Fast Approximation of Nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems

This paper proposes a very fast method for blindly approximating a nonlinear mapping which transforms a sum of random variables. The estimation is surprisingly good even when the basic assumption is not satisfied.We use the method for providing a good initialization for inverting post-nonlinear mixtures and Wiener systems. Experiments show that the algorithm speed is strongly improved and the asymptotic performance is preserved with a very low extra computational cost.

Initialisation of Nonlinearities for PNL and Wiener systems Inversion

This paper proposes a very fast method for blindly initial- izing a nonlinear mapping which transforms a sum of random variables. The method provides a surprisingly good approximation even when the basic assumption is not fully satis¯ed. The method can been used success- fully for initializing nonlinearity in post-nonlinear mixtures or in Wiener system inversion, for improving algorithm speed and convergence.

Estimación de funciones no lineales en mezclas post-no lineales

This paper proposes a new method for blindly inverting a nonlinear mapping which transforms a sum of random variables. This is the case of post-nonlinear (PNL) source separation mixtures. The importance of the method is based on the fact that it permits to decouple the estimation of the nonlinear part from the estimation of the linear one. Only the nonlinear part is inverted, without considering on the linear part. Hence the initial problem is transformed into a linear one that can then be solved with any convenient linear algorithm. The method is compared with other existing algorithms for blindly approximating nonlinear mappings. Experiments show that the proposed algorithm outperforms the results obtained with other algorithms and give a reasonably good linearized data

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

A nonlinear threshold model for the dependence of extremes of stationary sequences

One of the main implications of the efficient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stocks prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example. JEL classification: C12; C15; C22; C51 Keywords and Phrases: asymmetries, crises, extreme values, hypothesis testing, leverage effect, nonlinearities, threshold models

Do creative industries cluster? mapping creative local production systems in Italy

An important debate on the role of creativity and culture as factors of local economic development is distinctly emerging. Despite the emphasis put on the theoretical definition of these concepts, it is necessary to strengthen comparative research for the identification and analysis of the kind of creativity embedded in the territory as well as its determinants. Creative local production systems are identified in Italy and Spain departing from local labour markets as territorial units, and focusing on two different kinds of creative

Association mapping of candidate genes for drought tolerance in Mediterranean durum wheat landraces

Treball al que se li ha concedit el premi al millor póster del congrés

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.

A first attempt of geographically-distributed Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM): mapping human time and energy throughput in metropolitan Barcelona

This study presents a first attempt to extend the “Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM)” approach to a spatial dimension using GIS techniques in the Metropolitan area of Barcelona. We use a combination of census and commercial databases along with a detailed land cover map to create a layer of Common Geographic Units that we populate with the local values of human time spent in different activities according to MuSIASEM hierarchical typology. In this way, we mapped the hours of available human time, in regards to the working hours spent in different locations, putting in evidence the gradients in spatial density between the residential location of workers (generating the work supply) and the places where the working hours are actually taking place. We found a strong three-modal pattern of clumps of areas with different combinations of values of time spent on household activities and on paid work. We also measured and mapped spatial segregation between these two activities and put forward the conjecture that this segregation increases with higher energy throughput, as the size of the functional units must be able to cope with the flow of exosomatic energy. Finally, we discuss the effectiveness of the approach by comparing our geographic representation of exosomatic throughput to the one issued from conventional methods.

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.

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.

MR MAQ: algorisme de Read Mapping utilitzant la plataforma Hadoop

L’èxit del Projecte Genoma Humà (PGH) l’any 2000 va fer de la “medicina personalitzada” una realitat més propera. Els descobriments del PGH han simplificat les tècniques de seqüenciació de tal manera que actualment qualsevol persona pot aconseguir la seva seqüència d’ADN complerta. La tecnologia de Read Mapping destaca en aquest tipus de tècniques i es caracteritza per manegar una gran quantitat de dades. Hadoop, el framework d’Apache per aplicacions intensives de dades sota el paradigma Map Reduce, resulta un aliat perfecte per aquest tipus de tecnologia i ha sigut l’opció escollida per a realitzar aquest projecte. Durant tot el treball es realitza l’estudi, l’anàlisi i les experimentacions necessàries per aconseguir un Algorisme Genètic innovador que utilitzi tot el potencial de Hadoop.