At the heart of statistical learning lies the concept of uncertainty. Similarly, embodied agents such as robots and animals must likewise address uncertainty, as sensation is always only a partial reflection of reality. This thesis addresses the role that uncertainty can play in a central building block of intelligence: categorization. Cognitive agents are able to perform tasks like categorical perception through physical interaction (active categorical perception; ACP), or passively at a distance (distal categorical perception; DCP). It is possible that the former scaffolds the learning of the latter. However, it is unclear whether DCP indeed scaffolds ACP in humans and animals, nor how a robot could be trained to likewise learn DCP from ACP. Here we demonstrate a method for doing so which involves uncertainty: robots perform ACP when uncertain and DCP when certain. Furthermore, we demonstrate that robots trained in such a manner are more competent at categorizing novel objects than robots trained to categorize in other ways. This suggests that such a mechanism would also be useful for humans and animals, suggesting that they may be employing some version of this mechanism.

The R package coin implements a unified approach to permutation tests providing a huge class of independence tests for nominal, ordered, numeric, and censored data as well as multivariate data at mixed scales. Based on a rich and exible conceptual framework that embeds different permutation test procedures into a common theory, a computational framework is established in coin that likewise embeds the corresponding R functionality in a common S4 class structure with associated generic functions. As a consequence, the computational tools in coin inherit the exibility of the underlying theory and conditional inference functions for important special cases can be set up easily. Conditional versions of classical tests|such as tests for location and scale problems in two or more samples, independence in two- or three-way contingency tables, or association problems for censored, ordered categorical or multivariate data|can easily be implemented as special cases using this computational toolbox by choosing appropriate transformations of the observations. The paper gives a detailed exposition of both the internal structure of the package and the provided user interfaces along with examples on how to extend the implemented functionality. (authors' abstract)

The R package coin implements a unified approach to permutation tests providing a huge class of independence tests for nominal, ordered, numeric, and censored data as well as multivariate data at mixed scales. Based on a rich and flexible conceptual framework that embeds different permutation test procedures into a common theory, a computational framework is established in coin that likewise embeds the corresponding R functionality in a common S4 class structure with associated generic functions. As a consequence, the computational tools in coin inherit the flexibility of the underlying theory and conditional inference functions for important special cases can be set up easily. Conditional versions of classical tests - such as tests for location and scale problems in two or more samples, independence in two- or three-way contingency tables, or association problems for censored, ordered categorical or multivariate data - can be easily be implemented as special cases using this computational toolbox by choosing appropriate transformations of the observations. The paper gives a detailed exposition of both the internal structure of the package and the provided user interfaces. / Series: Research Report Series / Department of Statistics and Mathematics

The aim of this diploma thesis is statistical processing of a sample of patients that have been hospitalized and treated for ureteropelvic junction obstruction at the urological department of ÚNV Prague in last 20 years and to determine the optimal treatment method. Evaluation of surgical techniques from the surgical and economical point of creates a comprehensive image of advantages and disadvantages connected with application of a particular method and enables all participating subjects to decide in case of doubt. In this case the statistical analysis is a proper instrument, leading to find answers, however, it also gives an opportunity for discussion.

A primeira noção de topos, a de topos de Grothendieck, surgiu há cerca de 50 anos a partir de uma generalização do conceito de feixe na geometria algébrica. Poucos anos mais tarde, uma axiomatização categorial de algumas das propriedades de um topos de Grothendieck deu origem a uma segunda noção de topos, a de topos elementar; e essa descrição permitiu estabelecer ligações entre essas categorias e teoria dos conjuntos e lógica. Neste trabalho, estudamos a teoria de topos com um foco especial na construção da lógica interna dos topoi, e exploramos sua relação com modelos Heyting-valorados. / The first definition of a topos, that of a Grothendieck topos, emerged roughly 50 years ago from a generalization of the notion of sheaves in algebraic geometry. Few years later, a categorical axiomatization of some properties of Grothendieck topoi gave rise to a second notion of topoi, that of an elementary topos; and this description made it possible to establish connections between these categories and set theory and logic. In this work, we study topos theory with a particular focus on the construction of the internal logic of topoi, and explore its relation to Heyting-valued models.

Made available in DSpace on 2016-07-27T13:48:27Z (GMT). No. of bitstreams: 1 ROBSON PEDRO VERAS.pdf: 768979 bytes, checksum: 6c213763a7ad5009a9198f90f3950092 (MD5) Previous issue date: 2013-12-19 / A pesquisa Kant e a Religião da Razão procura estabelecer um debate específico em Ciência da Religião, notadamente sobre a Religião da Razão. Para esse propósito será estabelecido uma temática específica em que elementos religiosos podem ser sistematizados e redimensionados para uma conjuntura moral. O texto foi elaborado a partir de uma interpretação que irá ser de recondução a um desdobramento do conceito sobre religião. Desse modo, a experiência religiosa do homem se mostrará como conseqüência de uma dimensão moral construída socialmente. A importância dessa análise é a de percebermos a moral e sua manifestação na religião como desdobramento do Imperativo Categórico. Desse modo, temos aqui uma proposta de demonstração da religião dentro de uma percepção racional, voltada, sobre tudo, para o cumprimento moral, da ação pelo dever e pela virtude. Para o cumprimento dessa tarefa será feita uma análise do arcabouço moral em Kant (1992), (1996) e (2011), em que a tese do autor fundamenta o argumento religioso especificamente. É com esse conjunto de argumentos que entendemos que a confirmação de qualquer hipótese que tenha o filósofo Kant como mediador epistemológico, necessita de certo redimensionamento do autor a práticas modernas. O desafio, por assim dizer, é podermos admitir a ação moral como única possibilidade do dever. Dessa forma, a pesquisa se estrutura em três capítulos: o primeiro capítulo apresenta a religião da razão, dividida, supostamente, em categorias: a Moral, a Razão, o Imperativo Categórico, descrição acerca da Justiça e o Bem e o Mal. No capítulo seguinte é apresentado o processo de recondução da religião ao fundamento da moral. Para o terceiro capítulo mostra a importância da crítica Kantiana sobre a religião para o debate do contexto das Ciências da Religião

The Slovenian Public Opinion survey (SPOS), which carried out in 1990, was used by the government of Slovenia as a benchmark to prepare for an upcoming plebiscite, which asked the respondents whether they support independence from Yugoslavia. However, the sample size was large and it is quite likely that the respondents and nonrespondents had divergent viewpoints. We first develop an ignorable nonresponse model which is an extension of a bivariate binomial model. In order to accommodate the nonrespondents, we then develop a nonignorable nonresponse model which is an extension of the ignorable model. Our methodology uses an EM algorithm to fit both the ignorable and nonignorable nonresponse models, and estimation is carried out using the bootstrap mechanism. We also perform sensitivity analysis to study different degrees of departures of the nonignorable nonresponse model from the ignorable nonresponse model. We found that the nonignorable nonresponse model is mildly sensitive to departures from the ignorable nonresponse model. In fact, our finding based on the nonignorable model is better than an earlier conclusion about another nonignorable nonresponse model fitted to these data.

Two applications of Category Theory are considered. The link between them is applications to Physics and more specifically to Entropy. The first research chapter is broader in scope and not explicitly about Physics, although connections to Statistical Mechanics are made towards the end of the chapter. Matroids are abstract structures that describe dependence, and strong maps are certain structure-preserving functions between them with desirable properties. We examine properties of various categories of matroids and strong maps: we compute limits and colimits; we find free and cofree constructions of various subcategories; we examine factorisation structures, including a translation principle from geometric lattices; we find functors with convenient properties to/from vector spaces, multisets of vectors, geometric lattices, and graphs; we determine which widely used operations on matroids are functorial (these include deletion, contraction, series and parallel connection, and a simplification monad); lastly, we find a categorical characterisation of the greedy algorithm. In conclusion, this project determines which aspects of Matroid Theory are most and least conducive to categorical treatment. The purpose of the second research chapter is to provide a categorical framework for generalising and unifying notions of Entropy in various settings, exploiting the fact that Entropy is a monotone subadditive function. A categorical characterisation of Entropy through a category of thermodynamical systems and adiabatic processes is found. A modelling perspective (adiabatic categories) that directly generalises an existing model is compared to an axiomatisation through topological and linear structures (topological weak semimodules), where the latter is based on a categorification of semimodules. Properties of each class of categories are examined; most notably a cancellation property of adiabatic categories generalising an existing result, and an adjunction between the categories of weak semimodules and symmetric monoidal categories. An adjunction between categories of adiabatic categories and topological weak semimodules is found. We examine in which cases each of these classes of categories constitutes a traced monoidal category. Lastly, examples of physical applications are provided. In conclusion, this project uncovers a way of, and makes progress towards, retrieving the statistical formulation of Entropy from simple axioms.

FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Este trabalho visa a caracterizar formal, semÃntica e pragmaticamente as construÃÃes com verbo-suporte botar; considerando que, dentro desse âguarda-chuvaâ que se denominou verbo-suporte, hà estruturas com comportamentos sintÃtico-semÃnticos distintos. A partir das caracterÃsticas sintÃtico-semÃnticas das construÃÃes com verbo-suporte, verificaram-se trÃs graus de fluidez categorial: construÃÃes com verbo-suporte que estÃo mais prÃximas das construÃÃes livres (grau 1), construÃÃes com verbo-suporte consideradas prototÃpicas (grau 2) e construÃÃes que estÃo mais prÃximas das expressÃes cristalizadas (grau 3). A pesquisa enfocou o uso das construÃÃes botar + SN/SP em PortuguÃs e define as propriedades morfossintÃticas e semÃnticas que botar assume ao se vincular à categoria de verbo-suporte. A investigaÃÃo criteriosa sobre as propriedades de seleÃÃo de botar e seu comportamento sintÃtico-semÃntico em construÃÃes botar + SN/SP forneceu ainda subsÃdios para se descreverem diferentes empregos de botar nesse tipo de estrutura e, assim, se delinear uma cadeia de gramaticalizaÃÃo desse verbo. A base teÃrica linguÃstica de exame à a teoria funcionalista da linguagem, a qual reformula o corte rÃgido entre os verbos plenos e verbos-suporte, tratando esta categoria em uma perspectiva escalar e nÃo discreta. Os corpora (Norpofor, Porcufort e o DUP) de anÃlise compreendem ocorrÃncias de Vsup nas modalidades formal e informal do portuguÃs do Brasil, sem que se fixe como objetivo do trabalho pesquisar especificamente diferenÃas entre essas modalidades, mas com a hipÃtese de que a complexidade das CVSup nÃo poderia representar-se da mesma forma nessas modalidades de lÃngua. Realizou-se, com esta pesquisa, uma sistematizaÃÃo semÃntico-sintÃtica de expressÃes com verbo-suporte botar que apresentam graus de fluidez categorial. Para tanto, recorreu-se a anÃlises mÃltiplas que envolvem a descriÃÃo semÃntico-sintÃtica das expressÃes e a verificaÃÃo de parÃmetros que influenciam a fluidez e a depreensÃo de seus nÃveis. Os resultados demonstram ainda que a produtividade de botar na norma popular à maior do que na norma culta. No portuguÃs culto de Fortaleza, constatamos uma frequÃncia menor do verbo botar, confirmando nossa hipÃtese de que o processo de gramaticalizaÃÃo à mais lento na modalidade culta, embora, mesmo em menor quantidade, jà haja indÃcios de gramaticalizaÃÃo. ApÃs uma anÃlise geral nos sÃculos XVIII, XIX e XX, constatamos que hà um aumento da frequÃncia do verbo botar ao longo dos sÃculos. Tal fato confirma que esse verbo està em processo de gramaticalizaÃÃo contÃnuo. A descriÃÃo de cada um desses nÃveis (com os parÃmetros definidos na anÃlise e os exemplos extraÃdos dos corpora) explicitou que o verbo botar, na categoria de verbos-suporte, pode fazer parte tanto de estruturas mais integradas quanto de estruturas menos integradas, conforme essas construÃÃes se aproximam ou se distanciam do protÃtipo de uma construÃÃo com verbo-suporte. / This work aims to provide some formal, semantic and pragmatic characterization of the support verb âbotarâ, since the wideness concerning this verb presents distinctive syntactical and semantical behaviors in its structure. From the characteristics of the syntactical and semantical constructions of the verb, three degrees of categorical flushness were explored: free constructions, prototypical constructions and structures which are nearly crystalize. The research was concentrated in the constructions âbotar+SN/SPâ in Brazilian Portuguese, establishing the morpho-syntactical and semantical which the verb âbotarâ assumes when it is constructed as a support verb. The rigorous investigation of the selection properties of âbotarâ and its syntactical and semantical behavior in the âbotar+SN/SPâ structure provided support to describe different employments of the verb, hence leading to a chain of grammatical structures. The linguistic theoretical base used is the functionalism theory of language, which allows to precisely separating ordinary verbs from the support verbs, by treating their aspects in a scalar, rather discrete perspective. The corpus used in the analysis consists of Vsup occurrences in formal and informal Brazilian Portuguese language, however without restricting to only the differences among these modalities, but also using the hypothesis that the CVSup complexity could not be represented in these language modalities. The research allowed to create a systematic syntactical and semantical of expression involving the support verb which present degrees of categorical flushness. In order to achieve that, multiple analyses were conducted in which the syntactical and semantical descriptions of the expressions, in addition to the use of parameters which influences the flushness and the comprehension. As a result of the research, the productivity of the verb is more evident in the popular rather than in the formal usage. In particular, in formal Portuguese of Fortaleza, we verified a lower frequency of use, which confirms our starting hypothesis that the grammaticalization is slower in the formal language, although we could note that it has started already. After detailed analyses in the XVIII, XIX and XX centuries, we concluded that the usage of the verb has been increasing in the past few centuries, in fact the verb is having a gradual continuous grammaticalization. According to the analysis parameters and the examples obtained from the corpus, the description of each of those levels showed that the verb âbotarâ, within the support verb category, can be part of both the less and more integrated structures, depending on the how close those constructions are from the prototype of a support verb construction.

This thesis studies some constructions for building new models of Martin-Löf type theory out of old. We refer to the main techniques as gluing and idempotent splitting. For each we give general conditions under which type constructors exist in the resulting model. These techniques are used to construct some examples of Dialectica models of type theory. The name is chosen by analogy with de Paiva's Dialectica categories, which semantically embody Gödel's Dialectica functional interpretation and its variants. This continues a programme initiated by von Glehn with the construction of the polynomial model of type theory. We complete the analogy between this model and Gödel's original Dialectica by using our techniques to construct a two-level version of this model, equipping the original objects with an extra layer of predicates. In order to do this we have to carefully build up the theory of finite sum types in a display map category. We construct two other notable models. The first is a model analogous to the Diller-Nahm variant, which requires a detailed study of biproducts in categories of algebras. To make clear the generalization from the categories studied by de Paiva, we illustrate the construction of the Diller-Nahm category in terms of gluing an indexed system of types together with a system of predicates. Following this we develop the general techniques needed for the type-theoretic case. The second notable model is analogous to the Dialectica category associated to the error monad as studied by Biering. This model has only weak dependent products. In order to get a model with full dependent products we use the idempotent splitting construction, which generalizes the Karoubi envelope of a category. Making sense of the Karoubi envelope in the type-theoretic case requires us to face up to issues of coherence in our models. We choose the route of making sure all of the constructions we use preserve strict coherence, rather than applying a general coherence theorem to produce a strict model afterwards. Our chosen method preserves more detailed information in the final model.