<p>This research is concerned with theoretical and methodological aspects of geographic information transformation between different user contexts. In this dissertation I present theories and methodological approaches that enable a context sensititve use and reuse of geographic data in geographic information systems.</p><p>A primary motive for the reported research is that the patrons interested in answering environmental questions have increased in number and been diversified during the last 10-15 years. The interest from international, national and regional authorities together with multinational and national corporations embrace a range of spatial and temporal scales from global to local, and from many-year/-decade perspectives to real time applications. These differences in spatial and temporal detail will be expressed as rather different questions towards existing data. It is expected that geographic information systems will be able to integrate a large number of diverse data to answer current and future geographic questions and support spatial decision processes. However, there are still important deficiencies in contemporary theories and methods for geographic information integration</p><p>Literature studies and preliminary experiments suggested that any transformation between different users’ contexts would change either the thematic, spatial or temporal detail, and the result would include some amount of semantic uncertainty. Consequently, the reported experiments are separated into studies of change in either spatial or thematic detail. The scope concerned with thematic detatil searched for approaches to represent indiscernibility between categories, and the scope concerned with spatial detail studied semantic effects caused by changing spatial granularity.</p><p>The findings make several contributions to the current knowledge about transforming geographic information between users’ contexts. When changing the categorical resolution of a geographic dataset, it is possible to represent cases of indiscernibility using novel methods of rough classification described in the thesis. The use of rough classification methods together with manual landscape interpretations made it possible to evaluate semantic uncertainty in geographic data. Such evaluations of spatially aggregated geographic data sets show both predictable and non-predictable effects. and these effects may vary for different environmental variables.</p><p>Development of methods that integrate crisp, fuzzy and rough data enables spatial decision support systems to consider various aspects of semantic uncertainty. By explicitly representing crisp, fuzzy and rough relations between datasets, a deeper semantic meaning is given to geographic databasses. The explicit representation of semantic relations is called a Geographic Concept Topology and is held as a viable tool for context transformation and full integration of geographic datasets.</p>

Title: Categorial methods in structure theory Author: Jakub Opršal Department / Institute: Mathematical Institute, Charles University Supervisor of the master thesis: prof. RNDr. Věra Trnková, DrSc. Abstract: In the first part of the thesis we investigate functor algebras. Initial algebras have distin- guished role in the study of these structures, and it can be constructed by certain transfinite construction, which is called initial algebra construction. Sooner this year Adámek and Trnková have prooved, that the construction stops in either at most three, or in κ steps where κ is a regular cardinal. We continue with their work, and we study the relation between the size of the algebra and the length of the convergence. We prove that the length of the convergence never exceeds the cardinality of the initial algebra. Another transfinite construction has been studied in 1980 by Kelly. He has described the construction of free algebras for a pointed functor and defined a class of well-pointed functors for which the construction is especially simple (and is in fact special case of the construction of relatively terminal coalgebra which has been recently defined by Adámek and Trnková). In the last chapter we describe all well-pointed functors in categories of sets and the dual category, and we provide list of...

Dans cette thèse, nous étudions le problème de l'inférence bayésienne dans les graphes factoriels, en particulier les codes LDPC, quasiment résolus par les algorithmes de message-passing. Nous réalisons en particulier une étude approfondie du Belief Propagation (BP) dont la question de la sous-optimalité est soulevée dans le cas où le graphe factoriel présente des boucles. A partir de l'équivalence entre le BP et l'approximation de Bethe en physique statistique qui se généralise à l'approximation basée régions, nous détaillons le Generalized Belief Propagation (GBP), un algorithme de message-passing entre des clusters du graphe factoriel. Nous montrons par des expériences que le GBP surpasse le BP dans les cas où le clustering est réalisé selon les structures topologiques néfastes qui empêchent le BP de bien décoder, à savoir les trapping sets. Au-delà de l'étude des performances en termes de taux d'erreur, nous confrontons les deux algorithmes par rapport à leurs dynamiques face à des événements d'erreur non triviaux, en particulier lorsqu'ils présentent des comportements chaotiques. Par des estimateurs classiques et originaux, nous montrons que l'algorithme du GBP peut dominer l'algorithme du BP. / This thesis addresses the problem of inference in factor graphs, especially the LDPC codes, almost solved by message-passing algorithms. In particular, the Belief Propagation algorithm (BP) is investigated as a particular message-passing algorithm whose suboptimality is discussed in the case where the factor graph has a loop-like topology. From the equivalence between the BP and the Bethe approximation in statistical physics that is generalized to the region-based approximation, is detailed the Generalized Belief Propagation algorithm (GBP), a message-passing algorithm between clusters of the factor graph. It is experimentally shown to surpass the BP in the cases where the clustering deals with the harmful topological structures that prevents the BP from rightly decoding any LDPC code, namely the trapping sets. We do not only confront the BP and the GBP algorithms according to their performance from the point of view of the channel coding with the error-rate, but also according to their dynamical behaviors for non-trivial error-events for which both algorithms can exhibit chaotic beahviors. By means of classical and original dynamical quantifiers, it is shown that the GBP algorithm can overcome the BP algorithm.

Cette thèse s’intéresse principalement à l’existence et à la régularité desensembles minimaux. On commence par montrer, dans le chapitre 3, que le problème de Plateau étudié par Reifenberg admet au moins une solution. C’est-à-dire que, si l’onse donne un ensemble compact B⊂R^n et un sous-groupe L du groupe d’homologie de Čech H_(d-1) (B;G) de dimension (d-1) sur un groupe abelien G, on montre qu’il existe un ensemble compact E⊃B tel que L est contenu dans le noyau de l’homomorphisme H_(d-1) (B;G)→H_(d-1) (E;G) induit par l’application d’inclusion B→E, et pour lequel la mesure de Hausdorff H^d (E∖B) est minimale (sous ces contraintes). Ensuite, on montre au chapitre 4, que pour tout ensemble presque minimal glissant E de dimension 2, dans un domaine régulier Σ ressemblant localement à un demi espace, associé à la frontière glissante ∂Σ, et tel que E⊃∂Σ, il se trouve qu’à la frontière E est localement équivalent, par un homéomorphisme biHöldérien qui préserve la frontière, à un cône minimal glissant contenu dans un demi plan Ω, avec frontière glissante ∂Ω. De plus les seuls cônes minimaux possibles dans ce cas sont ∂Ω seul, ou son union avec un cône de type P_+ ou Y_+. / This thesis focuses on the existence and regularity of minimal sets. First we show, in Chapter 3, that there exists (at least) a minimizerfor Reifenberg Plateau problems. That is, Given a compact set B⊂R^n, and a subgroup L of the Čech homology group H_(d-1) (B;G) of dimension (d-1)over an abelian group G, we will show that there exists a compact set E⊃B such that L is contained in the kernel of the homomorphism H_(d-1) (B;G)→H_(d-1) (E;G) induced by the natural inclusion map B→E, and such that the Hausdorff measure H^d (E∖B) is minimal under these constraints. Next we will show, in Chapter 4, that if E is a sliding almost minimal set of dimension 2, in a smooth domain Σ that looks locally like a half space, and with sliding boundary , and if in addition E⊃∂Σ, then, near every point of the boundary ∂Σ, E is locally biHölder equivalent to a sliding minimal cone (in a half space Ω, and with sliding boundary ∂Ω). In addition the only possible sliding minimal cones in this case are ∂Ω or the union of ∂Ω with a cone of type P_+ or Y_+.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-08-12T15:13:32Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) dissertacao rommel cc.pdf: 1665635 bytes, checksum: 9f894f847272036c011387e2de71507f (MD5) / Made available in DSpace on 2014-08-12T15:13:32Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) dissertacao rommel cc.pdf: 1665635 bytes, checksum: 9f894f847272036c011387e2de71507f (MD5) Previous issue date: 2009-03-12 / Given a graph G = (V;E) and a set of vertices D V, a vertice v 2 V is dominated by D if jN[v] \ Dj 1. When jN(v) \ Dj = 1 for all v 2 V, G is efficiently dominable. A generalization of this concept is called efficient multiple domination, which requires all vertices must be dominated by a set D V exactly k times. The aim of this dissertation is to study these topics, describing the theoretical knowledge needed for advanced researches. For this reason, many of the theorems and its proofs are detailed. Furthermore, some results on the efficient multiple domination are presented, including bounds for the size of efficient k-dominating sets, the complement and iterated line graphs of efficiently (r + 1)-dominable r-regular graphs and a N P-completeness proof for the efficient multiple domination problem in arbitrary graphs. It is expected that this work contribute to the development of future researches on the efficient domination and in the resolution of some open problems. / Dado um grafo G = (V;E) e um subconjunto de vértices D V, define-se D como um conjunto dominante de G se todo vértice v 2 V que não estiver incluído no conjunto D for adjacente a pelo menos um vértice de D. Na situação em que, para todo v 2 V, jN[v]\Dj = 1, diz-se que o grafo G é eficientemente dominado. Uma generalização desse conceito consiste na múltipla dominação eficiente, em que é requerido que todo vértice do grafo seja dominado exatamente k vezes. O objetivo deste trabalho é realizar um estudo exploratório sobre esses temas, de modo a reunir o conhecimento teórico requerido para pesquisas avançadas. Para isso, buscou-se a apresentação e o detalhamento das demonstrações dos teoremas estudados. Além disso, foram fornecidos alguns resultados sobre a múltipla dominação eficiente no que se refere aos limites para o tamanho de um conjunto k-dominante eficiente, à relação da k-dominação eficiente entre grafos regulares, seu complemento e seus grafos linha iterados, bem como à caracterização da N P-completude para o problema da múltipla dominação eficiente em grafos arbitrários. Espera-se que esta dissertação forneça subsídios teóricos para estudos futuros voltados à dominação eficiente, bem como à resolução de algumas questões em aberto.

This research is concerned with theoretical and methodological aspects of geographic information transformation between different user contexts. In this dissertation I present theories and methodological approaches that enable a context sensititve use and reuse of geographic data in geographic information systems. A primary motive for the reported research is that the patrons interested in answering environmental questions have increased in number and been diversified during the last 10-15 years. The interest from international, national and regional authorities together with multinational and national corporations embrace a range of spatial and temporal scales from global to local, and from many-year/-decade perspectives to real time applications. These differences in spatial and temporal detail will be expressed as rather different questions towards existing data. It is expected that geographic information systems will be able to integrate a large number of diverse data to answer current and future geographic questions and support spatial decision processes. However, there are still important deficiencies in contemporary theories and methods for geographic information integration Literature studies and preliminary experiments suggested that any transformation between different users’ contexts would change either the thematic, spatial or temporal detail, and the result would include some amount of semantic uncertainty. Consequently, the reported experiments are separated into studies of change in either spatial or thematic detail. The scope concerned with thematic detatil searched for approaches to represent indiscernibility between categories, and the scope concerned with spatial detail studied semantic effects caused by changing spatial granularity. The findings make several contributions to the current knowledge about transforming geographic information between users’ contexts. When changing the categorical resolution of a geographic dataset, it is possible to represent cases of indiscernibility using novel methods of rough classification described in the thesis. The use of rough classification methods together with manual landscape interpretations made it possible to evaluate semantic uncertainty in geographic data. Such evaluations of spatially aggregated geographic data sets show both predictable and non-predictable effects. and these effects may vary for different environmental variables. Development of methods that integrate crisp, fuzzy and rough data enables spatial decision support systems to consider various aspects of semantic uncertainty. By explicitly representing crisp, fuzzy and rough relations between datasets, a deeper semantic meaning is given to geographic databasses. The explicit representation of semantic relations is called a Geographic Concept Topology and is held as a viable tool for context transformation and full integration of geographic datasets.

The process of quantifying the robustness of a given nonlinear system is not necessarily trivial. If the dynamics of the system in question are not sufficiently involved, then a tight estimate of a bound on system performance may be obtained. As the dynamics of the system concerned become more and more involved, it is often found that using the results existing in the literature provides a very conservative bound on system performance. Therefore, the motivation for this work is to develop a general method to obtain a less conservative estimate of a bound on system performance, compared to the results already available in literature. The scope of this work is limited to two dimensions at present. Note that working in a two dimensional space does not necessarily make the objective easily achievable. This is because quantifying the robustness of a general nonlinear system perturbed by disturbances can very easily become intractable, even on a space with dimension as low as two. The primary contribution of this work is a computational algorithm, the points generated by which are conjectured to lie on the boundary of the smallest robust forward invariant set for a given nonlinear system. A well known path-planning algorithm, available in existing literature, is leveraged to make the algorithm developed computationally efficient. If the system dynamics are not accurately known, then the above computed approximation of an invariant set may cease to be invariant over the given finite time interval for which the computed set is expected to be invariant. Therefore, the secondary contribution of this work is an algorithm monitoring a computed approximation of an invariant set. It is shown that for a certain type of systems, this secondary monitoring algorithm can be used to detect that a computed approximation of an invariant set is about to cease to be invariant, even if the primary algorithm computed the set based on an unsophisticated dynamical model of a system under consideration. The work related to computing approximations of invariant sets is tested mainly with the curve tracking problem in two dimensions. The algorithm monitoring whether a computed approximation of an invariant set is about to cease to be invariant is inspired by work related to detecting Lithium-ion (Li-ion) battery terminal voltage collapse detection.

The hybridization of soft computing methods of Radial Basis Function (RBF) neural networks, Multi Layer Perceptron (MLP) neural networks with back-propagation learning, fuzzy sets and rough sets are studied in the scope of this thesis. Conventional MLP, conventional RBF, fuzzy MLP, fuzzy RBF, rough fuzzy MLP, and rough fuzzy RBF networks are compared. In the fuzzy neural networks implemented in this thesis, the input data and the desired outputs are given fuzzy membership values as the fuzzy properties &ldquo / low&rdquo / , &ldquo / medium&rdquo / and &ldquo / high&rdquo / . In the rough fuzzy MLP, initial weights and near optimal number of hidden nodes are estimated using rough dependency rules. A rough fuzzy RBF structure similar to the rough fuzzy MLP is proposed. The rough fuzzy RBF was inspected whether dependencies like the ones in rough fuzzy MLP can be concluded.

Systems are becoming more complicated, complex, and interrelated. Designers have recognized the need to develop systems from a holistic perspective and design them as Systems-of-Systems (SoS). The design of the SoS, especially in the conceptual design phase, is generally characterized by significant uncertainty. As a result, it is possible for all three types of uncertainty (aleatory, epistemic, and error) and the associated factors of uncertainty (randomness, sampling, confusion, conflict, inaccuracy, ambiguity, vagueness, coarseness, and simplification) to affect the design process. While there are a number of existing SoS design methods, several gaps have been identified: the ability to modeling all of the factors of uncertainty at varying levels of knowledge; the ability to consider both the pernicious and propitious aspects of uncertainty; and, the ability to determine the value of reducing the uncertainty in the design process. While there are numerous uncertainty modeling theories, no one theory can effectively model every kind of uncertainty. This research presents a Hybrid Uncertainty Modeling Method (HUMM) that integrates techniques from the following theories: Probability Theory, Evidence Theory, Fuzzy Set Theory, and Info-Gap theory. The HUMM is capable of modeling all of the different factors of uncertainty and can model the uncertainty for multiple levels of knowledge. In the design process, there are both pernicious and propitious characteristics associated with the uncertainty. Existing design methods typically focus on developing robust designs that are insensitive to the associated uncertainty. These methods do not capitalize on the possibility of maximizing the potential benefit associated with the uncertainty. This research demonstrates how these deficiencies can be overcome by identifying the most robust and opportunistic design. In a design process it is possible that the most robust and opportunistic design will not be selected from the set of potential design alternatives due to the related uncertainty. This research presents a process called the Value of Reducing Uncertainty Method (VRUM) that can determine the value associated with reducing the uncertainty in the design problem before a final decision is made by utilizing two concepts: the Expected Value of Reducing Uncertainty (EVRU) and the Expected Cost to Reducing Uncertainty (ECRU).

This paper aims to demystify, empirically, a statement widely shared in the political imaginary of the citizens of Santiago de Cali: candidates, who predominate in the popular sectors of the population, are the ones who win the elections for mayor («Aguablanca elects the mayor»). From an analysis with Qualitative Comparative Analysis (QCA) in their mode of fuzzy sets, it is shown that there are more complex scenarios of the electoral behavior in the elections for the municipal mayor in 2003, 2007 and 2011. Starting from this premise, from a«sociological perspective» it is proposed a classification of the strata of the city according to the pooled weighted average and candidate as elite/non elite, to analyze the electoral trends in terms of political preferences of each stratum. It also seeks to identify causal combinations that consents the election of a mayor, taking into account variables such as the profil elite/non elite of the candidates, levels of fragmentation in both segments of candidatures and finally, the dominance that each achieved in the different communes of the city. / El presente trabajo se propone desmitificar, empíricamente, un enunciado ampliamente compartido en el imaginario político de los ciudadanos de Santiago de Cali: los candidatos predominantes en los sectores populares son quienes ganarán las elecciones a la alcaldía («Aguablanca elige al alcalde»). A partir de un análisis realizado con Qualitative Comparative Analysis (QCA), en su modalidad de conjuntos difusos, se muestra que existen escenarios sensiblemente más complejos del comportamiento electoral en los comicios para la alcaldía municipal en 2003, 2007 y 2011. Partiendo de esta premisa, desde una «perspectiva sociológica» del análisis electoral, se propone una clasificación de los estratos de la ciudad acorde a la media ponderada agrupada y de los candidatos como élite/no élite, para analizar las tendencias electorales en términos de expresión de preferencias políticas por parte de cada estrato. Asimismo, se busca identificar cuáles son las combinaciones causales que consienten la elección de un alcalde, teniendo en cuenta variables como: el perfil élite/no élite de los candidatos, los niveles de fragmentación existentes en ambos segmentos de candidaturas y, finalmente, el predominio que cada uno de ellos logran en las diferentes comunas de la ciudad.