Default Invariance: Naïve Category of Law and Finance

Default invariance is the idea that default does not change at any scale of law and finance. Default is a conserved quantity in a universe where fundamental principles of law and finance operate. It exists at the micro-level as part of the fundamental structure of every financial transaction, and at the macro- level, as a fixed critical point within the relatively stable phases of the law and finance cycle. A key point is that default is equivalent to maximizing uncertainty at the micro-level and at the macro-level, is equivalent to the phase transition where unbearable fluctuations occur in all forms of risk transformation, including maturity, liquidity and credit. As such, default invariance is the glue that links the micro and macro structures of law and finance. In this essay, we apply naïve category theory (NCT), a type of mapping logic, to these types of phenomena. The purpose of using NCT is to introduce a rigorous (but simple) mathematical methodology to law and finance discourse and to show that these types of structural considerations are of prime practical importance and significance to law and finance practitioners. These mappings imply a number of novel areas of investigation. From the micro- structure, three macro-approximations are implied. These approximations form the core analytical framework which we will use to examine the phenomena and hypothesize rules governing law and finance. Our observations from these approximations are grouped into five findings. While the entirety of the five findings can be encapsulated by the three approximations, since the intended audience of this paper is the non-specialist in law, finance and category theory, for ease of access we will illustrate the use of the mappings with relatively common concepts drawn from law and finance, focusing especially on financial contracts, derivatives, Shadow Banking, credit rating agencies and credit crises.

同事关系质量及其作用机制

Although the research into coworker relationship quality has been recognized one of key factors related to organization performance, and has been thought a new trend in organization behavior research with the flatting of organization structure and complication of task assignment, there is relatively little empirical research on the mechanism between coworkers’ interaction, contraring to the fruitful results on member exchange research based on social network theory, say nothing of the influence of cultural differences such as GUANXI. This research developed the scale for the assessment of Coworker Relationship Quality by literature review, deep interview, and questionnaires, compared the predictable ability of Coworker Relationship Quality (CRQ) scale and Coworker Exchange (CWX) scale on employees’ work attitudes and behaviors. Finally, the mediating effect of Coworker Relationship Quality between employees’ similarities on personality and their work attitudes and behaviors was investigated. Following are main results. Firstly, we found that the interpersonal communication, trust, and mutual support are the key factors of coworker relationship quality, which is similar to the result getting from western samples. But Chinese people are more GUANXI ORIENTATION, means they want to build longtime relationship with others, not only when they are coworkers, but also when one of them left the organization. Secondly, though the core meaning of CRQ and CWX are same, their predictable ability on organization outcomes is different. CRQ is more powerful than CWX, especially on turnover intention. The result showed that after controlling the effect of demographic variables and CRQ, CWX cannot predict turnover intention significantly, but CRQ can still predict turnover intention significantly after controlling demographic variables and CWX. Thirdly, the partial mediating effect of CRQ between positive affectivity similarity and organizational citizenship behavior, coworker satisfaction, organizational commitment and turnover intention are validated, but we did not find the mediating effect of CRQ between demographic variable similarity and workers’ attitudes and behaviors. The Similarity Attraction Paradigm, Social Identity Theory, and Self Category Theory were supported.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.

Grothendieck et les topos : rupture et continuité dans les modes d'analyse du concept d'espace topologique

La thèse présente une analyse conceptuelle de l'évolution du concept d'espace topologique. En particulier, elle se concentre sur la transition des espaces topologiques hérités de Hausdorff aux topos de Grothendieck. Il en ressort que, par rapport aux espaces topologiques traditionnels, les topos transforment radicalement la conceptualisation topologique de l'espace. Alors qu'un espace topologique est un ensemble de points muni d'une structure induite par certains sous-ensembles appelés ouverts, un topos est plutôt une catégorie satisfaisant certaines propriétés d'exactitude. L'aspect le plus important de cette transformation tient à un renversement de la relation dialectique unissant un espace à ses points. Un espace topologique est entièrement déterminé par ses points, ceux-ci étant compris comme des unités indivisibles et sans structure. L'identité de l'espace est donc celle que lui insufflent ses points. À l'opposé, les points et les ouverts d'un topos sont déterminés par la structure de celui-ci. Qui plus est, la nature des points change: ils ne sont plus premiers et indivisibles. En effet, les points d'un topos disposent eux-mêmes d'une structure. L'analyse met également en évidence que le concept d'espace topologique évolua selon une dynamique de rupture et de continuité. Entre 1945 et 1957, la topologie algébrique et, dans une certaine mesure, la géométrie algébrique furent l'objet de changements fondamentaux. Les livres Foundations of Algebraic Topology de Eilenberg et Steenrod et Homological Algebra de Cartan et Eilenberg de même que la théorie des faisceaux modifièrent profondément l'étude des espaces topologiques. En contrepartie, ces ruptures ne furent pas assez profondes pour altérer la conceptualisation topologique de l'espace elle-même. Ces ruptures doivent donc être considérées comme des microfractures dans la perspective de l'évolution du concept d'espace topologique. La rupture définitive ne survint qu'au début des années 1960 avec l'avènement des topos dans le cadre de la vaste refonte de la géométrie algébrique entreprise par Grothendieck. La clé fut l'utilisation novatrice que fit Grothendieck de la théorie des catégories. Alors que ses prédécesseurs n'y voyaient qu'un langage utile pour exprimer certaines idées mathématiques, Grothendieck l'emploie comme un outil de clarification conceptuelle. Ce faisant, il se trouve à mettre de l'avant une approche axiomatico-catégorielle des mathématiques. Or, cette rupture était tributaire des innovations associées à Foundations of Algebraic Topology, Homological Algebra et la théorie des faisceaux. La théorie des catégories permit à Grothendieck d'exploiter le plein potentiel des idées introduites par ces ruptures partielles. D'un point de vue épistémologique, la transition des espaces topologiques aux topos doit alors être vue comme s'inscrivant dans un changement de position normative en mathématiques, soit celui des mathématiques modernes vers les mathématiques contemporaines.

La logique et les logiques : la question du pluralisme

Partant des travaux séminaux de Boole, Frege et Russell, le mémoire cherche à clarifier l‟enjeu du pluralisme logique à l‟ère de la prolifération des logiques non-classiques et des développements en informatique théorique et en théorie des preuves. Deux chapitres plus « historiques » sont à l‟ordre du jour : (1) le premier chapitre articule l‟absolutisme de Frege et Russell en prenant soin de montrer comment il exclut la possibilité d‟envisager des structures et des logiques alternatives; (2) le quatrième chapitre expose le chemin qui mena Carnap à l‟adoption de la méthode syntaxique et du principe de tolérance, pour ensuite dégager l‟instrumentalisme carnapien en philosophie de la Logique et des mathématiques. Passant par l‟analyse d‟une interprétation intuitive de la logique linéaire, le deuxième chapitre se tourne ensuite vers l‟établissement d‟une forme logico-mathématique de pluralisme logique à l‟aide de la théorie des relations d‟ordre et la théorie des catégories. Le troisième chapitre délimite le terrain de jeu des positions entourant le débat entre monisme et pluralisme puis offre un argument contre la thèse qui veut que le conflit entre logiques rivales soit apparent, le tout grâce à l‟utilisation du point de vue des logiques sous-structurelles. Enfin, le cinquième chapitre démontre que chacune des trois grandes approches au concept de conséquence logique (modèle-théorétique, preuve-théorétique et dialogique) forme un cadre suffisamment général pour établir un pluralisme. Bref, le mémoire est une défense du pluralisme logique.

Categorical quantum computation

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

A Categorical Framework for the Specification and the Verification of Aspect Oriented Systems

Un objectif principal du génie logiciel est de pouvoir produire des logiciels complexes, de grande taille et fiables en un temps raisonnable. La technologie orientée objet (OO) a fourni de bons concepts et des techniques de modélisation et de programmation qui ont permis de développer des applications complexes tant dans le monde académique que dans le monde industriel. Cette expérience a cependant permis de découvrir les faiblesses du paradigme objet (par exemples, la dispersion de code et le problème de traçabilité). La programmation orientée aspect (OA) apporte une solution simple aux limitations de la programmation OO, telle que le problème des préoccupations transversales. Ces préoccupations transversales se traduisent par la dispersion du même code dans plusieurs modules du système ou l’emmêlement de plusieurs morceaux de code dans un même module. Cette nouvelle méthode de programmer permet d’implémenter chaque problématique indépendamment des autres, puis de les assembler selon des règles bien définies. La programmation OA promet donc une meilleure productivité, une meilleure réutilisation du code et une meilleure adaptation du code aux changements. Très vite, cette nouvelle façon de faire s’est vue s’étendre sur tout le processus de développement de logiciel en ayant pour but de préserver la modularité et la traçabilité, qui sont deux propriétés importantes des logiciels de bonne qualité. Cependant, la technologie OA présente de nombreux défis. Le raisonnement, la spécification, et la vérification des programmes OA présentent des difficultés d’autant plus que ces programmes évoluent dans le temps. Par conséquent, le raisonnement modulaire de ces programmes est requis sinon ils nécessiteraient d’être réexaminés au complet chaque fois qu’un composant est changé ou ajouté. Il est cependant bien connu dans la littérature que le raisonnement modulaire sur les programmes OA est difficile vu que les aspects appliqués changent souvent le comportement de leurs composantes de base [47]. Ces mêmes difficultés sont présentes au niveau des phases de spécification et de vérification du processus de développement des logiciels. Au meilleur de nos connaissances, la spécification modulaire et la vérification modulaire sont faiblement couvertes et constituent un champ de recherche très intéressant. De même, les interactions entre aspects est un sérieux problème dans la communauté des aspects. Pour faire face à ces problèmes, nous avons choisi d’utiliser la théorie des catégories et les techniques des spécifications algébriques. Pour apporter une solution aux problèmes ci-dessus cités, nous avons utilisé les travaux de Wiels [110] et d’autres contributions telles que celles décrites dans le livre [25]. Nous supposons que le système en développement est déjà décomposé en aspects et classes. La première contribution de notre thèse est l’extension des techniques des spécifications algébriques à la notion d’aspect. Deuxièmement, nous avons défini une logique, LA , qui est utilisée dans le corps des spécifications pour décrire le comportement de ces composantes. La troisième contribution consiste en la définition de l’opérateur de tissage qui correspond à la relation d’interconnexion entre les modules d’aspect et les modules de classe. La quatrième contribution concerne le développement d’un mécanisme de prévention qui permet de prévenir les interactions indésirables dans les systèmes orientés aspect.

Analyse de la structure logique des inférences légales et modélisation du discours juridique

Thèse par articles.

As relações afetivas na prática tutorial e sua relações com a aprendizagem no curso a distância de licenciatura plena em Química

In distance learning degree in Chemistry in full of the Secretária de Educação a distância da Universidade Federal do Rio Grande do Norte (SEDIS / UFRN). The teacher-tutor to establish the experimental subjects closer relationships with students, mediating the pedagogical actions that develop in the distance learning course, with a view to achieving the principles of autonomy and learning, contributing to the creation of learning environments collaborative, guided by affection.The article presents the results of an empirical research on affectivity in practice this tutorial experimental classes in higher distance education in the full degree course in Chemistry Polo Currais Novos/ RN, held between 2009 and 2010. The study is based on qualitative methodology, whose data were collected through questionnaires and semi-structured interviews with 48 (forty eight) students involved in distance learning courses and selected in order to compose a group of subjects who showed variability, as guidelines that guide the sampling procedures in qualitative research. The results, based on category theory and empirical analysis of data from the interviews were supplemented by information obtained from participant observation which also served to guide the data collection of the corpus of this work. With the results we understand that there is clarity about what characterizes a loving relationship between those involved in the process of teaching and learning in experimental classes in high school chemistry Distance Education. Furthermore, it was also clear that the communication process in dialogic teaching and learning in higher distance education in chemistry at the trial need to mark out in balanced affective attitudes, the experimental error that value and respect the many possible construction of knowledge by movements social interaction of individual and collective

As relações afetivas na prática tutorial e sua relação com a aprendizagem no curso a distância de licenciatura plena em química

In distance learning degree in Chemistry in full of the Secretária de Educação a distância da Universidade Federal do Rio Grande do Norte (SEDIS / UFRN). The teacher-tutor to establish the experimental subjects closer relationships with students, mediating the pedagogical actions that develop in the distance learning course, with a view to achieving the principles of autonomy and learning, contributing to the creation of learning environments collaborative, guided by affection.The article presents the results of an empirical research on affectivity in practice this tutorial experimental classes in higher distance education in the full degree course in Chemistry Polo Currais Novos/ RN, held between 2009 and 2010. The study is based on qualitative methodology, whose data were collected through questionnaires and semi-structured interviews with 48 (forty eight) students involved in distance learning courses and selected in order to compose a group of subjects who showed variability, as guidelines that guide the sampling procedures in qualitative research. The results, based on category theory and empirical analysis of data from the interviews were supplemented by information obtained from participant observation which also served to guide the data collection of the corpus of this work. With the results we understand that there is clarity about what characterizes a loving relationship between those involved in the process of teaching and learning in experimental classes in high school chemistry Distance Education. Furthermore, it was also clear that the communication process in dialogic teaching and learning in higher distance education in chemistry at the trial need to mark out in balanced affective attitudes, the experimental error that value and respect the many possible construction of knowledge by movements social interaction of individual and collective

Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

Tratamiento N-categorial de la lógica de la programación

En el contexto de las técnicas de validación de programas, de las estructuras de axiomatización de la programación planteadas por Hoare y del desarrollo de la Lógica de la Programación que Dijkstra realiza con el operador wp, hemos dotado a los elementos esenciales que intervienen en dicho desarrollo de una estructura que permite su estudio en el ámbito de las categorias. En este trabajo se demuestra que el conjunto de precondiciones de un fragmento de programa anotado tiene estructura de N-categoría y que sucede lo mismo con el conjunto de postcondiciones. Más aún, se ha puesto de manifiesto (y probado) que el operador wp actúa como un funtor entre estos pares de N-categorías. Además, los conjuntos de guardas surgen de un modo natural en la lógica de la programación, han sido tratados desde el punto de vista de la semántica denotacional (Wlrth para el PASCAL y Scott y otros, después, en un enfoque más general) y presentados por Manes y Arbib en su semántica parcialmente aditiva. Pues bien, en este trabajo se demuestra que los conjuntos de guardas tienen también estructura de N-categoría y gue cualguier N-categoría dotada de una suma definida adecuadamente tiene estructura de conjunto de guardas, de tal modo, además, gue el preorden inducido por la suma en el conjunto de guardas coincide con la flecha de la N-categoría. Esta suma es, en concreto, la disyunción exclusiva, lo que adicionalmente supone una sorprendentemente sencilla definición alternativa a la suma de las categorías parcialmente aditivas definida por Manes y Arbib. Con todo esto, se aportan herramientas conceptuales para entender mejor y resolver más eficientemente los problemas que tiene planteados la lógica de la programación, pues se dispone de un punto de vista distinto y nuevo y de toda una familia de instrumentos adicionales.---ABSTRACT---In the context of program validation techniques, Hoare's systems for programming and Dijkstra's development of the logic of programming, based on the operator wp, we have endowed the essential features of this development with a structure that permits to study them in the frame of category theory. In this thesis we show that the set of preconditions of an annotated program segment is an N-category, and the same happens for the set of postconditions. Even more, it is shown that the operator wp acts as a functor between those pairs of Ncategories. Furthermore, guard sets come out in a natural way in the logic of programming, they have been considered from a denotational semantics point of view (Wirth for Pascal and afterwards Scott and al. in a more general setting) and they have been embodied by Manes and Arbib in their partially additive semantics. Then, it is shown in this thesis that the above mentioned guard sets also have the structure of an N-category and that any N-category with an appropiately defined sum has the structure of a guard set in such a way that, besides, the preorder defined in the guard set by the sum operation coincides with the arrows of the N-category. This sum is just the exclusive or of Boolean Logic and this fact adds a surprisingly simple alternative definition for the sum operation in Manes and Arbib partially additive categories. The present work, in summary, makes a contribution of conceptual tools for a better understanding and a more efficient solution of the problems posed to the logic of programming and it does so by providing a new different point of view and a whole family of additional techniques.

An approach to ontology for institutional facts in the semantic web

Refinement in software engineering allows a specification to be developed in stages, with design decisions taken at earlier stages constraining the design at later stages. Refinement in complex data models is difficult due to lack of a way of defining constraints, which can be progressively maintained over increasingly detailed refinements. Category theory provides a way of stating wide scale constraints. These constraints lead to a set of design guidelines, which maintain the wide scale constraints under increasing detail. Previous methods of refinement are essentially local, and the proposed method does not interfere very much with these local methods. The result is particularly applicable to semantic web applications, where ontologies provide systems of more or less abstract constraints on systems, which must be implemented and therefore refined by participating systems. With the approach of this paper, the concept of committing to an ontology carries much more force. (c) 2005 Elsevier B.V. All rights reserved.

Dating paleochannel iron ore by (U-Th)/He analysis of supergene goethite, Hamersley province, Australia

(U-Th)/He dating of late-stage authigenic goethite, combined with corrections for diffusive loss of He-4 by the He-4/He-3 methodology, reveals strong correlation between a sample's age and its depth in ferruginized channel sediments from the Yandicoogina deposit, Western Australia. Corrected ages, ranging from ca. 18 Ma near the surface to ca. 5 Ma at the bottom of the profile, indicate that ferruginization of the aggraded channels becomes progressively younger with depth. This trend is consistent with goethite precipitation at the groundwater-atmosphere interface during water table drawdown driven by the aridification of Western Australia during the Neogene. The results demonstrate that the (U-Th)/He system is ideal for dating goethite if diffusive loss corrections are applied. The approach is suitable for dating weathering reactions on Earth and should also be suitable for dating Fe oxyhydroxides in the Martian regolith.