Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.

The determinants of YIc's R&D activity

This paper examines the determinants of young innovative companies’ (YICs) R&D activities taking into account the autoregressive nature of innovation. Using a large longitudinal dataset comprising Spanish manufacturing firms over the period 1990-2008, we find that previous R&D experience is a fundamental determinant for mature and young firms, albeit to a smaller extent in the case of the YICs, suggesting that their innovation behaviour is less persistent and more erratic. Moreover, our results suggest that firm and market characteristics play a distinct role in boosting the innovation activity of firms of different age. In particular, while market concentration and the degree of product diversification are found to be important in boosting R&D activities in the sub-sample of mature firms only, YICs’ spending on R&D appears to be more sensitive to demand-pull variables, suggesting the presence of credit constraints. These results have been obtained using a recently proposed dynamic type-2 tobit estimator, which accounts for individual effects and efficiently handles the initial conditions problem.

Escola i diversitat lingüística i cultural: desafiaments i oportunitats. El paper d'un Servei Educatiu de Zona com a agent d'innovació i canvi

Davant dels nous reptes educatius que planteja l’augment de la diversitat lingüística i cultural al conjunt del Sistema Educatiu Català, el present treball descriu els resultats i experiències obtinguts en les tres primeres fases d’un projecte de recerca centrat en la identificació d’indicadors vàlids que permetin dissenyar i implementar estratègies educatives inclusives adequades per atendre la diversitat lingüística i cultural present als nostres centres. La part central de la memòria descriu les primeres dades d’un estudi quantitatiu , realitzat en diferents moments del període d’escolarització (Pàrvuls 5 anys , segon i sisè de Primària i segon d’ESO) a quatre centres públics de Vilafranca del Penedès a finals del curs 2009-2010 , sobre el coneixement de català i de castellà i les possibles influències que en aquest hi juguen els factors de diversitat lingüística i cultural. El segon bloc d’aquest projecte presenta un seguit d’experiències i propostes d’assessorament centrades en el procés de sensibilització inicial sobre les implicacions educatives a nivell d’aula i de centre de la diversitat lingüística i cultural. També es presenta, com a annex final, un recull dels principals materials emprats en aquest procés d’intervenció en centre. A la part final del treball, s’hi desenvolupa una reflexió sobre les condicions que poden afavorir la implementació d’aquestes estratègies a nivell de centre i de sistema educatiu; i sobre el paper que , en aquests processos de canvi i millora educativa , hi podrien jugar els Serveis Educatius de Zona del Departament d’Ensenyament de la Generalitat de Catalunya.

Creació d'un programari per la transformació de dades

L'objectiu d'aquest TFC ha estat crear un programari que permeti transformacions ràpides de gran volums de dades. Cada procés de transformació hauria de dependre d'un conjunt de regles de transformació preestablertes per subconjunts de dades, de manera que el procés fos repetible i verificable per a poder garantir la qualitat dels processos de transformació; les regles de transformació s'haurien de poder especificar de manera fàcil i pràctica per a usuaris sense coneixements de programació; les transformacions possibles haurien de cobrir requeriments derivats de la neteja, la transformació i la formatació de dades en els nivells de taula, registre i camp, i per a cada subconjunt de dades i regles de transformació inicials, que constitueixen l'entrada, el programari hauria de retornar el corresponent subconjunt de dades transformades.

Multiuser detection with an unknown number of active users: receiver design

In multiuser detection, the set of users active at any time may be unknown to the receiver. In these conditions, optimum reception consists of detecting simultaneously the set of activeusers and their data, problem that can be solved exactly by applying random-set theory (RST) and Bayesian recursions (BR). However, implementation of optimum receivers may be limited by their complexity, which grows exponentially with the number of potential users. In this paper we examine three strategies leading to reduced-complexity receivers.In particular, we show how a simple approximation of BRs enables the use of Sphere Detection (SD) algorithm, whichexhibits satisfactory performance with limited complexity.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

The role of mentoring in facilitating the process of repurposing OER

This paper presents the initial data analysis of a research that is work in progress. It discusses the role of mentoring and peer support in facilitating the process of repurposing open educational resources (OER). It also reports on the lessons so far learned from the analysis of two distinct but related case studies on working with learners to use and disseminate OER.

El plan de lengua y cohesión social en Catañunya: primeros datos de una investigación = Language and Social Cohesion Plan in Catalonia: Initial research data

Los programas de inmersión lingüística han constituido y constituyen dentro del Sistema Educativo catalánla principal forma para que el alumnado de lengua familiar no-catalana aprenda una nueva lengua, el catalán,sin que, en su proceso de aprendizaje, vea mermado ni el desarrollo de su propia lengua ni su rendimientoacadémico. El éxito de la inmersión lingüística en las décadas anteriores ha sido frecuentemente utilizado comouno de los argumentos orientativos para justificar la política lingüística que se sigue en la escolarización de lainfancia extranjera. Sin embargo, los resultados obtenidos por investigaciones recientes parece que no avalanempíricamente dicho argumento. Este artículo analiza dichos resultados y expone, a partir del Plan para laLengua y Cohesión Social puesto en marcha por el Departamento de Educación de la Generalitat de Cataluña,cuáles son los retos que se presentan a su Sistema Educativo dentro del nuevo marco que supone el aumento de ladiversidad cultural y lingüística en la actual sociedad catalana

Data size sufficiency analyses of haplotype inference algortihms

We present experimental and theoretical analyses of data requirements for haplotype inference algorithms. Our experiments include a broad range of problem sizes under two standard models of tree distribution and were designed to yield statistically robust results despite the size of the sample space. Our results validate Gusfield's conjecture that a population size of n log n is required to give (with high probability) sufficient information to deduce the n haplotypes and their complete evolutionary history. The experimental results inspired our experimental finding with theoretical bounds on the population size. We also analyze the population size required to deduce some fixed fraction of the evolutionary history of a set of n haplotypes and establish linear bounds on the required sample size. These linear bounds are also shown theoretically.