Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Un método de diferencias finitas generalizadas para simular la actividad eléctrica de un tejido cardiaco

Una evolución del método de diferencias finitas ha sido el desarrollo del método de diferencias finitas generalizadas (MDFG) que se puede aplicar a mallas irregulares o nubes de puntos. En este método se emplea una expansión en serie de Taylor junto con una aproximación por mínimos cuadrados móviles (MCM). De ese modo, las fórmulas explícitas de diferencias para nubes irregulares de puntos se pueden obtener fácilmente usando el método de Cholesky. El MDFG-MCM es un método sin malla que emplea únicamente puntos. Una contribución de esta Tesis es la aplicación del MDFG-MCM al caso de la modelización de problemas anisótropos elípticos de conductividad eléctrica incluyendo el caso de tejidos reales cuando la dirección de las fibras no es fija, sino que varía a lo largo del tejido. En esta Tesis también se muestra la extensión del método de diferencias finitas generalizadas a la solución explícita de ecuaciones parabólicas anisótropas. El método explícito incluye la formulación de un límite de estabilidad para el caso de nubes irregulares de nodos que es fácilmente calculable. Además se presenta una nueva solución analítica para una ecuación parabólica anisótropa y el MDFG-MCM explícito se aplica al caso de problemas parabólicos anisótropos de conductividad eléctrica. La evidente dificultad de realizar mediciones directas en electrocardiología ha motivado un gran interés en la simulación numérica de modelos cardiacos. La contribución más importante de esta Tesis es la aplicación de un esquema explícito con el MDFG-MCM al caso de la modelización monodominio de problemas de conductividad eléctrica. En esta Tesis presentamos un algoritmo altamente eficiente, exacto y condicionalmente estable para resolver el modelo monodominio, que describe la actividad eléctrica del corazón. El modelo consiste en una ecuación en derivadas parciales parabólica anisótropa (EDP) que está acoplada con un sistema de ecuaciones diferenciales ordinarias (EDOs) que describen las reacciones electroquímicas en las células cardiacas. El sistema resultante es difícil de resolver numéricamente debido a su complejidad. Proponemos un método basado en una separación de operadores y un método sin malla para resolver la EDP junto a un método de Runge-Kutta para resolver el sistema de EDOs de la membrana y las corrientes iónicas. ABSTRACT An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method that can be applied to irregular grids or clouds of points. In this method a Taylor series expansion is used together with a moving least squares (MLS) approximation. Then, the explicit difference formulae for irregular clouds of points can be easily obtained using a simple Cholesky method. The MLS-GFD is a mesh-free method using only points. A contribution of this Thesis is the application of the MLS-GFDM to the case of modelling elliptic anisotropic electrical conductivity problems including the case of real tissues when the fiber direction is not fixed, but varies throughout the tissue. In this Thesis the extension of the generalized finite difference method to the explicit solution of parabolic anisotropic equations is also given. The explicit method includes a stability limit formulated for the case of irregular clouds of nodes that can be easily calculated. Also a new analytical solution for homogeneous parabolic anisotropic equation has been presented and an explicit MLS- GFDM has been applied to the case of parabolic anisotropic electrical conductivity problems. The obvious difficulty of performing direct measurements in electrocardiology has motivated wide interest in the numerical simulation of cardiac models. The main contribution of this Thesis is the application of an explicit scheme based in the MLS-GFDM to the case of modelling monodomain electrical conductivity problems using operator splitting including the case of anisotropic real tissues. In this Thesis we present a highly efficient, accurate and conditionally stable algorithm to solve a monodomain model, which describes the electrical activity in the heart. The model consists of a parabolic anisotropic partial differential equation (PDE), which is coupled to systems of ordinary differential equations (ODEs) describing electrochemical reactions in the cardiac cells. The resulting system is challenging to solve numerically, because of its complexity. We propose a method based on operator splitting and a meshless method for solving the PDE together with a Runge-Kutta method for solving the system of ODE’s for the membrane and ionic currents.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

A hybrid data assimilation scheme for model parameter estimation: application to morphodynamic modelling

We present a novel algorithm for joint state-parameter estimation using sequential three dimensional variational data assimilation (3D Var) and demonstrate its application in the context of morphodynamic modelling using an idealised two parameter 1D sediment transport model. The new scheme combines a static representation of the state background error covariances with a flow dependent approximation of the state-parameter cross-covariances. For the case presented here, this involves calculating a local finite difference approximation of the gradient of the model with respect to the parameters. The new method is easy to implement and computationally inexpensive to run. Experimental results are positive with the scheme able to recover the model parameters to a high level of accuracy. We expect that there is potential for successful application of this new methodology to larger, more realistic models with more complex parameterisations.

'Lo que diga la asamblea'. El ritual político como fetiche en tiempos de crisis

La actual crisis sistémica ha operado como una estructura de oportunidad sobre la que han cristalizado nuevos discursos, nuevas prácticas y nuevas estructuras políticas. La irrupción del 15M, de la Plataforma de Afectados por la Hipoteca (PAH) o de las llamadas “mareas” han permitido la visibilización de modos de hacer política que marcan una diferencia explícita con las prácticas asociadas al establishment político del llamado “régimen del 78”. Algunas de las prácticas popularizadas por estos movimientos han llegado a ser asumidas por amplias capas de la población. Entre ellas, destaca la asamblea como método legítimo de toma de decisiones. En esta comunicación planteamos un análisis de la asamblea como ritual político, deteniéndonos en la descripción de sus lógicas organizativas, principios de legimitación y características formales. A través de datos etnográficos recabados en la ciudad de Alcalá de Guadaíra (Sevilla) rastreamos la trama específica de discursos, prácticas y relaciones observables en el seno de las asambleas organizadas por el movimiento 15M. Finalmente, y a través de estos datos, reflexionamos sobre el sentido político del ritual en tiempos de crisis.

Diffusion Gradient Temporal Difference for Cooperative Reinforcement Learning with Linear Function Approximation

We introduce a diffusion-based algorithm in which multiple agents cooperate to predict a common and global statevalue function by sharing local estimates and local gradient information among neighbors. Our algorithm is a fully distributed implementation of the gradient temporal difference with linear function approximation, to make it applicable to multiagent settings. Simulations illustrate the benefit of cooperation in learning, as made possible by the proposed algorithm.

Distinct conformational properties determined by implicit and explicit representation of protein-solvent interactions. An analytical and computer simulation study

In the protein folding problem, solvent-mediated forces are commonly represented by intra-chain pairwise contact energy. Although this approximation has proven to be useful in several circumstances, it is limited in some other aspects of the problem. Here we show that it is possible to achieve two models to represent the chain-solvent system. one of them with implicit and other with explicit solvent, such that both reproduce the same thermodynamic results. Firstly, lattice models treated by analytical methods, were used to show that the implicit and explicitly representation of solvent effects can be energetically equivalent only if local solvent properties are time and spatially invariant. Following, applying the same reasoning Used for the lattice models, two inter-consistent Monte Carlo off-lattice models for implicit and explicit solvent are constructed, being that now in the latter the solvent properties are allowed to fluctuate. Then, it is shown that the chain configurational evolution as well as the globule equilibrium conformation are significantly distinct for implicit and explicit solvent systems. Actually, strongly contrasting with the implicit solvent version, the explicit solvent model predicts: (i) a malleable globule, in agreement with the estimated large protein-volume fluctuations; (ii) thermal conformational stability, resembling the conformational hear resistance of globular proteins, in which radii of gyration are practically insensitive to thermal effects over a relatively wide range of temperatures; and (iii) smaller radii of gyration at higher temperatures, indicating that the chain conformational entropy in the unfolded state is significantly smaller than that estimated from random coil configurations. Finally, we comment on the meaning of these results with respect to the understanding of the folding process. (C) 2009 Elsevier B.V. All rights reserved.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

The invisible factors that can make the difference. Language management and knowledge transfer in multinational sites

The knowledge-based society we live in has stressed the importance of human capital and brought talent to the top of most wanted skills, especially to companies who want to succeed in turbulent environments worldwide. In fact, streams, sequences of decisions and resource commitments characterize the day-to-day of multinational companies (MNCs). Such decision-making activities encompass major strategic moves like internationalization and new market entries or diversification and acquisitions. In most companies, these strategic decisions are extensively discussed and debated and are generally framed, formulated, and articulated in specialized language often developed by the best minds in the company. Yet the language used in such deliberations, in detailing and enacting the implementation strategy is usually taken for granted and receives little if any explicit attention (Brannen & Doz, 2012) an can still be a “forgotten factor” (Marschan et al. 1997). Literature on language management and international business refers to lack of awareness of business managers of the impact that language can have not only in communication effectiveness but especially in knowledge transfer and knowledge management in business environments. In the context of MNCs, management is, for many different reasons, more complex and demanding than that of a national company, mainly because of diversity factors inherent to internationalization, namely geographical and cultural spaces, i.e, varied mindsets. Moreover, the way of functioning, and managing language, of the MNC depends on its vision, its values and its internationalization model, i.e on in the way the MNE adapts to and controls the new markets, which can vary essentially from a more ethnocentric to a more pluricentric focus. Regardless of the internationalization model followed by the MNC, communication between different business units is essential to achieve unity in diversity and business sustainability. For the business flow and prosperity, inter-subsidiary, intra-company and company-client (customers, suppliers, governments, municipalities, etc..) communication must work in various directions and levels of the organization. If not well managed, this diversity can be a barrier to global coordination and create turbulent environments, even if a good technological support is available (Feely et al., 2002: 4). According to Marchan-Piekkari (1999) the tongue can be both (i) a barrier, (ii) a facilitator and (iii) a source of power. Moreover, the lack of preparation for the barriers of linguistic diversity can lead to various costs, including negotiations’ failure and failure on internationalization.. On the other hand, communication and language fluency is not just a message transfer procedure, but above all a knowledge transfer process, which requires extra-linguistic skills (persuasion, assertiveness …) in order to promote credibility of both parties. For this reason, MNCs need a common code to communicate and trade information inside and outside the company, which will require one or more strategies, in order to overcome possible barriers and organization distortions.

Violent adolescents and their educational environment : a multilevel analysis ; et, Youths carrying a weapon or using a weapon in a fight : what makes the difference ?

Rapport de synthèse : Cette recherche s'intéresse (1) au port et à l'utilisation d'armes chez les adolescents ainsi que (2) aux rôles des facteurs environnementaux et individuels dans la violence juvénile. Les données étaient tirés de SMASH 2002 (Swiss multicenter adolescent survey on health 2002), étude dans laquelle un échantillon représentatif de 7548 étudiants et apprentis âgés entre 16 et 20 ans vivant en Suisse ont été interrogés Dans une première étude, les adolescents ayant porté une arme (couteau, masse, coup de poing américain, pistolet/autre arme à feu, spray) durant l'année précédant l'enquête étaient comparés avec ceux n'ayant pas porté d'arme. Ensuite, dans le sous-échantillon de porteurs d'armes, ceux ayant uniquement porté l'arme étaient comparés avec ceux ayant utilisé une arme dans une bagarre. Des facteurs individuels, familiaux, scolaires et sociaux ont été étudiés à l'aide d'analyses bivariées et multivariées. 13.7% des jeunes vivant en Suisse ont porté une arme dans l'année précédant l'enquête. 6.2% des filles porteuses d'armes et 19.9% des garçons porteurs d'armes ont fait usage de l'arme dans une bagarre. Chez les garçons et chez les filles, les porteurs d'armes étaient plus souvent délinquants et victimes de violence physique. Les garçons porteurs d'armes étaient plus souvent des apprentis, à la recherche de sensations fortes, porteurs de tatouages, avaient une mauvaise relation avec leurs parents, étaient dans des bagarres sous l'influence de substances, et avaient des relations sexuelles à risque. En comparaison avec les porteuses d'armes, les filles utilisatrices d'armes étaient plus souvent fumeuses quotidiennes. Les garçons ayant utilisé leur arme étaient plus souvent nés à l'étranger, vivaient dans un milieu urbain, étaient des apprentis, avaient un mauvais contexte scolaire, avaient des relations sexuelles à risque et étaient impliqués dans des bagarres sous l'influence de substances. Nos résultats montrent que porter une arme est un comportement relativement fréquent chez les adolescents vivant en Suisse et qu'une proportion non négligeable de ces porteurs d'armes ont utilisé l'arme dans une bagarre. De ce fait, une discussion sur le port d'arme devrait être incluse dans l'entretien clinique ainsi que dans les programmes de prévention visant les adolescents. Dans une deuxième étude, la violence juvénile était définie comme présente si l'adolescent avait commis au moins un des quatre délits suivants durant l'année précédant l'enquête: attaquer un adulte, arracher ou voler quelque chose, porter une arme ou utiliser une arme dans une bagarre. Des niveaux écologiques étaient testés et résultaient en un modèle à trois niveaux pour les garçons (niveau individuel, niveau classe et niveau école) et, à cause d'une faible prévalence de la violence chez les filles, en un modèle à un niveau (individuel) pour les filles. Des variables dépendantes étaient attribuées à chaque niveau, en se basant sur la littérature. Le modèle multiniveaux des garçons montrait que le niveau école (10%) et le niveau classe (24%) comptaient pour plus d'un tiers de la variance inter-individuelle dans le comportement violent. Les facteurs associés à ce comportement chez les filles étaient être victime de violence physique et la recherche de sensations fortes. Pour les garçons, les facteurs explicatifs de la violence étaient pratiquer des relations sexuelles à risque, être à la recherche de sensations fortes, être victime de violence physique, avoir une mauvaise relation avec les parents, être déprimé et vivre dans une famille monoparentale au niveau individuel, la violence et les actes antisociaux au niveau de la classe et être apprenti au niveau de l'école. Des interventions au niveau de la classe ainsi qu'un règlement explicit en ce qui concerne la violence et d'autres comportements à risque dans des écoles devraient être prioritaires pour la prévention de la violence chez les adolescents. En outre, la prévention devrait tenir compte des différences entre les sexes.

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Voluntary Explicit versus Involuntary Conceptual Memory Are Associated with Dissociable fMRI Responses in Hippocampus, Amygdala, and Parietal Cortex for Emotional and Neutral Word Pairs.

Although functional neuroimaging studies have supported the distinction between explicit and implicit forms of memory, few have matched explicit and implicit tests closely, and most of these tested perceptual rather than conceptual implicit memory. We compared event-related fMRI responses during an intentional test, in which a group of participants used a cue word to recall its associate from a prior study phase, with those in an incidental test, in which a different group of participants used the same cue to produce the first associate that came to mind. Both semantic relative to phonemic processing at study, and emotional relative to neutral word pairs, increased target completions in the intentional test, but not in the incidental test, suggesting that behavioral performance in the incidental test was not contaminated by voluntary explicit retrieval. We isolated the neural correlates of successful retrieval by contrasting fMRI responses to studied versus unstudied cues for which the equivalent "target" associate was produced. By comparing the difference in this repetition-related contrast across the intentional and incidental tests, we could identify the correlates of voluntary explicit retrieval. This contrast revealed increased bilateral hippocampal responses in the intentional test, but decreased hippocampal responses in the incidental test. A similar pattern in the bilateral amygdale was further modulated by the emotionality of the word pairs, although surprisingly only in the incidental test. Parietal regions, however, showed increased repetition-related responses in both tests. These results suggest that the neural correlates of successful voluntary explicit memory differ in directionality, even if not in location, from the neural correlates of successful involuntary implicit (or explicit) memory, even when the incidental test taps conceptual processes.