Evaluation of the performance of steel fibre reinforced self-compacting concrete in elevated slab systems; from the material to the structure

Degree of Doctor of Philosophy of Structural/Civil Engineering

Blow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism

"Available online 22 March 2016"

Verificación de Sistemas Basada en Teoría de Tipos. System verification in type theory

Este proyecto se enmarca en la utlización de métodos formales (más precisamente, en la utilización de teoría de tipos) para garantizar la ausencia de errores en programas. Por un lado se plantea el diseño de nuevos algoritmos de chequeo de tipos. Para ello, se proponen nuevos algoritmos basados en la idea de normalización por evaluación que sean extensibles a otros sistemas de tipos. En el futuro próximo extenderemos resultados que hemos conseguido recientemente [16,17] para obtener: una simplificación de los trabajos realizados para sistemas sin regla eta (acá se estudiarán dos sistemas: a la Martin Löf y a la PTS), la formulación de estos chequeadores para sistemas con variables, generalizar la noción de categoría con familia utilizada para dar semántica a teoría de tipos, obtener una formulación categórica de la noción de normalización por evaluación y finalmente, aplicar estos algoritmos a sistemas con reescrituras. Para los primeros resultados esperados mencionados, nos proponemos como método adaptar las pruebas de [16,17] a los nuevos sistemas. La importancia radica en que permitirán tornar más automatizables (y por ello, más fácilmente utilizables) los asistentes de demostración basados en teoría de tipos. Por otro lado, se utilizará la teoría de tipos para certificar compiladores, intentando llevar adelante la propuesta nunca explorada de [22] de utilizar un enfoque abstracto basado en categorías funtoriales. El método consistirá en certificar el lenguaje "Peal" [29] y luego agregar sucesivamente funcionalidad hasta obtener Forsythe [23]. En este período esperamos poder agregar varias extensiones. La importancia de este proyecto radica en que sólo un compilador certificado garantiza que un programa fuente correcto se compile a un programa objeto correcto. Es por ello, crucial para todo proceso de verificación que se base en verificar código fuente. Finalmente, se abordará la formalización de sistemas con session types. Los mismos han demostrado tener fallas en sus formulaciones [30], por lo que parece conveniente su formalización. Durante la marcha de este proyecto, esperamos tener alguna formalización que dé lugar a un algoritmo de chequeo de tipos y a demostrar las propiedades usuales de los sistemas. La contribución es arrojar un poco de luz sobre estas formulaciones cuyos errores revelan que el tema no ha adquirido aún suficiente madurez o comprensión por parte de la comunidad. This project is about using type theory to garantee program correctness. It follows three different directions: 1) Finding new type-checking algorithms based on normalization by evaluation. First, we would show that recent results like [16,17] extend to other type systems like: Martin-Löf´s type theory without eta rule, PTSs, type systems with variables (in addition to systems in [16,17] which are a la de Bruijn), systems with rewrite rules. This will be done by adjusting the proofs in [16,17] so that they apply to such systems as well. We will also try to obtain a more general definition of categories with families and normalization by evaluation, formulated in categorical terms. We expect this may turn proof-assistants more automatic and useful. 2) Exploring the proposal in [22] to compiler construction for Algol-like languages using functorial categories. According to [22] such approach is suitable for verifying compiler correctness, claim which was never explored. First, the language Peal [29] will be certified in type theory and we will gradually add funtionality to it until a correct compiler for the language Forsythe [23] is obtained. 3) Formilizing systems for session types. Several proposals have shown to be faulty [30]. This means that a formalization of it may contribute to the general understanding of session types.

Convex and toric geometry to analyze complex dynamics in chemical reaction systems

Convex cone, toric variety, graph theory, electrochemical catalysis, oxidation of formic acid, feedback-loopsbifurcations, enzymatic catalysis, Peroxidase reaction, Shil'nikov chaos

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Orthogonal systems in finite grahps

To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups.

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

EEG-based functional brain networks: does the network size matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks--whose nodes can vary from tens to hundreds--are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies.

The Inventor Balance and the Functional Specialization in Global Inventive Activities

We study the functional specialization whereby some countries contribute relatively more inventors vs. organizations in the production of inventions at a global scale. We propose a conceptual framework to explain this type of functional specialization, which posits the presence of feedbacks between two distinct sub-systems, each one providing inventors and organizations. We quantify the phenomenon by means of a new metric, the “inventor balance”, which we compute using patent data. We show that the observed imbalances, which are often conspicuous, are determined by several factors: the innovativeness of a country relative to its level of economic development, relative factor endowments, the degree of technological specialization and, last, cultural traits. We argue that the “inventor balance” is a useful indicator for policy makers, and its routine analysis could lead to better informed innovation policies.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Systems biology of plants : from intraspecific genome variation to computational morphodynamics

Recently, the introduction of second generation sequencing and further advance-ments in confocal microscopy have enabled system-level studies for the functional characterization of genes. The degree of complexity intrinsic to these approaches needs the development of bioinformatics methodologies and computational models for extracting meaningful biological knowledge from the enormous amount of experi¬mental data which is continuously generated. This PhD thesis presents several novel bioinformatics methods and computational models to address specific biological questions in Plant Biology by using the plant Arabidopsis thaliana as a model system. First, a spatio-temporal qualitative analysis of quantitative transcript and protein profiles is applied to show the role of the BREVIS RADIX (BRX) protein in the auxin- cytokinin crosstalk for root meristem growth. Core of this PhD work is the functional characterization of the interplay between the BRX protein and the plant hormone auxin in the root meristem by using a computational model based on experimental evidence. Hyphotesis generated by the modelled to the discovery of a differential endocytosis pattern in the root meristem that splits the auxin transcriptional response via the plasma membrane to nucleus partitioning of BRX. This positional information system creates an auxin transcriptional pattern that deviates from the canonical auxin response and is necessary to sustain the expression of a subset of BRX-dependent auxin-responsive genes to drive root meristem growth. In the second part of this PhD thesis, we characterized the genome-wide impact of large scale deletions on four divergent Arabidopsis natural strains, through the integration of Ultra-High Throughput Sequencing data with data from genomic hybridizations on tiling arrays. Analysis of the identified deletions revealed a considerable portion of protein coding genes affected and supported a history of genomic rearrangements shaped by evolution. In the last part of the thesis, we showed that VIP3 gene in Arabidopsis has an evo-lutionary conserved role in the 3' to 5' mRNA degradation machinery, by applying a novel approach for the analysis of mRNA-Seq data from random-primed mRNA. Altogether, this PhD research contains major advancements in the study of natural genomic variation in plants and in the application of computational morphodynamics models for the functional characterization of biological pathways essential for the plant. - Récemment, l'introduction du séquençage de seconde génération et les avancées dans la microscopie confocale ont permis des études à l'échelle des différents systèmes cellulaires pour la caractérisation fonctionnelle de gènes. Le degrés de complexité intrinsèque à ces approches ont requis le développement de méthodologies bioinformatiques et de modèles mathématiques afin d'extraire de la masse de données expérimentale générée, des information biologiques significatives. Ce doctorat présente à la fois des méthodes bioinformatiques originales et des modèles mathématiques pour répondre à certaines questions spécifiques de Biologie Végétale en utilisant la plante Arabidopsis thaliana comme modèle. Premièrement, une analyse qualitative spatio-temporelle de profiles quantitatifs de transcripts et de protéines est utilisée pour montrer le rôle de la protéine BREVIS RADIX (BRX) dans le dialogue entre l'auxine et les cytokinines, des phytohormones, dans la croissance du méristème racinaire. Le noyau de ce travail de thèse est la caractérisation fonctionnelle de l'interaction entre la protéine BRX et la phytohormone auxine dans le méristème de la racine en utilisant des modèles informatiques basés sur des preuves expérimentales. Les hypothèses produites par le modèle ont mené à la découverte d'un schéma différentiel d'endocytose dans le méristème racinaire qui divise la réponse transcriptionnelle à l'auxine par le partitionnement de BRX de la membrane plasmique au noyau de la cellule. Cette information positionnelle crée une réponse transcriptionnelle à l'auxine qui dévie de la réponse canonique à l'auxine et est nécessaire pour soutenir l'expression d'un sous ensemble de gènes répondant à l'auxine et dépendant de BRX pour conduire la croissance du méristème. Dans la seconde partie de cette thèse de doctorat, nous avons caractérisé l'impact sur l'ensemble du génome des délétions à grande échelle sur quatre souches divergentes naturelles d'Arabidopsis, à travers l'intégration du séquençage à ultra-haut-débit avec l'hybridation génomique sur puces ADN. L'analyse des délétions identifiées a révélé qu'une proportion considérable de gènes codant était affectée, supportant l'idée d'un historique de réarrangement génomique modelé durant l'évolution. Dans la dernière partie de cette thèse, nous avons montré que le gène VÏP3 dans Arabidopsis a conservé un rôle évolutif dans la machinerie de dégradation des ARNm dans le sens 3' à 5', en appliquant une nouvelle approche pour l'analyse des données de séquençage d'ARNm issue de transcripts amplifiés aléatoirement. Dans son ensemble, cette recherche de doctorat contient des avancées majeures dans l'étude des variations génomiques naturelles des plantes et dans l'application de modèles morphodynamiques informatiques pour la caractérisation de réseaux biologiques essentiels à la plante. - Le développement des plantes est écrit dans leurs codes génétiques. Pour comprendre comment les plantes sont capables de s'adapter aux changements environnementaux, il est essentiel d'étudier comment leurs gènes gouvernent leur formation. Plus nous essayons de comprendre le fonctionnement d'une plante, plus nous réalisons la complexité des mécanismes biologiques, à tel point que l'utilisation d'outils et de modèles mathématiques devient indispensable. Dans ce travail, avec l'utilisation de la plante modèle Arabidopsis thalicinci nous avons résolu des problèmes biologiques spécifiques à travers le développement et l'application de méthodes informatiques concrètes. Dans un premier temps, nous avons investigué comment le gène BREVIS RADIX (BRX) régule le développement de la racine en contrôlant la réponse à deux hormones : l'auxine et la cytokinine. Nous avons employé une analyse statistique sur des mesures quantitatives de transcripts et de produits de gènes afin de démontrer que BRX joue un rôle antagonisant dans le dialogue entre ces deux hormones. Lorsque ce-dialogue moléculaire est perturbé, la racine primaire voit sa longueur dramatiquement réduite. Pour comprendre comment BRX répond à l'auxine, nous avons développé un modèle informatique basé sur des résultats expérimentaux. Les simulations successives ont mené à la découverte d'un signal positionnel qui contrôle la réponse de la racine à l'auxine par la régulation du mouvement intracellulaire de BRX. Dans la seconde partie de cette thèse, nous avons analysé le génome entier de quatre souches naturelles d'Arabidopsis et nous avons trouvé qu'une grande partie de leurs gènes étaient manquant par rapport à la souche de référence. Ce résultat indique que l'historique des modifications génomiques conduites par l'évolution détermine une disponibilité différentielle des gènes fonctionnels dans ces plantes. Dans la dernière partie de ce travail, nous avons analysé les données du transcriptome de la plante où le gène VIP3 était non fonctionnel. Ceci nous a permis de découvrir le rôle double de VIP3 dans la régulation de l'initiation de la transcription et dans la dégradation des transcripts. Ce rôle double n'avait jusqu'alors été démontrée que chez l'homme. Ce travail de doctorat supporte le développement et l'application de méthodologies informatiques comme outils inestimables pour résoudre la complexité des problèmes biologiques dans la recherche végétale. L'intégration de la biologie végétale et l'informatique est devenue de plus en plus importante pour l'avancée de nos connaissances sur le fonctionnement et le développement des plantes.

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.