Le projet s’addresse à la résignification kantienne du concept de “metaphysique”, à partir de l’évolution de la notion d’ontologie dans les Vorlesungen über Metaphysik contenues dans le volume XXVIII de l’Akademie Ausgabe. Á la base de la recherche on entende mettre en relation Kant entre la tradition logique du siècle 17º et 18º, pour comprendre la façon dans laquelle Kant (peut) se confront avec la terminologie de la tradition, et en particulier avec la médiation de Wolff et Baumgarten de la metaphysique leibnizienne.An (peut) traiter de passer d’une conception de la metaphysique de façon deductive capable de rendre la raison de la réalité sur la base de principes qui s’imposent à celle-là, sans en être des déscrivés, à une conception inductive, dans laquelle est par l’examen de la réalité même qu’on peut en tirer les lois.Les Leçons semblent le lieu dans laquelle l’ontologie plus émerge comme instrument de cette résignification, qui voit intéressés: approche méthodologique, autonomie de la raison et l’absolue urgence d’une exigence normative. / The aim of the project is to study the new meaning gained by the concept of “metaphysics” through the evolution of the notion of ontology in the Vorlesungen über Metaphysik, placed in the XXVIII volume of the Akademie Ausgabe. As foundation of the research, we want to put into relationship Kant and the logical tradition of the 17º and 18º century, in order to understand the way in which Kant confronts himself with the technical terms of the tradition, in particular with the mediation of the leibnizian metaphysics represented by Wolff and Baumgarten. Here there is a step from a deductive conception of metaphysics to an inductive one. While the first can explain the reality starting from principles imposed on it, in the last the laws of reality are gained through an analysis of the reality the same.The lessons seem to be the place in which the ontology emerges in the best and clearest way as the instrument to get the new meaning of the metaphysics, we are target to: here we find a methodological approach, the autonomy of reason and the absolute urgency of a normative exigency.

The thesis has analytical - interpretative nature and focuses on paradigmatic dealing with body and bodiliness motive in the prose of Slovak author Leopold Lahola. The subject of analysis is Lahola's prose collection - Posledná vec (The Last Thing). The thesis also overlaps comparatively to broader Central European context. Texts of Arnošt Lustig (Czech Republic), Imre Kertész (Hungary) and Henryk Grynberg (Poland) are reflected. The subject of comparison is the motive of body and bodiliness, means of expression, narrative point of view, and the concept of fable and sujet. Key words: the category of body and bodiliness, narrative techniques, text composition

Doctor of Philosophy / Department of Mathematics / Louis Crane / In this thesis we explore the possibilities of obtaining Topological Quantum Field Theories using cobordisms with corners to break further down in the structure of manifolds of a given dimension. The algebraic data obtained is described in the language of higher category theory, more precisely in its cubical approach which we explore here as well. Interesting connections are proposed to some important objects in Physics: the representations of the Poincaré group. Finally we will describe in great details the topological tools needed to describe the categories of cobordisms with corners and give some conjectures on their nature.

This thesis is mostly about supervised visual recognition problems. Based on a general definition of categories, the contents are divided into two parts: one which models categories and one which is not category based. We are interested in data driven solutions for both kinds of problems. In the category-free part, we study novelty detection in temporal and spatial domains as a category-free recognition problem. Using data driven models, we demonstrate that based on a few reference exemplars, our methods are able to detect novelties in ego-motions of people, and changes in the static environments surrounding them. In the category level part, we study object recognition. We consider both object category classification and localization, and propose scalable data driven approaches for both problems. A mixture of parametric classifiers, initialized with a sophisticated clustering of the training data, is demonstrated to adapt to the data better than various baselines such as the same model initialized with less subtly designed procedures. A nonparametric large margin classifier is introduced and demonstrated to have a multitude of advantages in comparison to its competitors: better training and testing time costs, the ability to make use of indefinite/invariant and deformable similarity measures, and adaptive complexity are the main features of the proposed model. We also propose a rather realistic model of recognition problems, which quantifies the interplay between representations, classifiers, and recognition performances. Based on data-describing measures which are aggregates of pairwise similarities of the training data, our model characterizes and describes the distributions of training exemplars. The measures are shown to capture many aspects of the difficulty of categorization problems and correlate significantly to the observed recognition performances. Utilizing these measures, the model predicts the performance of particular classifiers on distributions similar to the training data. These predictions, when compared to the test performance of the classifiers on the test sets, are reasonably accurate. We discuss various aspects of visual recognition problems: what is the interplay between representations and classification tasks, how can different models better adapt to the training data, etc. We describe and analyze the aforementioned methods that are designed to tackle different visual recognition problems, but share one common characteristic: being data driven. / <p>QC 20140604</p>

Apresentamos neste trabalho uma definição de complexidade na categoria derivada de complexos (limitados superiormente) de módulos sobre uma k-álgebra de dimensão finita. Um dos resultados que conseguimos foi uma relação entre a complexidade de objetos indecomponíveis e a noção de dimensão global forte. Mais especificamente, mostramos que a existência de um objeto indecomponível na categoria derivada limitada superiormente com complexidade não nula é condição suficiente para que a respectiva álgebra tenha dimensão global forte infinita. Também investigamos se existe uma relação entre as dimensões global e global forte da classe das álgebras shod (Coelho e Lanzilotta, 2009). Fomos motivados pela caracterização da classe das álgebras quase inclinadas (Happel, Reiten e Smalo, 1996) em termos da sua dimensão global forte, dada por D. Happel e D. Zacharia (2008), e pelo fato das álgebras shod serem uma generalização das álgebras quase inclinadas. Nossa conclusão foi que não existe, em geral, uma caracterização das álgebras shod em termos de sua dimensão global forte. Isto é, mostramos que para cada inteiro d > 2 existe uma álgebra shod estrita cuja dimensão global forte é igual a d. / We introduce in this thesis a definition of complexity in the derived category of bounded above complexes of modules over a finite dimensional k-algebra. One of our result shows a relationship between the complexity of indecomposable objects and the notion of strong global dimension. More specifically, we prove that the existence of an indecomposable object in the category derived bounded above whose complexity is not zero is a sufficient condition for corresponding algebra being of infinite strong global dimension. We also investigate the existence of a relationship between the global dimension and the strong global dimension of shod algebras (Coelho and Lanzilotta, 1999). Our motivation came from characterization of quasitilted algebras (Happel, Reiten and Smalo, 1996) by its strong global dimension, given by D. Happel and D. Zacharia (2008), and from the fact that shod algebras are a generalization of quasitilted algebras. Our conclusion was that there is not in general a characterization of shod algebras in terms of its strong global dimension. This conclusion comes from the fact that we showed that for each integer d > 2 there exists a strictly shod algebra whose strong global dimension is d.

O objetivo desta tese é descrever a temporalização em língua de sinais brasileira (libras), no âmbito da teoria semiótica de linha francesa. Para tanto, a proposta é analisar seis textos narrativos sinalizados por surdos ou intérpretes fluentes na língua. Os estudos sobre as línguas de sinais, como os de Liddell (2003), de Finau (2004), de Johnston & Schembri (2007), de Sinte (2013), têm apontado que as línguas sinalizadas contam com os mecanismos gerais de enunciação; que não há marcas morfológicas de flexãode tempoem seus verbos, e que há outros elementosgramaticais e discursivos envolvidos na construção das relações temporais no interior de seus textos, como gestos manuais (os itens lexicaisdicionarizadosque têm função de advérbio, como HOJE, ONTEM, AMANHÃ, etc.), e como outros gestosnão manuais,como movimentos do tronco, localização das mãos e direção do olhar do sinalizador. Esta tese vai tratar de mostrar a especificidade da organização do tempo no plano do conteúdo dos textos em libras. O estudo parte das pesquisas mencionadas e toma como base para a análise o trabalho realizado por Fiorin (2002) no português, para apresentar uma descrição dos mecanismos de instauração e organização do sistema temporal de cada um dos textos selecionados, mostrando como foram marcados o MR (momento de referência) e os diferentes momentos que compõem essas histórias. A proposta foi levantar todas as formas como a libras expressa o presente, o passado e o futuro em seus discursos, descrevendo, assim, o que Greimas & Courtés (2012) denominam como sendo a localização temporal em um texto e os efeitos de sentido da instauração do tempo. Os dados analisados foram transcritos no software ELAN (EUDICO Language Annotator), seguindo a proposta de McCleary, Viotti & Leite (2010). As análises feitas mostram que, em alguns textos do corpus, a marcação do tempo é feita por itens lexicais de tempo dicionarizados, por meio de debreagens enunciativas e enuncivas, e, em outros casos, quando não há uma marca temporal específica, a língua conta com outro mecanismo discursivo, uma embreagem heterocategórica, que permite que, por meio de uma neutralização das categorias da enunciação (pessoa, espaço, tempo), o tempo seja construído espacialmente e entendido a partir de elementos que tipicamente instauram pessoa e criam diferentes espaços nos textos. / The objective of this thesis is to describe the timing in Brazilian sign language Libras within the framework of French Semiotics. As such, the proposal is to analyze six narrative texts signaled by deaf people or fluent interpreters of the language. Studies of sign languages, such as those of Liddell (2003), Finau (2004), Johnston & Schembri (2007), and Sinte (2013), have pointed out that sign languages use the general mechanisms of enunciation, that there are no morphological markers of tense inflection of verbs in these languages, and that there are other grammatical and discursive elements involved in the construction of temporal relationships within signed texts, such as hand gestures (lexical items listed in dictionaries as adverbs, such as TODAY, YESTERDAY, TOMORROW, etc.) and other non-manual gestures, such as upper-body movements, hand positions, and the direction of the signers gaze. This thesis intends to demonstrate the specificity of the organization of time in the content of the texts in Libras. The present study takes the aforementioned studies as a starting point and uses the work of Fiorin (2002) about Portuguese Language as a basis for the analysis to present a description of the mechanisms for establishing and organizing the temporal system of each of the texts selected, showing how the MR (moment of reference) and the different moments that make up these stories were marked. The proposal was to survey all the forms by which Libras expresses the present, past and future in its discourses, thus describing what Greimas & Courtés (2012) call the temporal localization in a text and the effects of meaning in terms of establishing time. The analyzed data were transcribed in the ELAN (EUDICO Language Annotator)software following the proposal of McCleary, Viotti & Leite (2010). The analyses performed showed that in some texts of the corpus the marking of time is effected by dictionarized temporal lexical items, by means of enunciative and enuncive débrayages (shifting out), and, in other cases where there is no specific temporal marker, the language uses another discursive mechanismheterocategorical embrayage (shifting in)which uses a neutralization of enunciation categories (person, space, time) to allow time to be constructed spatially and understood based on elements that typically establish the person and create different spaces in the texts.

[pt] Considere os seguintes dois tipos de transformções em demonstrações: 1) tornar uma prova mais incompleta, apagando um lema ou uma construção que sejam parte da prova e pondo no lugar um aviso dizendo isso é óbvio; 2) pegar um passo que foi provado por um isso é óbvio, aplicar algum algoritmo que encontre uma demonstração para esse passo, e trocar o aviso pela demonstração de verdade. Nós vamos considerar que a primeira operação vai em direção ao esqueleto da demonstração, e que ela é como uma projeção; a segunda operação é um levantamento de um esqueleto para uma demonstração um pouco mais completa com aquele esqueleto. Nós só estamos interessados em esqueletos que possam ser levantados até provas completas usando algum algoritmo conhecido. Nesta tese descrevemos uma linguagem - o sistema DNC - que permite provar vários fatos sobre categorias usando esqueletos. O método para o levantamento é, a grosso modo, o seguinte: a partir do nome de um termo em DNC nós podemos obter o seu tipo; por uma espécie de Isomorfismo de Curry-Howard um tipo desses pode ser visto como uma preposição numa certa lógica; um algoritmo que obtenha uma demonstração para essa proposição retorna uma árvore de demonstração (uma derivação) num certo sistema de Dedução Natural, e essa árvore pode ser lida como um lambda- termo do tipo dado - ela dá uma construção natural para um objeto daquele tipo, e esse objeto muito frequentemente é exatamente o objeto que esperávamos obter. Derivações em DNC podem ser traduzidas para derivações num Pure Type System com Dicionários (PTSD), e derivações em PTSDs podem ser traduzidas para derivações em Pure Type Systems (PTSs); daí, questões sobre a teoria da prova de DNC se tornam questões sobre a teoria da prova de PTSs, que é bastante bem-conhecida. Não só temos um levantamento de nomes de termos em DNC para provas completas, mas também temos um modo formal de levantar diagramas categóricos expressos na linguagem do DNC para termos em DNC e daí para provas completas; e se mudamos o dicionário embutido num PTSD podemos fazer com que o mesmo esqueleto em DNC represente provas em contextos diferentes; por exemplo, algumas provas que aparentemente estão sendo feitas sobre a categoria dos conjuntos podem ser reinterpretados como provas sobre um topos arbitrário. Usamos essa idéia para apresentar de uma forma simples - em que os passos óbvios omitidos são óbvios num sentido muito preciso - a semântica categárica para alguns PTSs, incluindo PTSs com polimorfismo e tipos dependentes, e os PTSs para quais as derivações em DNC são traduzidas. / [en] Consider the following two kinds of transformation on proofs; the first is to make a a proof more incomplete, by erasing a lemma or a construction from it and replacing it by a tag saying this is obvious; the second kind of transformation takes a step that is proved by a this is obvious tag, applies some kind of prof-search algorithm to it, and replaces the tag by a real proof for that step. We will consider that the first operation goes toward the skeleton towards a more complete proof that had that skeleton as a projection. We are only interested in skeletons can be lifted back to full proofs using some known algorithm. In this thesis we can describe a language - DNC - that lets us prove several categorical facts using skeletons. The method for lifting these skeletons goes like this: from the name of a DNC term we can obtain its type; by a kind of Curry-Howard isomorphism a such type can be seen as a proposition in a certain logic; proof-search for that proposition will obtain a proof-tree for it in a certain system of Natural Deduction, and that proof-tree can be read as a lambda-term of given type - the proof-tree gives a natural construction for an object of the given type, that very often is exactly the object that we were looking for. Derivations in DNC can be translated into derivations in a Pure Type System with Dictionaries (PTSD), and derivations in PTSDs can be translated into derivations in Pure Type Systems (PTSs); so questions about the proof- theory of DNC become questions about the proof-theory of PTSs, whose properties are quite well-known. Also, not only we can lift names of terms in DNC to full proofs in different settings; for example, some proofs that apparently are happening over the category of sets can be reinterpreted as proofs over an arbitrary topos. We use that idea to give a simple presentation (in which the omitted obvious steps are obvious in a very precise sense) of the categorical semantics for some PTSs - and that includes PTSs into which the DNC derivations are translated.

Esta pesquisa tem como objetivo descrever e analisar, a partir das construções linguísticas usadas para marcar a introdução de um texto dissertativo-argumentativo, pela perspectiva da Gramaticalização e da Cognição, as categorias linguísticas mais frequentes. Para isso usamos um corpus que totaliza 1600 redações de vestibular da FUVEST (Fundação para o vestibular USP), produzidas no período de 2004 a 2011, sendo 50% delas as melhores e as outras 50% as piores consideradas pela banca corretora. Teoricamente, fundamentamos esta pesquisa nos estudos sobre Cognição, a partir de Tomasello (2003), Damásio (2011), Del Nero (1997) e sobre Gramaticalização Heine, Claudi e Hünnemeyer (1991), Bybee (2010). Todo o material analisado teve tratamento quantitativo e qualitativo e chegou-se à determinação de que a categoria espaço é a categoria cognitiva mais frequente na defesa de uma tese e difere da categoria lugar. Foi possível, assim, constatar que espaço, embora em vários contextos seja utilizado como sinônimo de lugar, sob o ponto de vista linguístico-cognitivo lugar tem caráter mais concreto, por determinar localização física, enquanto espaço situa-se mais à direita do continuum das categorias cognitivas propostas por Heine, Claudi e Hünnemeyer (1991), após a categoria tempo, apontando para maior grau de abstração metafórica. Pudemos evidenciar que o processamento cognitivo para a produção textual envolve vários fatores mentais como o protosself (condição básica ao indivíduo), self central (todo o conhecimento adquirido) e self autobiográfico (a forma de externalizar o conhecimento adquirido em texto escrito). Destacamos também, a forma como o candidato começa uma dissertação, procurando criar um espaço conjunto de atenção, que é resultado de todos esses selves trabalhando juntos para a (inter)subjetividade materializada via categorias cognitivas. / This research has as aim to describe and analyze, from the linguistic constructs used to mark the introduction of a argumentative essay text, from the perspective of Grammaticalization and Cognition, the most frequent linguistic categories . So we use a corpus of essays totaling 1600 entrance FUVEST exam (Foundation for the exam - USP) , produced in the period 2004-2011 , 50% of them the best and the other 50% considered the worst by the examining board. Theoretically this research is based on studies about Cognition, from Tomasello (2003), Damasio (2011), and Del Nero (1997), about Grammaticalization, the bases are Heine, Claudi and Hünnemeyer (1991) , and Bybee (2010). All analyzed material had quantitative and qualitative treatment, from this was found a determination that the space category is the most frequent cognitive category in the defense of a thesis and differs from place category. It was thus possible to observe that space, although in various contexts is used as a synonym of place, from the linguistic-cognitive point of view place has more concrete aspect, for determining physical location, while space is located more to the right cognitive categories continuum proposed by Heine, Claudi and Hünnemeyer (1991), after the time category, pointing to a higher degree of metaphorical abstraction. We found that the cognitive processing for text production involves several factors such as mental protosself (basic condition to the individual), core self (all acquired knowledge) and autobiographical self (how to externalize the knowledge acquired in the written text). We also note how the candidate begins an essay, trying to create a space set of attention, which is a result of all these selves working together for the (inter) subjectivity materialized via cognitive categories.

Cluster categories, introduced by Buan–Marsh–Reineke–Reiten–Todorov and later generalised by Amiot, are certain 2-Calabi–Yau triangulated categories that model the combinatorics of cluster algebras without frozen variables. When frozen variables do occur, it is natural to try to model the cluster combinatorics via a Frobenius category, with the indecomposable projective-injective objects corresponding to these special variables. Amiot–Iyama–Reiten show how Frobenius categories admitting (d-1)-cluster-tilting objects arise naturally from the data of a Noetherian bimodule d-Calabi–Yau algebra A and an idempotent e of A such that A/< e > is finite dimensional. In this work, we observe that this phenomenon still occurs under the weaker assumption that A and A^op are internally d-Calabi–Yau with respect to e; this new definition allows the d-Calabi–Yau property to fail in a way controlled by e. Under either set of assumptions, the algebra B=eAe is Iwanaga–Gorenstein, and eA is a cluster-tilting object in the Frobenius category GP(B) of Gorenstein projective B-modules. Geiß–Leclerc–Schröer define a class of cluster algebras that are, by construction, modelled by certain Frobenius subcategories Sub(Q_J) of module categories over preprojective algebras. Buan–Iyama–Reiten–Smith prove that the endomorphism algebra of a cluster-tilting object in one of these categories is a frozen Jacobian algebra. Following Keller–Reiten, we observe that such algebras are internally 3-Calabi–Yau with respect to the idempotent corresponding to the frozen vertices, thus obtaining a large class of examples of such algebras. Geiß–Leclerc–Schröer also attach, via an algebraic homogenization procedure, a second cluster algebra to each category Sub(Q_J), by adding more frozen variables. We describe how to compute the quiver of a seed in this cluster algebra via approximation theory in the category Sub(Q_J); our alternative construction has the advantage that arrows between the frozen vertices appear naturally. We write down a potential on this enlarged quiver, and conjecture that the resulting frozen Jacobian algebra A and its opposite are internally 3-Calabi–Yau. If true, the algebra may be realised as the endomorphism algebra of a cluster-tilting object in a Frobenius category GP(B) as above. We further conjecture that GP(B) is stably 2-Calabi–Yau, in which case it would provide a categorification of this second cluster algebra.

In the 1980s and 1990s, Joyal and Street developed a graphical notation for various flavours of monoidal category using graphs drawn in the plane, commonly known as string diagrams. In particular, their work comprised a rigorous topological foundation of the notation. In 2007, Harmer, Hyland and Melliès gave a formal mathematical foundation for game semantics using a notions they called ⊸-schedules, ⊗-schedules and heaps. Schedules described interleavings of plays in games formed using ⊸ and ⊗, and heaps provided pointers used for backtracking. Their definitions were combinatorial in nature, but researchers often draw certain pictures when working in practice. In this thesis, we extend the framework of Joyal and Street to give a formal account of the graphical methods already informally employed by researchers in game semantics. We give a geometric formulation of ⊸-schedules and ⊗-schedules, and prove that the games they describe are isomorphic to those described in Harmer et al.’s terms, and also those given by a more general graphical representation of interleaving across games of multiple components. We further illustrate the value of the geometric methods by demonstrating that several proofs of key properties (such as that the composition of ⊸-schedules is associative) can be made straightforward, reflecting the geometry of the plane, and overstepping some of the cumbersome combinatorial detail of proofs in Harmer et al.’s terms. We further extend the framework of formal plane diagrams to account for the heaps and pointer structures used in the backtracking functors for O and P.