Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

Las agencias de calificación crediticia (Las hijas de Elena: La triple a)

En este trabajo, en primer lugar, se analiza la estructura (accionariado), funcionalidad (cómo funcionan y emiten sus opiniones) y el comportamiento (cómo actúan en los mercados) de las tres agencias más importantes de calificación de activos financieros, de emisores y emisiones de activos financieros. En segundo término, se señalan sus poco, si algo, científicas evaluaciones basadas en conceptos y actuaciones tan poco adecuadas como: profecía autocumplida, carencia de fecha de caducidad, catastrofismo, que, a veces, imponen con comportamientos gansteriles. Asimismo, se destaca la importancia y trascendencia que suponen las opiniones que emiten dichas agencias, auténticos ucases, que las convierten, de facto, en auténticos señores de horca y caudillo que acondicionan la vida y hacienda de inversores y emisores. En realidad, su comportamiento es tan deplorable y funesto, que como las hijas de Elena, de ahí el título del trabajo, ninguna es buena. Finalmente, se presenta, en forma de decálogo, los hechos, irrefutables, que justifican el calificativo de malvadas de dichas agencias: S&P, Moody?s y Fitch, hasta el punto de que son el antimefistofelismo personificado. Mefistófeles se definía a sí mismo como un pobre diablo que pretendiendo hacer el mal, acababa haciendo el bien, justo al revés que las hijas de Elena.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Inositol 1,4,5-trisphosphate receptor subtype 3 in pancreatic islet cell secretory granules revisited.

It has been reported that the inositol 1,4,5-trisphosphate receptor subtype 3 is expressed in islet cells and is localized to both insulin and somatostatin granules [Blondel, O., Moody, M. M., Depaoli, A. M., Sharp, A. H., Ross, C. A., Swift, H. & Bell, G. I. (1994) Proc. Natl. Acad. Sci. USA 91, 7777-7781]. This subcellular localization was based on electron microscope immunocytochemistry using antibodies (affinity-purified polyclonal antiserum AB3) directed to a 15-residue peptide of rat inositol trisphosphate receptor subtype 3. We now show that these antibodies cross-react with rat, but not human, insulin. Accordingly, the anti-inositol trisphosphate receptor subtype 3 (AB3) antibodies label electron dense cores of mature (insulin-rich) granules of rat pancreatic beta cells, and rat granule labeling was blocked by preabsorption of the AB3 antibodies with rat insulin. The immunostaining of immature, Golgi-associated proinsulin-rich granules with AB3 antibodies was very weak, indicating that cross-reactivity is limited to the hormone and not its precursor. Also, the AB3 antibodies labeled pure rat insulin crystals grown in vitro but failed to stain crystals grown from pure human insulin. By immunoprecipitation, the antibodies similarly displayed a higher affinity for rat than for human insulin. We could not confirm the labeling of somatostatin granules using AB3 antibodies.

Equações de onda generalizadas e quantização funtorial para teorias de campo escalar livre

Nesta dissertação apresentamos um método de quantização matemática e conceitualmente rigoroso para o campo escalar livre de interações. Trazemos de início alguns aspéctos importantes da Teoria de Distribuições e colocamos alguns pontos de geometria Lorentziana. O restante do trabalho é dividido em duas partes: na primeira, estudamos equações de onda em variedades Lorentzianas globalmente hiperbólicas e apresentamos o conceito de soluções fundamentais no contexto de equações locais. Em seguida, progressivamente construímos soluções fundamentais para o operador de onda a partir da distribuição de Riesz. Uma vez estabelecida uma solução para a equação de onda em uma vizinhança de um ponto da variedade, tratamos de construir uma solução global a partir da extensão do problema de Cauchy a toda a variedade, donde as soluções fundamentais dão lugar aos operadores de Green a partir da introdução de uma condição de contorno. Na última parte do trabalho, apresentamos um mínimo da Teoria de Categorias e Funtores para utilizar esse formalismo na contrução de um funtor de segunda quantização entre a categoria de variedades Lorentzianas globalmente hiperbólicas e a categoria de redes de álgebras C* satisfazendo os axiomas de Haag-Kastler. Ao fim, retomamos o caso particular do campo escalar quântico livre.

Sobre a evasão estudantil na Escola Politécnica da Universidade de São Paulo: identificação e possíveis causas.

A evasão estudantil afeta as universidades, privadas e públicas, no Brasil, trazendo-lhes prejuízos financeiros proporcionais à incidência, respectivamente, de 12% e de 26% no âmbito nacional e de 23% na Universidade de São Paulo (USP), razão pela qual se deve compreender as variáveis que governam o comportamento. Neste contexto, a pesquisa apresenta os prejuízos causados pela evasão e a importância de pesquisá-la na Escola Politécnica da USP (EPUSP): seção 1, desenvolve revisão bibliográfica sobre as causas da evasão (seção 2) e propõe métodos para obter as taxas de evasão a partir dos bancos de dados do Governo Federal e da USP (seção 3). Os resultados estão na seção 4. Para inferir sobre as causas da evasão na EPUSP, analisaram-se bancos de dados que, descritos e tratados na seção 5.1, contêm informações (P. Ex.: tipo de ingresso e egresso, tempo de permanência e histórico escolar) de 16.664 alunos ingressantes entre 1.970 e 2.000, bem como se propuseram modelos estatísticos e se detalharam os conceitos dos testes de hipóteses 2 e t-student (seção 5.2) utilizados na pesquisa. As estatísticas descritivas mostram que a EPUSP sofre 15% de evasão (com maior incidência no 2º ano: 24,65%), que os evadidos permanecem matriculados por 3,8 anos, que a probabilidade de evadir cresce após 6º ano e que as álgebras e os cálculos são disciplinas reprovadoras no 1º ano (seção 5.3). As estatísticas inferenciais demonstraram relação entre a evasão - modo de ingresso na EPUSP e evasão - reprovação nas disciplinas do 1º ano da EPUSP, resultados que, combinados com as estatísticas descritivas, permitiram apontar o déficit vocacional, a falta de persistência, a falta de ambientação à EPUSP e as deficiências na formação predecessora como variáveis responsáveis pela evasão (seção 5.4).

1800, Catalogus eorum qui in Universitate Harvardiana, Cantabrigiae, in republica Massachusettensi, ab anno MDCXLII, ad annum MDCCC, alicujus gradû laureâ donati sunt.

Marbled paper cover. Includes a biographical note on Joshua Moody (Harvard AB 1707), and a few additional annotations. Asterisks added next to the names of alumni who died after the Catalogue's publication.

Letter of recommendation for Amos Main from Joseph Moodey to Nathan Prince, 1725 July 2

Handwritten letter sent by Joseph Moody, schoolmaster in York, to Harvard Tutor Nathan Prince recommending student Amos Main for acceptance to the College. In the letter, Moody requests Prince give Main an examination for admission, with the caveat that though Main has been studying Latin and Greek he has a difficult home life and is "somewhat Raw; yet I hope you'l wink at it." The letter, dated July 2, 1725, is written on a folded folio-sized leaf; there are handwritten notes about Massachusetts towns on the verso.

Lowell, Massachusetts, 1850 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Plan of the city of Lowell, Massachusetts, from actual surveys by Sidney & Neff. It was published by S. Moody in 1850. Scale [ca. 1:3,450]. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Massachusetts State Plane Coordinate System, Mainland Zone (in Feet) (Fipszone 2001) coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, canals, drainage, public buildings, schools, churches, parks, industry locations (e.g. mills, factories, etc.), private buildings with names of property owners, and more. Relief shown by hachures. Includes also illustrations of local buildings in margins.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.

Marshfield, Massachusetts, 1838 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of Marshfield, Mass., surveyed by John Ford Jr. ; on stone by J.E. Moody. It was published by Thomas Moore's Lithography in 1838. Scale [1:19,800]. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Massachusetts State Plane Coordinate System, Mainland Zone (in Feet) (Fipszone 2001). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, or other information associated with the principal map. This map shows features such as roads, railroads, drainage, public buildings, schools, churches, cemeteries, industry locations (e.g. mills, factories, mines, etc.), private buildings with names of property owners, town boundaries and more. Relief is shown by hachures. This layer is part of a selection of digitally scanned and georeferenced historic maps of Massachusetts from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of regions, originators, ground condition dates (1755-1922), scales, and purposes. The digitized selection includes maps of: the state, Massachusetts counties, town surveys, coastal features, real property, parks, cemeteries, railroads, roads, public works projects, etc.

A tiny spark /

Poems.

Issues and innovations in distance learning /

"September 1998"--T.p. verso.

How to analyze railroad reports,

Mode of access: Internet.