Despite decades of theoretical and experimental investigation, the fundamental interactions between nucleons remains poorly understood. While the strong interaction is responsible for binding quarks into nucleons, and nucleons into nuclei, there is no consistent description of these processes. At the low energies where nucleon binding occurs, the interactions are in principle calculable from quantum chromodynamics, but the required non-perturbative calculations are not possible. Instead, different models have been created to describe different phenomena. These models require experimental input to constrain them. As the expected weak interaction effects are not seen in the strangeness-conserving systems as have been seen in other systems, it is believed that the strong interaction interferes with the weak interaction. Therefore by measuring parity-violating observables that occur due to the weak interaction, information can be gained about the strong interaction. The NPDGamma and n3He experiments are two complementary experiments that measured a parity violating observables in a few nucleon system. They ran on the Fundamental Neutron Physics Beamline at the Spallation Neutron Source. The NPDGamma experiment measured the parity violating directional asymmetry in the gamma ray's emission direction after polarized cold neutron capture on a liquid parahydrogen target using an array of 48 CsI detectors. The n3He experiment measured the parity violating directional asymmetry in the proton emission direction after polarized cold neutron capture on a gaseous $^{3}$He target. The capture occurs inside an ionization chamber that measures the proton emission direction. Both experiments have completed data taking with data analysis in an advanced state. These experiments should be able to be used with a number of already existing experimental results to constrain the models. I designed and assembled a pair of $^{3}$He ionization chambers that were used as beam monitors during the experiments. Using the lessons learned from the beam monitors, I then designed and assembled the ionization chamber that is the combined target and detector for the n3He experiment. The monitors and target chamber were examined to determine their charge collection properties and linearity after installation. One of the monitors was calibrated to determine the neutron flux from the output current. / February 2017

Este trabalho aborda a formulação geométrica das teorias clássicas de calibre, ou Yang-Mills, considerando-as como uma importante classe de modelos que deve ser incluída em qualquer tentativa de estabelecer um formalismo matemático geral para a teoria clássica dos campos. Tal formulação deve vir em (pelo menos) duas variantes: a versão hamiltoniana, que passou por uma fase de desenvolvimento rápido durante os últimos 10-15 anos, levando ao que hoje é conhecido como o ``formalismo multissimplético\'\', e a mais tradicional versão lagrangiana utilizada nesta tese. O motivo principal justificando tal investigação é que teorias de calibre constituem os mais importantes exemplos de sistemas dinâmicos que são altamente relevantes na Física e onde a equivalência entre a versão lagrangiana e a versão hamiltoniana, que no caso de sistemas não-singulares é estabelecida pela transformação de Legendre, deixa de ser óbvia, pois teorias de calibre são sistemas degenerados do ponto de vista lagrangiano e são sistemas vinculados do ponto de vista hamiltoniano. Esta propriedade característica das teorias de calibre é uma consequência direta do seu alto grau de simetria, isto é, da sua invariância de calibre. No entanto, numa formulação plenamente geométrica da teoria clássica dos campos, capaz de incorporar situações topologicamente não-triviais, a invariância sob transformações de calibre locais (transformações de calibre de segunda espécie) e, surpreendentemente, até mesmo a invariância sob as transformações de simetria globais correspondentes (transformações de calibre de primeira espécie) não podem ser adequadamente descritas em termos de grupos de Lie e suas ações em variedades, mas requerem a introdução e o uso sistemático de um novo conceito, a saber, fibrados de grupos de Lie e suas ações em fibrados (sobre a mesma variedade base). A meta principal da presente tese é tomar os primeiros passos no desenvolvimento de ferramentas matemáticas adequadas para lidar com este novo conceito de simetria e, como uma primeira aplicação, dar uma definição clara e simples do procedimento de ``acoplamento mínimo\'\' e uma demonstração simples do teorema de Utiyama, segundo o qual lagrangianas para potenciais de calibre (conexões) de primeira ordem (i.e., que dependem apenas dos próprios potenciais de calibre e de suas derivadas parciais até primeira ordem) que são invariantes sob transformações de calibre são necessariamente funções dos campos de calibre (i.e., do tensor de curvatura) invariantes sob as transformações de simetria globais correspondentes. / This thesis deals with the geometric formulation of classical gauge theories, or Yang-Mills theories, regarded as an important class of models that must be included in any attempt to establish a general mathematical framework for classical field theory. Such a formulation must come in (at least) two variants: the hamiltonian version which has gone through a phase of rapid development during the last 10-15 years, leading to what is now known as the ``multisymplectic formalism\'\', and the more traditional lagrangian version studied in this thesis. The main motivation justifying this kind of investigation is that gauge theories constitute the most important examples of dynamical systems that are highly relevant in physics and where the equivalence between the lagrangian and the hamiltonian version, which for non-singular systems is established through the Legendre trans% formation, is far from obvious, since gauge theories are degenerate systems from the lagrangian point of view and are constrained systems from the hamiltonian point of view. This characteristic property of gauge theories is a direct consequence of their high degree of symmetry, that is, of gauge invariance. However, in a fully geometric formulation of classical field theory, capable of incorporating topologically non-trivial situations, invariance under local gauge transformations (gauge transformations of the second kind) and, surprisingly, even invariance under the corresponding global symmetry transformations (gauge transformations of the first kind) cannot be described adequately in terms of Lie groups and their actions on manifolds but requires the introduction and systematic use of a new concept, namely Lie group bundles and their actions on fiber bundles (over the same base manifold). The main goal of the present thesis is to take the first steps in developing adequate mathematical tools for handling this new concept of symmetry and, as a first application, give a simple clear-cut definition for the prescription of ``minimal coupling\'\' and a simple proof of Utiyama´s theorem, according to which lagrangians for gauge potentials (connections) that are gauge invariant and of first order, i.e., dependent only on the gauge potentials themselves and on their partial derivatives up to first order, are necessarily functions of the gauge field strengths (i.e., the curvature tensor) invariant under the corresponding global symmetry transformations.

Nesta tese, mostramos que o modelo estocástico binário para expressão gênica, por um gene auto-regulado, possui solução completa. A solução dependente do tempo é escrita via expansão em termos das funções de Heun confluentes. Apresentamos um exemplo de dinâmica estocástica desse gene. Para tal, desenvolvemos uma relação de recorrência entre derivadas arbitrárias das funções de Heun confluentes. Mostramos também que o regime estacionário deste modelo possui simetria de Lie SO(2, 1) tipo Lorentz. Esta simetria é análoga à simetria do momento angular, porém com um sinal errado. O invariante desta álgebra define a meia-vida relativa do regime dinâmico do gene. O equivalente do momento angular azimutal é uma medida indireta do nível de atividade do gene. Os operadores levantamento e abaixamento conectam diferentes processos estocásticos de expressão proteínica. As flutuações destes processos estocásticos são classificadas em termos das relações entre os etiquetadores de um elemento da representação da álgebra. No arcabouço da teoria dos grupos, o modelo estocástico para um gene externamente regulado aparece como um caso particular do modelo para um gene auto-regulado. Mostramos, por fim, uma comparação entre estas duas estratégias de regulação. Demonstramos que um gene auto-regulado pode expressar proteínas em regimes sub Poisson, Poisson ou super Poisson. Por seu turno, o gene externamente regulado somente expressa proteínas em regimes Poisson ou super Poisson. Portanto, num processo estocástico, a auto-regulação mostra-se como uma forma de controle mais precisa. Também mostramos que a dinâmica de genes auto-regulados possui meia-vida mais curta que a de genes externamente regulados. Ou seja, a auto-regulação permite respostas mais rápidas à perturbações externas. / In this thesis we show that the stochastic binary model to protein synthesis by na auto-regulated gene is completely solvable. The time-dependent solution is written in terms of the confluent Heun functions. We present an example of probability dynamics to this gene. To get that, we developed a recurrence relation between arbitrary derivatives of the confluent Heun functions. We also show the existence of a Lorentz-like Lie symmetry SO(2, 1). This is an analogous to the angular momentum symmetry but presenting one wrong sign in its preserved form. This invariant defines the relative half-life of the dynamical regime of the gene. The equivalent of the azimuth angular momentum measures indirectly the activity level of the gene. The ladder operators connect distinct stochastic processes of protein synthesis. The fluctuations of these processes are classified in terms of the relation between labeling numbers of a representation of the algebra. In the group theory formalism, the stochastic model to an externally regulated gene is a particular case of the model to an auto-regulated gene. We compare these two gene regulation strategies, and show that the auto-regulated gene can synthesize proteins into the super Poisson, Poisson, and sub Poisson fluctuating regimes. The externally regulated gene only presents the super Poisson and Poisson regimes. Therefore, the auto-regulation is responsible for a more precise control of gene expression. We also show that the dynamics of the auto-regulated genes has a shorter half-life. Thus, the auto-regulation permits faster responses of the system to external perturbation.

La méthode dite de la fonctionnelle de la densité d'énergie (EDF) est l'outil théorique de référence pour l'étude systématique de la structure des noyaux atomiques de masse A>20. La méthode EDF est formulée en deux étapes successives consistant à briser puis à restaurer les symétries du Hamiltonien nucléaire sous-jacent. La technique de restauration des symétries n'est cependant rigoureusement formulée que si la fonctionnelle d'énergie dérive explicitement d'une interaction effective, i.e. d'un pseudo-potentiel, ce qui constitue un cas particulier de la méthode EDF plus générale. Ainsi, et comme cela a été démontré récemment, l'utilisation des paramétrisations existantes des fonctionnelles d'énergie conduit à l'obtention de résultats non physiques. Le pouvoir prédictif limité des fonctionnelles d'énergie existantes et leur inocuité relative à la restauration des symétries, nécessitent aujourd'hui de repenser leur méthode de construction. La première partie de ce travail a été dédié à l'analyse approfondie du problème associé à la restauration de symétrie et à l'identification de pistes permettant de contraindre la forme analytique des fonctionnelles d'énergie ne dérivant pas d'un pseudo-potentiel indépendant du système. La seconde partie a consisté à développer un pseudo-potentiel rendant la restauration des symétries automatiquement bien définie. Les difficultés de ce travail ont résidé dans (i) l'identification de la complexité minimale du pseudo-potentiel nécessaire à l'obtention d'une fonctionnelle d'énergie assez flexible pour égaler, et si possible améliorer, les performances des paramétrisations existantes, (ii) la dérivation analytique de la fonctionnelle et des champs à un corps découlant de celle ci, (iii) l'implémentation de ces derniers dans les codes de calculs, et dans (iv) le développement d'un protocole d'ajustement des paramètres adapté à la nouvelle fonctionnelle d'énergie ainsi développée. Les premiers résultats obtenus ont permis de valider l'approche en démontrant la flexibilité suffisante du pseudo-potentiel au niveau des calculs réalisés sans restauration des symétries. / The theoretical tool of choice for the microscopic description of all medium- and heavy-mass nuclei is the Energy Density Functional (EDF) method. Such a method relies on the concept of spontaneous symmetry breaking and restoration. In that sense, it is intrinsically a two-step approach. However, the symmetry restoration procedure is only well-defined in the particular case where the energy functional derives from a pseudo-potential. Thereby and as it has been recently shown, existing parameterizations of the energy functional provides unphysical results. Such a problem as well as the lack of predictive power call for developing new families of functionals. The first part of the present work is devoted to a study of the symmetry restoration problem and to the identification of properties that could constrain the analytic form of energy functionals that do not derive from a pseudo-potential. The second part deals with the construction of an energy functional that derives from a pseudo potential. The difficulties of such work are (i) the identification of the minimal complexity of the pseudo-potential necessary to obtain an energy functional that is flexible enough to provide high-quality EDF parameterizations, (ii) the tedious analytical derivation of the functional and of the associated one-body fields, (iii) the implementation of the latter in existing codes, and (iv) the development of an efficient fitting procedure. Eventually, it seems possible to generate a parameterization that strictly derives from a pseudo-potential and that provides as good results as state-of-the-art (quasi) bilinear functionals.

The theoretical tool of choice for the microscopic description of all medium- and heavy-mass nuclei is the Energy Density Functional (EDF) method. Such a method relies on the concept of spontaneous symmetry breaking and restoration. In that sense, it is intrinsically a two-step approach. However, the symmetry restoration procedure is only well-defined in the particular case where the energy functional derives from a pseudo-potential. Thereby and as it has been recently shown, existing parameterizations of the energy functional provides unphysical results. Such a problem as well as the lack of predictive power call for developing new families of functionals. The first part of the present work is devoted to a study of the symmetry restoration problem and to the identification of properties that could constrain the analytic form of energy functionals that do not derive from a pseudo-potential. The second part deals with the construction of an energy functional that derives from a pseudo potential. The difficulties of such work are (i) the identification of the minimal complexity of the pseudo-potential necessary to obtain an energy functional that is flexible enough to provide high-quality EDF parameterizations, (ii) the tedious analytical derivation of the functional and of the associated one-body fields, (iii) the implementation of the latter in existing codes, and (iv) the development of an efficient fitting procedure. Eventually, it seems possible to generate a parameterization that strictly derives from a pseudo-potential and that provides as good results as state-of-the-art (quasi) bilinear functionals.

<p>There are several methods avaliable to find areas of interest, but most fail at detecting such areas in cluttered scenes. In this paper two methods will be presented and tested in a qualitative perspective. The first is the darg operator, which is used to detect three dimensional convex or concave objects by calculating the derivative of the argument of the gradient in one direction of four rotated versions. The four versions are thereafter added together in their original orientation. A multi scale version is recommended to avoid the problem that the standard deviation of the Gaussians, combined with the derivatives, controls the scale of the object, which is detected. </p><p>Another feature detected in this paper is rotational symmetries with the help of approximative polynomial expansion. This approach is used in order to minimalize the number and sizes of the filters used for a correlation of a representation of the orientation and filters matching the rotational symmetries of order 0, 1 and 2. With this method a particular type of rotational symmetry can be extracted by using both the order and the orientation of the result. To improve the method’s selectivity a normalized inhibition is applied on the result, which causes a much weaker result in the two other resulting pixel values when one is high. </p><p>Both methods are not enough by themselves to give a definite answer to if the image consists of an area of interest or not, since several other things have these types of features. They can on the other hand give an indication where in the image the feature is found.</p>

<p>Gaze tracking means to detect and follow the direction in which a person looks. This can be used in for instance human-computer interaction. Most existing systems illuminate the eye with IR-light, possibly damaging the eye. The motivation of this thesis is to develop a truly non-intrusive gaze tracking system, using only a digital camera, e.g. a web camera.</p><p>The approach is to detect and track different facial features, using varying image analysis techniques. These features will serve as inputs to a neural net, which will be trained with a set of predetermined gaze tracking series. The output is coordinates on the screen.</p><p>The evaluation is done with a measure of accuracy and the result is an average angular deviation of two to four degrees, depending on the quality of the image sequence. To get better and more robust results, a higher image quality from the digital camera is needed.</p>

In 2008 a large statistics sample of approximately 1·107 η-decays has been collected with the WASA detector at COSY using the pd→3Heη reaction at the beam kinetic energy of 1 GeV. These data are being used to study the not so rare η decays involving charged pions, like η→π+π-π0. This decay proceeds mainly via a strong isospin violating contribution, where the decay width is proportional to the light quark mass difference squared, (md-mu)2. In addition this decay can be used to search for C-violating effects. The analysis is presented and the Dalitz plot parameters with statistical and systematical uncertainties are determined from a sample of 1.33·105 η→π+π-π0 events in the Dalitz plot. The asymmetry parameters with statistical uncertainties are presented which show no evidence of C-violation. / WASA-at-COSY

Aquesta tesi es situa en el marc de la teoriaqualitativadelssistemesd’equacionsdiferencials en el pla. Cada capítol conté un aspectediferent, però en totsells es tractenproblemes, la soluciódelsqualsestà basada en el rol que hi juguen les simetriesdiscretes i continues (reversibilitat o simetries de Lie) de campsvectorialsplans. A la introducció, es dóna un resumdelsresultatsmésconeguts i s’hiintrodueix la notació que es fa servir al llarg de la tesi. En el segon i tercer capítol, s’aborda el problema de trobarl’expressió explícita del canvilinealitzant o orbitalmentlinealitzantd#un camp vectorial suau a partir del coneixementd’uncommutador, en el cas de la linealització, o una simetria de Lie, en el cas de la linealització orbital. Cada capítol finalitzaambexemplesil.lustratius del procedimentconstructiudelscanvis. Al Capítol 5 s’apliquenelsresultatsdelscapítolsanteriors, combinatsamblinealitzacionsDarbouxianes. Concretament, es considera un sistema quadràtictipusLotka-Volterra i es caracteritzen les selles linealitzables i orbitalmentlinealitzablesmitjançant la troballadelscanvislinealitzants o orbitalmentlinealitzants. En el sisè capítol, s’utilitzal’existènciad’unàlgebra de simetriespuntuals de Lie per donar informació sobre l’existència i localitzaciód’òrbitesperiòdiques. En particular, quanl’àlgebra de simetriespuntuals de Lie d’unaequació diferencial escalar de segónordreautònoma i suau té dimensiómajor o igual a dos, definim les anomenadesfuncionsfonamentals que enspermeten estudiar les òrbitesperiòdiques al pla de fases. En el cas particular d’equacionspolinomials de Liénard, mostrem la no existència de cicles límit en tot el pla de fases. Finalment, al Capítol 7 es relacionen elssistemes reversibles amb el problema del centre aixícomamb el problema de la integrabilitat analítica. Consideremsistemesd’equacionsdiferencialsanalíticsamb centres degenerats i mostrem que poden transformar-se, després d’un reescalat del temps, en un sistema lineal i reversible. El coneixement de integralsprimeresens proporciona un procediment per caracteritzar, en alguns casos, la condició de reversibilitat del centre degenerat. D’altra banda, relacioneml’existència de integralsprimeresanalítiquesamb la reversibilitat orbital analítica en el cas de singularitatsdèbils no degenerades.

This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational purposes, it has been used to explain and control the dynamics in various physical systems. In order to use the quantum walk to its fullest potential, it is important to know and optimize the properties purely due to quantum dynamics and in presence of noise. Various studies of its dynamics in the absence and presence of noise have been reported. We propose new approaches to optimize the dynamics, discuss symmetries and effect of noise on the quantum walk. Making use of its properties, we propose the use of quantum walk as an efficient new tool for various applications in physical systems and quantum information processing. In the first and second part of this dissertation, we discuss evolution process of the quantum walks, propose and demonstrate the optimization of discrete-time quantum walk using quantum coin operation from SU(2) group and discuss some of its properties. We investigate symmetry operations and environmental effects on dynamics of the walk on a line and an $n-$cycle highlighting the interplay between noise and topology. Using the properties and behavior of quantum walk discussed in part two, in part three we propose the application of quantum walk to realize quantum phase transition in optical lattice, that is to efficiently control and redistribute ultracold atoms in optical lattice. We also discuss the implementation scheme. Another application we consider is creation of spatial entanglement using quantum walk on a quantum many body system.