The method we developed in the previous section generalizes easily to systems of the form

We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of $\mathbb{R}^n$. Th…

Tree-like structures such as retinal images are widely studied in computer-aided diagnosis systems for large-scale screening programs. Despite severa…

Nowhere dense graph classes provide one of the least restrictive notions of sparsity for graphs. Several equivalent characterizations of nowhere dens…

Archdeacon (1987) proved that graphs embeddable on a fixed surface can be $3$-coloured so that each colour class induces a subgraph of bounded maximu…

Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Ne\v{s}et\v{r}il and Osso…

A sequence of graphs is FO-convergent if the probability of satisfaction of every first-order formula converges. A graph modeling is a graph, whose d…

In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the V1 simpl…

In this article we study some spectral properties of the linear operator $\mathcal{L}\_{\Omega}+a$ defined on the space $C(\bar\Omega)$ by :$$ \mathcal{L}\_{\Omega}[\varphi] +a\varphi:=\int\_{\Omega}K(x,y)\varphi(y)\,dy+a(x)\varphi(x)$$ where $\Omeg…

In this article we study some spectral properties of the linear operator $\mathcal{L}\_{\Omega}+a$ defined on the space $C(\bar\Omega)$ by :$$ \mathc…

The recent increase of interest in the graph invariant called tree-depth and in its applications in algorithms and logic on graphs led to a natural q…

The arboricity of a graph G is the minimum number of colours needed to colour the edges of G so that every cycle gets at least two colours. Given a p…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractabl…

We consider (e1,…,en) an orthonormal basis of Rn, (x1,…,xn) the associated variables, and we set vi:=∂xiu for i∈{1,⋯,n}. As a consequence of Lemma and Lemma, we have the following result.

This paper establishes some properties for stable solutions of a semilin-ear elliptic equation with homogeneous Neumann boundary conditions in unboun…

The notion of left convergent sequences of graphs introduced by Lov\' asz et al. (in relation with homomorphism densities for fixed patterns and Szem…

This paper quantitatively explores the social and socio-semantic patterns of constitution of academic collaboration teams. To this end, we broadly un…

Given finitely many connected polygonal obstacles $O_1,\dots,O_k$ in the plane and a set $P$ of points in general position and not in any obstacle, t…

The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks…

In this paper we develop a geometrical model of functional architecture for the processing of spatio-temporal visual stimuli. The model arises from t…

Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures call…

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with…

We study in details the turnout rate statistics for 77 elections in 11 different countries. We show that the empirical results established in a previ…

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