Exceptional graphs for the random walk

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We study the behaviour of a natural measure defined on the leaves of the genealogical tree of some branching processes, namely self-similar growth-fragmentation processes. Each particle, or cell, is attributed a positive mass that evolves in continuous tim ...

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to t ...

Accurately quantifying extreme rainfall is important for the design of hydraulic structures, for flood mapping and zoning and for disaster management. In order to produce maps of estimates of 25-year rainfall return levels in Brazil, we selected 893 shorte ...

How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given r-edge-coloured graph G? These problems were introduced in the 1960s and were intensively studied by various researchers over the last 50 years. In this pa ...

Graphs offer a simple yet meaningful representation of relationships between data. This representation is often used in machine learning algorithms in order to incorporate structural or geometric information about data. However, it can also be used in an i ...

Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant patterns. On the other ...

This paper introduces a new algorithm for consensus optimization in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. All decentralized algorithms rely on communications between adjacent nodes. ...

We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and allows us to reco ...

Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...

We study in this thesis the asymptotic behavior of optimal paths on a random graph model, the configuration model, for which we assign continuous random positive weights on its edges. We start by describing the asymptotic behavior of the diameter and the f ...

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

A bootstrap percolation process on a graph is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least infected neighbours becomes infected and remai ...

A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph G, (cr) over bar (G), is the mi ...

The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of ...

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

We study the extinction time tau of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degr ...

Transport of suprathermal ions is examined from the Levy walk perspective in a simple magnetized toroidal plasma. Depending on their energy, these suprathermal ions exhibit superdiffusive, diffusive, or subdiffusive dispersion as a result of the complex in ...

The topic of this thesis is the study of several stochastic control problems motivated by sailing races. The goal is to minimize the travel time between two locations, by selecting the fastest route in face of randomly changing weather conditions, such as ...

Exceptional graphs for the random walk

Chattez avec Graph Search

Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces

On the robustness of the metric dimension of grid graphs to adding a single edge

Practical issues with modeling extreme Brazilian rainfall

Covering Graphs by Monochromatic Trees and Helly-Type Results for Hypergraphs

Representing graphs through data with learning and optimal transport

Partition and Code: learning how to compress graphs

Special Issue: "Data Science versus Classical Inference: Prediction, Estimation, and Attribution", honouring Prof. Brad Efron's International Prize in Statistics in 2019 Discussion

Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization

Ensemble Kalman Filter For Multiscale Inverse Problems

Normal approximation of the solution to the stochastic heat equation with Levy noise

Non-Exponential Variations for Classical Results in First Passage Percolation

The n-term Approximation of Periodic Generalized Levy Processes

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Bootstrap Percolation in Power-Law Random Graphs

Approximating the rectilinear crossing number

The Range of a Random Walk on a Comb

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility

Exponential extinction time of the contact process on finite graphs

Lévy walk description of suprathermal ion transport

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization