The Large Deviation Principle for Coarse-Grained Processes

The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in statistical mechanics by exploiting the long-range nature of the interaction function defining such models. In particular, the large deviation principle is used in a companion paper to derive the variational principles that characterize equilibrium macrostates in statistical models of two-dimensional and quasi-geostrophic turbulence. Such macrostates correspond to large-scale, long-lived flow structures, the description of which is the goal of the statistical equilibrium theory of turbulence. The large deviation bounds for the coarse-grained process under consideration are shown to hold with respect to the strong $L^2$ topology, while the associated rate function is proved to have compact level sets with respect to the weak topology. This compactness property is nevertheless sufficient to establish the existence of equilibrium macrostates for both the microcanonical and canonical ensembles.Comment: 19 page

Linguistic analysis of the valence, arousal and dominance of auditory hallucinations and internal thoughts in schizophrenia: Implications for psychoeducation and CBT

70% of patients with schizophrenia suffer from auditory verbal hallucinations (AVH) which are frequently described as distressing and disabling. The content of AVH, in relation to internal thought, has never been linguistically tested in a self-monitoring study. The aim of this preliminary study was to establish if there was a significant difference between AVH and inner thoughts on the key linguistic parameters of valence (pleasantness), dominance (control) and arousal (intensity of emotion produced). Six volunteers with a diagnosis of schizophrenia from voice hearing support groups produced real-time, detailed diaries of AVH and inner thoughts using randomised/fixed timers. Analysis of content was completed using an established linguistic database. AVH were significantly more unpleasant and controlling but not more emotionally arousing than inner thoughts. Psychoeducation around the experience of hallucination in schizophrenia should include information that the voices will be significantly more unpleasant and controlling than their own thoughts but not more emotionally arousing. CBT might therefore include the use of compassion focussed techniques to help with the unpleasantness of AVH and schema level techniques to improve coping with the dominance of AVH

On The Differentiation Of A Log-Liklihood Function Using Matrix Calculus

Simple theorems based on a mathematical property of vecY/vecX provide powerful tools for obtaining matrix calculus results. By way of illustration, new results are obtained for matrix derivatives involving vecA, vechA, v(A) and vecX where X is a symmetric matrix. The analysis explains exactly how a log-likelihood function should be differentiated using matrix calculus.

A Mean-field statistical theory for the nonlinear Schrodinger equation

A statistical model of self-organization in a generic class of one-dimensional nonlinear Schrodinger (NLS) equations on a bounded interval is developed. The main prediction of this model is that the statistically preferred state for such equations consists of a deterministic coherent structure coupled with fine-scale, random fluctuations, or radiation. The model is derived from equilibrium statistical mechanics by using a mean-field approximation of the conserved Hamiltonian and particle number for finite-dimensional spectral truncations of the NLS dynamics. The continuum limits of these approximated statistical equilibrium ensembles on finite-dimensional phase spaces are analyzed, holding the energy and particle number at fixed, finite values. The analysis shows that the coherent structure minimizes total energy for a given value of particle number and hence is a solution to the NLS ground state equation, and that the remaining energy resides in Gaussian fluctuations equipartitioned over wavenumbers. Some results of direct numerical integration of the NLS equation are included to validate empirically these properties of the most probable states for the statistical model. Moreover, a theoretical justification of the mean-field approximation is given, in which the approximate ensembles are shown to concentrate on the associated microcanonical ensemble in the continuum limit.Comment: 24 pages, 2 figure

De la formulation de cas à la prévention de rechute : une thérapie cognitive systématique de la schizophrénie

Cet article discute du statut actuel de la recherche sur la thérapie cognitive (TC) de la schizophrénie. Après avoir passé en revue l'étendue des recherches indiquant l'efficacité de la thérapie cognitive pour ce trouble, on présente le processus thérapeutique typique. Les techniques clés en thérapie cognitive de la schizophrénie sont décrites de même que des exemples typiques de cas et des mises en garde contre des blocages éventuels en thérapie. Les techniques clés ici décrites sont l'engagement dans la relation thérapeutique, le développement d'explications, l'introduction du doute, le questionnement périphérique, les devoirs d'expérimentation comportementale, les approches axées sur les schémas, et la prévention de la rechute. La TC de la schizophrénie est considérée comme acceptable, efficace et solide en complémentarité avec les neuroleptiques et d'autres interventions de nature psychosociale.This paper discusses the current status of cognitive therapy research in schizophrenia. After reviewing the extent of the evidence base indicating the efficacy of CT in this disorder, the typical process of therapy is outlined. The key techniques of CT in schizophrenia are described along with typical case examples and caveats concerning possible blocks in therapy. The key techniques described are engaging, developing explanations, introducing doubt, peripheral questioning, behavioural homework experiments, schema focussed approaches and relapse prevention. CT for schizophrenia is proposed as an acceptable, effective and safe adjunct to neuroleptic and other psychosocial interventions.Este articulo discute del estatuto actual de la investigaciôn sobre la terapia cognoscitiva (TC) de la esquizofrenia. Después de haber pasado en revista la vastedad de investigaciones que indican Io eficaz de la terapia cognoscitiva de este desorden, se présenta el proceso terapéutico tïpico. Se describen las técnicas claves de la terapia cognoscitiva de la esquizofrenia con ejemplos de casos tipicos y con advertencias contra los eventuales bloqueos durante la terapia. las técnicas claves que se describen son el compromiso en la relaciôn terapéutica, el desarrollo de explicaciones, la introduccion de la duda, el interrogarse periférico, las tareas de experimentacion del comportamiento, los enfoques centrados en los esquemas, la prevencion de la recaîda. LaTC de la esquizofrenia es considerada como algo aceptable, solido y eficaz que se comple-menta con los neurolépticos y con otras intervenciones de naturaleza psicosocial

Reduction in jejunal fluid absorption in vivo through distension and cholinergic stimulation not attributable to enterocyte secretion

Jejunal fluid absorption in vivo was reduced by distension and by hydrostatic pressure and further declined on adding E. coli STa enterotoxin but no net fluid secretion was detected. Luminal atropine reduced pressure mediated reductions in fluid absorption to normal values but intravenous hexamethonium was without effect. A neural component to inhibition of absorption by pressure (though not stretch) may be mediated by axon reflexes within cholinergic neurons.Perfusion of cholinergic compounds also reduced net fluid absorption but did not cause secretion. In order to show that these actions were not secretory processes stimulated by cholinergic compounds that offset normal rates of absorption, these compounds were tested for their ability to cause net secretion in loops that were perfused with solutions in which choline substituted for sodium ion. In addition, these perfusates additionally contained E. coli STa enterotoxin or EIPA (ethyl-isopropyl-amiloride) to minimize absorption.In these circumstances, where it might be expected to do so if it were acting through a secretory rather than an absorptive mechanism, carbachol did not cause net fluid secretion. Cholinergic stimulation and pressure induced distension are thought to reduce net fluid absorption through inducing secretion but are found only to reduce fluid absorption.In conclusion, distension and cholinergic stimulation of the small intestine are two further circumstances in which fluid secretion is assumed to explain their action on fluid movement, as required by the enterocyte secretion model of secretion but, which like STa enterotoxin, instead are only able to reduce fluid absorption. This casts further doubt on the widespread validity of the enterocyte secretion model for fluid appearance in the lumen in diarrhoeal diseases

Brownian theory of 2D turbulence and generalized thermodynamics

We propose a new parametrization of 2D turbulence based on generalized thermodynamics and Brownian theory. Explicit relaxation equations are obtained that should be easily implementable in numerical simulations for three typical types of turbulent flows. Our parametrization is related to previous ones but it removes their defects and offers attractive new perspectives.Comment: Submitted to Phys. Rev. Let