http://hdl.handle.net/2072/98 http://www.recercat.net/retrieve/2418 http://hdl.handle.net/2072/98 Search the Channel s http://www.recercat.net/simple-search http://hdl.handle.net/2072/67882 title: Sobolev mappings, degree, homotopy classes and rational homology spheres authors: Goldstein, Pawel; Hajlasz, Piotr <br>abstract: "Vegeu el resum a l'inici del document del fitxer adjunt." <br> Mon, 29 Mar 2010 22:58:59 GMT http://hdl.handle.net/2072/67881 title: Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension authors: Calvez, Vincent; Corrias, Lucilla; Ebde, Mohamed Abderrahman <br>abstract: "Vegeu el resum a l'inici del document del fitxer adjunt." <br> Mon, 29 Mar 2010 22:58:59 GMT http://hdl.handle.net/2072/67880 title: A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics authors: Cáceres, María J.; Carrillo, José A.; Tao, Louis <br>abstract: To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory. <br> Fri, 26 Feb 2010 22:58:59 GMT http://hdl.handle.net/2072/67879 title: On the number of higher order Delaunay triangulations authors: Mitsche, Dieter; Saumell, Maria; Silveira, Rodrigo I. <br>abstract: "Vegeu el resum a l'inici del document del fitxer adjunt." <br> Fri, 26 Feb 2010 22:58:59 GMT