Le but de cette thèse est d’étudier profondément le repliement des protéines, au moyendes concepts d’invariance de jauge et d’universalité. La structure de jauge émerge del’équation de Frenet qui est utilisée pour décrire la forme de la chaîne principale de laprotéine. Le principe d’invariance de jauge conduit à une fonctionnelle d’énergieeffective pour une protéine, développée dans le but d’extraire les propriétésuniverselles des protéines repliées durant la phase d’effondrement, et qui estcaractérisée par la loi d’échelle du rayon de giration au niveau tertiaire de la structureprotéique. Dans cette thèse, on étudie l’existence d’une large universalité au niveausecondaire de la structure protéique. La fonctionnelle d’énergie invariante de jaugealliée à l’équation de Frenet discrète conduit à une solution solitonique, identifiéecomme un motif hélice-boucle-hélice dans la protéine. / The purpose of this thesis is to investigate protein folding, by means of the general concepts of gauge invariance and universality. The gauge structure emerges in the Frenet equation which is utilized to describe the shape of protein backbone. The gauge invariance principle leads us an effective energy functional for a protein, which bas been found to catch the universal properties of folded proteins in their collapse phase,characterized by the scaling law of gyration radius on the tertiary level of proteinstructure. In this thesis, the existence of wide universality on the secondary level of protein structure is investigated. The synthesis of the gauge-invariant energy functional with the discrete Frenet equation leads to a soliton solution, which is identified as the helix-loop-helix motif in protein.

This paper aims to “demonstrate” that whereas man does not have a universalized conceptionof justice based on intercultural consensus, he must seek it dialogically. Nowadays, themulticultural nature of society requires rules to ensure reasonable coexistence among individuals.To achieve this goal, it is necessary to have a consensual conception of justice thatprovides criteria for dialogue and intergroup coexistence. / Este trabajo intenta “demostrar” que si bien el hombre no tiene una concepción universalizablede justicia que posea consenso intercultural, este debe buscarla dialógicamente. Elcarácter multicultural de las sociedades de hoy en día exige normas que permitan garantizarla convivencia razonable entre los individuos. Para alcanzar este objetivo es necesario contarcon una concepción consensuada de justicia que proporcione criterios para el diálogo yla convivencia intergrupal.

[pt] A presente dissertação é uma investigação acerca da validade universal do juízo do belo, tratado por Kant na Critica da faculdade do juízo. Tal investigação se faz necessária para esclarecer a proposta kantiana sobre um juízo que é singular, fundado no sentimento de prazer, mas que ergue uma pretensão à validade universal. Para dar conta da universalidade do juízo do belo, a dissertação lida com as duas Introduções, a primeira e a publicada, e com a Analítica do belo. Ela procura explicitar as razões pelas quais Kant fundamenta o juízo do belo no sentimento de prazer. Esse sentimento envolve as faculdades cognitivas da imaginação e do entendimento, faculdades que, no caso do juízo do belo, estão como que num jogo livre. Esse jogo livre é possível porque o juízo acerca do belo é um juízo reflexivo, que não parte de conceitos, mas do singular dado e vai procurar um conceito para esse singular. Nesse sentido, justificar a validade universal do juízo do belo é o desafio principal e o objetivo da dissertação. / [en] This dissertation is an investigation about the universal validity of the judgment of the beautiful, as treated by Kant in his Critique of Judgment. Such investigation is needed to clarify the Kantian proposal for this judgment that is singular and grounded on the feeling of pleasure, which raises a claim for its universal validity as well. To be able to manage the universality of the judgment of the beautiful, this work deals with the two Introductions, the first and the published one, and with the Analytic of the Beautiful. It seeks to explain the terms in which Kant grounds the judgment of the beautiful over the feeling of pleasure. In the case of the judgment of the beautiful the cognitive faculties of imagination and understanding are in a free play. This free play is possible because the judgment of the beautiful is a reflective judgment, which doesn t come from concepts but it actually must seek a concept for the singular given. In this sense, to justify the universal validity of the judgment of the beautiful is the main challenge and purpose of this dissertation.

Classical and quantum spin systems are widely used models in both experimental and theoretical condensed matter physics. In many materials, the electronic interactions can be difficult to model exactly. However, in some insulators (Mott insulators), the magnetic (spin) interactions can be captured well with spin-only models. Several models are studied in this thesis. First, I report the solution of a long-standing issue in a classical frustrated spin model (i.e., where the quantum effects are neglected and the complexity is due to competing interactions): the nature of the thermal phase transition to a stripe state in the two dimensional (2D) J1-J2 model. Here J1 and J2 are nearest- and next-nearest-neighbor couplings. Monte Carlo simulations with single-spin updates are used for the calculations, and an extended-ensemble method, a generalization of the Wang-Landau algorithm, is also developed and tested. I focus on the study of "weak universality" behavior (continuously varying critical exponents, with one of the exponents staying fixed), for which I show a correspondence with a known class of conformal field theories with charge c = 1. Next, moving to quantum spins, to shed light on magnetic systems studied experimentally and to investigate new types of quantum states of interest in developing theories of quantum magnetism, I study the S = 1/2 Heisenberg model on the 2D square lattice with added six-spin interactions (the so-called J-Q3 model) as well as a set of 3D quantum antiferromagnets on dimerized lattices. Here I use the stochastic series expansion quantum Monte Carlo method. In the study of the J-Q3 model, I report on a similar weak-universality behavior as in the classical J1-J2 model, but with a mapping to a different known class of c = 1 conformal field theories. The critical behavior of the system again shows continuously changing exponents, in a way which corresponds to a gradual weakening of Z4 symmetry-breaking to an emergent U(1) symmetry. In the study of dimerized antiferromagnets, I report on a universal behavior of the Néel temperature TN, which can be related to ground state parameters independently of the microscopic interaction details in several different models.

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In the thesis, the joint universality of periodic Hurwitz zeta-functions as well as that jointly with the Riemann zeta-functions of normalized cusp forms is obtained. / Darbe yra įrodomas jungtinis universalumas periodinėms Hurvico dzeta funkcijoms, taip pat bendras universalumas su Rymano dzeta funkcija ir normuotų parabolinių formų dzeta funkcija.

Darbe yra įrodomas jungtinis universalumas periodinėms Hurvico dzeta funkcijoms, taip pat bendras universalumas su Rymano dzeta funkcija ir normuotų parabolinių formų dzeta funkcija. / In the thesis, the joint universality of periodic Hurwitz zeta-functions as well as that jointly with the Riemann zeta-function or zeta functions of normalized cusp forms is obtained.

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Cette thèse adresse les problèmes d'universalité et de complétude computationelle pour plusieurs modèles de calcul inspirés par la biologie. Il s'agit principalement des systèmes d'insertion/effacement, réseaux de processeurs évolutionnaires, ainsi que des systèmes de réécriture de multi-ensembles. Les résultats décrits se classent dans deux catégories majeures : l'étude de la puissance de calcul des opérations d'insertion et d'effacement avec ou sans mécanismes de contrôle, et la construction des systèmes de réécriture de multi-ensembles universels de petite taille. Les opérations d'insertion et d'effacement consistent à rajouter ou supprimer une sous-chaîne dans une chaîne de caractères dans un contexte donné. La motivation pour l'étude de ces opérations vient de la biologie, ainsi que de la linguistique et de la théorie des langages formels. Dans la première partie de ce manuscrit nous examinons des systèmes d'insertion/effacement correspondant à l'édition de l'ARN, un processus qui insère ou supprime des fragments de ces molécules. Une particularité importante de l'édition de l'ARN est que le endroit auquel se font les modifications est déterminé par des séquences de nucléotides se trouvant toujours du même côté du site de modification. En termes d'insertion et d'effacement, ce phénomène se modéliserait par des règles possédant le contexte uniquement d'un seul côté. Nous montrons qu'avec un contexte gauche de deux caractères il est possible d'engendrer tous les langages rationnels. D'autre part, nous prouvons que des contextes plus longs n'augmentent pas la puissance de calcul du modèle. Nous examinons aussi les systèmes d’insertion/effacement utilisant des mécanismes de contrôle d’application des règles et nous montrons l'augmentation de la puissance d'expression. Les opérations d'insertion et d'effacement apparaissent naturellement dans le domaine de la sécurité informatique. Comme exemple on peut donner le modèle des grammaires gauchistes (leftist grammar), qui ont été introduites pour l'étude des systèmes critiques. Dans cette thèse nous proposons un nouvel instrument graphique d'analyse du comportement dynamique de ces grammaires. La deuxième partie du manuscrit s'intéresse au problème d'universalité qui consiste à trouver un élément concret capable de simuler le travail de n'importe quel autre dispositif de calcul. Nous commençons par le modèle de réseaux de processeurs évolutionnaires, qui abstrait le traitement de l'information génétique. Nous construisons des réseaux universels ayant un petit nombre de règles. Nous nous concentrons ensuite sur les systèmes de réécriture des multi-ensembles, un modèle qui peut être vu comme une abstraction des réactions biochimiques. Pour des raisons historiques, nous formulons nos résultats en termes de réseaux de Petri. Nous construisons des réseaux de Petri universels et décrivons des techniques de réduction du nombre de places, de transitions et d'arcs inhibiteurs, ainsi que du degré maximal des transitions. Une bonne partie de ces techniques repose sur une généralisation des machines à registres introduite dans cette thèse et qui permet d'effectuer plusieurs tests et opérations en un seul changement d'état / The present thesis considers the problems of computational completeness and universality for several biologically-inspired models of computation: insertion-deletion systems, networks of evolutionary processors, and multiset rewriting systems. The presented results fall into two major categories: study of expressive power of the operations of insertion and deletion with and without control, and construction of universal multiset rewriting systems of low descriptional complexity. Insertion and deletion operations consist in adding or removing a subword from a given string if this subword is surrounded by some given contexts. The motivation for studying these operations comes from biology, as well as from linguistics and the theory of formal languages. In the first part of the present work we focus on insertion-deletion systems closely related to RNA editing, which essentially consists in inserting or deleting fragments of RNA molecules. An important feature of RNA editing is the fact that the locus the operations are carried at is determined by certain sequences of nucleotides, which are always situated to the same side of the editing site. In terms of formal insertion and deletion, this phenomenon is modelled by rules which can only check their context on one side and not on the other. We show that allowing one-symbol insertion and deletion rules to check a two-symbol left context enables them to generate all regular languages. Moreover, we prove that allowing longer insertion and deletion contexts does not increase the computational power. We further consider insertion-deletion systems with additional control over rule applications and show that the computational completeness can be achieved by systems with very small rules. The motivation for studying insertion-deletion systems also comes from the domain of computer security, for the purposes of which a special kind of insertion-deletion systems called leftist grammars was introduced. In this work we propose a novel graphical instrument for visual analysis of the dynamics of such systems. The second part of the present thesis is concerned with the universality problem, which consists in finding a fixed element able to simulate the work any other computing device. We start by considering networks of evolutionary processors (NEPs), a computational model inspired by the way genetic information is processed in the living cell, and construct universal NEPs with very few rules. We then focus on multiset rewriting systems, which model the chemical processes running in the biological cell. For historical reasons, we formulate our results in terms of Petri nets. We construct a series of universal Petri nets and give several techniques for reducing the numbers of places, transitions, inhibitor arcs, and the maximal transition degree. Some of these techniques rely on a generalisation of conventional register machines, proposed in this thesis, which allows multiple register checks and operations to be performed in a single state transition