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May 26, 2010
Analysis of PDEs

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

Nonexistence of positive supersolutions of elliptic equations via the…

We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of $\mathbb{R}^n$. Th…
Aug 29, 2016
Computer Vision

Curvature Integration in a 5D Kernel for Extracting Vessel Connection…

Tree-like structures such as retinal images are widely studied in computer-aided diagnosis systems for large-scale screening programs. Despite severa…
Aug 18, 2017
Combinatorics
Discrete Mathematics

Nowhere Dense Graph Classes and Dimension

Nowhere dense graph classes provide one of the least restrictive notions of sparsity for graphs. Several equivalent characterizations of nowhere dens…
Nov 28, 2016
Combinatorics

Defective colouring of graphs excluding a subgraph or minor

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…
Feb 19, 2009
Combinatorics

Characterisations and Examples of Graph Classes with Bounded Expansion

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…
Jul 30, 2016
Combinatorics

Existence of Modeling Limits for Sequences of Sparse Structures

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…
Oct 11, 2019
Neurons and Cognition
Computer Vision
Analysis of PDEs
Differential Geometry
Metric Geometry

A sub-Riemannian model of the visual cortex with frequency and phase

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…
Dec 21, 2015
Analysis of PDEs

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…

On the definition and the properties of the principal eigenvalue of s…

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…
Jul 03, 2017
Logic in Computer Science
Discrete Mathematics
Combinatorics

Shrub-depth: Capturing Height of Dense Graphs

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…
Aug 08, 2011
Combinatorics

Colouring Edges with many Colours in Cycles

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…
Oct 04, 2018
Discrete Mathematics
Logic in Computer Science
Combinatorics

First-order interpretations of bounded expansion classes

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractabl…
Oct 19, 2018
Analysis of PDEs

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.

Stable solutions of semilinear elliptic equations in unbounded domains

This paper establishes some properties for stable solutions of a semilin-ear elliptic equation with homogeneous Neumann boundary conditions in unboun…
May 12, 2015
Combinatorics

Limits of Structures and the Example of Tree-Semilattices

The notion of left convergent sequences of graphs introduced by Lov\' asz et al. (in relation with homomorphism densities for fixed patterns and Szem…
Apr 20, 2010
Physics and Society

Academic team formation as evolving hypergraphs

This paper quantitatively explores the social and socio-semantic patterns of constitution of academic collaboration teams. To this end, we broadly un…
Jun 21, 2017
Combinatorics

Obstacle Numbers of Planar Graphs

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…
Jul 03, 2014
Computer Vision
Neural and Evolutionary Computation
Neurons and Cognition
Machine Learning

Cortical spatio-temporal dimensionality reduction for visual grouping

The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks…
Jan 15, 2013
Analysis of PDEs
Symplectic Geometry
Neurons and Cognition

A cortical-inspired geometry for contour perception and motion inte…

In this paper we develop a geometrical model of functional architecture for the processing of spatio-temporal visual stimuli. The model arises from t…
Dec 02, 2013
Combinatorics

Modeling Limits in Hereditary Classes: Reduction and Application to …

Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures call…
Dec 21, 2015
Computer Vision

Local and global gestalt laws: A neurally based spectral approach

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with…
Jan 03, 2012
Physics and Society
Statistical Mechanics
Data Analysis
Statistics and Probability

Election turnout statistics in many countries: similarities, differ…

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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