No description available.

Traditional methods for predicting transient stability of power systems such as the direct method, the time domain approach, and the energy function methods do not work well for online transient stability predictions problems. With the advent of Phasor Measurement Units (PMUs) in power systems, it is now possible to monitor the behavior of the system in real time and provide important information for transient stability assessment and enhancement. Techniques such as the rotor oscillation prediction method based on time series have made the prediction of system stability possible for real-time applications. However, methods of this type require more than 300 milliseconds after the start of a transient event to make reliable predictions. The dissertation provides an alternate prediction method for transient stability by taking advantage of the available PMUs data. It predicts transient stability using apparent impedance trajectories obtained from PMUs, decision trees, and FLDSD method. This method enables to find out the strategic locations for PMUs installation in the power system to rapidly predict transient stability. From the simulations performed, it is realized that system stability can be predicted in approximately 200 milliseconds (12 cycles). The main advantage of this method is its simplicity as the PMUs can record the apparent impedance trajectories in real-time without any previous calculations. Moreover, using decision trees built in CART, transient stability prediction becomes straightforward and computationally very fast. The optimum locations for PMUs placement can also be determined using this technique. After the transient instability prediction by the apparent impedance trajectories, a slow- coherency based intelligent controlled islanding scheme is also developed to restore the stability of system. It enables the generators in the same island to stay in synchronism and the imbalance between the generators and load demand is minimized. / Ph. D.

Spanwise nonuniformity effects are modeled in the cross-sectional analysis of beam theory. This modeling adheres to an established numerical framework on cross-sectional analysis of uniform beams with arbitrary cross-sections. This framework is based on two concepts: decomposition of the rotation tensor and the variational-asymptotic method. Allowance of arbitrary materials and geometries in the cross-section is from discretization of the warping field by finite elements. By this approach, dimensional reduction from three-dimensional elasticity is performed rigorously and the sectional strain energy is derived to be asymptotically-correct. Elastic stiffness matrices are derived for inputs into the global beam analysis. Recovery relations for the displacement, stress, and strain fields are also derived with care to be consistent with the energy. Spanwise nonuniformity effects appear in the form of pointwise and sectionwise derivatives, which are approximated by finite differences. The formulation also accounts for the effects of spanwise variations in initial twist and/or curvature. A linearly tapered isotropic strip is analyzed to demonstrate spanwise nonuniformity effects on the cross-sectional analysis. The analysis is performed analytically by the variational-asymptotic method. Results from beam theory are validated against solutions from plane stress elasticity. These results demonstrate that spanwise nonuniformity effects become significant as the rate at which the cross-sections vary increases. The modeling of transverse shear modes of deformation is accomplished by transforming the strain energy into generalized Timoshenko form. Approximations in this transformation procedure from previous works, when applied to uniform beams, are identified. The approximations are not used in the present work so as to retain more accuracy. Comparison of present results with those previously published shows that these approximations sometimes change the results measurably and thus are inappropriate. Static and dynamic results, from the global beam analysis, are calculated to show the differences between using stiffness constants from previous works and the present work. As a form of validation of the transformation procedure, calculations from the global beam analysis of initially twisted isotropic beams from using curvilinear coordinate axes featuring twist are shown to be equivalent to calculations using Cartesian coordinates.

No description available.

Technologies such as micro-expression arrays and high-throughput sequenc- ing assays have accelerated research of genetic transcription in biological cells. Furthermore, many links between the gene expression levels and the pheno- typic characteristics of cells have been discovered. Our current understanding of transcriptomics as an intermediate regulatory layer between genomics and proteomics raises hope that we will soon be able to decipher many more cel- lular mechanisms through the exploration of gene transcription. However, although large amounts of expression data are measured, only lim- ited information can be extracted. One general problem is the large set of considered genomic features. Expression levels are often analyzed individually because of limited computational resources and unknown statistical dependen- cies among the features. This leads to multiple testing issues or can lead to overfitting models, commonly referred to as the “curse of dimensionality.” Another problem can arise from ignorance of measurement uncertainty. In particular, approaches that consider statistical significance can suffer from underestimating uncertainty for weakly expressed genes and consequently re- quire subjective manual measures to produce consistent results (e.g., domain- specific gene filters). In this thesis, we lay out a theoretical foundation for a Bayesian interpretation of gene expression data based on subtle assumptions. Expression measure- ments are related to latent information (e.g., the transcriptome composition), which we formulate as a probability distribution that represents the uncer- tainty over the composition of the original sample. Instead of analyzing univariate gene expression levels, we use the multivari- ate transcriptome composition space. To realize computational feasibility, we develop a scalable dimensional reduction that aims to produce the best approximation that can be used with the computational resources available. To enable the deconvolution of gene expression, we describe subtissue specific probability distributions of expression profiles. We demonstrate the suitabil- ity of our approach with two deconvolution applications: first, we infer the composition of immune cells, and second we reconstruct tumor-specific ex- pression patterns from bulk-RNA-seq data of prostate tumor tissue samples.:1 Introduction 1 1.1 State of the Art and Motivation 2 1.2 Scope of this Thesis 5 2 Notation and Abbreviations 7 2.1 Notations 7 2.2 Abbreviations 9 3 Methods 10 3.1 The Convolution Assumption 10 3.2 Principal Component Analysis 11 3.3 Expression Patterns 11 3.4 Bayes’ Theorem 12 3.5 Inference Algorithms 13 3.5.1 Inference Through Sampling 13 3.5.2 Variationa lInference 14 4 Prior and Conditional Probabilities 16 4.1 Mixture Coefficients 16 4.2 Distribution of Tumor Cell Content 18 4.2.1 Optimal Tumor Cell Content Drawing 20 4.3 Transcriptome Composition Distribution 21 4.3.1 Sequencing Read Distribution 21 4.3.1.1 Empirical Plausibility Investigation 25 4.3.2 Dirichletand Normality 29 4.3.3 Theta◦logTransformation 29 4.3.4 Variance Stabilization 32 4.4 Cell and Tissue-Type-Specific Expression Pattern Distributions 32 4.4.1 Method of Moments and Factor Analysis 33 4.4.1.1 Tumor Free Cells 33 4.4.1.2 Tumor Cells 34 4.4.2 Characteristic Function 34 4.4.3 Gaussian Mixture Model 37 4.5 Prior Covariance Matrix Distribution 37 4.6 Bayesian Survival Analysis 38 4.7 Demarcation from Existing Methods 40 4.7.1 Negative Binomial Distribution 40 4.7.2 Steady State Assumption 41 4.7.3 Partial Correlation 41 4.7.4 Interaction Networks 42 5 Feasibility via Dimensional Reduction 43 5.1 DR for Deconvolution of Expression Patterns 44 5.1.1 Systematically Differential Expression 45 5.1.2 Internal Distortion 46 5.1.3 Choosinga DR 46 5.1.4 Testing the DR 47 5.2 Transformed Density Functions 49 5.3 Probability Distribution of Mixtures in DR Space 50 5.3.1 Likelihood Gradient 51 5.3.2 The Theorem 52 5.3.3 Implementation 52 5.4 DR for Inference of Cell Composition 53 5.4.1 Problem Formalization 53 5.4.2 Naive PCA 54 5.4.3 Whitening 55 5.4.3.1 Covariance Inflation 56 5.4.4 DR Through Optimization 56 5.4.4.1 Starting Point 57 5.4.4.2 The Optimization Process 58 5.4.5 Results 59 5.5 Interpretation of DR 61 5.6 Comparison to Other DRs 62 5.6.1 Weighted Correlation Network Analysis 62 5.6.2 t-Distributed Stochastic Neighbor Embedding 65 5.6.3 Diffusion Map 66 5.6.4 Non-negativeMatrix Factorization 66 5.7 Conclusion 67 6 Data for Example Application 68 6.1 Immune Cell Data 68 6.1.1 Provided List of Publicly Available Data 68 6.1.2 Obtaining the Publicly Available RNA-seq Data 69 6.1.3 Obtaining the Publicly Available Expression Microarray Data 71 6.1.4 Data Sanitization 71 6.1.4.1 A Tagging Tool 72 6.1.4.2 Tagging Results 73 6.1.4.3 Automatic Sanitization 74 6.1.5 Data Unification 75 6.1.5.1 Feature Mapping 76 6.1.5.2 Feature Selection 76 6.2 Examples of Mixtures with Gold Standard 79 6.2.1 Expression Microarray Data 81 6.2.2 Normalized Expression 81 6.2.3 Composition of the Gold Standard 82 6.3 Tumor Expression Data 82 6.3.1 Tumor Content 82 6.4 Benchmark Reference Study 83 6.4.1 Methodology 83 6.4.2 Reproduction 84 6.4.3 Reference Hazard Model 85 7 Bayesian Models in Example Applications 87 7.1 Inference of Cell Composition 87 7.1.1 The Expression Pattern Distributions (EPDs) 88 7.1.2 The Complete Model 89 7.1.3 Start Values 89 7.1.4 Resource Limits 90 7.2 Deconvolution of Expression Patterns 91 7.2.1 The Distribution of Expression Pattern Distribution 91 7.2.2 The Complete Model 92 7.2.3 SingleSampleDeconvolution 93 7.2.4 A Simplification 94 7.2.5 Start Values 94 8 Results of Example Applications 96 8.1 Inference of Cell Composition 96 8.1.1 Single Composition Output 96 8.1.2 ELBO Convergence in Variational Inference 97 8.1.3 Difficulty-Divergence 97 8.1.3.1 Implementing an Alternative Stick-Breaking 98 8.1.3.2 Using MoreGeneral Inference Methods 99 8.1.3.3 UsingBetterData 100 8.1.3.4 Restriction of Variance of Cell-Type-Specific EPDs 100 8.1.3.5 Doing Fewer Iterations 100 8.1.4 Difficulty-Bias 101 8.1.5 Comparison to Gold Standard 101 8.1.6 Comparison to Competitors 101 8.1.6.1 Submission-Aginome-XMU 105 8.1.6.2 Submission-Biogem 105 8.1.6.3 Submission-DA505 105 8.1.6.4 Submission-AboensisIV 105 8.1.6.5 Submission-mittenTDC19 106 8.1.6.6 Submission-CancerDecon 106 8.1.6.7 Submission-CCB 106 8.1.6.8 Submission-D3Team 106 8.1.6.9 Submission-ICTD 106 8.1.6.10 Submission-Patrick 107 8.1.6.11 Conclusion for the Competitor Review 107 8.1.7 Implementation 107 8.1.8 Conclusion 108 8.2 Deconvolution of Expression Patterns 108 8.2.1 Difficulty-Multimodality 109 8.2.1.1 Order of Kernels 109 8.2.1.2 Posterior EPD Complexity 110 8.2.1.3 Tumor Cell Content Estimate 110 8.2.2 Difficulty-Time 110 8.2.3 The Inference Process 111 8.2.3.1 ELBO Convergence in Variational Inference 111 8.2.4 Posterior of Tumor Cell Content 112 8.2.5 Posterior of Tissue Specific Expression 112 8.2.6 PosteriorHazardModel 113 8.2.7 Gene Marker Study with Deconvoluted Tumor Expression 115 8.2.8 Hazard Model Comparison Overview 116 8.2.9 Implementation 116 9 Discussion 117 9.1 Limitations 117 9.1.1 Simplifying Assumptions 117 9.1.2 Computation Resources 118 9.1.3 Limited Data and Suboptimal Format 118 9.1.4 ItIsJustConsistency 119 9.1.5 ADVI Uncertainty Estimation 119 9.2 Outlook 119 9.3 Conclusion 121 A Appendix 123 A.1 Optimalα 123 A.2 Digamma Function and Logarithm 123 A.3 Common Normalization 124 A.3.1 CPMNormalization 124 A.3.2 TPMNormalization 124 A.3.3 VSTNormalization 125 A.3.4 PCA After Different Normalizations 125 A.4 Mixture Prior Per Tissue Source 125 A.5 Data 125 A.6 Cell Type Characterization without Whitening 133 B Proofs 137 Bibliography 140

3相3元データとは，対象，変量，条件の3つの有限集合組によって表現されるデータの総称であり，マーケティングリサーチ，心理学，経済学などの様々な分野で観測されるデータである．本論文では，多変量解析手法の一つである正準共分散分析を3相3元データに拡張し，その適用例および既存手法との比較を行った． / Three-mode three-way data exist in various research areas, such as psychology and marketing research. We propose new dimensional reduction methods for three-mode three-way data based on canonical covariance analysis in this study. In addition, we include a simulation study and apply the proposed method to real data. / 博士(文化情報学) / Doctor of Culture and Information Science / 同志社大学 / Doshisha University

Descrevemos os processos de captura, criação e micromanipulação cirúrgica das moscas Chrysomya megacephala. Apresentamos os processos de geração de estímulo e registro da atividade dos dois neurônios H1 localizados na placa lobular de seu cérebro. Um primeiro resultado apresentado refere-se a acuidade de seu sistema visual. Desenvolvemos um procedimento para comparar sua taxa de disparos espontâneos com as respostas do neurônio H1 quando sujeito a estímulos de excitação e inibição. Mostramos que o sistema visual da mosca não está apenas adaptado a detectar grandes fluxos ópticos mas também, é capaz de detectar pequenas velocidades de aproximadamente 1, 5o.s-1 e de apenas 0,25o de amplitude. Estes valores mostram que a mosca é capaz de detectar deslocamentos angulares muito menores do que sua abertura omatidial, = 1 2o. Outro resultado apresentado é obtido ao estudarmos o processo de codificação-decodificação neural. Alguns sistemas sensoriais agem como um conversor analógico-digital, recebendo um estímulo S(t) e codificando-o em uma sequência de pulsos, spikes. O processo de decodificação da resposta neural consiste em receber este conjunto pulsos e gerar uma estimativa Se(t) do estmulo. Este processo requer a computação e subsequente inversão de funções de correlação de alta ordem. A dimensão das matrizes que representam estas funções pode se tornar proibitivamente grande. Apresentamos um eficiente método para reduzir estas funções de correlação. Esta aproximação tem baixo custo computacional, evita a inversão de grandes matrizes e nos da um excelente resultado para a reconstrução do estímulo. Testamos a qualidade de nossa reconstrução sobre estímulos de rotação e translação. A contribuição dos núcleos de segunda ordem para a reconstrução do estímulo é de apenas 8% da contribuição dos núcleos de primeira ordem. Entretanto, em instantes específicos, a adição destes núcleos pode representar uma contribuição de ate 100%. Finalmente, investigamos quais atributos do estímulo são codificados pelos neurônios H1. Nosso espaço de estímulos possui um conjunto da ordem de 2 × 1096 elementos. É impossível imaginar que o sistema formado pelos dois neurônios H1 seja capaz de codificar eficientemente esta enorme quantidade de elementos. É razoável considerar que este sistema seja ao menos capaz de codificar um atributo essencial do movimento, seu sentido - rotações horizontais para direita ou para esquerda. Desta forma, apresentamos dois estímulos distintos para a mosca, um no qual suas velocidades são retiradas de uma distribuição Gaussiana e outro que contem apenas o sentido deste movimento. Obtemos uma correlação da ordem de 80 - 90% entre as estimativas de ambos os estímulos, estimativas obtidas através do processo de reconstrução linear. Obtemos aproximadamente 85% de eficiência na predição do sentido deste movimento. Ao utilizarmos a Teoria da Informação, encontramos uma diferença de apenas 10% entre as taxas de informação transmitida sobre os estímulos Gaussiano e sua versão reduzida. Concluímos que a propriedade comum a estes dois estímulos, o sentido do movimento, é o atributo relevante a ser codificado pelos neurônios H1. / We describe the practices of capturing, creation, and microsurgery of the flies Chrysomya megacephala. We present the procedures of stimulus generation and recording of the activity of the two H1 neurons in the lobula plate of its brain. One first result presented is related to its visual system acuity. We developed a method to compare its spontaneous firing rate with the H1s responses to excitatory and inhibitory stimuli. We show that the flys visual system is not only adapted to detect large optic flows but is also capable to detect small velocities about 1, 5o.s-1 with just 0, 25o of amplitude. These values show that the fly is capable to detect angular displacements much smallers than its ommatidial aperture, = 1 2o. Another relevant result is attained studying the processes of neural encode-decode. Some sensorial systems act as an analog-to-digital conversor, these systems encode the input stimulus S(t) in a sequence of action potential, spikes. The decoding process of the neural response consists of capturing this set of spikes and to generate an estimate Se(t) of the stimulus. This process requires the computation and subsequent inversion of high order correlations functions. The dimension of the matrixes that represent these functions can become prohibitively large. We present an efficient method to reduce these correlation functions. This approximation has low computational cost, avoids large matrixes inversion and give to us an excellent result to the stimulus reconstruction. We tested the reconstruction quality of rotational and translational stimuli. The contribution of second order stimulus reconstruction kernels is just 8% of first order kernels contribution. However, in specific times, the addition of these kernels may represent a 100% contribution. Finally, we investigate which stimulus features are codified by the H1 neurons. The stimulus space has a set of about 2 × 1096 elements. It is impossible to imagine that the system formed by the two H1 neurons could be able to encode efficiently this amount of elements. It is reasonable to consider that this system is at least able to encode an essencial characteristic of movement, its direction horizontal rotations to the right or to the left. Therefore, we presente two different stimuli to the fly, one which have velocities taken from a Gaussian distribution and another which contains just the direction of this movement. We obtain about 80 - 90% correlation between the estimates of both stimuli, estimates obtained through linear reconstruction methods. We obtain about 85% of efficiency in the prediction of stimulus direction. We find just a 10% difference between the information rate transmitted about the Gaussian stimulus and its reduced version using Information Theory. We conclude that the common attribute of these stimuli, the direction of movement, is the relevant attribute to be codified by the H1 neurons.

Descrevemos os processos de captura, criação e micromanipulação cirúrgica das moscas Chrysomya megacephala. Apresentamos os processos de geração de estímulo e registro da atividade dos dois neurônios H1 localizados na placa lobular de seu cérebro. Um primeiro resultado apresentado refere-se a acuidade de seu sistema visual. Desenvolvemos um procedimento para comparar sua taxa de disparos espontâneos com as respostas do neurônio H1 quando sujeito a estímulos de excitação e inibição. Mostramos que o sistema visual da mosca não está apenas adaptado a detectar grandes fluxos ópticos mas também, é capaz de detectar pequenas velocidades de aproximadamente 1, 5o.s-1 e de apenas 0,25o de amplitude. Estes valores mostram que a mosca é capaz de detectar deslocamentos angulares muito menores do que sua abertura omatidial, = 1 2o. Outro resultado apresentado é obtido ao estudarmos o processo de codificação-decodificação neural. Alguns sistemas sensoriais agem como um conversor analógico-digital, recebendo um estímulo S(t) e codificando-o em uma sequência de pulsos, spikes. O processo de decodificação da resposta neural consiste em receber este conjunto pulsos e gerar uma estimativa Se(t) do estmulo. Este processo requer a computação e subsequente inversão de funções de correlação de alta ordem. A dimensão das matrizes que representam estas funções pode se tornar proibitivamente grande. Apresentamos um eficiente método para reduzir estas funções de correlação. Esta aproximação tem baixo custo computacional, evita a inversão de grandes matrizes e nos da um excelente resultado para a reconstrução do estímulo. Testamos a qualidade de nossa reconstrução sobre estímulos de rotação e translação. A contribuição dos núcleos de segunda ordem para a reconstrução do estímulo é de apenas 8% da contribuição dos núcleos de primeira ordem. Entretanto, em instantes específicos, a adição destes núcleos pode representar uma contribuição de ate 100%. Finalmente, investigamos quais atributos do estímulo são codificados pelos neurônios H1. Nosso espaço de estímulos possui um conjunto da ordem de 2 × 1096 elementos. É impossível imaginar que o sistema formado pelos dois neurônios H1 seja capaz de codificar eficientemente esta enorme quantidade de elementos. É razoável considerar que este sistema seja ao menos capaz de codificar um atributo essencial do movimento, seu sentido - rotações horizontais para direita ou para esquerda. Desta forma, apresentamos dois estímulos distintos para a mosca, um no qual suas velocidades são retiradas de uma distribuição Gaussiana e outro que contem apenas o sentido deste movimento. Obtemos uma correlação da ordem de 80 - 90% entre as estimativas de ambos os estímulos, estimativas obtidas através do processo de reconstrução linear. Obtemos aproximadamente 85% de eficiência na predição do sentido deste movimento. Ao utilizarmos a Teoria da Informação, encontramos uma diferença de apenas 10% entre as taxas de informação transmitida sobre os estímulos Gaussiano e sua versão reduzida. Concluímos que a propriedade comum a estes dois estímulos, o sentido do movimento, é o atributo relevante a ser codificado pelos neurônios H1. / We describe the practices of capturing, creation, and microsurgery of the flies Chrysomya megacephala. We present the procedures of stimulus generation and recording of the activity of the two H1 neurons in the lobula plate of its brain. One first result presented is related to its visual system acuity. We developed a method to compare its spontaneous firing rate with the H1s responses to excitatory and inhibitory stimuli. We show that the flys visual system is not only adapted to detect large optic flows but is also capable to detect small velocities about 1, 5o.s-1 with just 0, 25o of amplitude. These values show that the fly is capable to detect angular displacements much smallers than its ommatidial aperture, = 1 2o. Another relevant result is attained studying the processes of neural encode-decode. Some sensorial systems act as an analog-to-digital conversor, these systems encode the input stimulus S(t) in a sequence of action potential, spikes. The decoding process of the neural response consists of capturing this set of spikes and to generate an estimate Se(t) of the stimulus. This process requires the computation and subsequent inversion of high order correlations functions. The dimension of the matrixes that represent these functions can become prohibitively large. We present an efficient method to reduce these correlation functions. This approximation has low computational cost, avoids large matrixes inversion and give to us an excellent result to the stimulus reconstruction. We tested the reconstruction quality of rotational and translational stimuli. The contribution of second order stimulus reconstruction kernels is just 8% of first order kernels contribution. However, in specific times, the addition of these kernels may represent a 100% contribution. Finally, we investigate which stimulus features are codified by the H1 neurons. The stimulus space has a set of about 2 × 1096 elements. It is impossible to imagine that the system formed by the two H1 neurons could be able to encode efficiently this amount of elements. It is reasonable to consider that this system is at least able to encode an essencial characteristic of movement, its direction horizontal rotations to the right or to the left. Therefore, we presente two different stimuli to the fly, one which have velocities taken from a Gaussian distribution and another which contains just the direction of this movement. We obtain about 80 - 90% correlation between the estimates of both stimuli, estimates obtained through linear reconstruction methods. We obtain about 85% of efficiency in the prediction of stimulus direction. We find just a 10% difference between the information rate transmitted about the Gaussian stimulus and its reduced version using Information Theory. We conclude that the common attribute of these stimuli, the direction of movement, is the relevant attribute to be codified by the H1 neurons.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-08-23T18:04:55Z No. of bitstreams: 1 EduardoCarvalho.pdf: 588274 bytes, checksum: c6f59c7f025b5de8d00feac1696b6979 (MD5) / Made available in DSpace on 2017-08-23T18:04:55Z (GMT). No. of bitstreams: 1 EduardoCarvalho.pdf: 588274 bytes, checksum: c6f59c7f025b5de8d00feac1696b6979 (MD5) Previous issue date: 2011-07-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The CPT-even abelian gauge sector of the Standard Model Extension is represented by the Maxwell term supplemented by KF )µνρσ FµνFρσ, where the Lorentz-violating background tensor, (KF )µνρσ, possesses the symmetries of the Riemann tensorand a double null trace. In the present work, it is examined the planar version of this theory, obtained by means of a dimensional reduction procedure to (1 + 2) dimensions. The resulting planar electrodynamics is composed of a gauge sector containing six Lorentz-violating coe¢ cients, a scalar …eld endowed with a noncanonical kinetic term, and a coupling term that links the scalar and gauge sectors. The parity of the components of the Lorentz violating tensors is analyzed, following the de…nition of the parity operator in (1 +2) dimensions. The equations of motion of the theory are also found, where the electromagnetic …eld appears coupled to scalar …eld. This coupling however appears only as a second order e¤ect on the violation coe¢ cients and thus it is neglected. The energy-momentum tensor of the theory is calculated, revealing contributions of scalar, gauge and coupling sectors. From this tensor it is found a positive energy density de…ned for small violation parameters. The wave equations for the …elds E and B and the potential A0 and A are written and solved in the steady state by the method of Green. It is observed that the Lorentz-violating parameters do not alter the asymptotic behavior of the …elds but induce an angular dependence not observed in the Maxwell planar theory. It is also observed that electrical charges generate static magnetic …eld, as well as stationary currents generate electric …eld, a property already present in the original theory in (1 +3) dimensions. The dispersion relation also is determined, revealing that the six parameters related to the pure electromagnetic sector do not yield birefringence at …rst order. In this model, the birefringence may appear only as a second order efect associated with the coupling tensor linking the gauge and scalar sectors. / O setor de gauge abeliano CPT-Par do Modelo Padrão Estendido é representado pelo termo de Maxwell suplementado por (KF )µνρσ FµνFρσ, onde o tensor de campo de fundo violador de Lorentz, (KF )µνρσ, possui as simetrias do tensor de Riemann e um duplo traço nulo. No presente trabalho é examinada a versão planar dessa teoria, obtida por meio do procedimento de redução dimensional para (1+2) dimensões. A eletrodinâmica planar resultante é composta de um setor de gauge contendo seis coe…ficientes de violação de Lorentz, um campo escalar regido por um termo cinético não canônico, e um termo de acoplamento que interliga os dois setores. A paridades das componentes dos tensores violadores de Lorentz é analisada. Também são encontradas as equações de movimento da teoria, onde o campo eletromagnético aparece acoplado ao campo escalar. Este acoplamento, no entanto, aparece apenas como um efeito de segunda ordem nas equações de movimento e por isso é descartado. O tensor de energia-momento da teoria é calculado, apresentando contribuições tanto dos setores escalar e de gauge quanto do de acoplamento. A partir deste tensor é encontrada uma densidade de energia positiva de…nida apenas para pequenas parâmetros de violação. As equações de onda para, os campos E e B e potenciais A0 e A, são escritas e resolvidas no regime estacionário, via o método de Green. Observa-se que os parâmetros de violação de Lorentz não alteram o comportamento assimptótico dos campos, mas induzem uma dependência angular não observada na teoria planar de Maxwell. É também observado que cargas estáticas geram campo magnético, assim como correntes estacionárias geram campo elétrico, uma propriedade já presente na teoria original em (1+3) dimensões. A relação de dispersão também é determinada, revelando que os seis parâmetros relacionados ao setor eletromagnético puro não produzem birrefringência. Neste modelo, a birrefringência pode aparecer apenas como um efeito de segunda ordem associado ao tensor de acoplamento que liga os campos escalar e de gauge.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-08-23T18:24:30Z No. of bitstreams: 1 RoemirMoreira.pdf: 689688 bytes, checksum: 82f6a2259d4db9b3772731a4618fdc96 (MD5) / Made available in DSpace on 2017-08-23T18:24:30Z (GMT). No. of bitstreams: 1 RoemirMoreira.pdf: 689688 bytes, checksum: 82f6a2259d4db9b3772731a4618fdc96 (MD5) Previous issue date: 2011-09-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The gauge sector of the Standard Model Extended (MPE) has been investigated in many respects in recent years, discussing the effects of Lorentz symmetry violation in physical systems and the limitations on the magnitude of the parameters of violation. This work revisited some planar theories derived from the dimensional reduction of the gauge sector of the MPE, and perform an original contribution: the dimensional reduction of the CPT-even and nonbirefringent gauge sector of the MPE, composed of nine components. The resulting planar theory includes a gauge sector and scalar sector (which has an nonsual kinetic term), coupled together by a 3-vector Cα Lorentz violation. Both sectors, gauge and scale, are affected by the six components of a symmetric tensor violates Lorentz, kµρ. The energy-momentum tensor is explicitly calculated, revealing that the energy of the gauge and scalar sectors is stable for small values of the parameters of violation. The equations of motion for the electric and magnetic elds, as well as the potentials, are written and analyzed in the steady state. Then employ the method of Green to get the stationary solutions of classical electrodynamics to rst order in the parameters of violation. It is observed that the coe cients of Lorentz violation does not alter the asymptotic behavior of the elds, but does not induce an angular dependence observed in the planar theory of Maxwell. The dispersion relation is exactly computed and is compatible with a theory does not birefringent, and demonstrating that the theory is stable, but in general, not causal. Finally, we calculate the Feynman propagator for the gauge elds and scalar theory of planar, accurately, using a set of 11 projectors that form a closed algebra. We use the expression of the Feynman propagator to analyze the consistency of the theory regarding its stability, causality and unitarity. / O setor de gauge do Modelo Padrão Estendido (MPE) tem sido investigado em muitos aspectos nos últimos anos, discutindo os efeitos da violação da simetria de Lorentz em sistemas físicos e as limitações da magnitude dos parâmetros de violação. Neste trabalho, rediscutimos algumas teorias planares obtidas a partir da redução dimensional do setor de gauge do MPE, e realizamos uma contribuição original: a redução dimensional do setor de gauge CPT-par e não-birrefringente do MPE, composto por nove componentes. A resultante teoria planar abarca um setor de gauge e um setor escalar (dotado de um termo cinético não usual), acoplados entre si por um 3-vetor Cα de violação de Lorentz (LV). Ambos os setores, de gauge e escalar, são afetados pelas seis componentes de um tensor simétrico violador de Lorentz, kµρ. O tensor de energia-momento É explicitamente calculado, revelando que a energia dos setores de gauge e escalar são estáveis para pequenos valores dos parâmetros de violação. As equações de movimento para os campos elétrico e magnético, assim como para os potenciais, são escritas e analisadas no regime estacionário. Empregamos então o método de Green para obter as soluções clássicas estacionárias desta eletrodinâmica em primeira ordem nos parâmetros de violação. É observado que os coefi cientes de violação de Lorentz não alteram o comportamento assintótico dos campos, mas induzem uma dependência angular não observada na teoria planar de Maxwell. A relação de dispersão é exatamente computada, sendo compatível com uma teoria não birrefringente, e demonstrando que a teoria é estável, mas, em geral, não causal. Por fim, calculamos o propagador de Feynman para os campos de gauge e escalar desta teoria planar, de forma exata, usando um conjunto de 11 projetores que formam uma álgebra fechada. Usamos a expressão do propagador de Feynman para analisar a consistência da teoria no que concerne a sua estabilidade, causalidade e unitariedade.