By consideration of the information processing task faced by the central nervous system in estimating body spatial orientation and in controlling active body movement using an internal model referenced control strategy, a mathematical model for sensory conflict generation is developed. The model postulates a major dynamic functional role for sensory conflict signals in movement control, as well as in sensory-motor adaptation. It accounts for the role of active movement in creating motion sickness symptoms in some experimental circumstance, and in alleviating them in others. The relationship between motion sickness produced by sensory rearrangement and that resulting from external motion disturbances is explicitly defined. A nonlinear conflict averaging model is proposed which describes dynamic aspects of experimentally observed subjective discomfort sensation, and suggests resulting behaviours. The model admits several possibilities for adaptive mechanisms which do not involve internal model updating. Further systematic efforts to experimentally refine and validate the model are indicated.

/pdf/a-heuristic-mathematical-model-for-the-dynamics-of-sensory-4e5uay3fgz.pdf

A heuristic mathematical model for the dynamics of sensory conflict and motion sickness

In this work we review the present status of numerical methods for partial differential equations on vector and parallel computers. A discussion of the relevant aspects of these computers and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial-boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. A brief discussion of application areas utilizing these computers is included.

/pdf/solution-of-partial-differential-equations-on-vector-and-3mkk75xyo6.pdf

Solution of Partial Differential Equations on Vector and Parallel Computers

Theoremes de points fixes dans les treillis complets, etude du comportement d'un systeme dynamique discret, analyse semantique exacte des programmes et applications. Methodes constructives d'approximation de points fixes d'operateurs monotone sur un treillis complet. Analyse semantique approchee des programmes et applications. Analyse semantique des procedures recursives.

Méthodes itératives de construction et d'approximation de points fixes d'opérateurs monotones sur un treillis, analyse sémantique des programmes

For purposes of evaluation and manipulation, mathematical functions f are commonly replaced by approximation polynomials p. Examples include floating-point implementations of elementary functions, integration, ordinary differential equations (ODE) solving. For that, a wide range of numerical methods exists. We consider the application of such methods in the context of rigorous computing, where we need guarantees on the accuracy of the result, with respect to both the truncation and rounding errors.A rigorous polynomial approximation (RPA) for a function f defined over an interval [a,b] is a couple (P, Delta) where P is a polynomial and Delta is an interval such that f(x)-P(x) belongs to Delta, for all x in [a,b]. In this work we analyse and bring forth several ways of obtaining RPAs for univariate functions. Firstly, we analyse and refine an existing approach based on Taylor expansions. Secondly, we replace them with better approximations such as minimax approximations, Chebyshev truncated series or interpolation polynomials.Several applications are presented: one from standard functions implementation in mathematical libraries (libm), another regarding the computation of Chebyshev series expansions solutions of linear ODEs with polynomial coefficients, and finally an automatic process for function evaluation with guaranteed accuracy in reconfigurable hardware.

/pdf/rigorous-polynomial-approximations-and-applications-2irkvim7tq.pdf

Rigorous Polynomial Approximations and Applications

Les fonctions D-finies (ou holonomes) a une variable sont les solutions d'equations differentielles lineaires a coefficients polynomiaux. En calcul formel, il s'est avere fructueux depuis une vingtaine d'annees d'en developper un traitement algorithmique unifie. Cette these s'inscrit dans cette optique, et s'interesse a l'evaluation numerique des fonctions D-finies ainsi qu'a quelques problemes apparentes. Elle explore trois grandes directions. La premiere concerne la majoration des coefficients des developpements en serie de fonctions D-finies. On aboutit a un algorithme de calcul automatique de majorants accompagne d'un resultat de finesse des bornes obtenues. Une seconde direction est la mise en pratique de l'algorithme " bit burst " de Chudnovsky et Chudnovsky pour le prolongement analytique numerique a precision arbitraire des fonctions D-finies. Son implementation est l'occasion de diverses ameliorations techniques. Ici comme pour le calcul de bornes, on s'attache par ailleurs a couvrir le cas des points singuliers reguliers des equations differentielles. Enfin, la derniere partie de la these developpe une methode pour calculer une approximation polynomiale de degre impose d'une fonction D-finie sur un intervalle, via l'etude des developpements en serie de Tchebycheff de ces fonctions. Toutes les questions sont abordees avec un triple objectif de rigueur (resultats numeriques garantis), de generalite (traiter toute la classe des fonctions D-finies) et d'efficacite. Pratiquement tous les algorithmes etudies s'accompagnent d'implementations disponibles publiquement.

https://pastel.archives-ouvertes.fr/pastel-00663017/document

Autour de l'évaluation numérique des fonctions D-finies

Ultra-arithmetic I: Function data types

Ultra-arithmetic II: intervals of polynomials

Parallel methods for solving equations

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Ultra-arithmetic I: Function data types

Ultra-arithmetic II: intervals of polynomials

Parallel methods for solving equations