Towards improving cluster-based feature selection with a simplified silhouette filter

This paper proposes a filter-based algorithm for feature selection. The filter is based on the partitioning of the set of features into clusters. The number of clusters, and consequently the cardinality of the subset of selected features, is automatically estimated from data. The computational complexity of the proposed algorithm is also investigated. A variant of this filter that considers feature-class correlations is also proposed for classification problems. Empirical results involving ten datasets illustrate the performance of the developed algorithm, which in general has obtained competitive results in terms of classification accuracy when compared to state of the art algorithms that find clusters of features. We show that, if computational efficiency is an important issue, then the proposed filter May be preferred over their counterparts, thus becoming eligible to join a pool of feature selection algorithms to be used in practice. As an additional contribution of this work, a theoretical framework is used to formally analyze some properties of feature selection methods that rely on finding clusters of features. (C) 2011 Elsevier Inc. All rights reserved.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Número Irracionais e transcendentes

Pós-graduação em Matemática - IBILCE

Lindelof spaces which are indestructible, productive, or D

We discuss relationships in Lindelof spaces among the properties "indestructible". "productive", "D", and related properties. (C) 2011 Elsevier B.V. All rights reserved.

A countably compact free Abelian group of size continuum that admits a non-trivial convergent sequence

We show that it is consistent with ZFC that the free Abelian group of cardinality c admits a topological group topology that makes it countably compact with a non-trivial convergent sequence. (C) 2011 Elsevier B.V. All rights reserved.

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML

Exact Unification and Admissibility

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.

Negative ternary set-sharing

The Set-Sharing domain has been widely used to infer at compiletime interesting properties of logic programs such as occurs-check reduction, automatic parallelization, and flnite-tree analysis. However, performing abstract uniflcation in this domain requires a closure operation that increases the number of sharing groups exponentially. Much attention has been given to mitigating this key inefflciency in this otherwise very useful domain. In this paper we present a novel approach to Set-Sharing: we define a new representation that leverages the complement (or negative) sharing relationships of the original sharing set, without loss of accuracy. Intuitively, given an abstract state sh\> over the finite set of variables of interest V, its negative representation is p(V) \ shy. Using this encoding during analysis dramatically reduces the number of elements that need to be represented in the abstract states and during abstract uniflcation as the cardinality of the original set grows toward 2 . To further compress the number of elements, we express the set-sharing relationships through a set of ternary strings that compacts the representation by eliminating redundancies among the sharing sets. Our experiments show that our approach can compress the number of relationships, reducing signiflcantly the memory usage and running time of all abstract operations, including abstract uniflcation.

Relationship among research collaboration, number of documents and number of citations. A case study in Spanish computer science production in 2000-2009.

This paper analyzes the relationship among research collaboration, number of documents and number of citations of computer science research activity. It analyzes the number of documents and citations and how they vary by number of authors. They are also analyzed (according to author set cardinality) under different circumstances, that is, when documents are written in different types of collaboration, when documents are published in different document types, when documents are published in different computer science subdisciplines, and, finally, when documents are published by journals with different impact factor quartiles. To investigate the above relationships, this paper analyzes the publications listed in the Web of Science and produced by active Spanish university professors between 2000 and 2009, working in the computer science field. Analyzing all documents, we show that the highest percentage of documents are published by three authors, whereas single-authored documents account for the lowest percentage. By number of citations, there is no positive association between the author cardinality and citation impact. Statistical tests show that documents written by two authors receive more citations per document and year than documents published by more authors. In contrast, results do not show statistically significant differences between documents published by two authors and one author. The research findings suggest that international collaboration results on average in publications with higher citation rates than national and institutional collaborations. We also find differences regarding citation rates between journals and conferences, across different computer science subdisciplines and journal quartiles as expected. Finally, our impression is that the collaborative level (number of authors per document) will increase in the coming years, and documents published by three or four authors will be the trend in computer science literature.

Sized Type Analysis for Logic Programs (Technical Communication)

We present a novel analysis for relating the sizes of terms and subterms occurring at diferent argument positions in logic predicates. We extend and enrich the concept of sized type as a representation that incorporates structural (shape) information and allows expressing both lower and upper bounds on the size of a set of terms and their subterms at any position and depth. For example, expressing bounds on the length of lists of numbers, together with bounds on the values of all of their elements. The analysis is developed using abstract interpretation and the novel abstract operations are based on setting up and solving recurrence relations between sized types. It has been integrated, together with novel resource usage and cardinality analyses, in the abstract interpretation framework in the Ciao preprocessor, CiaoPP, in order to assess both the accuracy of the new size analysis and its usefulness in the resource usage estimation application. We show that the proposed sized types are a substantial improvement over the previous size analyses present in CiaoPP, and also benefit the resource analysis considerably, allowing the inference of equal or better bounds than comparable state of the art systems.

Modelado y Comparación de Colecciones en la Web Semántica

En esta tesis se estudia la representación, modelado y comparación de colecciones mediante el uso de ontologías en el ámbito de la Web Semántica. Las colecciones, entendidas como agrupaciones de objetos o elementos con entidad propia, son construcciones que aparecen frecuentemente en prácticamente todos los dominios del mundo real, y por tanto, es imprescindible disponer de conceptualizaciones de estas estructuras abstractas y de representaciones de estas conceptualizaciones en los sistemas informáticos, que definan adecuadamente su semántica. Mientras que en muchos ámbitos de la Informática y la Inteligencia Artificial, como por ejemplo la programación, las bases de datos o la recuperación de información, las colecciones han sido ampliamente estudiadas y se han desarrollado representaciones que responden a multitud de conceptualizaciones, en el ámbito de la Web Semántica, sin embargo, su estudio ha sido bastante limitado. De hecho hasta la fecha existen pocas propuestas de representación de colecciones mediante ontologías, y las que hay sólo cubren algunos tipos de colecciones y presentan importantes limitaciones. Esto impide la representación adecuada de colecciones y dificulta otras tareas comunes como la comparación de colecciones, algo crítico en operaciones habituales como las búsquedas semánticas o el enlazado de datos en la Web Semántica. Para solventar este problema esta tesis hace una propuesta de modelización de colecciones basada en una nueva clasificación de colecciones de acuerdo a sus características estructurales (homogeneidad, unicidad, orden y cardinalidad). Esta clasificación permite definir una taxonomía con hasta 16 tipos de colecciones distintas. Entre otras ventajas, esta nueva clasificación permite aprovechar la semántica de las propiedades estructurales de cada tipo de colección para realizar comparaciones utilizando las funciones de similitud y disimilitud más apropiadas. De este modo, la tesis desarrolla además un nuevo catálogo de funciones de similitud para las distintas colecciones, donde se han recogido las funciones de (di)similitud más conocidas y también algunas nuevas. Esta propuesta se ha implementado mediante dos ontologías paralelas, la ontología E-Collections, que representa los distintos tipos de colecciones de la taxonomía y su axiomática, y la ontología SIMEON (Similarity Measures Ontology) que representa los tipos de funciones de (di)similitud para cada tipo de colección. Gracias a estas ontologías, para comparar dos colecciones, una vez representadas como instancias de la clase más apropiada de la ontología E-Collections, automáticamente se sabe qué funciones de (di)similitud de la ontología SIMEON pueden utilizarse para su comparación. Abstract This thesis studies the representation, modeling and comparison of collections in the Semantic Web using ontologies. Collections, understood as groups of objects or elements with their own identities, are constructions that appear frequently in almost all areas of the real world. Therefore, it is essential to have conceptualizations of these abstract structures and representations of these conceptualizations in computer systems, that define their semantic properly. While in many areas of Computer Science and Artificial Intelligence, such as Programming, Databases or Information Retrieval, the collections have been extensively studied and there are representations that match many conceptualizations, in the field Semantic Web, however, their study has been quite limited. In fact, there are few representations of collections using ontologies so far, and they only cover some types of collections and have important limitations. This hinders a proper representation of collections and other common tasks like comparing collections, something critical in usual operations such as semantic search or linking data on the Semantic Web. To solve this problem this thesis makes a proposal for modelling collections based on a new classification of collections according to their structural characteristics (homogeneity, uniqueness, order and cardinality). This classification allows to define a taxonomy with up to 16 different types of collections. Among other advantages, this new classification can leverage the semantics of the structural properties of each type of collection to make comparisons using the most appropriate (dis)similarity functions. Thus, the thesis also develops a new catalog of similarity functions for the different types of collections. This catalog contains the most common (dis)similarity functions as well as new ones. This proposal is implemented through two parallel ontologies, the E-Collections ontology that represents the different types of collections in the taxonomy and their axiomatic, and the SIMEON ontology (Similarity Measures Ontology) that represents the types of (dis)similarity functions for each type of collection. Thanks to these ontologies, to compare two collections, once represented as instances of the appropriate class of E-Collections ontology, we can know automatically which (dis)similarity functions of the SIMEON ontology are suitable for the comparison. Finally, the feasibility and usefulness of this modeling and comparison of collections proposal is proved in the field of oenology, applying both E-Collections and SIMEON ontologies to the representation and comparison of wines with the E-Baco ontology.

On the stability of Voronoi cells

Let T be a given subset of ℝ n , whose elements are called sites, and let s∈T. The Voronoi cell of s with respect to T consists of all points closer to s than to any other site. In many real applications, the position of some elements of T is uncertain due to either random external causes or to measurement errors. In this paper we analyze the effect on the Voronoi cell of small changes in s or in a given non-empty set P⊂T\{s}. Two types of perturbations of P are considered, one of them not increasing the cardinality of T. More in detail, the paper provides conditions for the corresponding Voronoi cell mappings to be closed, lower and upper semicontinuous. All the involved conditions are expressed in terms of the data.

Étude de l’orientation cardinale sud dans les sépultures mayas de la Période Classique

Ce mémoire porte sur l’étude de l’orientation des sépultures mayas de la Période Classique (250 - 900/1000 de notre ère). Il s’agit d’une recherche visant à comprendre le choix d’une orientation sud des défunts dans la vallée du Belize et ses environs. L’intérêt porté à cette région vient du fait que l’orientation sud des défunts est un phénomène que l’on retrouve rarement sur le territoire maya, sauf à cet endroit. Alors que la présence de la cardinalité en lien avec la cosmovision maya est attestée dans l’architecture, le plan des sites, la forme et la fonction des divinités, dans l’agriculture, etc., il est plutôt rare qu’elle soit analysée dans les études du traitement funéraire. Ainsi, le but de cette recherche est de saisir l’ampleur de la pratique de l’orientation sud des défunts sur le territoire maya, de comprendre son origine et sa ou ses possible(s) signification(s). Les données des sépultures de la Période Classique de cinq sites de la vallée du Belize (Baking Pot, Barton Ramie, Blackman Eddy, Cahal Pech et Xunantunich), de quatre sites du Plateau Vaca (Minanha, Pacbitun, Mountain Cow et Caracol) et de trois sites situés à l’ouest (Holmul) et au nord (San José et Altun Ha) de ces deux régions sont compilées. Les résultats révèlent que le coeur de cette pratique se trouve dans la vallée du Belize, bien qu’une orientation sud des défunts ait été retrouvée partout. Cette pratique semble apparaitre à la fin de la Période Préclassique et les analyses ne révèlent pas de lien entre l’orientation sud et certaines variables (âge, sexe, position du défunt). Finalement, on arrive à la conclusion qu’il est possible que cette orientation sud des défunts soit en lien avec le passage des défunts dans l’inframonde et que cela forme un choix culturel local en lien avec le statut et l’identité du défunt.

Explora: A Visualisation Tool for Metric Analysis of Software Corpora

When analysing software metrics, users find that visualisation tools lack support for (1) the detection of patterns within metrics; and (2) enabling analysis of software corpora. In this paper we present Explora, a visualisation tool designed for the simultaneous analysis of multiple metrics of systems in software corpora. Explora incorporates a novel lightweight visualisation technique called PolyGrid that promotes the detection of graphical patterns. We present an example where we analyse the relation of subtype polymorphism with inheritance and invocation in corpora of Smalltalk and Java systems and find that (1) subtype polymorphism is more likely to be found in large hierarchies; (2) as class hierarchies grow horizontally, they also do so vertically; and (3) in polymorphic hierarchies the length of the name of the classes is orthogonal to the cardinality of the call sites.