Influence Assessment in Twitter Multi-relational Network

International audience; Influence in Twitter has become recently a hot research topic since this micro-blogging service is widely used to share and disseminate information. Some users are more able than others to influence and persuade peers. Thus, studying most influential users leads to reach a large-scale information diffusion area, something very useful in marketing or political campaigns. In this paper, we propose a new approach for influence assessment on Twitter network, it is based on a modified version of the conjunctive combination rule in belief functions theory in order to combine different influence markers such as retweets, mentions and replies. We experiment the proposed meth…

A la recherche des mini-publics : un problème de communautés, de singularités et de sémantique

International audience

Clique Percolation Method: Memory Efficient Almost Exact Communities

Automatic detection of relevant groups of nodes in large real-world graphs, i.e. community detection, has applications in many fields and has received a lot of attention in the last twenty years. The most popular method designed to find overlapping communities (where a node can belong to several communities) is perhaps the clique percolation method (CPM). This method formalizes the notion of community as a maximal union of $k$-cliques that can be reached from each other through a series of adjacent $k$-cliques, where two cliques are adjacent if and only if they overlap on $k-1$ nodes. Despite much effort CPM has not been scalable to large graphs for medium values of $k$. Recent work has sho…

Papersᵞ, Discussing board for scientific papers

International audience

Descent distribution on Catalan words avoiding a pattern of length at most three

Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern $p$ we provide a bivariate generating function where the coefficient of $x^ny^k$ in its series expansion is the number of length $n$ Catalan words with $k$ descents and avoiding $p$. As a byproduct, we enumerate the set of Catalan words avoiding $p$, and we provide the popularity of descents on this set. Some of the obtained enumerating sequences are not yet recorded in the On-line En…

Pattern distribution in faro words and permutations

International audience

Towards A Twitter Observatory: A Multi-Paradigm Framework For Collecting, Storing And Analysing Tweets

International audience; In this article we show how a multi-paradigm framework can fulfil the requirements of tweets analysis and reduce the waiting time for researchers that use computational resources and storage systems to support large-scale data analysis. The originality of our approach is to combine concerns about data harvesting, data storage, data analysis and data visualisation into a framework that supports inductive reasoning in multidisciplinary scientific research. Our main contribution is a polyglot storage system with a generic data model to support logical data independence and a set of tools that can provide a suitable solution for mixing different types of algorithms in or…

Évaluation de l’influence dans un réseau multi-relationnel : le cas de Twitter

International audience

SNFreezer: a Platform for Harvesting and Storing Tweets in a Big Data Context

International audience

Packing coloring and subsets preserving path distance

International audience

The pure descent statistic on permutations

International audience; We introduce a new statistic based on permutation descents which has a distribution given by the Stirling numbers of the first kind, i.e., with the same distribution as for the number of cycles in permutations. We study this statistic on the sets of permutations avoiding one pattern of length three by giving bivariate generating functions. As a consequence, new classes of permutations enumerated by the Motzkin numbers are obtained. Finally, we deduce results about the popularity of the pure descents in all these restricted sets. (C) 2017 Elsevier B.V. All rights reserved.

Pattern statistics in faro words and permutations

We study the distribution and the popularity of some patterns in $k$-ary faro words, i.e. words over the alphabet $\{1, 2, \ldots, k\}$ obtained by interlacing the letters of two nondecreasing words of lengths differing by at most one. We present a bijection between these words and dispersed Dyck paths (i.e. Motzkin paths with all level steps on the $x$-axis) with a given number of peaks. We show how the bijection maps statistics of consecutive patterns of faro words into linear combinations of other pattern statistics on paths. Then, we deduce enumerative results by providing multivariate generating functions for the distribution and the popularity of patterns of length at most three. Fina…

(Re)constuire la temporalité d’un événement médiatique sur Twitter : une étude contrastive

International audience; En examinant la temporalité d’un « événement » sur Twitter, à travers les tweets d’acteurs politiques dans quatre pays, cette étude contribue à enrichir notre compréhension du processus de médiatisation de la communication politique via les réseaux socio-numériques. A partir des traces laissées sur le réseau par ses utilisateurs, la contribution cherche à identifier un « événement » médiaté qui se manifesterait dans des discours des acteurs politiques comparés à la twittosphère. This study proposes to enrich our understanding of the mediatization of political communication via digital social networks, by examining the temporality of an “event” on Twitter, through the…

Évaluation de l’influence polarisée dans un réseau multi-relationnel : application à twitter

International audience

Temporal density of complex networks and ego-community dynamics

International audience

Pattern avoiding permutations modulo pure descent

International audience

Q-bonacci words and numbers

We present a quite curious generalization of multi-step Fibonacci numbers. For any positive rational $q$, we enumerate binary words of length $n$ whose maximal factors of the form $0^a1^b$ satisfy $a = 0$ or $aq > b$. When $q$ is an integer we rediscover classical multi-step Fibonacci numbers: Fibonacci, Tribonacci, Tetranacci, etc. When $q$ is not an integer, obtained recurrence relations are connected to certain restricted integer compositions. We also discuss Gray codes for these words, and a possibly novel generalization of the golden ratio.

Evaluation de l’influence sur Twitter: Application au projet « Twitter aux Elections Européennes 2014 »

International audience

Grand Dyck paths with air pockets

Grand Dyck paths with air pockets (GDAP) are a generalization of Dyck paths with air pockets by allowing them to go below the $x$-axis. We present enumerative results on GDAP (or their prefixes) subject to various restrictions such as maximal/minimal height, ordinate of the last point and particular first return decomposition. In some special cases we give bijections with other known combinatorial classes.

Enumeration of Łukasiewicz paths modulo some patterns

Abstract For any pattern α of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length n ≥ 0 where two paths are equivalent whenever the occurrence positions of α are identical on these paths. As a byproduct, we give a constructive bijection between Motzkin paths and some equivalence classes of Łukasiewicz paths.

Évaluation de l’influence dans un réseau multi-relationnel

L'influence sur Twitter est devenue un sujet de recherche important. Certains utilisateurs révèlent plus de capacité que d'autres pour influencer les personnes avec lesquelles ils sont connectés. Ainsi, trouver les utilisateurs les plus influents peut permettre une diffusion efficace de l'information à grande échelle, action très utile dans le marketing ou les campagnes politiques. Dans cet article, nous proposons une nouvelle approche pour l'évaluation de l'influence dans les réseaux multi-relationnels tels que Twitter. Notre méthode est basée sur la règle de combinaison conjonctive de la théorie des fonctions de croyance qui permet de fusionner différents types de relations. Nous expérime…

Fibonacci q-decreasing words: enumerative results and Gray codes

Qubonacci words

International audience

Dyck paths with a first return decomposition constrained by height

International audience; We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height k with a flat (resp. with no flats) at the maximal height. (C) 2018 Elsevier B.V. All rights reserved.KeywordsKeyWords Plus:STATISTICS; STRINGS

Motzkin Paths With a Restricted First Return Decomposition

International audience

Asymptotic bit frequency in Fibonacci words

It is known that binary words containing no $k$ consecutive 1s are enumerated by $k$-step Fibonacci numbers. In this note we discuss the expected value of a random bit in a random word of length $n$ having this property.

Un observatoire pour la modélisation et l’analyse des réseaux multi-relationnels. Une application à l'étude du discours politique sur Twitter

International audience

A web application for event detection and exploratory data analysis for Twitter data

International audience

Forests and pattern-avoiding permutations modulo pure descents

Abstract We investigate an equivalence relation on permutations based on the pure descent statistic. Generating functions are given for the number of equivalence classes for the set of all permutations, and the sets of permutations avoiding exactly one pattern of length three. As a byproduct, we exhibit a permutation set in one-to-one correspondence with forests of ordered binary trees, which provides a new combinatorial class enumerated by the single-source directed animals on the square lattice. Furthermore, bivariate generating functions for these sets are given according to various statistics.