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Article
Tropical Reproducing Kernels and Optimization
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several equivalent characterizations. ...
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Chapter and Conference Paper
Computing Transience Bounds of Emergency Call Centers: A Hierarchical Timed Petri Net Approach
A fundamental issue in the analysis of emergency call centers is to estimate the time needed to return to a congestion-free regime after an unusual event with a massive arrival of calls. Call centers can gener...
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Article
Spectral Inequalities for Nonnegative Tensors and Their Tropical Analogues
We extend some characterizations and inequalities for the eigenvalues of nonnegative matrices, such as Donsker–Varadhan, Friedland–Karlin, Karlin–Ost inequalities, to nonnegative tensors. Our approach involves...
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Article
Tropical Spectrahedra
We introduce tropical spectrahedra, defined as the images by the nonarchimedean valuation of spectrahedra over the field of real Puiseux series. We provide an explicit polyhedral characterization of generic tr...
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Chapter and Conference Paper
Piecewise Affine Dynamical Models of Timed Petri Nets – Application to Emergency Call Centers
We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive map**s to ana...
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Chapter and Conference Paper
A Convex Programming Approach to Solve Posynomial Systems
We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collecti...
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Article
The Operator Approach to Entropy Games
Entropy games and matrix multiplication games have been recently introduced by Asarin et al. They model the situation in which one player (Despot) wishes to minimize the growth rate of a matrix product, wherea...
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Article
Algèbre de groupe en caractéristique 1 et distances invariantes sur un groupe fini
Les distances et plus généralement les métriques invariantes sur un groupe fini, utilisées en particulier en statistique, sont étroitement liées aux idempotents de l’algèbre du groupe sur le semi-corps idempot...
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Article
Open AccessExploration of the role of the virulence factor ElrA during Enterococcus faecalis cell infection
Enterococcus faecalis, an organism generally not pathogenic for healthy humans, has the potential to cause disease in susceptible hosts. While it seems to be equipped to interact with and circumvent host immune d...
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Article
Maximizing concave piecewise affine functions on the unitary group
We show that a convex relaxation, introduced by Sridharan, McEneaney, Gu and James to approximate the value function of an optimal control problem arising from quantum gate synthesis, is exact. This relaxation...
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Article
Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model
We consider a cell population described by an age-structured partial differential equation with time periodic coefficients. We assume that division only occurs within certain time intervals at a rate ...
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Article
Certification of real inequalities: templates and sums of squares
We consider the problem of certifying lower bounds for real-valued multivariate transcendental functions. The functions we are dealing with are nonlinear and involve semialgebraic operations as well as some tr...
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Article
Open AccessOverexpression of Enterococcus faecalis elr operon protects from phagocytosis
Mechanisms underlying the transition from commensalism to virulence in Enterococcus faecalis are not fully understood. We previously identified the enterococcal leucine-rich protein A (ElrA) as a virulence factor...
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Article
Dobrushin’s Ergodicity Coefficient for Markov Operators on Cones
Doeblin and Dobrushin characterized the contraction rate of Markov operators with respect the total variation norm. We generalize their results by giving an explicit formula for the contraction rate of a Marko...
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Chapter and Conference Paper
Performance Evaluation of an Emergency Call Center: Tropical Polynomial Systems Applied to Timed Petri Nets
We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a func...
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Chapter and Conference Paper
The Tropical Shadow-Vertex Algorithm Solves Mean Payoff Games in Polynomial Time on Average
We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every s...
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Article
The level set method for the two-sided max-plus eigenproblem
We consider the max-plus analogue of the eigenproblem for matrix pencils, A ⊗ x = λ ⊗ B ⊗ x. We show that the spectrum of (A,B) (i.e., the set of possible values of λ), which is a finite union of intervals, can b...
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Article
Computing the Vertices of Tropical Polyhedra Using Directed Hypergraphs
We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, const...
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Chapter
Is the Distance Geometry Problem in NP?
Given a weighted undirected graph \(G = (V,E,d)\) with $$d : E \rightarr...
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Chapter and Conference Paper
Certification of Bounds of Non-linear Functions: The Templates Method
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof...
