Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

The Accessibility City. When Transport Infrastructure Matters in Urban Spatial Structure

Suburbanization is changing the urban spatial structure and less monocentric metropolitan regions are becoming the new urban reality. Focused only on centers, most works have studied these spatial changes neglecting the role of transport infrastructure and its related location model, the “accessibility city”, in which employment and population concentrate in low-density settlements and close to transport infrastructure. For the case of Barcelona, we consider this location model and study the population spatial structure between 1991 and 2006. The results reveal a mix between polycentricity and the accessibility city, with movements away from the main centers, but close to the transport infrastructure.

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.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Structure theorems for subgroups of homeomorphism groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

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.

Technology, business models and network structure in the airline industry

Network airlines have been increasingly focusing their operations on hub airports through the exploitation of connecting traffic, allowing them to take advantage of economies of traffic density, which are unequivocal in the airline industry. Less attention has been devoted to airlines? decisions on point-to-point thin routes, which could be served using different aircraft technologies and different business models. This paper examines, both theoretically and empirically, the impact on airlines ?networks of the two major innovations in the airline industry in the last two decades: the regional jet technology and the low-cost business model. We show that, under certain circumstances, direct services on point-to-point thin routes can be viable and thus airlines may be interested in deviating passengers out of the hub.

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give sufficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.

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.

Technology, business models and network structure in the airline industry

Network airlines have been increasingly focusing their operations on hub airports through the exploitation of connecting traffic, allowing them to take advantage of economies of traffic density, which are unequivocal in the airline industry. Less attention has been devoted to airlines' decisions on point-to-point thin routes, which could be served using different aircraft technologies and different business models. This paper examines, both theoretically and empirically, the impact on airlines' networks of the two major innovations in the airline industry in the last two decades: the regional jet technology and the low-cost business model. We show that, under certain circumstances, direct services on point-to-point thin routes can be viable and thus airlines may be interested in deviating passengers out of the hub. Keywords: regional jet technology; low-cost business model; point-to-point network; hub-and-spoke network JEL Classi…fication Numbers: L13; L2; L93

Spatio-temporal variations in reproductive patterns and population structure of Pasiphaea multidentata (Decapoda: Caridea) in the Blanes canyon and adjacent margin, North-western Mediterranean Sea

The bathyal faunal communities of the NW Mediterranean slopes have been studied consistently in the last two decades, with a special focus on population structure, trophic dynamics and benthopelagic coupling of commercial deep-sea decapod crustaceans and fishes (reviewed in Sardà et al. 2004) and associated species (Cartes and Sardà, 1993; Company and Sardà, 1997, 2000; Cartes et al., 2001; Company et al., 2001, 2003, 2004). One of the major topographic features in the North-western Mediterranean slope is the presence of submarine canyons. Canyons play a major role in funnelling energy and organic matter from the shelf to bathyal and abyssal depths (Puig et al., 2000), but the implications of this enhanced organic supply in the deep-sea benthic communities is still mostly unknown. Trophic supply can follow two major pathways – vertical deposition in the water column (Billett et al., 1983; Baldwin et al., 1998; Lampitt et al., 2001) or down-slope advection on the margins (Puig et al., 2001; Bethoux et al., 2002; Canals et al., 2006) – and can be a limiting factor in the deep-sea, being especially important in the oligotrophic Mediterranean Sea (Sardà et al., 2004). Differences in the quantity, quality and timing of organic matter input to the deep seafloor have been used to explain patterns of biomass and abundance in benthic communities (Levin et al., 1994; Gooday & Turley, 1990; Billett et al., 2001; Galéron et al., 2001; Puig et al., 2001; Gage, 2003) as well as other biological process and in particular the existence of seasonal reproduction (Tyler et al., 1994; Company et al., 2004 (MEPS). Reproduction is a highly energetic process tightly linked to food availability and quality.

Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deteriorates

Population genetic structure and demography analysis in palinurus elephas populations from atlantic and mediterranean waters

Report for the scientific sojourn at the University of Reading, United Kingdom, from January until May 2008. The main objectives have been firstly to infer population structure and parameters in demographic models using a total of 13 microsatellite loci for genotyping approximately 30 individuals per population in 10 Palinurus elephas populations both from Mediterranean and Atlantic waters. Secondly, developing statistical methods to identify discrepant loci, possibly under selection and implement those methods using the R software environment. It is important to consider that the calculation of the probability distribution of the demographic and mutational parameters for a full genetic data set is numerically difficult for complex demographic history (Stephens 2003). The Approximate Bayesian Computation (ABC), based on summary statistics to infer posterior distributions of variable parameters without explicit likelihood calculations, can surmount this difficulty. This would allow to gather information on different demographic prior values (i.e. effective population sizes, migration rate, microsatellite mutation rate, mutational processes) and assay the sensitivity of inferences to demographic priors by assuming different priors.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.