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1	Quantization Dimension for Probability Definitions Lindsay, Larry J. 12 1900 (has links) The term quantization refers to the process of estimating a given probability by a discrete probability supported on a finite set. The quantization dimension Dr of a probability is related to the asymptotic rate at which the expected distance (raised to the rth power) to the support of the quantized version of the probability goes to zero as the size of the support is allowed to go to infinity. This assumes that the quantized versions are in some sense ``optimal'' in that the expected distances have been minimized. In this dissertation we give a short history of quantization as well as some basic facts. We develop a generalized framework for the quantization dimension which extends the current theory to include a wider range of probability measures. This framework uses the theory of thermodynamic formalism and the multifractal spectrum. It is shown that at least in certain cases the quantization dimension function D(r)=Dr is a transform of the temperature function b(q), which is already known to be the Legendre transform of the multifractal spectrum f(a). Hence, these ideas are all closely related and it would be expected that progress in one area could lead to new results in another. It would also be expected that the results in this dissertation would extend to all probabilities for which a quantization dimension function exists. The cases considered here include probabilities generated by conformal iterated function systems (and include self-similar probabilities) and also probabilities generated by graph directed systems, which further generalize the idea of an iterated function system. Geometric quantization. Probabilities. Fractals. Quantization iterated function systems graph directed sets fractals multifractals
2	Elementos de Semántica Denotacional de Lenguajes de Programación con Datos Borrosos Sánchez Álvarez, Daniel 01 October 1999 (has links) A fin de diseñar e implementar lenguajes de programación que tengan en cuenta el paradigma borroso modificaremos el lambda cálculo clásico, adjuntando a cada término un grado, y redefiniendo la beta-reducción, obteniendo que para que el nuevo cálculo verifique la propiedad de Church-Rosser la transmisión de los grados debe hacerse por medio de una función que sea una t-norma o s-conorma. Utilizando esta nueva herramienta diseñamos un lenguaje no determinista que satisface los requerimientos de la programación con datos borrosos. / With the aim of designing and implementing programming languages that take into account the fuzzy paradigm we will modify the classical lambda calculus by adding a degree to each term and by redefining the b-reduction. Thus, for the new calculus to verify the Church-Rosser property, the degree computed with can be made through a function that is a t-norm or an s-conorm. With this new tool we design a nondeterminist language that satisfies fuzzy dataprogramming requirements, and an example of its behaviour is shown. trapezoidal numbers Church numbers numerical system fuzzy numbers powerdomain directed sets fuzzy sets fuzzy boolean denotational semantics labelled tree s-conorma t-norma separabilidad sustitución reducción de Church-Rosser powerdomain número trapezoidal número de Church número borroso normalización ideal principal extensión cilíndrica dominio potencia conjunto dirigido conjunto borroso semántica denotacional booleano borroso árbol etiquetado Church-Rosser property abstract syntax guarded command substitutions reductions linguistic values linguistic variables t-norm s-conorm 621.3 68

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Quantization Dimension for Probability Definitions

Elementos de Semántica Denotacional de Lenguajes de Programación con Datos Borrosos