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.

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Suboptimal filtering and nonlinear time scale transformation for the analysis of multiexponential decays

Multiexponential decays may contain time-constants differing in several orders of magnitudes. In such cases, uniform sampling results in very long records featuring a high degree of oversampling at the final part of the transient. Here, we analyze a nonlinear time scale transformation to reduce the total number of samples with minimum signal distortion, achieving an important reduction of the computational cost of subsequent analyses. We propose a time-varying filter whose length is optimized for minimum mean square error

On the consequences of misspecifing assumptions concerning residuals distribution in a repeated measures and nonlinear mixed modelling context

In this paper we describe the results of a simulation study performed to elucidate the robustness of the Lindstrom and Bates (1990) approximation method under non-normality of the residuals, under different situations. Concerning the fixed effects, the observed coverage probabilities and the true bias and mean square error values, show that some aspects of this inferential approach are not completely reliable. When the true distribution of the residuals is asymmetrical, the true coverage is markedly lower than the nominal one. The best results are obtained for the skew normal distribution, and not for the normal distribution. On the other hand, the results are partially reversed concerning the random effects. Soybean genotypes data are used to illustrate the methods and to motivate the simulation scenarios

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate.

Post-Nonlinear Mixtures and Beyond

Although sources in general nonlinear mixturm arc not separable iising only statistical independence, a special and realistic case of nonlinear mixtnres, the post nonlinear (PNL) mixture is separable choosing a suited separating system. Then, a natural approach is based on the estimation of tho separating Bystem parameters by minimizing an indcpendence criterion, like estimated mwce mutual information. This class of methods requires higher (than 2) order statistics, and cannot separate Gaarsian sources. However, use of [weak) prior, like source temporal correlation or nonstationarity, leads to other source separation Jgw rithms, which are able to separate Gaussian sourra, and can even, for a few of them, works with second-order statistics. Recently, modeling time correlated s011rces by Markov models, we propose vcry efficient algorithms hmed on minimization of the conditional mutual information. Currently, using the prior of temporally correlated sources, we investigate the fesihility of inverting PNL mixtures with non-bijectiw non-liacarities, like quadratic functions. In this paper, we review the main ICA and BSS results for riunlinear mixtures, present PNL models and algorithms, and finish with advanced resutts using temporally correlated snu~sm

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

The Analysis of interval censoring and double censoring via Markov chain Monte Carlo methods

L'Anàlisi de la supervivència s'utilitza en diferents camps per analitzar el temps transcorregut entre dos esdeveniments. El que distingeix l'anàlisi de la supervivència d'altres àrees de l'estadística és que les dades normalment estan censurades. La censura en un interval apareix quan l'esdeveniment final d'interès no és directament observable i només se sap que el temps de fallada està en un interval concret. Un esquema de censura més complex encara apareix quan tant el temps inicial com el temps final estan censurats en un interval. Aquesta situació s'anomena doble censura. En aquest article donem una descripció formal d'un mètode bayesà paramètric per a l'anàlisi de dades censurades en un interval i dades doblement censurades així com unes indicacions clares de la seva utilització o pràctica. La metodologia proposada s'ilustra amb dades d'una cohort de pacients hemofílics que es varen infectar amb el virus VIH a principis dels anys 1980's.

Eliciting and fostering learners' metacognitive knowledge about language learning in self-directed learning programs: a review of data collection methods and procedures

Són molts els estudis que avui en dia incideixen en la necessitat d’oferir un suport metodològic i psicològic als aprenents que treballen de manera autònoma. L’objectiu d’aquest suport és ajudar-los a desenvolupar les destreses que necessiten per dirigir el seu aprenentatge així com una actitud positiva i una major conscienciació envers aquest aprenentatge. En definitiva, aquests dos tipus de preparació es consideren essencials per ajudar els aprenents a esdevenir més autònoms i més eficients en el seu propi aprenentatge. Malgrat això, si bé és freqüent trobar estudis que exemplifiquen aplicacions del suport metodològic dins els seus programes, principalment en la formació d’estratègies o ajudant els aprenents a desenvolupar un pla de treball, aquest no és el cas quan es tracta de la seva preparació psicològica. Amb rares excepcions, trobem estudis que documentin com s’incideix en les actituds i en les creences dels aprenents, també coneguts com a coneixement metacognitiu (CM), en programes que fomenten l’autonomia en l’aprenentatge. Els objectius d’aquest treball son dos: a) oferir una revisió d’estudis que han utilitzat diferents mitjans per incidir en el CM dels aprenents i b) descriure les febleses i avantatges dels procediments i instruments que utilitzen, tal com han estat valorats en estudis de recerca, ja que ens permetrà establir criteris objectius sobre com i quan utilitzar-los en programes que fomentin l’aprenentatge autodirigit.

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.

Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.

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

Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

Empirical studies in industrial location: an assessment of their methods and results

This paper surveys recent evidence on the determinants of (national and/or foreign) industrial location. We find that the basic analytical framework has remained essentially unaltered since the early contributions of the early 1980's while, in contrast, there have been significant advances in the quality of the data and, to a lesser extent, the econometric modelling. We also identify certain determinants (neoclassical and institutional factors) that tend to provide largely consistent results across the reviewed studies. In light of this evidence, we finally suggest future lines of research.