Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Fontaine modules and F-T-crystals, a dévissage

Das Hauptziel der Arbeit ist es, die Beziehung zwischen Fontaine Modulen und F-T-Kristall zu studieren. Im ersten Kapitel wird die Definition von Fontaine Modulen, die auf die inversen Cartier Transform setzt erinnern wir von Ogus und Vologodsky errichtet. Neben der Erinnerung an die urspruengliche Konstruktion des inversen Cartier Transform, eine direktere Konstruktion, die wir auch vorstellen von G.T. Lan, M. Sheng und K. Zuo. Darueber hinaus beweisen wir diernGleichwertigkeit der beiden Konstruktion.rnrnrnIm zweiten Kapitel werden wir uns daran erinnern, den Konstruktion von inversen Cartier Transform in der Log Einstellung von D. Schepler und verallgemeinern die Lan-Sheng-Zuo Konstruktion an dieser Einstellung. Darueber hinaus geben wir eine Definition von Log FontainernModulen. Im dritten Kapitel werden wir erinnern an die Definition von F-T-Kristall und beweisen das wichtigste Ergebnis dieser Arbeit: Sei $Y$ eine glatte $S_{nu}$-Schema, wobei $S_{nu}$ ist eine flache $W_{nu+1}(k)$-Schema, $nugeq1$, und $X/S_0$ seine Reduction modulo $p$ sein. Bei einem F-T-Kristall $(E,Phi,B)$ auf $Y$ der Breite von weniger als $p$ und let $(E_Y ,B_Y ,nabla_Y)$ die entsprechende gefilterte $O_Y$-modulen mit einer integrierbar Zusammenhang ausgestattet. Anschliesend wird die Reduktion dieses Objekt modulo $p$ definiert eine Fontaine Modulen auf $X/S_0$ im dem Sinnernder Ogus und Vologodsky.

Nanoparticular iron complex drugs for parenteral administration - physicochemical characterization, biological distribution and pharmacological safety

Iron deficiency is the most common deficiency disease worldwide with many patients who require intravenous iron. Within the last years new kind of parenteral iron complexes as well as generic preparations entered the market. There is a high demand for methods clarifying benefit to risk profiles of old and new iron complexes. It is also necessary to disclose interchangeability between originator and intended copies to avoid severe anaphylactic and anaphylactoid side reaction and assure equivalence of therapeutic effect.rnrnThe investigations presented in this work include physicochemical characterization of nine different parenteral iron containing non-biological complex drugs. rnWe developed an in-vitro assay, which allows the quantification of labile iron in the different complexes and thus it is a useful tool to estimate the pharmaclogical safety regarding iron related adverse drug events. This assay additionally allowed the estimation of complex stability by evaluation of degradation kinetics at the applied conditions.rnrnAn in-ovo study was performed to additionally compare different complexes in respect to body distribution. This in combination with complex stability information allowed the risk estimation of potential local acute and chronic reactions to iron overload.rnrnInformation obtained by the combination of the methods within this work are helpful to estimate the safety and efficacy profile of different iron containing non-biological complex drugs. rnrnPhysicochemical differences between the complexes were demonstrated in respect to size of the inorganic fraction, size and size distribution of the complete particles, structure of the inorganic iron fraction, morphology of the complexes and charge of the complexes. And furthermore significant differences in the biological behavior of different complexes were demonstrated. rnrnThe combination of complex stability and biodistribution as well as the combination of structure, size and stability represent helpful tools for the physicochemical characterization of iron containing non-biological complex drugs and for the estimation of pharmacological safety. This work thus represents an up to date summary of some relevant methods for the characterization of intravenous iron complex drugs in respect to pharmaceutical quality, pharmacological safety and aspects of efficacy. rnrnProspectively, it is worthwhile that the methods within this work will contribute to the development and/or characterization of iron containing nanoparticular formulations with beneficial efficacy and safety profiles.rn

Line focusing for soft x-ray laser-plasma lasing

A computational study of line-focus generation was done using a self-written ray-tracing code and compared to experimental data. Two line-focusing geometries were compared, i.e., either exploiting the sagittal astigmatism of a tilted spherical mirror or using the spherical aberration of an off-axis- illuminated spherical mirror. Line focusing by means of astigmatism or spherical aberration showed identical results as expected for the equivalence of the two frames of reference. The variation of the incidence angle on the target affects the line-focus length, which affects the amplification length such that as long as the irradiance is above the amplification threshold, it is advantageous to have a longer line focus. The amplification threshold is physically dependent on operating parameters and plasma-column conditions and in the present study addresses four possible cases.

Mortality associated with diabetes and cardiovascular disease in older women

Background Current guidelines for the prevention of cardiovascular disease (CVD) recommend diabetes as a CVD risk equivalent. However, reports that have examined the risk of diabetes in comparison to pre-existing CVD are lacking among older women. We aimed to assess whether diabetes was associated with a similar risk of total and cause-specific mortality as a history of CVD in older women. Methodology/Principal Findings We studied 9218 women aged 68 years or older enrolled in a prospective cohort study (Study of Osteoporotic Fracture) during a mean follow-up period of 11.7 years and compared all-cause, cardiovascular and coronary heart disease mortality among 4 groups: non-diabetic women with and without existing CVD, diabetic women with and without existing CVD. Mean (SD) age of the participants was 75.2 (5.3) years, 3.5% reported diabetes and 6.8% reported existing CVD. During follow-up, 5117 women died with 36% from CVD. The multivariate adjusted risk of cardiovascular mortality was increased among both non-diabetic women with CVD (hazard ratio (HR) 2.32, 95% CI: 1.97–2.74, P<0.001) and diabetic women without CVD (HR 2.06, CI: 1.62–2.64, P<0.001) compared to non-diabetic women without existing CVD. All-cause, cardiovascular and coronary mortality of non-diabetic women with CVD were not significantly different from diabetic women without CVD. Conclusions/Significance Older diabetic women without CVD have a similar risk of cardiovascular mortality compared to non-diabetic women with pre-existing CVD. The equivalence of diabetes and CVD seems to extend to older women, supporting current guidelines for cardiovascular prevention.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

Electron transport through catechol-functionalized molecular rods

The charge transport properties of a catechol-type dithiol-terminated oligo-phenylene-ethynylene was investigated by cyclic voltammetry (CV) and by the scanning tunnelling microscopy break junction technique (STM-BJ). Single molecule charge transport experiments demonstrated the existence of high and low conductance regions. The junction conductance is rather weakly dependent on the redox state of the bridging molecule. However, a distinct dependence of junction formation probability and of relative stretching distances of the catechol- and quinone-type molecular junctions is observed. Substitution of the central catechol ring with alkoxy-moieties and the combination with a topological analysis of possible π-electron pathways through the respective molecular skeletons lead to a working hypothesis, which could rationalize the experimentally observed conductance characteristics of the redox-active nanojunctions.

Synthetic versus natural curcumin: bioequivalence in an in vitro oral mucositis model

BACKGROUND Curcumin (CUR) is a dietary spice and food colorant (E100). Its potent anti-inflammatory activity by inhibiting the activation of Nuclear Factor-kappaB is well established. METHODS The aim of this study was to compare natural purified CUR (nCUR) with synthetically manufactured CUR (sCUR) with respect to their capacity to inhibit detrimental effects in an in vitro model of oral mucositis. The hypothesis was to demonstrate bioequivalence of nCUR and sCUR. RESULTS The purity of sCUR was HPLC-confirmed. Adherence and invasion assays for bacteria to human pharyngeal epithelial cells demonstrated equivalence of nCUR and sCUR. Standard assays also demonstrated an identical inhibitory effect on pro-inflammatory cytokine/chemokine secretion (e.g., interleukin-8, interleukin-6) by Detroit pharyngeal cells exposed to bacterial stimuli. There was bioequivalence of sCUR and nCUR with respect to their antibacterial effects against various pharyngeal species. CONCLUSION nCUR and sCUR are equipotent in in vitro assays mimicking aspects of oral mucositis. The advantages of sCUR include that it is odorless and tasteless, more easily soluble in DMSO, and that it is a single, highly purified molecule, lacking the batch-to-batch variation of CUR content in nCUR. sCUR is a promising agent for the development of an oral anti-mucositis agent.

From Broadstone to Zackenberg

Ecological networks are typically complex constructions of species and their interactions. During the last decade, the study of networks has moved from static to dynamic analyses, and has attained a deeper insight into their internal structure, heterogeneity, and temporal and spatial resolution. Here, we review, discuss and suggest research lines in the study of the spatio-temporal heterogeneity of networks and their hierarchical nature. We use case study data from two well-characterized model systems (the food web in Broadstone Stream in England and the pollination network at Zackenberg in Greenland), which are complemented with additional information from other studies. We focus upon eight topics: temporal dynamic space-for-time substitutions linkage constraints habitat borders network modularity individual-based networks invasions of networks and super networks that integrate different network types. Few studies have explicitly examined temporal change in networks, and we present examples that span from daily to decadal change: a common pattern that we see is a stable core surrounded by a group of dynamic, peripheral species, which, in pollinator networks enter the web via preferential linkage to the most generalist species. To some extent, temporal and spatial scales are interchangeable (i.e. networks exhibit ‘ergodicity’) and we explore how space-for-time substitutions can be used in the study of networks. Network structure is commonly constrained by phenological uncoupling (a temporal phenomenon), abundance, body size and population structure. Some potential links are never observed, that is they are ‘forbidden’ (fully constrained) or ‘missing’ (a sampling effect), and their absence can be just as ecologically significant as their presence. Spatial habitat borders can add heterogeneity to network structure, but their importance has rarely been studied: we explore how habitat generalization can be related to other resource dimensions. Many networks are hierarchically structured, with modules forming the basic building blocks, which can result in self-similarity. Scaling down from networks of species reveals another, finer-grained level of individual-based organization, the ecological consequences of which have yet to be fully explored. The few studies of individual-based ecological networks that are available suggest the potential for large intraspecific variance and, in the case of food webs, strong size-structuring. However, such data are still scarce and more studies are required to link individual-level and species-level networks. Invasions by alien species can be tracked by following the topological ‘career’ of the invader as it establishes itself within a network, with potentially important implications for conservation biology. Finally, by scaling up to a higher level of organization, it is possible to combine different network types (e.g. food webs and mutualistic networks) to form super networks, and this new approach has yet to be integrated into mainstream ecological research. We conclude by listing a set of research topics that we see as emerging candidates for ecological network studies in the near future.

Entre la lingüística y la filología : El análisis sintáctico-pragmático. Una mirada diacrónica a las preposiciones con y sin

Este artículo forma parte de una investigación mayor cuyo propósito es estudiar el empleo y la evolución de las preposiciones con y sin en la historia de la lengua española peninsular y americana. Además de describir el empleo de las preposiciones en diferentes contextos formales y pragmáticos, el trabajo tiene un propósito explicativo en tanto intenta dar cuenta de frecuencias de uso de las formas lingüísticas en relación con el género y el tema del discurso. Considera, asimismo, la equivalencia funcional (parcial) de con / contra; con / no sin para delimitar estrategias de selección y propone la posibilidad de estudiar la variación de formas (parcialmente) antónimas como reflejo de perspectiva cognitiva.

Entre la lingüística y la filología : El análisis sintáctico-pragmático. Una mirada diacrónica a las preposiciones con y sin

Este artículo forma parte de una investigación mayor cuyo propósito es estudiar el empleo y la evolución de las preposiciones con y sin en la historia de la lengua española peninsular y americana. Además de describir el empleo de las preposiciones en diferentes contextos formales y pragmáticos, el trabajo tiene un propósito explicativo en tanto intenta dar cuenta de frecuencias de uso de las formas lingüísticas en relación con el género y el tema del discurso. Considera, asimismo, la equivalencia funcional (parcial) de con / contra; con / no sin para delimitar estrategias de selección y propone la posibilidad de estudiar la variación de formas (parcialmente) antónimas como reflejo de perspectiva cognitiva.

Entre la lingüística y la filología : El análisis sintáctico-pragmático. Una mirada diacrónica a las preposiciones con y sin

Este artículo forma parte de una investigación mayor cuyo propósito es estudiar el empleo y la evolución de las preposiciones con y sin en la historia de la lengua española peninsular y americana. Además de describir el empleo de las preposiciones en diferentes contextos formales y pragmáticos, el trabajo tiene un propósito explicativo en tanto intenta dar cuenta de frecuencias de uso de las formas lingüísticas en relación con el género y el tema del discurso. Considera, asimismo, la equivalencia funcional (parcial) de con / contra; con / no sin para delimitar estrategias de selección y propone la posibilidad de estudiar la variación de formas (parcialmente) antónimas como reflejo de perspectiva cognitiva.

Arquitectura cognitiva basada en el gradiente sensorial y su aplicación a la robótica móvil

El objetivo de esta tesis es el desarrollo de un sistema completo de navegación, aprendizaje y planificación para un robot móvil. Dentro de los innumerables problemas que este gran objetivo plantea, hemos dedicado especial atención al problema del conocimiento autónomo del mundo. Nuestra mayor preocupación ha sido la de establecer mecanismos que permitan, a partir de información sensorial cruda, el desarrollo incremental de un modelo topológico del entorno en el que se mueve el robot. Estos mecanismos se apoyan invariablemente en un nuevo concepto propuesto en esta tesis: el gradiente sensorial. El gradiente sensorial es un dispositivo matemático que funciona como un detector de sucesos interesantes para el sistema. Una vez detectado uno de estos sucesos, el robot puede identificar su situación en un mapa topológico y actuar en consecuencia. Hemos denominado a estas situaciones especiales lugares sensorialmente relevantes, ya que (a) captan la atención del sistema y (b) pueden ser identificadas utilizando la información sensorial. Para explotar convenientemente los modelos construidos, hemos desarrollado un algoritmo capaz de elaborar planes internalizados, estableciendo una red de sugerencias en los lugares sensorialmente relevantes, de modo que el robot encuentra en estos puntos una dirección recomendada de navegación. Finalmente, hemos implementado un sistema de navegación robusto con habilidades para interpretar y adecuar los planes internalizados a las circunstancias concretas del momento. Nuestro sistema de navegación está basado en la teoría de campos de potencial artificial, a la que hemos incorporado la posibilidad de añadir cargas ficticias como ayuda a la evitación de mínimos locales. Como aportación adicional de esta tesis al campo genérico de la ciencia cognitiva, todos estos elementos se integran en una arquitectura centrada en la memoria, lo que pretende resaltar la importancia de ésta en los procesos cognitivos de los seres vivos y aporta un giro conceptual al punto de vista tradicional, centrado en los procesos. The general objective of this thesis is the development of a global navigation system endowed with planning and learning features for a mobile robot. Within this general objective we have devoted a special effort to the autonomous learning problem. Our main concern has been to establish the necessary mechanisms for the incremental development of a topological model of the robot’s environment using the sensory information. These mechanisms are based on a new concept proposed in the thesis: the sensory gradient. The sensory gradient is a mathematical device which works like a detector of “interesting” environment’s events. Once a particular event has been detected the robot can identify its situation in the topological map and to react accordingly. We have called these special situations relevant sensory places because (a) they capture the system’s attention and (b) they can be identified using the sensory information. To conveniently exploit the built-in models we have developed an algorithm able to make internalized plans, establishing a suggestion network in the sensory relevant places in such way that the robot can find at those places a recommended navigation direction. It has been also developed a robust navigation system able to navigate by means of interpreting and adapting the internalized plans to the concrete circumstances at each instant, i.e. a reactive navigation system. This reactive system is based on the artificial potential field approach with the additional feature introduced in the thesis of what we call fictitious charges as an aid to avoid local minima. As a general contribution of the thesis to the cognitive science field all the above described elements are integrated in a memory-based architecture, emphasizing the important role played by the memory in the cognitive processes of living beings and giving a conceptual turn in the usual process-based approach.

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.