Sergey Kirgizov

Influence Assessment in Twitter Multi-relational Network

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 largescale 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 method on a large amount of data gathered from Twitter in the context of the European Elections 2014 and deduce top influential candidates.

Patterns in treeshelves

We study the distribution and the popularity of left children on sets of treeshelves avoiding a pattern of size three. (Treeshelves are ordered binary increasing trees where every child is connected to its parent by a left or a right link.) The considered patterns are sub-treeshelves, and for each such a pattern we provide exponential generating function for the corresponding distribution and popularity. Finally, we present constructive bijections between treeshelves avoiding a pattern of size three and some classes of simpler combinatorial objects.

Information fusion-based approach for studying influence on Twitter using belief theory

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 study, we propose a new approach for multi-level influence assessment on multi-relational networks, such as Twitter. We define a social graph to model the relationships between users as a multiplex graph where users are represented by nodes, and links model the different relations between them (e.g., retweets, mentions, and replies). We explore how relations between nodes in this graph could reveal about the influence degree and propose a generic computational model to assess influence degree of a certain node. This is based on the conjunctive combination rule from the belief functions theory to combine different types of relations. We experiment the proposed method on a large amount of data gathered from Twitter during the European Elections 2014 and deduce top influential candidates. The results show that our model is flexible enough to to consider multiple interactions combination according to social scientists needs or requirements and that the numerical results of the belief theory are accurate. We also evaluate the approach over the CLEF RepLab 2014 data set and show that our approach leads to quite interesting results.

Suppression distance computation for hierarchical clusterings

We generalize the suppression distance defined for partitions to hierarchical clusterings.We reduce its computation to the minimum vertex cover problem.We prove this problem can be solved in polynomial time and provide a recursive algorithm. We discuss the computation of a distance between two hierarchical clusterings of the same set. It is defined as the minimum number of elements that have to be removed so the remaining clusterings are equal. The problem of distance computing was extensively studied for partitions. We prove it can be solved in polynomial time in the case of hierarchies as it gives birth to a class of perfect graphs. We also propose an algorithm based on recursively computing maximum assignments.

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.

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

Dyck paths with a first return decomposition constrained by height

p

The pure descent statistic on permutations

we provide a bivariate generating function where the coefficient of

The complexity of deciding whether a graph admits an orientation with fixed weak diameter

x^ny^k

Enumeration of \L{}ukasiewicz paths modulo some patterns.

in its series expansion is the number of length