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Special Issue of the Journal of Mathematical Structures in Computer Science dedicated to a selection of papers presented at the 18th International Workshop on Expressiveness in Concurrency (EXPRESS'11)
No full textInternational audienceThis issue of Mathematical Structures in Computer Science contains a selection of papers presented at the 18th International Workshop on Expressiveness in Concurrency (EXPRESS'11), a satellite event of CONCUR'11, held on September 5th, 2011 in Aachen, German
Generic uniqueness of the bias vector of mean-payoff zero-sum games
No full textInternational audienceZero-sum mean payoff games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair (u,λ) solution of T(u)=λ1+u where T:Rn→Rn is the Shapley (dynamic programming) operator, λ is a scalar, 1 is the unit vector, and u∈Rn. The scalar λ yields the mean payoff per time unit, and the vector u, called the bias, allows one to determine optimal stationary strategies. The existence of the eigenpair (u,λ) is generally related to ergodicity conditions. A basic issue is to understand for which classes of games the bias vector is unique (up to an additive constant). In this paper, we consider perfect information zero-sum stochastic games with finite state and action spaces, thinking of the transition payments as variable parameters, transition probabilities being fixed. We identify structural conditions on the support of the transition probabilities which guarantee that the spectral problem is solvable for all values of the transition payments. Then, we show that the bias vector, thought of as a function of the transition payments, is generically unique (up to an additive constant). The proof uses techniques of max-plus (tropical) algebra and nonlinear Perron-Frobenius theory
Investments and Liability Regimes in Payment Platforms
No full textSupplementary data to this article can be found online at http://dx.doi.org/10.1016/j.ijindorg.2014.06.003International audienceIn this paper, we discuss how fraud losses impact the price structure chosen by a monopolistic payment platform, if merchants can invest in fraud detection technologies. We show that liability rules bias the structure of the prices charged by the platform to consumers and merchants with respect to a case in which such a responsibility regime is not implemented. If consumers are liable for fraud, the profit-maximizing price structure is neither biased in favor of consumers nor merchants. If consumers are not liable for fraud, the platform lowers the price for merchants to provide them with investment incentives. Under the zero liability rule for consumers, the profit-maximizing allocation of fraud losses maximizes social welfare
Characterization of Glioma Microcirculation and Tissue Features Using Intravoxel Incoherent Motion Magnetic Resonance Imaging in a Rat Brain Model
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Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media
No full textInternational audienceWe consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first transmission eigenvalue with respect to the thickness of the thin layer. Our convergence analysis is based on a Max–Min principle and an iterative approach which involves estimates on the corresponding eigenfunctions. We provide explicit expressions for the terms in the asymptotic expansion up to order 3
Assessing the enrichment significance of a Position Weight Matrix along a DNA sequence
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A bijection for plane graphs and its applications
No full textInternational audienceThis paper is concerned with the counting and random sampling of plane graphs (simple planar graphs embedded in the plane). Our main result is a bijection between the class of plane graphs with triangular outer face, and a class of oriented binary trees. The number of edges and vertices of the plane graph can be tracked through the bijection. Consequently, we obtain counting formulas and an efficient random sampling algorithm for rooted plane graphs (with arbitrary outer face) according to the number of edges and vertices. We also obtain a bijective link, via a bijection of Bona, between rooted plane graphs and 1342-avoiding permutations. 1 Introduction A planar graph is a graph that can be embedded in the plane (drawn in the plane without edge crossing). A pla-nar map is an embedding of a connected planar graph considered up to deformation. The enumeration of pla-nar maps has been the subject of intense study since the seminal work of Tutte in the 60's [20] showing that many families of planar maps have beautiful counting formulas. Starting with the work of Cori and Vauquelin [10] and then Schaeffer [18, 19], bijective constructions have been discovered that provide more transparent proofs of such formulas. The enumeration of planar graphs has also been the focus of a lot of efforts, culminating with the asymptotic counting formulas obtained by Giménez and Noy [16]. In this paper we focus on simple planar maps (planar maps without loops nor multiple edges), which are also called plane graphs. This family of planar maps has, quite surprisingly, not been considered until fairly recently. This is probably due to the fact that loops and multiple edges are typically allowed in studies about planar maps, whereas they are usually forbidden in studies about planar graphs. At any rate, the first result about plane graphs was an exact algebraic expressio
Periodic planar straight-frame drawings with polynomial resolution
No full textInternational audienceWe present a new algorithm to compute periodic (planar) straight-line drawings of toroidal graphs. Our algorithm is the first to achieve two important aesthetic criteria: the drawing fits in a straight rectangular frame, and the grid area is polynomial, precisely the grid size is O(n 4 × n 4). This solves one of the main open problems in a recent paper by Duncan et al. [3]
Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow
No full textInternational audienceThe fundamental free-space 2D steady creeping MHD flow produced by a concentrated point force of strength g located at a so-called source point x0 in an unbounded conducting Newtonian liquid with uniform viscosity μ and conductivity σ>0 subject to a prescribed uniform ambient magnetic field B=Be1 is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field σ are expressed at any observation point x≠x0 in terms of usual modified Bessel functions, the vectors g,x−x0 and the so-called Hartmann layer thickness d=(μ/σ−−−√)/B (see Hartmann (1937)). The resulting basic flows obtained for g either parallel with or normal to the magnetic field B are examined and found to exhibit quite different properties