Bertrand Jouve

Quantitative Analysis of Connectivity in the Visual Cortex: Extracting Function from Structure

It is generally agreed that information flow through the cortex is constrained by a hierarchical architecture. Lack of precise data on areal connectivity leads to indeterminacy of existing models. The authors introduce two quantitative parameters (SLN and FLN) that hold the promise of resolving such indeterminacy. In the visual system, using a very incomplete database, provisional hierarchies are in line with the recent proposal of higher functions of area V1 and suggest a hitherto unsuspected central function of the frontal eye field.

Simplicial simple-homotopy of flag complexes in terms of graphs

A flag complex can be defined as a simplicial complex whose simplices correspond to complete subgraphs of its 1-skeleton taken as a graph. In this article, by introducing the notion of s-dismantlability, we shall define the s-homotopy type of a graph and show in particular that two finite graphs have the same s-homotopy type if, and only if, the two flag complexes determined by these graphs have the same simplicial simple-homotopy type. This result is closely related to similar results established by Barmak and Minian [J.A. Barmak, E.G. Minian, Simple homotopy types and finite spaces, Adv. Math. 218 (1) (2008) 87-104. doi:10.1016/j.aim.2007.11.019] in the framework of posets and we give the relation between the two approaches. We conclude with a question about the relation between the s-homotopy and the graph homotopy defined in [B. Chen, S.-T. Yau, Y.-N. Yeh, Graph homotopy and Graham homotopy, Selected papers in honor of Helge Tverberg, Discrete Math. 241 (1-3) (2001) 153-170. doi:10.1016/S0012-365X(01)00115-7.]

Transitive convex subsets in large tournaments

Abstract A convex subset of vertices of a tournament T is such that any vertex not in the subset either dominates or is dominated by all of the vertices in the convex subset. Given a large tournament T, we explore the structure of T by looking for its transitive convex subsets. In a majority voting tournament some isolated inconsistencies may appear in such subsets. We propose a way to reveal such “nearly” transitive convex subsets. They are the subsets of a partition which optimizes the inertia of a geometrical embedding of T.

s-homotopy for finite graphs

Abstract We introduce the notion of “s-dismantlability” which will give in the category of finite graphs an analogue of formal deformations defining the simple-homotopy type in the category of finite simplicial complexes. More precisely, s-dismantlability allows us to define an equivalence relation whose equivalence classes are called “s-homotopy types” and we get a correspondence between s-homotopy types in the category of graphs and simple-homotopy types in the category of simplicial complexes by the way of classical functors between these two categories (theorem 3.6). Next, we relate these results to similar results obtained by Barmak and Minian (2006) within the framework of posets (theorem 4.2).

Online Firefighting on Trees

In the Firefighter problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the Fractional Firefighter game where the amount of protection allocated to a vertex lies between 0 and 1. We introduce the online version of both Firefighter and Fractional Firefighter, in which the number of firefighters available at each turn is revealed over time. We show that the greedy algorithm on finite trees, which maximises at each turn the amount of vertices protected, is 1/2-competitive for both online versions; this was previously known only in special cases of Firefighter. We also show that, for Firefighter, the optimal competitive ratio of online algorithms ranges between 1/2 and the inverse of the golden ratio. The greedy algorithm is optimal if the number of firefighters is not bounded and we propose an optimal online algorithm which reaches the inverse of the golden ratio if at most 2 firefighters are available. Finally, we show that on infinite trees with linear growth, any firefighter sequence stronger than a non-zero periodic sequence is sufficient to contain the fire, even when revealed online.

Role detection in online forums based on growth models for trees

Some structural characteristics of online discussions have been successfully modeled in the recent years. When parameters of these models are properly estimated, the models are able to generate synthetic discussions that are structurally similar to the real discussions. A common aspect of these models is that they consider that all users behave according to the same model. In this paper, we combine a growth model with an Expectation–Maximization algorithm that finds different parameters for different latent groups of users. We use this method to find the different roles that coexist in the community. Moreover, we analyze whether we can predict users behaviors based on their roles. Indeed, we show that predictions are improved for some of the roles when compared with a simple growth model.

Behind the Communities, a Focus on the Sparse Part of a Network

We propose a method that allows to detect the subset of the sparse nodes in a complex network, providing supplementary informations about its structure and features. The aim is to produce a complementary approach to the classical ones dealing with dense communities, and in the end to develop mixed models of community classification which are articulated around the network’s sparse skeleton. We will present in this article different metrics that measure sparsity in a network, and introduce a method that uses these metrics to extract the sparse part from it, which we tested on a toy network and on data coming from the real world.

Non-parametric clustering over user features and latent behavioral functions with dual-view mixture models

We present a dual-view mixture model to cluster users based on their features and latent behavioral functions. Every component of the mixture model represents a probability density over a feature view for observed user attributes and a behavior view for latent behavioral functions that are indirectly observed through user actions or behaviors. Our task is to infer the groups of users as well as their latent behavioral functions. We also propose a non-parametric version based on a Dirichlet Process to automatically infer the number of clusters. We test the properties and performance of the model on a synthetic dataset that represents the participation of users in the threads of an online forum. Experiments show that dual-view models outperform single-view ones when one of the views lacks information.

Critically Twin Primitive 2-Structures

Unlike graphs, digraphs or binary relational structures, the 2-structures do not define precise links between vertices. They only yield an equivalence between links. Also 2-structures provide a suitable generalization in the framework of clan decomposition. Let