An Approximation Problem in Multiplicatively Invariant Spaces

Let $\mathcal{H}$ be Hilbert space and $(\Omega,\mu)$ a $\sigma$-finite measure space. Multiplicatively invariant (MI) spaces are closed subspaces of $L^2(\Omega, \mathcal{H})$ that are invariant under point-wise multiplication by functions in a fix subset of $L^{\infty}(\Omega).$ Given a finite set of data $\mathcal{F}\subseteq L^2(\Omega, \mathcal{H}),$ in this paper we prove the existence and construct an MI space $M$ that best fits $\mathcal{F}$, in the least squares sense. MI spaces are related to shift invariant (SI) spaces via a fiberization map, which allows us to solve an approximation problem for SI spaces in the context of locally compact abelian groups. On the other hand, we introduce the notion of decomposable MI spaces (MI spaces that can be decomposed into an orthogonal sum of MI subspaces) and solve the approximation problem for the class of these spaces. Since SI spaces having extra invariance are in one-to-one relation to decomposable MI spaces, we also solve our approximation problem for this class of SI spaces. Finally we prove that translation invariant spaces are in correspondence with totally decomposable MI spaces.Comment: 18 pages, To appear in Contemporary Mathematic

Linear combinations of frame generators in systems of translates

A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose integer translates form a frame for $V$. In this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators. Surprisingly the results are very different to the recently studied case when the property to be a frame is not required.Comment: 13 pages, To appear in J. Math. Anal. App

Advances In Time Series Analysis With Hydrological Applications

The objective of this thesis is to develop and refine statistical methods which can be used for solving a variety of challenging problems which arise in the field of stochastic hydrology and elsewhere. Four areas in stochastic hydrology where more research is required are long term memory processes and the Hurst phenomenon, seasonal geophysical processes, bootstrapping time series models and nonlinear and/or nonGaussian features present in geophysical time series.;For addressing the first problem, we study the family of fractionally differencing autoregressive and moving-average processes (FARMA). Specifically, we characterize the efficiency of the sample mean and the efficiency of ordinary least squares estimates of regression parameters when the statistical error belongs to the FARMA family. Also, we prove that for FARMA models it is true that the logarithm of the determinant of the autocovariance matrix, divided by the number of observations converges to the logarithm of the variance of the white noise. Finally, the finite sample properties of the maximum likelihood method of estimation are compared with the average likelihood method.;For the second problem in stochastic hydrology stated above, we investigate the family of periodic autoregressive and moving-average models (PARMA). We characterize these processes from the point of view of the state-space formulation. We give an exact maximum likelihood algorithm for fitting a PARMA model. Also, we give algorithms for computing the autocovariance matrix, the inverse autocorrelations, and the information matrix associated with the PARMA model.;An additional problem that initially was formulated for its relevance to stochastic hydrology is an improved bootstrapping procedure to investigate parameter uncertainty. We generalize and study some of the asymptotic properties of this procedure.;With respect to the fourth problem in stochastic hydrology, we investigate nonparametric function fitting when applied to time series processes. We give strong approximation results for these estimates, subject to certain mixing properties of the stochastic process. We extend a data based method for choosing the smoothing constant, and propose another method for doing this. We investigate a convex combination of a parametric estimate plus a nonparametric function estimate. Also, we study within a time series context a semi-parametric approach for function estimation. Finally, we use the kernel method for estimating state-dependent models

A pragmatic logic of transparency: development of a model for a compared study of public policy texts in Latin American countries

This article aims to the logical development of a practical and applicable analysis model of argumentative transparency, specifically for the study of public policies. To this end, we draw upon a “political concept of transparency” which redefines pragmatic logic operations in contexts of trust and cooperation between actors. The model combines a principal-agent framework, non-linear assumptions of production of information, and conversational maxims of use of language. This results in an analysis that is focused on the actors’ capacity and their relation. The model also finds a necessary link between active and passive transparency processes, where the building of trust arising from transparency is directly associated with the reduction of control costs. In addition, this article intends to be an applied model, with visual tools related to transparent decision-making processes, protocols for marking up transparency in texts and, finally, an empirical analysis of transparency in the argument of specific public policies. The combination of multiple frameworks and the deduction of a logical model presents an original work for the study of public policies.Fil: Mosquera Sadleir, Carlos Mariano. Universidad Católica de Córdoba. Facultad de Ciencia Política y Relaciones Internacionales; Argentin

El cambio didáctico en profesores universitarios de química a través de un programa de actividades basado en la enseñanza por investigación orientada

Se muestra aquí una experiencia de investigación aplicada en el campo de la formación continuada de profesores universitarios de ciencias, concretamente de aquellos encargados de la formación inicial de profesores de química en una Facultad de Ciencias y Educación en Colombia. Se parte de la consideración del cambio didáctico desde la perspectiva de cambios en la epistemología y en la práctica docente de los profesores. Este cambio ha supuesto la identificación, como punto de partida, de algunas concepciones y actitudes habituales de los profesores intervenidos hacia la ciencia, la función de la historia de la ciencia y la enseñanza y el aprendizaje de la ciencia; de igual forma se han caracterizado algunas prácticas docentes habituales. A partir de los conocimientos actuales en Didáctica de las Ciencias se ha elaborado y aplicado un Programa de Actividades para la formación continuada de Profesores Universitarios de Química basado en el modelo de enseñanza por investigación orientada el cual ha favorecido que los profesores intervenidos cambien hacia concepciones y actitudes más innovadoras hacia la ciencia y hacia su enseñanza, y hayan manifestado prácticas docentes más próximas a lo esperado por la investigación contemporánea en Didáctica de las Ciencias Experimentales