A Monge–Kantorovich mass transport problem for a discrete distance

AbstractThis paper is concerned with a Monge–Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obtain, taking limits in the rescaled nonlocal formulation, the PDE formulation given by Evans–Gangbo for the classical problem

On a dual formulation for the growing sandpile problem

International audienceIn this paper, we are interested in the mathematical and numerical study of the Prigozhinmodel for a growing sandpile. Based on implicit Euler discretization in time, we give a simpleimprovement of theoretical and numerical analyses of the dual formulation for the problem.By using this model, we also give some application to the Monge–Kantorovich problem foroptimal mass transportation

Utilisation of the Array-OL specification language for self-generation of a memory controller especially for the H.264/AVC

International audienceH.264/AVC has been introduced in recent years to decrease the bit-rate and to increase the flexibility of implementations. After careful study and analysis, we have concluded that the complexity of this video codec depends mainly on its multidimensional data dependency, its elementary processing modules and its various profiles and levels. In this paper, we have proposed several Array-OL models especially for the modelling of data flow between the processing modules for self-generation of vhdl code of a memory controller for H.264/AVC. The controller will be adapted to the application profiles and levels and the used external memory. The proposed models combined with high level modelling tools should be used to perform embedded systems; the goal is the automatic generation of the Netlist from a high level description. The methodology is demonstrated by an example in which a specific level of the H.264/AVC is generated from information given by the proposed Array-OL models. The generated vhdl code is synthesised using two FPGA development board with ratios of used LUTs that do not exceed 10% and verified to work at 263 MHz frequency

A Free Boundary Problem: contributions from modern analysis

We exemplify the role of Free Boundary Problems as an important source of ideas in modern analysis. With the help of a model problem we illustrate the use of analytical, algebraic and geometrical techniques obtaining uniqueness of weak solutions via the use of entropy inequalities, existence through nonlinear semigroup theory, and regularity using a method, called intrinsic scaling, based on interpreting a partial differential equation in a geometry dictated by its own structur