Séminaires de probabilités et statistiques (SAMM, 2009-2010‪)‬ Université Paris 1 Panthéon-Sorbonne

This talk is concerned with issues related to social diversity in urban environments. We introduce a model of real estate transactions between agents which are heterogeneous in their willingness to pay. A key feature of the model is the assumption that agents preferences for a location depend both on an intrinsic attractiveness of the location, and on the social characteristics of its neighborhood. Focusing on the case of a monocentric city, the stationary state is analytically characterized and gives the distribution of income over space. The model is studied through numerical simulations as well

Cities are constellations of human processes that give rise to a multitude of dynamic behaviours manifesting themselves in rapid, abrupt, surprising, fast, slow and smooth changes across many temporal and spatial scales.

Formation and evolution of transportation networks, in the particular case of subway network.

The Sparse Coding principle together with novel theoretical insights like the "L1-norm miracle" have led to the new field of "Compressed Sensing". In this talk I will introduce the main ideas and main methods of compressed sensing and give an overview of the main applications of this exciting new field

We give sufficient conditions under which the convergence of finite difference approximations in the space variable of the solution to the Cauchy problem for stochastic PDEs of parabolic type can be accelerated to any given order of convergence by Richardson's method.

Manifold learning with sparse coding, applications to image reconstruction.