For a fuzzy uniform space, the notion of a Cauchy prefilter, a precompact fuzzy set, a complete fuzzy set and a bounded fuzzy set are defined in such a way that these notions are good extensions of the corresponding notions for a uniform space. A theory of fuzzy uniform spaces is developed which generalises the theory of uniform spaces.

We start by discussing fuzzy sets and the algebra of fuzzy sets. We consider some properties of fuzzy modeling tools. This is followed by considering the Mamdani and Sugeno models for designing fuzzy controllers. Various methods for using sets of data for desining controllers are discussed. This is followed by a chapter illustrating the use of genetic algorithms in designing and optimizing fuzzy controllers.Finally we look at some previous applications of fuzzy control in telecommunication networks, and illustrate a simple application that was developed as part of the present work.

Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence are called Mycielski-regular. We show that the self-similar measure generated by a finite family of contracting similitudes and which up to a constant is the Hausdorff measure in its dimension on an invariant set C is Mycielski-regular.

Many computational problems require reasoning about relational structures. Examples include high-level system design, architectural configuration of network systems, reasoning about ontologies, and verification of programs with linked data structures. Traditionally, relational models are translated to propositional formulas and then solved by leveraging SAT solvers. However, SAT solvers can only reason about problems within a finite scope, i.e, concrete cardinality bounds on the relations involved. SMT solvers, on the other hand, are efficient tools that can check automatically the satisfiability of complex constraints over several domains without scope restrictions. They are used as the back-end solvers in many verification tools. To break the limitation of bounded analysis, this thesis presents a many-sorted relational logic in SMT where relations of arity n are defined as sets of n-tuples with parametrized sorts for tuple elements. We define a version of this logic as a first-order theory of finite relations where relation terms are built from relation constants and variables, set operators, and relational operators such as join, transpose, product, and transitive closure. We also present a deductive calculus for that theory and provide proofs of refutation soundness and model soundness of our calculus. In addition, we implement the calculus as a relational solver in the SMT solver CVC4, expanding its already large set of built-in theories, and evaluate the relational solver in two applications: Alloy and Ontology, showing promising results. Moreover, with the goal of improving the performance of SMT solvers in general, we present a symmetry detection algorithm to detect symmetries in SMT formulas and present a symmetry breaking algorithm to generate blocking constraints that eliminate those symmetries. We then discuss an experimental evaluation of our implementation of these algorithms in CVC4 against SMT-LIB benchmarks.

Tesis para optar al grado de Magíster en Ciencias de la Ingeniería, Mención Eléctrica / Memoria para optar al título de Ingeniero Civil Eléctrico / Esta tesis se enfoca en resolver el problema del multi-target tracking en ambientes altamente dinámicos, y utilizando robots que poseen baja capacidad de procesamiento y sensores limi- tados. Para esto se utiliza un nuevo método de realizar tracking baso en Random Finite Sets (RFS). La utilización de este método supone diferentes mejoras como la eliminación del data association problem o la utilización de la información negativa de los sensores. La hipótesis que se desea probar es que la utilización de este nuevo método puede obtener mejores resultados que los clásicos métodos de tracking, como el EKF multi-hipótesis. Además se desea demostrar que es posible realizar un tracking de este estilo en robots de poco procesamiento computacional y que este resultado se puede mejorar aún más si un conjunto de robots comparten sus estimaciones para generar una estimación global. Para esto se utiliza el robot Nao, el cual es utilizado en la competencia RoboCup, la cual corresponde a una competencia de fútbol robótico. Es en este escenario donde se implementa un método de tracking, basado en RFS, que se utiliza para ubicar todos los robots de la cancha, con tal de realizar un mapa de obstáculos. La implementación de este método la caracterización de cada sensor del robot, los cuales son utilizados como inputs del sistema. Finalmente, se realizan diversas pruebas, ya sea con robots reales o con simulaciones realistas, la cuales constan de escenarios ficticios y de partidos reales. En cada una de estas, se compara el mapa de obstáculos obtenido con las posiciones reales de los robots con la cancha. Esta comparación se realiza utilizando una medida de distancia especialmente diseñada para comparar conjuntos, llamada OSPA. Los resultados obtenidos demuestran que el método propuesto en esta tesis supera en general a los métodos clásicos, ya sea tanto cualitativa como cuantitativamente. Se pueden observar claramente las ventajas de la utilización negativa de los sensores, así como la no necesidad de resolver el data association problem. También se puede observar la mejora generada al utilizar la información compartida entre robots, lo que genera un mapa de obstáculos más preciso. / Fondecyt 1161500

Philosophiae Doctor - PhD / Understanding the geometries of points in space has been attractive to mathematicians for ages. As a model, twelve years ago, Kurz and Meyer [32] considered point sets in the m-dimensional a ne space Fmq over a nite eld Fq with q = pr elements, p prime, where each squared Euclidean distance of two points is a square in Fq: The latter points are said to be at integral distance in Fmq , and the sets above are called integral point sets.

When we scan image data by ultrasound, we have a little information of displayed scene. For understanding content of the image we try to separate the observed objects of interest from the background. Obtaining information of these objects is called a process called segmentation. This work is focused on the segmentation of ultrasound image sequences using geometric active contours solved by the method of level sets. For better representation is also dealing with image preprocessing. The result is an implementation of segmentation methods on simulated and real data.

Given a graph with domination number γ, we find bounds on the maximum number of minimum dominating sets. First, for γ≥3, we obtain lower bounds on the number of γ-sets that do not dominate a graph on n vertices. Then, we show that γ-fold lexicographic product of the complete graph on n1/γ vertices has domination number γ and γn-O(nγ-γ/1) dominating sets of size γ. Finally, we see that a certain random graph has, with high probability, (i) domination number γ; and (ii) all but o(nγ) of its γ-sets being dominating.

This thesis is separated into two parts: threshold graphs and inertia sets. First we present an algorithmic approach to finding the minimum rank of threshold graphs and then progress to counting the number of threshold graphs with a specific minimum rank. Second, we find an algorithmic and more automated way of determining the inertia set of graphs with seven or fewer vertices using theorems and lemmata found in previous papers. Inertia sets are a relaxation of the inverse eigenvalue problem. Instead of determining all the possible eigenvalues that can be obtained by matrices with a specific zero/nonzero pattern we restrict to counting the number of positive and negative eigenvalues.

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