Convergence towards asymptotic state in 1-D mappings: a scaling investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Learning flexible sensori-motor mappings in a complex network

Given the complex structure of the brain, how can synaptic plasticity explain the learning and forgetting of associations when these are continuously changing? We address this question by studying different reinforcement learning rules in a multilayer network in order to reproduce monkey behavior in a visuomotor association task. Our model can only reproduce the learning performance of the monkey if the synaptic modifications depend on the pre- and postsynaptic activity, and if the intrinsic level of stochasticity is low. This favored learning rule is based on reward modulated Hebbian synaptic plasticity and shows the interesting feature that the learning performance does not substantially degrade when adding layers to the network, even for a complex problem.

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Lineability of the set of holomorphic mappings with dense range

Let U be an open subset of a separable Banach space. Let F be the collection of all holomorphic mappings f from the open unit disc D � C into U such that f(D) is dense in U. We prove the lineability and density of F in appropriate spaces for diferent choices of U. RESUMEN. Sea U un subconjunto abierto de un espacio de Banach separable. Sea F el conjunto de funciones holomorfas f definidas en el disco unidad D del plano complejo con valores en U tales que f(D) es denso en U. En el artículo se demuestra la lineabilidad y densidad del conjunto F para diferentes elecciones de U.

Descubrimiento de mappings en recursos geoespaciales

La integración de fuentes de información heterogéneas ha sido un problema abordado en diferentes tipos de fuentes a lo largo de las décadas de diferentes maneras. Una de ellas es el establecimiento de unas relaciones semánticas que permitan poder unir la información de las fuentes relacionadas. A estos enlaces, claves en la integración, se les ha llamado generalmente mappings. Los mappings se han usado en multitud de trabajos y se han abordado, de manera más práctica que teórica en muchos casos, diferentes soluciones para su descubrimiento, su almacenaje, su explotación, etc. Sin embargo, aunque han sido muchas las contribuciones sobre mappings, no hay una definición generalizada y admitida por la comunidad que cubra todos los aspectos vinculados a los mappings. Además, en su proceso de descubrimiento, no existe un marco teórico que defina metódicamente los procesos a seguir y sus características. Igualmente, la actual forma de evaluar el descubrimiento de mappings no es suficiente para toda la casuística existente. En este trabajo se aporta una definición de mapping génerica que engloba todos los sistemas actuales, la especificación detallada del proceso de descubrimiento y el análisis y la propuesta de un proceso de evaluación del descubrimiento. La validez de estos aportes se comprueba con la formulación de hipótesis y su comprobación mediante un estudio cuantitativo sobre un caso de uso con recursos geoespaciales heterogéneos. ABSTRACT The integration of heterogeneous information resources has been an issue addressed in different types of sources over the decades in different ways. One of them is the establishment of semantic relations which allow information from different related resources to be linked. These links, crucial pieces of this integration, are usually known as mappings. These mappings have been widely used in many applications, and different solutions for their discovery, storing, explotation, etc. have been presented, following rather a more practical than theoretical way in many cases. However, although mappings have been widely applied by many researchers, there is a lack of a generally accepted definition that can cover all the aspects related to mappings. Moreover, in the process of mapping discovery, there is not a theoretical framework that defines methodically the processes to be followed and their characteristics. Similarly, the current way of assessing or evaluating the discovery of mappings is insufficient for all the existing use cases. The main contributions of this work are threefold. On the one hand, it presents a general definition of "mapping" which covers all current systems. On the other hand, it describes a detailed specification of the discovery process, and, finally, it faces the analysis and the purpose of the evaluation of this discovery process. The validity of these contributions has been checked with the formulation of hypothesis which have been verified by using heterogeneous geospatial resources in a quantitative study.

Methods and Techniques for the Generation and Eficient Exploitation of RDB2RDF Mappings

RDB to RDF Mapping Language (R2RML) es una recomendación del W3C que permite especificar reglas para transformar bases de datos relacionales a RDF. Estos datos en RDF se pueden materializar y almacenar en un sistema gestor de tripletas RDF (normalmente conocidos con el nombre triple store), en el cual se pueden evaluar consultas SPARQL. Sin embargo, hay casos en los cuales la materialización no es adecuada o posible, por ejemplo, cuando la base de datos se actualiza frecuentemente. En estos casos, lo mejor es considerar los datos en RDF como datos virtuales, de tal manera que las consultas SPARQL anteriormente mencionadas se traduzcan a consultas SQL que se pueden evaluar sobre los sistemas gestores de bases de datos relacionales (SGBD) originales. Para esta traducción se tienen en cuenta los mapeos R2RML. La primera parte de esta tesis se centra en la traducción de consultas. Se propone una formalización de la traducción de SPARQL a SQL utilizando mapeos R2RML. Además se proponen varias técnicas de optimización para generar consultas SQL que son más eficientes cuando son evaluadas en sistemas gestores de bases de datos relacionales. Este enfoque se evalúa mediante un benchmark sintético y varios casos reales. Otra recomendación relacionada con R2RML es la conocida como Direct Mapping (DM), que establece reglas fijas para la transformación de datos relacionales a RDF. A pesar de que ambas recomendaciones se publicaron al mismo tiempo, en septiembre de 2012, todavía no se ha realizado un estudio formal sobre la relación entre ellas. Por tanto, la segunda parte de esta tesis se centra en el estudio de la relación entre R2RML y DM. Se divide este estudio en dos partes: de R2RML a DM, y de DM a R2RML. En el primer caso, se estudia un fragmento de R2RML que tiene la misma expresividad que DM. En el segundo caso, se representan las reglas de DM como mapeos R2RML, y también se añade la semántica implícita (relaciones de subclase, 1-N y M-N) que se puede encontrar codificada en la base de datos. Esta tesis muestra que es posible usar R2RML en casos reales, sin necesidad de realizar materializaciones de los datos, puesto que las consultas SQL generadas son suficientemente eficientes cuando son evaluadas en el sistema gestor de base de datos relacional. Asimismo, esta tesis profundiza en el entendimiento de la relación existente entre las dos recomendaciones del W3C, algo que no había sido estudiado con anterioridad. ABSTRACT. RDB to RDF Mapping Language (R2RML) is a W3C recommendation that allows specifying rules for transforming relational databases into RDF. This RDF data can be materialized and stored in a triple store, so that SPARQL queries can be evaluated by the triple store. However, there are several cases where materialization is not adequate or possible, for example, if the underlying relational database is updated frequently. In those cases, RDF data is better kept virtual, and hence SPARQL queries over it have to be translated into SQL queries to the underlying relational database system considering that the translation process has to take into account the specified R2RML mappings. The first part of this thesis focuses on query translation. We discuss the formalization of the translation from SPARQL to SQL queries that takes into account R2RML mappings. Furthermore, we propose several optimization techniques so that the translation procedure generates SQL queries that can be evaluated more efficiently over the underlying databases. We evaluate our approach using a synthetic benchmark and several real cases, and show positive results that we obtained. Direct Mapping (DM) is another W3C recommendation for the generation of RDF data from relational databases. While R2RML allows users to specify their own transformation rules, DM establishes fixed transformation rules. Although both recommendations were published at the same time, September 2012, there has not been any study regarding the relationship between them. The second part of this thesis focuses on the study of the relationship between R2RML and DM. We divide this study into two directions: from R2RML to DM, and from DM to R2RML. From R2RML to DM, we study a fragment of R2RML having the same expressive power than DM. From DM to R2RML, we represent DM transformation rules as R2RML mappings, and also add the implicit semantics encoded in databases, such as subclass, 1-N and N-N relationships. This thesis shows that by formalizing and optimizing R2RML-based SPARQL to SQL query translation, it is possible to use R2RML engines in real cases as the resulting SQL is efficient enough to be evaluated by the underlying relational databases. In addition to that, this thesis facilitates the understanding of bidirectional relationship between the two W3C recommendations, something that had not been studied before.

Sets, sequences, and mappings: the basic concepts of analysis

Mode of access: Internet.