Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig

Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras

Formal methods applied to the analysis of phylogenies: Phylogenetic model checking

Los árboles filogenéticos son abstracciones útiles para modelar y caracterizar la evolución de un conjunto de especies o poblaciones respecto del tiempo. La proposición, verificación y generalización de hipótesis sobre un árbol filogenético inferido juegan un papel importante en el estudio y comprensión de las relaciones evolutivas. Actualmente, uno de los principales objetivos científicos es extraer o descubrir los mensajes biológicos implícitos y las propiedades estructurales subyacentes en la filogenia. Por ejemplo, la integración de información genética en una filogenia ayuda al descubrimiento de genes conservados en todo o parte del árbol, la identificación de posiciones covariantes en el ADN o la estimación de las fechas de divergencia entre especies. Consecuentemente, los árboles ayudan a comprender el mecanismo que gobierna la deriva evolutiva. Hoy en día, el amplio espectro de métodos y herramientas heterogéneas para el análisis de filogenias enturbia y dificulta su utilización, además del fuerte acoplamiento entre la especificación de propiedades y los algoritmos utilizados para su evaluación (principalmente scripts ad hoc). Este problema es el punto de arranque de esta tesis, donde se analiza como solución la posibilidad de introducir un entorno formal de verificación de hipótesis que, de manera automática y modular, estudie la veracidad de dichas propiedades definidas en un lenguaje genérico e independiente (en una lógica formal asociada) sobre uno de los múltiples softwares preparados para ello. La contribución principal de la tesis es la propuesta de un marco formal para la descripción, verificación y manipulación de relaciones causales entre especies de forma independiente del código utilizado para su valoración. Para ello, exploramos las características de las técnicas de model checking, un paradigma en el que una especificación expresada en lógica temporal se verifica con respecto a un modelo del sistema que representa una implementación a un cierto nivel de detalle. Se ha aplicado satisfactoriamente en la industria para el modelado de sistemas y su verificación, emergiendo del ámbito de las ciencias de la computación. Las contribuciones concretas de la tesis han sido: A) La identificación e interpretación de los árboles filogeneticos como modelos de la evolución, adaptados al entorno de las técnicas de model checking. B) La definición de una lógica temporal que captura las propiedades filogenéticas habituales junto con un método de construcción de propiedades. C) La clasificación de propiedades filogenéticas, identificando categorías de propiedades según estén centradas en la estructura del árbol, en las secuencias o sean híbridas. D) La extensión de las lógicas y modelos para contemplar propiedades cuantitativas de tiempo, probabilidad y de distancias. E) El desarrollo de un entorno para la verificación de propiedades booleanas, cuantitativas y paramétricas. F) El establecimiento de los principios para la manipulación simbolica de objetos filogenéticos, p. ej., clados. G) La explotación de las herramientas de model checking existentes, detectando sus problemas y carencias en el campo de filogenia y proponiendo mejoras. H) El desarrollo de técnicas "ad hoc" para obtener ganancia de complejidad alrededor de dos frentes: distribución de los cálculos y datos, y el uso de sistemas de información. Los puntos A-F se centran en las aportaciones conceptuales de nuestra aproximación, mientras que los puntos G-H enfatizan la parte de herramientas e implementación. Los contenidos de la tesis están contrastados por la comunidad científica mediante las siguientes publicaciones en conferencias y revistas internacionales. La introducción de model checking como entorno formal para analizar propiedades biológicas (puntos A-C) ha llevado a la publicación de nuestro primer artículo de congreso [1]. En [2], desarrollamos la verificación de hipótesis filogenéticas sobre un árbol de ejemplo construido a partir de las relaciones impuestas por un conjunto de proteínas codificadas por el ADN mitocondrial humano (ADNmt). En ese ejemplo, usamos una herramienta automática y genérica de model checking (punto G). El artículo de revista [7] resume lo básico de los artículos de congreso previos y extiende la aplicación de lógicas temporales a propiedades filogenéticas no consideradas hasta ahora. Los artículos citados aquí engloban los contenidos presentados en las Parte I--II de la tesis. El enorme tamaño de los árboles y la considerable cantidad de información asociada a los estados (p.ej., la cadena de ADN) obligan a la introducción de adaptaciones especiales en las herramientas de model checking para mantener un rendimiento razonable en la verificación de propiedades y aliviar también el problema de la explosión de estados (puntos G-H). El artículo de congreso [3] presenta las ventajas de rebanar el ADN asociado a los estados, la partición de la filogenia en pequeños subárboles y su distribución entre varias máquinas. Además, la idea original del model checking rebanado se complementa con la inclusión de una base de datos externa para el almacenamiento de secuencias. El artículo de revista [4] reúne las nociones introducidas en [3] junto con la implementación y resultados preliminares presentados [5]. Este tema se corresponde con lo presentado en la Parte III de la tesis. Para terminar, la tesis reaprovecha las extensiones de las lógicas temporales con tiempo explícito y probabilidades a fin de manipular e interrogar al árbol sobre información cuantitativa. El artículo de congreso [6] ejemplifica la necesidad de introducir probabilidades y tiempo discreto para el análisis filogenético de un fenotipo real, en este caso, el ratio de distribución de la intolerancia a la lactosa entre diversas poblaciones arraigadas en las hojas de la filogenia. Esto se corresponde con el Capítulo 13, que queda englobado dentro de las Partes IV--V. Las Partes IV--V completan los conceptos presentados en ese artículo de conferencia hacia otros dominios de aplicación, como la puntuación de árboles, y tiempo continuo (puntos E-F). La introducción de parámetros en las hipótesis filogenéticas se plantea como trabajo futuro. Referencias [1] Roberto Blanco, Gregorio de Miguel Casado, José Ignacio Requeno, and José Manuel Colom. Temporal logics for phylogenetic analysis via model checking. In Proceedings IEEE International Workshop on Mining and Management of Biological and Health Data, pages 152-157. IEEE, 2010. [2] José Ignacio Requeno, Roberto Blanco, Gregorio de Miguel Casado, and José Manuel Colom. Phylogenetic analysis using an SMV tool. In Miguel P. Rocha, Juan M. Corchado Rodríguez, Florentino Fdez-Riverola, and Alfonso Valencia, editors, Proceedings 5th International Conference on Practical Applications of Computational Biology and Bioinformatics, volume 93 of Advances in Intelligent and Soft Computing, pages 167-174. Springer, Berlin, 2011. [3] José Ignacio Requeno, Roberto Blanco, Gregorio de Miguel Casado, and José Manuel Colom. Sliced model checking for phylogenetic analysis. In Miguel P. Rocha, Nicholas Luscombe, Florentino Fdez-Riverola, and Juan M. Corchado Rodríguez, editors, Proocedings 6th International Conference on Practical Applications of Computational Biology and Bioinformatics, volume 154 of Advances in Intelligent and Soft Computing, pages 95-103. Springer, Berlin, 2012. [4] José Ignacio Requeno and José Manuel Colom. Model checking software for phylogenetic trees using distribution and database methods. Journal of Integrative Bioinformatics, 10(3):229-233, 2013. [5] José Ignacio Requeno and José Manuel Colom. Speeding up phylogenetic model checking. In Mohd Saberi Mohamad, Loris Nanni, Miguel P. Rocha, and Florentino Fdez-Riverola, editors, Proceedings 7th International Conference on Practical Applications of Computational Biology and Bioinformatics, volume 222 of Advances in Intelligent Systems and Computing, pages 119-126. Springer, Berlin, 2013. [6] José Ignacio Requeno and José Manuel Colom. Timed and probabilistic model checking over phylogenetic trees. In Miguel P. Rocha et al., editors, Proceedings 8th International Conference on Practical Applications of Computational Biology and Bioinformatics, Advances in Intelligent and Soft Computing. Springer, Berlin, 2014. [7] José Ignacio Requeno, Gregorio de Miguel Casado, Roberto Blanco, and José Manuel Colom. Temporal logics for phylogenetic analysis via model checking. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 10(4):1058-1070, 2013

A 3d geoscience information system framework

Two-dimensional geographical information systems are extensively used in the geosciences to create and analyse maps. However, these systems are unable to represent the Earth's subsurface in three spatial dimensions. The objective of this thesis is to overcome this deficiency, to provide a general framework for a 3d geoscience information system (GIS), and to contribute to the public discussion about the development of an infrastructure for geological observation data, geomodels, and geoservices. Following the objective, the requirements for a 3d GIS are analysed. According to the requirements, new geologically sensible query functionality for geometrical, topological and geological properties has been developed and the integration of 3d geological modeling and data management system components in a generic framework has been accomplished. The 3d geoscience information system framework presented here is characterized by the following features: - Storage of geological observation data and geomodels in a XML-database server. According to a new data model, geological observation data can be referenced by a set of geomodels. - Functionality for querying observation data and 3d geomodels based on their 3d geometrical, topological, material, and geological properties were developed and implemented as plug-in for a 3d geomodeling user application. - For database queries, the standard XML query language has been extended with 3d spatial operators. The spatial database query operations are computed using a XML application server which has been developed for this specific purpose. This technology allows sophisticated 3d spatial and geological database queries. Using the developed methods, queries can be answered like: "Select all sandstone horizons which are intersected by the set of faults F". This request contains a topological and a geological material parameter. The combination of queries with other GIS methods, like visual and statistical analysis, allows geoscience investigations in a novel 3d GIS environment. More generally, a 3d GIS enables geologists to read and understand a 3d digital geomodel analogously as they read a conventional 2d geological map

The algebra of semi-flows: a tale of two topologies

To capture the global structure of a dynamical system we reformulate dynamics in terms of appropriately constructed topologies, which we call flow topologies; we call this process topologization. This yields a description of a semi-flow in terms of a bi-topological space, with the first topology corresponding to the (phase) space and the second to the flow topology. A study of topology is facilitated through discretization, i.e. defining and examining appropriate finite sub-structures. Topologizing the dynamics provides an elegant solution to their discretization by discretizing the associated flow topologies. We introduce Morse pre-orders, an instance of a more general bi-topological discretization, which synthesize the space and flow topologies, and encode the directionality of dynamics. We describe how Morse pre-orders can be augmented with appropriate (co)homological information in order to describe invariance of the dynamics; this ensemble provides an algebraization of the semi-flow. An illustration of the main ingredients of the paper is provided by an application to the theory of discrete parabolic flows. Algebraization yields a new invariant for positive braids in terms of a bi-graded differential module which contains Morse theoretic information of parabolic flows

Image analysis for detecting the transverse profile of worn-out rails

Over its useful life a railway track is subject tomany mechanical and environmental stresses which graduallylead to its deterioration. Monitoring the wear condition of therailway superstructure is one of the key points to guarantee anadequate safety level of the railway transport system; in thisfield, the use of high-efficiency laser techniques has becomeconsolidated and implemented in diagnostic trains (e.g. the“Archimede train” and the “Talete train” ) which allow to detectthe track geometric parameters (gauge, alignment, longitudinallevel, cross level, superelevation defect, etc.) and the state of railwear (vertical, horizontal, 45-degree etc.) with very highaccuracy. The objective of this paper is to describe a new nonconventionalprocedure for detecting the transverse profile ofworn-out rails by means of image-processing technique. Thismethodological approach is based on the analysis of theinformation contained in high-resolution photographic images ofrails and on specific algorithms which allow to obtain the exactgeometric profile and the measurement of the relevant deviationscompared to new rails of the same typology.The analyses and the first results, obtained from laboratoryresearches, concern rails cross sections taken from railway linesunder upgrading. The procedure has shown high precision in thewear evaluation as well as great rapidity in being performed