学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2856号 ; 請求記号: 新制/工/1420 ; 整理番号: 25541 / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13385号 / 工博第2856号 / 新制||工||1420(附属図書館) / 25541 / UT51-2007-Q786 / 京都大学大学院工学研究科建築学専攻 / (主査)教授 加藤 直樹, 教授 上谷 宏二, 准教授 大﨑 純 / 学位規則第4条第1項該当

Constraint programming is an invaluable tool for solving many of the complex NP-complete problems that we need solutions to. These problems can be easily described as Constraint Satisfaction Problems (CSPs) and then passed to constraint solvers: complex pieces of software written to solve general CSPs efficiently. Many of the problems we need solutions to are real world problems: planning (e.g. vehicle routing), scheduling (e.g. job shop schedules) and timetabling problems (e.g. staff rotas) to name but a few. In the real world, we place structure on objects to make them easier to deal with. This manifests itself as symmetry. The symmetry in these real world problems make them easier to deal with for humans. However, they lead to a great deal of redundancy when using computational methods of problem solving. Thus, this thesis examines some of the many aspects of utilising the symmetry of CSPs to reduce the amount of computation needed by constraint solvers. In this thesis we look at the ease of use of previous symmetry breaking methods. We introduce a new and novel method of describing the symmetries of CSPs. We look at previous methods of symmetry breaking and show how we can drastically reduce their computation while still breaking all symmetry. We give the first detailed investigation into the behaviour of breaking only subsets of all symmetry. We look at how this affects the performance of constraint solvers before discovering the properties of a good symmetry. We then present an original method for choosing the best symmetries to use. Finally, we look at areas of redundant computation in constraint solvers that no other research has examined. New ways of dealing with this redundancy are proposed with results of an example implementation which improves efficiency by several orders of magnitude.

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.

The non-linear Hartree-Fock (HF) equations are usually solved via the iterative self-consistent field method. However, there is no a priori guarantee of convergence, especially in systems with strong electron correlation where symmetry breaking occurs. This work focuses on closed- shell systems in the HF approximation and the (in)stability of the found solutions, and proposes new deterministic methods for the localization of both symmetry-adapted and broken symmetry solutions. We employ a perturbative method and show how one can always obtain a symmetry-adapted solution of the HF equations. We also determine the radius of convergence, related to the existence of at least one bound state, of the perturbative series. Next, we rederive the matrix of stability and adapt it to spin and orbital symmetry. Calculation of higher energy variations follows, first in terms of spin-orbitals and then orbitals. Motivated by the investigation of the structure of a broken-symmetry solution, we propose a new deterministic method for the localization of a broken-symmetry solution. The general expressions are verified by reformulating the stability conditions for simple cases. The proposed methods are successfully applied to helium-, beryllium- and neon-like systems.

Made available in DSpace on 2014-06-11T19:25:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-09-27Bitstream added on 2014-06-13T19:12:27Z : No. of bitstreams: 1 woitekjunior_m_me_ift.pdf: 9022411 bytes, checksum: 88726cc3ceec91a0d503f0b0557e5add (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Uma das características mais importantes das teorias de gauge não-Abelianas é a não-linearidade das equações de campo clássicas. Mostra-se no contexto da teoria de Yang-Mills que essa característica pode fazer com que o campo de gauge apresente comportamento caótico. Isso pode acontecer mesmo quando estivermos considerando a dinâmica do campo na ausência de fontes, isto é, o vácuo da teoria de Yang-Mills. Discutimos a relação entre os comportamentos caótico e ergódico. Em seguida, introduzimos a formulação de Berdichevsky da Mecânica Estatística Clássica para sistemas dinâmicos Hamiltonianos que são ergódicos e possuem poucos graus de liberdade. A Mecânica Estatística de Berdichevsky é usada para estudar a situação mais simples numa teoria de gauge não-Abeliana onde as variáveis de campo são caóticas e o espaço de fase correspondente tem a propriedade geométrica necessária. Mostramos que, para os propósitos desse estudo, um par de campos escalares complexos deve ser incluído no problema. Mais precisamente, analisamos o modelo de Higgs não-Abeliano; a Lagrangiana da teoria considerada possui uma simetria SU(2). A transição de uma descrição dinâmica do sistema de YangMills-Higgs (fora do equilíbrio termodinâmico) para uma descrição termodinâmica (quando ele atingiu o equilíbrio) é investigada numericamente. Mostra-se que depois de um tempo suficientemente longo as soluções numéricas se comportam de tal maneira que o sistema pode ser descrito de um jeito mais simples através de grandezas como a temperatura, calculadas de acordo com as prescriçõees da Mecânica Estatística de equilíbrio. Estas são previstas analiticamente para comparção com os resultados numéricos... / One of the most important features of non-Abelian gauge theories is the non-linearity of the classical field equations. In the context of Yang-Mills theory it is shown that this feature can cause the gauge field to show chaotic behavior. That can happen even when we are considering the field dynamics in the absence of sources, i.e., the vacuum of the Yang-Mills theory. We discuss the connection between chaotic and ergodic behaviors. Then we introduce Berdichevsky’s formulation of Classical Statistical Mechanics for Hamiltonian dynamical systems that are both ergodic and low-dimensional. Berdichevsky’s theory of Statistical Mechanics is used to study the simplest situation in a non-Abelian gauge theory where the field variables are chaotic and the corresponding phase space has the necessary geometric property. We show that, for the purposes of this study, a pair of complex scalar fields must be introduced in the problem. More precisely, we analyse the so-called non-Abelian Higgs model; the Lagrangian of the theory we are considering has a SU(2) symmetry. The transition from a non-equilibrium dynamical description of the Yang-Mills-Higgs system to a thermodynamical description when it reaches equilibrium is numerically investigated. It is shown that after a sufficiently long time the numerical solutions behave in such a manner that the system can be described by quantities like the temperature, determined in accordance with the prescriptions of equilibrium Statistical Mechanics. These are predicted analytically for comparison with the numerical results. It is verified that there is agreement between analytical and numerical predictions so that the thermalization of the Yang-Mills-Higgs system can be explained with the aid of Berdichevsky’s Statistical Mechanics. A dynamical approach to the study... (Complete abstract click electronic access below)

Made available in DSpace on 2014-06-11T19:32:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-04Bitstream added on 2014-06-13T21:03:27Z : No. of bitstreams: 1 santos_vgcs_dr_guara.pdf: 603356 bytes, checksum: 48d0890069648043a713c383f62ba614 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nesta tese procuramos veri car e aprofundar os limites de validade dos chamados sistemas quânticos com simetria PT. Nestes tem-se, por exemplo, sistemas cuja hamiltoniana é não-hermitiana mas apresenta um espectro de energia real. Tal característica é usualmente justi cada pela presença da simetria PT (paridade e inversão temporal), muito embora não haja ainda uma demonstração bem aceita na literatutra desta propriedade de tais sistemas. Inicialmente estudamos sistemas quânticos não-relativísticos dependentes do tempo, sistemas em mais dimensões espaciais, a m de veri car possíveis limites da simetria PT na garantia da realidade do espectro. Logo depois estudamos sistemas quânticos relativísticos em 1+1D que possuem simetria PT com uma mistura adequada de potenciais: vetor, escalar e pseudo-escalar, sendo o potencial vetor complexo. Em seguida trabalhamos com densidades de lagrangiana com potenciais não-hermitianos em 1+1 dimensões espaço-temporais e em dimensões mais altas. A vantagem das baixas dimensões é que alguns sistemas possuem soluções não-perturbativas exatas. Finalmente, mostramos que não somente é possível ter um modelo consistente com dois campos escalares, mas também que a introdução de um número maior de campos permite que a densidade de energia também permaneça real. / In this thesis we verify and try to deepen the limits of validity of the so called quantum systems with PT-symmetry. These are systems whose Hamiltonians are non-Hermitian but present real energy spectra. Such characteristic usually is justi ed by the presence of PT symmetry (parity and time inversion), despite of the fact that there is no well accepted demonstration in literature of this property of such systems yet. Initially we study timedependent non-relativistic quantum systems in one spatial dimension in order to verify possible limits for which the PT symmetry grants the reality of the spectra. Soon later we study relativistic quantum systems in 1+1D that they possess symmetry PT with an convenient mixing of complex vector plus scalar plus pseudoscalar potentials is considered. After that, we work with a Lagrangian density with such features in 1+1 space-time dimensions and higher dimensions, in the context of eld theory. The advantage of working in low dimensions is that, in such dimensions, some systems possess exact nonperturbative solutions. Finally, we show that not only it is possible to have a consistent model with two scalar elds, but also that the introduction of a bigger number of elds allows that the energy density also remains real.

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-02Bitstream added on 2014-06-13T20:03:15Z : No. of bitstreams: 1 pupin_jc_dr_ift.pdf: 1428942 bytes, checksum: d6abaa838d7800612f4a795ffa313ad7 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Utilizando a simetria quiral, calculamos a contribuição dominante ao potencial nucleon-nucleon (NN) devido à troca de três píons não correlacionados. Esta contribuição é isovetorial com as componentes pseudoescalar e axial. A pseudoescalar é dominante, tem um alcance de 1.0 fm e contribui no canal de píon. No mesmo contexto, estudamos a produção de um píon na interação nucleon-nucleon devida à troca de dois píons. O termo dominante do Kernel da produção é construído a partir da mesma interação básica usada no potencial NN devido à troca de três píons. Relacionamos este termo à componente central do potencial NN devido à troca de dois píons e mostramos que esta, por sua vez, é dominada pelo fator de forma escalar píon-nucleon. O Kernel obtido foi aplicado para o limiar da produção e na construção de um potencial de três nucleons. Os resultados foram generalizados para um potencial NN central qualquer e comparados ao potencial de Argonne e àquele devido à troca de um méson escalar...ctício / Abstracts: Using the chiral symmetry, we calculated the dominant contribution to the nucleon-nucleon (NN) potential due to the exchange of three non-correlated pions (3o). This contribution is isovetor with pseudoscalar and axial components. The pseudoscalar component is dominant, it has a range of 1.0 fm and it contributes in the pion channel. In the same context, we studied the pion production in the nucleon-nucleon interaction due to the exchange of two pions (2o). The dominant term of the production Kernel is built from the same basic interaction used in the 3o-exchange NN potential. We related this term to the central component of the 2o-exchange NN potential and we showed that the latter, on its turn, is dominated by the pion-nucleon scalar form factor. The obtained Kernel was applied at the threshold and in the constructioin of a three-nucleon potential. The results were generalized foa a central NN potential of any kind and compared to the potentials of Argonne and to that due to the exchange of one ...ctitious scalar meson

En relation avec le désordre de leur structure, les composés relaxeurs révèlent une dualité entre les échelles locale et globale. L'ordre polaire qui se développe localement ne se manifeste pas à l'échelle globale, la structure globale demeurant cubique. Bien que pertinente au vu de ses capacités à saisir la dualité d'échelle, une incorporation directe de la symétrie locale à l'appareil d'étude des relaxeurs reste absente. C'est autour de cette lacune que s'articule la thèse, en ce qu'elle constitue une implémentation explicite de la symétrie locale dans l'Hamiltonien effectif. Elle porte sur l'analyse du rôle de la symétrie locale à sous-tendre l'ordre locale dont les propriétés macroscopiques émergent. Une question sous-jacente s'adjoint à ces considérations et concerne la possible formulation du problème d'un point de vue topologique / Concomitantly with lattice disorder, there is a discrepancy between local and global scales in relaxor ferroelectrics, in that structural distortions occurring at the local scale are not reflected in the average global structure which remains cubic. There is an absence of direct implementation of the local symmetry in the modeling of relaxors, despite its considerable, but often unacknowledged, ability to encode local features. Central to the thesis is an explicit account for local gauge symmetry within the first-principles-derived effective Hamiltonian approach. The thesis thus aims to consider how an extended symmetry allowing independent transformations at different points in space can effectively bridge local features and macroscopical properties. An underlying question the thesis also seeks to answer is whether the disorder-induced non-trivial interplay between local and global scales can be described from a topological point of view

O principal objetivo deste trabalho é estudar a quantização covariante da corda bosônica e da supercorda RNS, explorando as simetrias envolvidas, ou seja, as simetrias BRST e conforme no caso da corda bosônica e as generalizações correspondentes para a corda fermiônica. Em particular, discutimos alguns aspectos perturbativos da teoria bosônica e a construção de operadores de vértice da corda fermiônica. / The main goal of this work is to study the covariant quantization of the bosonic and RNS string theories by exploiting the involved symmetries, namely, the BRST and conformal invariance for the bosonic string and the corresponding supersymmetric generalizations for the fermionic case. In particular, we discuss some perturbative aspects of the bosonic theory and the construction of vertex operators for the fermionic string.

Neste trabalho, estuda-se propriedades e implementações de duas importantes representações de formas denominadas curvatura e eixos de simetria (ou esqueletos), relacionando-as ao clássico modelo de processamento da informação visual proposto por Marr. Para tanto, fez-se necessária uma releitura dos critérios para a representação de formas já existentes, além da proposição e comparação de algumas abordagens numéricas através das quais curvaturas e esqueletos são calculados, com especial atenção dada a características como robustez e invariância. No caso da curvatura, que é uma medida clássica da geometria diferencial sem divergências quanto a sua definição e interpretação, foi dado maior enfoque à robustez dos métodos quanto à presença de ruídos de diversas naturezas e quanto a sensibilidade na escolha dos parâmetros que levaram aos resultados mais precisos. Além disso, propôs-se uma versão não-derivativa da curvatura (denominada circularidade local) a fim de contornar o problema advindo das instabilidades do cálculo de derivadas de dados reais amostrados. Ainda relativamente à curvatura, um método baseado na transformada de Fourier bidimensional foi proposto e comparado à abordagem unidimensional já estabelecida e a outro método padrão (&#946-Splines/ Medioni) de cálculo de curvatura de contornos digitais. Já no caso dos esqueletos, a existência de diversas interpretações geométricas e matemáticas para o conceito e as inúmeras abordagens numéricas para o cálculo dos mesmos demandaram a revisão da literatura sob a luz do modelo inicialmente introduzido para que se pudesse impor uniformidade à terminologia e situar as diferentes abordagens e implementações dentro de um panorama comum, sendo que dois novos métodos para o cálculo de esqueletos foram criados quando do desenvolvimento deste trabalho (esqueletos por dilatações exatas e esqueletos afins baseados em áreas). / In this work, properties and implementations of two important shape representa¬tions had been studied: curvature and symmetry axis (or skeletons) and they had been related to the Marr\'s classical visual information processing model. Thus, it was necessary a re-interpretation of previously existent criteria for shape represen¬tation in addition to the proposition and comparison of some numerical approaches for curvature and skeletons calculations with special attention given to robustness and invariance characteristics. In the curvature case, a classic measure from dif¬ferential geometry with no divergence about its definition and interpretation, we focused mainly on the numerical methods robustness in presence of several noise categories and on the best parameter set choice sensibility. Additionally, a no derivative version of curvature (also called local circularity) was proposed in order to circumvent problems related to the sampled real data derivatives numerical ins¬tabilities. Still talking about curvature, a 2D Fourier transform based method had been proposed and assessed in comparison to the 1D approach and other standard digital contour curvature calculation method (&#946-Splines/ Medioni). In the skeleton\'s case, the existence of several geometrical and mathematical interpretations of the concept and the innumerable numeric approaches to their calculation demanded a literature survey regarding the initially introduced model to impose uniformity to the terminology and to situate the different approaches and implementations into a common framework where two new methods to skeleton\'s calculations had been created (exact dilations based skeletons and area based affine skeletons).