d$-distinguishing coloring. A distinguishing $d$-coloring is a coloring $c:V(G)\rightarrow\{1,...,d\}$ invariant only under the trivial automorphism. In this paper, we introduce a game variant of the distinguishing number. The distinguishing game is a game with two players, the Gentle and the Rascal, with antagonist goals. This game is played on a graph $G$ with a set of $d\in\mathbb N^*$ colors. Alternately, the two players choose a vertex of $G$ and color it with one of the $d$ colors. The game ends when all the vertices have been colored. Then the Gentle wins if the coloring is distinguishing and the Rascal wins otherwise. This game leads to define two new invariants for a graph $G$, which are the minimum numbers of colors needed to ensure that the Gentle has a winning strategy, depending on who starts. These invariants could be infinite, thus we start by giving sufficient conditions to have infinite game distinguishing numbers. We also show that for graphs with cyclic automorphisms group of prime odd order, both game invariants are finite. After that, we define a class of graphs, the involutive graphs, for which the game distinguishing number can be quadratically bounded above by the classical distinguishing number. The definition of this class is closely related to imprimitive actions whose blocks have size $2$. Then, we apply results on involutive graphs to compute the exact value of these invariants for hypercubes and even cycles. Finally, we study odd cycles, for which we are able to compute the exact value when their order is not prime. In the prime order case, we give an upper bound of $3$

Optimal accessing and non-accessing structures for graph protocols

An accessing set in a graph is a subset B of vertices such that there exists D subset of B, such that each vertex of V\B has an even number of neighbors in D. In this paper, we introduce new bounds on the minimal size kappa'(G) of an accessing set, and on the maximal size kappa(G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly kappa(G) and kappa'(G) for several families of graphs. Finally, we show that the corresponding decision problems are NP-Complete

Hierarchical topic structuring: from dense segmentation to topically focused fragments via burst analysis

International audienceTopic segmentation traditionally relies on lexical cohesion measured through word re-occurrences to output a dense segmen-tation, either linear or hierarchical. In this paper, a novel organization of the topical structure of textual content is proposed. Rather than searching for topic shifts to yield dense segmentation, we propose an algorithm to extract topically focused fragments organized in a hierarchical manner. This is achieved by leveraging the temporal distribution of word re-occurrences, searching for bursts, to skirt the limits imposed by a global counting of lexical re-occurrences within segments. Comparison to a reference dense segmentation on varied datasets indicates that we can achieve a better topic focus while retrieving all of the important aspects of a text

Quantum Secret Sharing with Graph States

Revised Selected Papers - http://www.memics.cz/2012/International audienceWe study the graph-state-based quantum secret sharing protocols [24,17] which are not only very promising in terms of physical implementation, but also resource efficient since every player's share is composed of a single qubit. The threshold of a graph-state-based protocol admits a lower bound: for any graph of order n, the threshold of the corresponding n-player protocol is at least 0.506n. Regarding the upper bound, lexicographic product of the C 5 graph (cycle of size 5) are known to provide n-player protocols which threshold is n − n 0.68. Using Paley graphs we improve this bound to n − n 0.71. Moreover, using probabilistic methods, we prove the existence of graphs which associated threshold is at most 0.811n. Albeit non-constructive, probabilistic methods permit to prove that a random graph G of order n has a threshold at most 0.811n with high probability. However, verifying that the threshold of a given graph is acually smaller than 0.811n is hard since we prove that the corresponding decision problem is NP-Complete. These results are mainly based on the graphical characterization of the graph-state-based secret sharing properties, in particular we point out strong connections with domination with parity constraints

Investigating domain-independent NLP techniques for precise target selection in video hyperlinking

International audienceAutomatic generation of hyperlinks in multimedia video data is a subject with growing interest, as demonstrated by recent work undergone in the framework of the Search and Hyperlinking task within the Mediaeval benchmark initiative. In this paper, we compare NLP-based strategies for precise target selection in video hyperlinking exploiting speech material, with the goal of providing hyperlinks from a specified anchor to help information retrieval. We experimentally compare two approaches enabling to select short portions of videos which are relevant and possibly complementary with respect to the anchor. The first approach exploits a bipartite graph relating utterances and words to find the most relevant utterances. The second one uses explicit topic segmentation, whether hierarchical or not, to select the target segments. Experimental results are reported on the Mediaeval 2013 Search and Hyperlinking dataset which consists of BBC videos, demonstrating the interest of hierarchical topic segmentation for precise target selection

IRISA and KUL at MediaEval 2014: Search and Hyperlinking Task

International audienceThis paper presents our approach and results in the hyper-linking sub-task at MediaEval 2014. A two step approach is implemented: relying on a topic segmentation technique, the first step consists in generating potential target segments; then, for each anchor, the best 20 target segments are selected according to two distinct strategies: the first one focuses on the identification of very similar targets using n-grams and named entities; the second one makes use of an intermediate structure built from topic models, which offers the possibility to control serendipity and to explain the links created

Méthadone ou torture ?

Pour la première fois, la Cour européenne des droits de l’homme basée à Strasbourg se penche sur la question de savoir si les patients dépendants à l’héroïne ont un droit à poursuivre leur traitement à base de méthadone lorsqu’ils sont privés de leur liberté. S’appuyant sur l’art. 3 de la Convention, lequel interdit la torture comme les autres traitements inhumains et dégradants, la Cour estime que c’est à l’Etat, qui entend refuser l’accès à la méthadone, de prouver – sur la base d’une expertise indépendante – qu’une approche médicale autre que celle fondée sur un médicament agoniste aurait de sérieuses chances de succès dans le traitement de la dépendance du patient en cause. La présente contribution discute la portée et les limites de cet arrêt