Transmitting quantum information across quantum channels is an important task. However quantum information is delicate, and is easily corrupted. We address the task of protecting quantum information from an information theoretic perspective -- we encode some message qudits into a quantum code, send the encoded quantum information across the noisy quantum channel, then recover the message qudits by decoding. In this dissertation, we discuss the coding problem from several perspectives.} The noisy quantum channel is one of the central aspects of the quantum coding problem, and hence quantifying the noisy quantum channel from the physical model is an important problem. We work with an explicit physical model -- a pair of initially decoupled quantum harmonic oscillators interacting with a spring-like coupling, where the bath oscillator is initially in a thermal-like state. In particular, we treat the completely positive and trace preserving map on the system as a quantum channel, and study the truncation of the channel by truncating its Kraus set. We thereby derive the matrix elements of the Choi-Jamiolkowski operator of the corresponding truncated channel, which are truncated transition amplitudes. Finally, we give a computable approximation for these truncated transition amplitudes with explicit error bounds, and perform a case study of the oscillators in the off-resonant and weakly-coupled regime numerically. In the context of truncated noisy channels, we revisit the notion of approximate error correction of finite dimension codes. We derive a computationally simple lower bound on the worst case entanglement fidelity of a quantum code, when the truncated recovery map of Leung et. al. is rescaled. As an application, we apply our bound to construct a family of multi-error correcting amplitude damping codes that are permutation-invariant. This demonstrates an explicit example where the specific structure of the noisy channel allows code design out of the stabilizer formalism via purely algebraic means. We study lower bounds on the quantum capacity of adversarial channels, where we restrict the selection of quantum codes to the set of concatenated quantum codes. The adversarial channel is a quantum channel where an adversary corrupts a fixed fraction of qudits sent across a quantum channel in the most malicious way possible. The best known rates of communicating over adversarial channels are given by the quantum Gilbert-Varshamov (GV) bound, that is known to be attainable with random quantum codes. We generalize the classical result of Thommesen to the quantum case, thereby demonstrating the existence of concatenated quantum codes that can asymptotically attain the quantum GV bound. The outer codes are quantum generalized Reed-Solomon codes, and the inner codes are random independently chosen stabilizer codes, where the rates of the inner and outer codes lie in a specified feasible region. We next study upper bounds on the quantum capacity of some low dimension quantum channels. The quantum capacity of a quantum channel is the maximum rate at which quantum information can be transmitted reliably across it, given arbitrarily many uses of it. While it is known that random quantum codes can be used to attain the quantum capacity, the quantum capacity of many classes of channels is undetermined, even for channels of low input and output dimension. For example, depolarizing channels are important quantum channels, but do not have tight numerical bounds. We obtain upper bounds on the quantum capacity of some unital and non-unital channels -- two-qubit Pauli channels, two-qubit depolarizing channels, two-qubit locally symmetric channels, shifted qubit depolarizing channels, and shifted two-qubit Pauli channels -- using the coherent information of some degradable channels. We use the notion of twirling quantum channels, and Smith and Smolin's method of constructing degradable extensions of quantum channels extensively. The degradable channels we introduce, study and use are two-qubit amplitude damping channels. Exploiting the notion of covariant quantum channels, we give sufficient conditions for the quantum capacity of a degradable channel to be the optimal value of a concave program with linear constraints, and show that our two-qubit degradable amplitude damping channels have this property.

Video editing and object recognition are two significant fields in computer vi- sion: the first has remarkably assisted digital production and post-production tasks of a digital video footage; the second is considered fundamental to image classification or image based search in large databases (e.g. the web). In this thesis, we address two problems, namely we present a novel formulation that tackles video editing tasks and we develop a mechanism that allows to generate more robust descriptors for objects in an image. Concerning the first problem, this thesis proposes two variational models to perform temporally coherent video editing. These models are applied to change an object’s (rigid or non-rigid) texture throughout a given video sequence. One model is based on propagating color information from a given frame (or be- tween two given frames) along the motion trajectories of the video; while the other is based on propagating gradient domain information. The models we present in this thesis require minimal user intervention and they automatically accommodate for illumination changes in the scene. Concerning the second problem, this thesis addresses the problem of affine invariance in object recognition. We introduce a way to generate geometric affine invariant quantities that are used in the construction of feature descrip- tors. We show that when these quantities are used they do indeed achieve a more robust recognition than the state of the art descriptors. i / La edición de vídeo y el reconocimiento de objetos son dos áreas fundamentales en el campo de la visión por computador: la primera es de gran utilidad en los procesos de producción y post-producción digital de vídeo; la segunda es esencial para la clasificación o búsqueda de imágenes en grandes bases de datos (por ejemplo, en la web). En esta tesis se acometen ambos problemas, en concreto, se presenta una nueva formulación que aborda las tareas de edición de vídeo y se desarrolla un mecanismo que permite generar descriptores más robustos para los objetos de la imagen. Con respecto al primer problema, en esta tesis se proponen dos modelos variacionales para llevar a cabo la edición de vídeo de forma coherente en el tiempo. Estos modelos se aplican para cambiar la textura de un objeto (rígido o no) a lo largo de una secuencia de vídeo dada. Uno de los modelos está basado en la propagación de la información de color desde un determinado cuadro de la secuencia de vídeo (o entre dos cuadros dados) a lo largo de las trayectorias de movimiento del vídeo. El otro modelo está basado en la propagación de la información en el dominio del gradiente. Ambos modelos requieren una intervención mínima por parte del usuario y se ajustan de manera automática a los cambios de iluminación de la escena. Con respecto al segundo problema, esta tesis aborda el problema de la invariancia afín en el reconocimiento de objetos. Se introduce un nuevo método para generar cantidades geométricas afines que se utilizan en la generación de descriptores de características. También se demuestra que el uso de dichas cantidades proporciona mayor robustez al reconocimiento que los descriptores existentes actualmente en el estado del arte.

Visual information from a speaker's mouth region is known to improve automatic speech recognition (ASR) robustness, especially in the presence of acoustic noise. Currently, the vast majority of audio-visual ASR (AVASR) studies assume frontal images of the speaker's face, which is a rather restrictive human-computer interaction (HCI) scenario. The lack of research into AVASR across multiple views has been dictated by the lack of large corpora that contains varying pose/viewpoint speech data. Recently, research has concentrated on recognising human be- haviours within &quotmeeting " or &quotlecture " type scenarios via &quotsmart-rooms ". This has resulted in the collection of audio-visual speech data which allows for the recognition of visual speech from both frontal and non-frontal views to occur. Using this data, the main focus of this thesis was to investigate and develop various methods within the confines of a lipreading system which can recognise visual speech across multiple views. This reseach constitutes the first published work within the field which looks at this particular aspect of AVASR. The task of recognising visual speech from non-frontal views (i.e. profile) is in principle very similar to that of frontal views, requiring the lipreading system to initially locate and track the mouth region and subsequently extract visual features. However, this task is far more complicated than the frontal case, because the facial features required to locate and track the mouth lie in a much more limited spatial plane. Nevertheless, accurate mouth region tracking can be achieved by employing techniques similar to frontal facial feature localisation. Once the mouth region has been extracted, the same visual feature extraction process can take place to the frontal view. A novel contribution of this thesis, is to quantify the degradation in lipreading performance between the frontal and profile views. In addition to this, novel patch-based analysis of the various views is conducted, and as a result a novel multi-stream patch-based representation is formulated. Having a lipreading system which can recognise visual speech from both frontal and profile views is a novel contribution to the field of AVASR. How- ever, given both the frontal and profile viewpoints, this begs the question, is there any benefit of having the additional viewpoint? Another major contribution of this thesis, is an exploration of a novel multi-view lipreading system. This system shows that there does exist complimentary information in the additional viewpoint (possibly that of lip protrusion), with superior performance achieved in the multi-view system compared to the frontal-only system. Even though having a multi-view lipreading system which can recognise visual speech from both front and profile views is very beneficial, it can hardly considered to be realistic, as each particular viewpoint is dedicated to a single pose (i.e. front or profile). In an effort to make the lipreading system more realistic, a unified system based on a single camera was developed which enables a lipreading system to recognise visual speech from both frontal and profile poses. This is called pose-invariant lipreading. Pose-invariant lipreading can be performed on either stationary or continuous tasks. Methods which effectively normalise the various poses into a single pose were investigated for the stationary scenario and in another contribution of this thesis, an algorithm based on regularised linear regression was employed to project all the visual speech features into a uniform pose. This particular method is shown to be beneficial when the lipreading system was biased towards the dominant pose (i.e. frontal). The final contribution of this thesis is the formulation of a continuous pose-invariant lipreading system which contains a pose-estimator at the start of the visual front-end. This system highlights the complexity of developing such a system, as introducing more flexibility within the lipreading system invariability means the introduction of more error. All the works contained in this thesis present novel and innovative contributions to the field of AVASR, and hopefully this will aid in the future deployment of an AVASR system in realistic scenarios.

Thesis (MComm (Industrial Psychology))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: The choice of career path could create a stressful situation for many individuals. Researchers seem to agree that if a person is able to find fit between what they would like to do and what a job (work environment) involves then a person is likely to perform their chosen occupation well. Interest assessment is a method that assists in making personal and organisational career related decisions. The Campbell Interest and Skill Survey (CISS, Campbell, Hyne & Nilsen, 1992) is a well-known interest assessment instrument that can be used for such decisions. Even though interest assessment can assist, these instruments have been criticised for being gender biased and typically forcing people into stereotypical gendered type occupations. Bias is indicated as nuisance factors that threaten the validity of cross-group (cultural) comparisons (Van de Vijver & Leung, 1997). These nuisance factors could be due to construct bias, method bias and/or item bias. Therefore, due to the importance of the decisions made, it would seem essential that the information provided by test results apply equally across different reference groups – this would imply equivalent measurement. Equivalence is achieved at three levels: Configural, metric and scalar (Vandenberg & Lance, 2000; Vandenberg, 2002). Full measurement invariance (achieved when scalar invariance is found) implies the ability to compare observed scores directly. By making use of confirmatory factor analytic techniques suggested by Vandenberg and Lance (2000), increasing constraints of equivalence were proposed for the CISS measurement model. While adequate model fit was found for the CISS Basic scales, the sample size did not afford independent gender sample confirmatory factor analyses (CFAs) and consequent measurement invariance tests to be conducted on the Basic scales. The CISS Orientation scales were then subjected to CFA on the combined gender sample and then were subjected to independent CFAs on the separate gender samples. Unfortunately poor model fit was found at this global level of measurement in the CISS. This prevented the researcher from completing the necessary measurement invariance tests on the Orientation scales for the CISS. The implications of the results are discussed, limitations are indicated and areas for further research are highlighted. / AFRIKAANSE OPSOMMING: Die maak van ‘n loopbaankeuse kan spanning veroorsaak in baie mense. Dit wil voorkom of navorsers saamstem dat indien ‘n person se werklike beroep ooreenstem met dit wat hy/sy graag sou wou doen – dan sal die persoon waarskynlik goed presteer in die gekose beroep. Die benutting van belangstellingsvraelyste kan individue help om effektiewe persoonlike en beroepsgerigte keuses te maak. Die “Campbell Interest and Skill Survey” (CISS, Campbell, Hyne & Nilsen, 1992) is ‘n bekende belangstellingsvraelys wat gebruik kan word om ondersteuning te bied om bogenoemde keuses te maak. Alhoewel belangstellingsvraelyste oor die algemeen waardevolle hulpbronne is in die maak van beroepskeuses, is hierdie vraelyste al gekritiseer dat hulle sydig kan wees op grond van geslag en as sulks mense kan lei om geslagsgetipeerde beroepskeuses te maak. “Sydigheid” in toetse kan beskryf word as “lastige” faktore wat die geldigheid van kruiskulturele vergelykings bedreig (Van de Vijver & Leung, 1997). Hierdie faktore kan veroorsaak word deur konstruksydigheid, metodesydigheid en/of itemsydigheid. Dit is dus noodsaaklik dat die informasie wat verskaf word deur die toetsresultate dieselfde betekenis moet hê oor al die verskillende verwysingsgroepe en dit noodsaak ekwivalente meting. Ekwivalensie kan bereik word op drie vlakke: konfiguraal, metries en skalêr (Vandenberg & Lance, 2000; Vandenberg, 2002). Volle invariansie van meting (wat bereik word wanneer skalêre invariansie bevind word) impliseer dat waargenome metings direk met mekaar vergelyk kan word. Deur gebruik te maak van bevestigende faktoranalitiese tegnieke voorgestel deur Vandenberg en Lance (2000), is toenemende ekwivalensiebeperkinge voorgestel vir die “CISS” metingsmodel. Alhoewel ’n bevredigende passing gevind is vir die “CISS Basic scales” model, het die grootte van die steekproef nie toegelaat dat die “CISS Basic scales” model onafhanklik op die twee geslagsgroepe gepas word nie en ook nie toegelaat dat die metingsinvariansie van die model oor die twee geslagsgroepe ondersoek word nie. Die “CISS Orientation scales” is toe blootgestel aan bevestigende faktorontleding op die gekombineerde geslagsteekproef en asook op die onderskeie geslagsgroepe. Op hierdie globale vlak kon daar egter nie bevredigende modelpassing gevind word nie. Die gebrekkige modelpassing het gevolglik die navorser verhoed om enige verdere metingsvariansie toetse op die “Orientation scales” te doen. Die implikasies van die resultate word bespreek, beperkinge word aangedui en verdere moonlike navorsingsgebiede word uitgelig.

Este trabalho apresenta uma extensão do princípio de invariância para sistemas chaveados contínuos no tempo. Esta extensão fornece estimativas de atratores e suas respectivas áreas de atração para sistemas chaveados compostos por um número finito de subsistemas, a qual é obtida através de uma função auxiliar comum e múltiplas funções auxiliares que desempenham o mesmo papel que as funções de Lyapunov. As principais características desses novos resultados, são que a derivada da função auxiliar ou das múltiplas funções auxiliares podem assumir valores positivos em alguns conjuntos e também são usados para analisar o comportamento assintótico da solução do sistema chaveado. Resultados para sistemas chaveados com subsistemas com incertezas paramétricas também foram obtidos. Neste caso, as estimativas dos atratores e suas respectivas áreas de atração independem do parâmetro incerto. Analisando as propriedades da função auxiliar comum ao longo de um sistema formado pela combinação convexa de todos os subsistemas, os resultados passam a fornecer estimativas de atratores e suas áreas de atração mesmo na presença de subsistemas que não são ultimamente limitados. Este último resultado pode não evitar o chaveamento rápido, então surge o problema da existência da solução. Esta dificuldade pôde ser superada com o uso da teoria de sistemas descontínuos para garantir que sua solução seja definida para todo tempo mesmo que o chaveamento rápido ocorra. Portanto, uma escolha apropriada da lei de chaveamento possibilita o uso da solução de Krasovskii para garantir a existência da solução para todo tempo. Ainda, representando cada subsistema por um modelo fuzzy T-S, o comportamento assintótico da solução do sistema chaveado pôde ser estudado apenas verificando propriedades de alguns conjuntos do espaço de estado e a factibilidade de um conjunto de desigualdades matriciais lineares. / This work presents an extension of the invariance principle for continuous time switched systems. This extension is useful to obtain estimates of the attractor and basin of attraction for switched systems composed by a finite number of subsystems, which are obtained by using a common auxiliary function or multiple auxiliary functions which play the same hole as the Lyapunov function. The main feature of these new results are that the common auxiliary function or the multiple auxiliary functions can be positive in some sets and are used to analyze the asymptotic behavior of the switching solution. Results for switched systems with parametric uncertainties were also obtained. The estimates of the attractor and basin of attraction does not depend on the uncertain parameter. Analysing the auxiliary function along the solutions of the convex combination of the subsystems, estimates of the attractor and basin of attraction for switched systems with subsystems which are not necessarily ultimately bounded were given. This last result can not avoid the fast switching, then the switched solution may not exist for all time. This difficulty was overcome with the use of the theory of discontinuous systems to guarantee the existence of the switching system solution for all time. Furthemore, using a T-S fuzzy model approach, the asymptotic behavior of the switched solution could be analyzed only by checking properties of some sets and the feasibility of a set of linear matrix inequalities.

This thesis addresses the task of developing automatic algorithms for analysing the two-dimensional ultrasound video footage obtained from fetal heart screening scans. These scans are typically performed in the second trimester of pregnancy to check for congenital heart anomalies and require significant training and anatomical knowledge to perform. The aim is to develop a tool that runs at high frame rates with no user initialisation and infers the visibility, position, orientation, view classification, and cardiac phase of the heart, and additionally the locations of cardiac structures of interest (such as valves and vessels) in a manner that is robust to the various sources of variation that occur in real-world ultrasound scanning. This is the first work to attempt such a detailed automated analysis of these videos. The problem is posed as a Bayesian filtering problem, which provides a principled framework for aggregating uncertain measurements across a number of frames whilst exploiting the constraints imposed by anatomical feasibility. The resulting inference problem is solved approximately with a particle filter, whose state space is partitioned to reduce the problems associated with filtering in high-dimensional spaces. Rotation-invariant features are captured from the videos in an efficient way in order to tackle the problem of unknown orientation. These are used within random forest learning models, including a novel formulation to predict circular-valued variables. The algorithm is validated on an annotated clinical dataset, and the results are compared to estimates of inter- and intra-observer variation, which are significant in both cases due to the inherent ambiguity in the imagery. The results suggest that the algorithm's output approaches these benchmarks in several respects, and fall slightly behind in others. The work presented here is an important first step towards developing automated clinical tools for the detection of congenital heart disease.

In this master s thesis, we have studied the possibility of Lorentz invariance violation by considering some terms of the standard-model extesion (SME), specifically, those terms which refer to the quantum electrodynamics extension. We have performed quantum corrections in the fermionic sector of the usual quantum electrodynamics with added terms which violate the Lorentz and CPT symmetries in two different configurations. Firstly, adding operators governed by the coefficient gκλμ and, in a later time, adding operators governed by the coefficient bμ. In the theory with the coefficient gκλμ, we have performed quantum corrections in order to induce, in the bosonic sector of the theory, the conventional Chern-Simons and the higher-derivative terms, and analyze the behavior of both terms in the finite temperature regime, by using the method of derivative expansion and the Matsubara formalism. On the other hand, in the model with the coefficient bμ, we have performed quantum corrections in order to induce, in the bosonic sector, the higher-derivative Chern-Simons term, by using the method of derivative expansion and, subsequently, analyze the behavior of this term in the finite temperatura regime, where we have used the Matsubara formalism again. Thus, for the first case, we have observed that the conventional Chern-Simons term is nonzero only at finite temperature, whereas the higher-derivative term is finite at zero temperature, however, this term goes to zero when the temperature increases infinitely. In the second part of our study, we have shown that the higher-derivative Chern-Simons term is induced at zero temperature, nevertheless, this term goes to zero when the temperature increases too much. / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nesta dissertação, estudamos a possibilidade de violação da invariância de Lorentz levando em conta alguns termos do modelo padrão estendido, mais especificamente, da parte deste modelo que trata da eletrodinâmica quântica estendida. Realizamos correções quânticas no setor fermiônico da eletrodinâmica quântica usual adicionada de termos que violam as simetrias de Lorentz e CPT em duas configurações diferentes. Primeiramente, adicionando operadores governados pelo coeficiente gκλμ e, em um momento posterior, adicionando operadores governados pelo coeficiente bμ. Para a teoria com o coeficiente gκλμ, realizamos correções quânticas com a intenção de induzir, no setor bosônico da teoria, os termos de Chern-Simons convencional e o de derivada superior, e analisar o comportamento de ambos os termos no regime de temperatura finita, fazendo o uso do método da expansão derivativa e do formalismo de Matsubara. Já para o modelo com o coeficiente bμ, realizamos correções quânticas a fim de induzir, no setor bosônico, o termo de Chern-Simons de derivada superior, usando o método da expansão derivativa e, posteriormente, analisar o comportamento deste termo no regime de temperatura finita, ao utilizarmos novamente o formalismo de Matsubara. Assim, para o primeiro caso, notamos que o termo de Chern-Simons convencional é diferente de zero apenas à temperatura finita, enquanto que, o termo de derivada superior é finito em temperatura zero, porém, tal termo vai a zero quando a temperatura cresce infinitamente. Na segunda parte do nosso estudo, mostramos que o termo de Chern-Simons de derivada superior é induzido no regime de temperatura zero, contudo, tal termo vai a zero quando a temperatura cresce muito.

The effective action of Euler Heisenberg describes the nonlinear dynamics of electromagnetic fields in vacuum. Such action takes into account the polarization in a vacuum for a bond, in addition to describing also the photon propagation through arbitrary electromagnetic fields that vary slowly. So, since its discovery, the effective action of Euler Heisenberg has been studied in various contexts, such as the scattering of light by light, pair production in a vacuum, Division of photons, birefringence in vacuum, effective action in gravity and string theory, among others. In this work we performed a study on the Lorentz transformations of observer and grains, showing that, in the presence of a field, the revolutions and changes of speed (boost) break the equivalence between these two transformations (Observer and particle). We studied also the violation of Lorentz invariance by consideration of some terms related to the extended standard model, with a focus on quantum electrodynamics extended. We carry out a Perturbative calculation in the cμν coefficient, a coefficient of this responsible for violation of Lorentz symmetry of particle, however impose rotational invariance. From the results of this calculation, we can retrieve the Perturbative result to the effect of the Division of photons in a vacuum, as well as the effective action of Euler Heisenberg with Lorentz violation, the linear coefficient c00. / Conselho Nacional de Desenvolvimento Científico e Tecnológico / A ação efetiva de Euler-Heisenberg descreve a dinâmica não linear de campos eletromagnéticos no vácuo. Tal ação leva em conta a polarização no vácuo para um laço, além de descrever também a propagação de fótons através de campos eletromagnéticos arbitrários que variam lentamente. Então, desde a sua descoberta, a ação efetiva de Euler-Heisenberg tem sido estudada em vários contextos, tais como o espalhamento da luz pela luz, produção de pares no vácuo, divisão de fótons, birrefringência no vácuo, ação efetiva em gravidade e teoria de cordas, dentre outros. Neste trabalho realizamos inicialmente um estudo sobre as transformações de Lorentz de observador e de partícula, mostrando que, na presença de um campo de fundo, as rotações e mudanças de velocidade (boost) quebram a equivalência entre essas duas transformações (observador e partícula). Estudamos também a violação da invariância de Lorentz através da consideração de alguns termos referentes ao modelo padrão estendido, com foco na eletrodinâmica quântica estendida. Efetuamos um cálculo não perturbativo no coeficiente cμν , coeficiente este responsável pela violação da simetria de Lorentz de partícula, no entanto impomos invariância rotacional. A partir dos resultados desse cálculo, conseguimos recuperar o resultado perturbativo para o efeito da divisão de fótons no vácuo, assim como a ação efetiva de Euler-Heisenberg com violação de Lorentz, linear no coeficiente c00.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-11-05T20:45:40Z No. of bitstreams: 1 WAGNER OLIVEIRA DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2017.pdf: 707943 bytes, checksum: f2f7e6d2f28889fe9d5b1bf8b99fbbcd (MD5) / Made available in DSpace on 2018-11-05T20:45:40Z (GMT). No. of bitstreams: 1 WAGNER OLIVEIRA DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2017.pdf: 707943 bytes, checksum: f2f7e6d2f28889fe9d5b1bf8b99fbbcd (MD5) Previous issue date: 2017-08-09 / Capes / Nesta dissertação consideramos a proposta de modificação dos setores do fóton e do férmion via à teoria de campos efetiva de Myers-Pospelov. Esta abordagem tem como principal característica a violação da simetria de Lorentz através da introdução de operadores de altas ordens derivativas de dimensão-5 e campos constantes. Consequentemente,a quebra desta importante simetria conduz a relações de dispersão que sondam efeitos na escala de energia de Planck, onde efeitos da gravidade quântica devem ser relevantes. Isso nos motiva a estudar as possíveis consequências destas relações de dispersão modificadas no comportamento termodinâmico de gases compostos por fótons ou férmions. Será mostrado que a violação da simetria de Lorentz pode ser interpretada como uma pseudo-interação repulsiva ou atrativa entre as partículas. Mostraremos também, por exemplo, que a relação de dispersão modificada do fóton, implica em um aumento da entropia do sistema, isto é, a quebra da simetria de Lorentz pode conduzir a um aumento no número de estados acessíveis do sistema. Além disso, aplicamos as propriedades destes gases a radiação de corpo negro e a dinâmica estelar de anãs brancas no modelo de Chandrasekhar. / In this dissertation, we consider a proposal which modifies the gauge and fermion sectors via Myers-Pospelov effective field theory. The main feature of this approach is the Lorentz symmetry violation through the introduction of higher-derivatives operators of dimension-5 and constant fields. Hence, breaking this important symmetry leads to dispersion relations probing effects in the Planck energy scale, that in turn, sets the limit for which the quantum description of space-time becomes to be relevant. It motivate us to study the possible implications of these modified dispersion relations on thermodynamic behavior of photons and fermions gases. It will be shown that the breakdown of Lorentz invariance can be interpreted as a repulsive or attractive pseudo-interaction among the particles. Additionally, for instance, it will be shown that the presence of a deformed dispersion relation for photons entails an increase in the entropy of the system, e.g., the Lorentz symmetry violation may lead to an increase in the number of microstates available to the system. In addition, we apply the properties of these gases to black body radiation and stellar dynamics of white dwarfs in the Chandrasekhar model.

Submitted by DANIELE ALESSANDRA REGHINI GAZETTA null (daniellygaze@hotmail.com) on 2016-01-15T17:36:23Z No. of bitstreams: 1 diss-daniele.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) / Rejected by Ana Paula Grisoto (grisotoana@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: No campo “Versão a ser disponibilizada online imediatamente” foi informado que seria disponibilizado o texto completo porém no campo “Data para a disponibilização do texto completo” foi informado que o texto completo deverá ser disponibilizado apenas 6 meses após a defesa. Caso opte pela disponibilização do texto completo apenas 6 meses após a defesa selecione no campo “Versão a ser disponibilizada online imediatamente” a opção “Texto parcial”. Esta opção é utilizada caso você tenha planos de publicar seu trabalho em periódicos científicos ou em formato de livro, por exemplo e fará com que apenas as páginas pré-textuais, introdução, considerações e referências sejam disponibilizadas. Se optar por disponibilizar o texto completo de seu trabalho imediatamente selecione no campo “Data para a disponibilização do texto completo” a opção “Não se aplica (texto completo)”. Isso fará com que seu trabalho seja disponibilizado na íntegra no Repositório Institucional UNESP. Por favor, corrija esta informação realizando uma nova submissão. Agradecemos a compreensão. on 2016-01-15T19:12:27Z (GMT) / Submitted by DANIELE ALESSANDRA REGHINI GAZETTA null (daniellygaze@hotmail.com) on 2016-01-16T16:43:56Z No. of bitstreams: 2 diss-daniele.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) daniele-dissert.pdf: 585710 bytes, checksum: 222237614b39411bc9b9a3e82ad6ab17 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-01-18T16:33:44Z (GMT) No. of bitstreams: 1 gazetta_dar_me_sjrp.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) / Made available in DSpace on 2016-01-18T16:33:44Z (GMT). No. of bitstreams: 1 gazetta_dar_me_sjrp.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) Previous issue date: 2016-01-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O principal resultado dessa dissertação é o Teorema de Poincaré-Bendixson para campos de vetores planares suaves por partes, que nos diz quais são os tipos de conjuntos limite. Estudaremos também detalhes a respeito dos conceitos de conjuntos minimais e caóticos em campos de vetores planares suaves por partes. / The main result of this work is the Poincaré - Bendixson Theorem for planar piecewise smooth vector fields, which tell us what kind of limit sets arise in this context. We will also study details about the concepts of minimal and chaotic sets in planar piecewise smooth vector fields.