The direct sum decomposition of tensor products for SU(3) has many applications in physics, and the problem has been studied extensively. This has resulted in many decomposition methods, each with its advantages and disadvantages. The description given here is geometric in nature and it describes both the constituents of the direct sum and their multiplicities. In addition to providing decompositions of specific tensor products, this approach is very well suited to studying tensor products as the parameters vary, and drawing general conclusions. After a description and proof of the method, several applications are discussed and proved. The decompositions are also studied further for the special cases of tensor products of an irreducible representation with itself or with its conjugate. In particular, questions regarding multiplicities are considered. As an extension of this diagrammatic method, the repeated tensor product of N copies of the fundamental representation is studied, and a method for its decomposition is provided. Again, questions regarding multiplicities are considered.

In der vorliegenden Arbeit wird der Hypothalamus, eine kleine, aber bedeutsame Struktur des Zwischenhirns untersucht. Er spielt unter anderem eine Rolle bei der Regulation des Schlaf-Wach-Rhythmus, des Sexualverhaltens, der Stimmungslage, autonomer und Stoffwechsel-Funktionen. Veränderungen einzelner oder mehrerer spezifischer Kerngruppen sind bei neuropsychiatrischen bzw. -endokrinologischen Erkrankungen, wie Narkolepsie, Schizophrenie, affektiver Störung, Demenz, Borderline-Persönlichkeitsstörung, Pädophilie oder Adipositas zu beobachten. Die Substrukturierung und Darstellung der einzelnen Kerngruppen gelang bisher nur in Postmortem-Studien. Im Rahmen dieser Studie konnte mit Hilfe der Diffusions-Tensor-Bildgebung erstmals eine in-vivo Substrukturierung des Hypothalamus konsistent bei zehn gesunden Probanden vorgenommen werden. Dabei wurden nach einem Algorithmus zunächst die Segmentierung und anschließend die Parzellierung durchgeführt, woraus sich drei konsistente Cluster ergaben. Der topografische Vergleich der erhaltenen Cluster mit Postmortem-Studien der Literatur ergab vergleichbare und anatomisch plausible Korrelate. Mit der von uns entwickelten Methode könnten anhand einer größeren Patientengruppe pathophysiologische Zusammenhänge neuropsychiatrischer und –endokrinologischer Störungen genauer eruiert werden und zu einem besseren Verständnis des Krankheitsverlaufs und der Therapie beitragen.

The direct sum decomposition of tensor products for SU(3) has many applications in physics, and the problem has been studied extensively. This has resulted in many decomposition methods, each with its advantages and disadvantages. The description given here is geometric in nature and it describes both the constituents of the direct sum and their multiplicities. In addition to providing decompositions of specific tensor products, this approach is very well suited to studying tensor products as the parameters vary, and drawing general conclusions. After a description and proof of the method, several applications are discussed and proved. The decompositions are also studied further for the special cases of tensor products of an irreducible representation with itself or with its conjugate. In particular, questions regarding multiplicities are considered. As an extension of this diagrammatic method, the repeated tensor product of N copies of the fundamental representation is studied, and a method for its decomposition is provided. Again, questions regarding multiplicities are considered.

Esclerose Múltipla (MS) é uma doença neurodegenerativa que tem ganhado grande atenção nas últimas décadas, sendo o diagnóstico por imagens de ressonância magnética (MRI) um grande aliado para a avaliação da doença.Porém, um dos principais desafios é garantir uma maior sensibilidade e especificidade para detecção de diferentes lesões no sistema nervoso central (CNS) e assim classificar as diferentes variantes da MS, auxiliando na tomada de decisão para o tratamento farmacológico. Nas últimas décadas, a técnica de imagens ponderadas por difusão (DWI), em especial a técnica de imagem por tensor de difusão (DTI), têm sido evidenciada com grande potencial para o estudo da MS, apresentando uma melhora significativa para a detecção de lesões sutis, ainda em estágios iniciais da MS. Desta forma, as técnicas de processamento de imagens estão em constante aprimoramento para que sejam adaptados às novas modalidades de aquisição de imagens. Neste estudo focamos o desenvolvimento de uma técnica de processamento digital de imagens multimodais a fim de proporcionar uma solução viável para a rotina de diagnóstico por imagem em MS. Um conjunto de 25 pacientes de uma variante de MS foi selecionado aleatoriamente do banco de imagens do HCFMRP. Três modalidades de imagens foram coletadas para a avaliação da segmentação automatica (T1, T2-FLAIR e DTI), assim como a segmentação manual do especialista para cada paciente. Três métodos de segmentação multimodal automática de lesões foram analisados (Bayesiano, Frequentista e Agrupamento) afim de analisar a sensibilidade e especificidade de detecção de lesões na substância branca aparentemente normal (NAWM). Os resultados sugerem que o método de segmentação Bayesiano apresenta maior robustes e precisão na definição tanto de lesões visivelmente contrastantes em T1 e T2-FLAIR (i.e. lesões hipo e hiperintensas) assim como lesões da NAWM evidentes nos mapas quantitativos de DTI (FA e ADC). O erro associado à técninca automática de segmentação ficou em torno de 1.51 +- 0.51 % do volume total de lesões marcadas pelo especialista. Concluímos que o uso de ferramentas multimodais de segmentação de imagens MRI alcançou patamares razoáveis de detecção de lesões de MS, tornando assim uma ferramenta computacional hábil para uso no diagnóstico clínico. / Multiple sclerosis (MS) is a neurodegenerative disease that has gained great attention in the last decades, which magnetic resonance imaging (MRI) have shown as an important tool for the disease evaluation. However, one of the main challenges is guaranteeing greater lesion detection sensitivity and specificity in the whole central nervous system (CNS) and thus classify the different variants of MS, which aids in decision making for pharmacological treatment. In the last decades, the diffusion-weighted imaging (DWI) technique, especially the diffusion tensor imaging approach (DTI), has been evidenced with great potential for the study of MS, presenting a significant improvement for the detection of lesions even in early stages of MS. Hence, the techniques of image processing are constantly improving in order to be adapted on a multimodal image evaluation. In this study, the development of a multimodal digital image processing technique to provide a viable solution to the MS imaging routine was focused. A set of 25 patients from a MS variant was randomly selected from the HCFMRP imaging database. Three MR imaging modalities were collected for the evaluation of our automatic segmentation (T1, T2-FLAIR and DTI), as well as manual segmentation of the specialist for each patient. Three methods of automatic multimodal segmentation of MS lesions were analyzed (Bayesian, Frequentist and Clustering) in order to analyze the sensitivity and specificity of lesion detection in the apparently normal white matter (NAWM). The results suggest that the Bayesian segmentation method presented greater robustness and precision in the definition of visibly contrasting lesions in T1 and T2-FLAIR (i.e. hypo and hyperintense lesions) as well as NAWM lesions that are evident in quantitative DTI (FA and ADC). The error associated with the automatic segmentation technique was around 1.51 +- 0.51 % of the total lesion volume being evaluated by the a specialist. We conclude that the use of multimodal MRI images can be used in an automatic segmentation tools, reaching reasonable levels of MS lesion detection, thus making it a useful tool for clinical diagnosis.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2018-06-29T18:43:00Z No. of bitstreams: 2 Tese - Marcos Tulio Alves de Carvalho - 2018.pdf: 2579945 bytes, checksum: 29a08a3db199f6061cf6020d90ce9213 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-07-03T15:18:43Z (GMT) No. of bitstreams: 2 Tese - Marcos Tulio Alves de Carvalho - 2018.pdf: 2579945 bytes, checksum: 29a08a3db199f6061cf6020d90ce9213 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-07-03T15:18:43Z (GMT). No. of bitstreams: 2 Tese - Marcos Tulio Alves de Carvalho - 2018.pdf: 2579945 bytes, checksum: 29a08a3db199f6061cf6020d90ce9213 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-06-12 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / In this work we study two problems: the first one involving the prescribed Schouten tensor and the second one the prescribed curvature operator. The first problem was inspired by the works Deturck and Yang, [6], which consist of: Given a tensor T of order 2 in the pseudo-Euclidean space ( ,g), n ≥ 3, with coordinates x = ( ), and metric g, where , = ±1, find a metric as = g, such that the tensor of Schouten be T. The second problem is the problem of the prescribed curvature tensor consist of: Let Euclidean space ( ;g), n ≥ 3, with coordinates x = ( ), is , the R a tensor of order 4 of the form , where T = , with differentiable functions.We want to find a metric = g, such that = , where is the tensor curvature of the metric . Considering that the solutions are invariant by translation and rotation, we find necessary and sufficient conditions for both problems to have solution. / Neste trabalho estudamos dois problemas: o primeiro envolvendo o tensor de Schouten prescrito e o segundo o tensor curvatura prescrito. O primeiro problema foi inspirado no trabalho de Deturck e Yang, [6], que consiste em: Dado um tensor T de ordem 2 no espaço pseudo-Euclidiano ( ;g), n ≥ 3, com coordenadas x = ( ), e métrica g, onde , = ±1, encontrar uma métrica conforme = g, tal que o tensor de Schouten da métrica seja T. O segundo problema é o problema do tensor curvatura prescrito que consiste em: Seja o espaço Euclidiano ( ;g), n ≥ 3, com coordenadas x = ( ), e , e R um tensor de ordem 4 da forma onde T = , com funções diferenciáveis. Queremos encontrar uma métrica = g, tal que = , onde é o tensor curvatura da métrica . Considerando que as soluções sejam invariantes por translação e rotação, encontramos condições necessárias e suficientes para que ambos os problemas tenham solução.

Grothendieck published an extraordinary paper entitled ”Resume de la theorie metrique des pro¬duits tensoriels topologiques” in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck Inequality. Following Kirivine, in this article, we give the proof of Grothendieck Inequality. We refor¬mulate it in different forms. We also investigate the famous Grothendieck constant KG. The Grothendieck constant was achieved by taking supremum over a special class of matrices. But our attempt will be to investigate it, considering a smaller class of matrices, namely only the positive definite matrices in this class. Actually we want to use it to get a counterexample of Matsaev’s conjecture, which was proved to be right by Von Neumann in some specific cases. In chapter 1, we shall state and prove the Grothendieck Inequality. In chapter 2, we shall introduce tensor product of vector spaces and different tensor norms. In chapter 3, we shall formulate Grothendieck Inequality in different forms and use the notion of tensor norms for its equivalent formation .In the last chapteri.ein chapter4we shall investigate on the Grothendieck constant.

Orientadores: Anelyssa Cysne Frota D'Abreu, Fernando Cendes / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Ciências Médicas / Made available in DSpace on 2018-08-27T01:17:26Z (GMT). No. of bitstreams: 1 Pinheiro_GiordannaLuizaSelingardi_M.pdf: 1372164 bytes, checksum: e02f4b5ec43afe35e676ab843e98cda0 (MD5) Previous issue date: 2015 / Resumo: A distonia é uma síndrome caracterizada por espasmos e contrações musculares, prolongados e involuntários, causando movimentos de torção e posturas anormais, frequentemente dolorosos. A distonia craniocervical (DCC) ocorre quando há contração das musculaturas da cabeça, face e pescoço; podendo ser focal ou segmentar. Estas são as distonias mais frequentes em indivíduos adultos. O tratamento com a toxina botulínica é o mais indicado para a DCC, mas seu efeito é temporário. Disfunção ou lesão dos gânglios da base sempre foi considerado o componente central na sua fisiopatologia, porém estudos mais recentes mostram o envolvimento de diversas outras regiões cerebrais como o córtex sensorio-motor e cerebelo. O presente estudo avaliou as alterações estruturais da substância branca em 40 pacientes comparando-os a 40 controles saudáveis. Secundariamente os mesmos pacientes foram divididos em 4 grupos: blefarospasmo, blefarospasmo + oromandibular, blefarospasmo + oromandibular + cervical e cervical. Todos passaram por uma avaliação clínica detalhada, envolvendo revisão do histórico, exame neurológico e exame de ressonância magnética. As análises da técnica de imagem por tensor de difusão (DTI) foram feitas através do software Trato baseado em estatística espacial (TBSS), onde foram avaliados anisotropia fracional (FA) e difusividade média (MD). Também foram realizadas técnicas baseada em região de interesse (ROI) e tractografia nesses pacientes. Não encontramos diferenças significativas no FA e MD nas análises realizadas, sugerindo que a microestrutura da substância branca dos pacientes com DCC encontra-se preservada. Futuros estudos utilizando análises funcionais podem desvendar um acometimento funcional dos circuitos cerebrais, sem que haja necessariamente acometimento estrutural da substância branca / Abstract: Dystonia is a syndrome characterized by involuntary muscle contractions, causing twisting movements and abnormal postures, which are often painful. Craniocervical dystonia (CCD) involves the contraction of the head and neck muscles. It is the most frequent dystonia in adults, and it can be focal or segmental. Botulinum toxin is the best treatment for CCD, although the effect is temporary. Classically considered secondary to a dysfunction or lesion in the basal ganglia circuit, recent studies have shown the involvement of the sensorimotor areas and the cerebellum. In the present study, we evaluated the structural brain changes in 40 patients comparing them to 40 healthy controls. Secondarily, we divided the patients into 4 groups based on dystonia localization: blepharospasm, blepharospasm + oromandibular, blepharospasm + oromandibular + cervical and cervical. Patients and controls underwent the same MRI acquisition protocol in a 3T Philips Achieva MRI scanner. All patients were assessed by an experienced neurologist specialized in Movement Disorders. We performed DTI analyzes with Tract-Based Spatial Statistics (TBSS) and we evaluated the fractional anisotropy and the mean diffusivity. We performed two confirmatory analyses using a ROI based approach and tractography. There were no microstructural alterations neither in the primary nor the secondary analysis. We did not find microstructure changes in the white matter of subjects with craniocervical dystonia. Further studies should evaluate the presence of functional and connectivity abnormalities in these subjects / Mestrado / Fisiopatologia Médica / Mestra em Ciências

As the technology underlying modern electronics advances, it is unlikely that previous rates of power use and computational speed improvement can be maintained. Devices using the spin of an electron or hole, "spintronic" systems, can begin to address these problems, creating new devices which can be used as a continuation and augmentation of existing electronic systems. In addition, spintronic devices could make special use of coherent quantum states, making it feasible to address certain problems which are computationally intractable using classical electronic components. Unlike higher-dimensional nanostructures such as quantum wires and wells, quantum dots allow a single electron or hole to be confined to the dot. Through the spin-orbit effect, the electron and hole g-tensor can be influenced by quantum dot shape and applied electric fields, leading to the possibility of gating a single quantum dot and using a single electron or hole spin for quantum information storage or manipulation. In this thesis, the spin of electrons and holes in isolated semiconductor quantum dots are investigated in the presence of electric and magnetic fields using realspace numerical 8-band strain-dependent k · p theory. The calculations of electron and hole g-tensors are then used to predict excitonic g-tensors as a function of electric field. These excitonic g-factors are then compared against existing experimental work, and show that in-plane excitonic g-factor dependence on electric field is dominated by the hole g-factor. The dependence of the electron and hole g-tensors on the applied electric field are then used to propose a class of novel quantum dot devices which manipulate the electron or hole spins in either a resonant or a non-resonant mode. Because of the highly parabolic dependence of some components of the hole g-tensor on the applied electric field, a shift in the Larmor frequency and an additional resonance are predicted, with additional shifts and resonances occurring for higher-order dependencies. Spin manipulation times down to 3.9ns for electrons and 180ps for holes are reported using these methods.

The semester thesis describes the basic principles of MRI, methods for measuring diffusion coefficients and creating DWI and DTI images. As a result a practical implementation of program was implemented in Matlab, based on theoretical knowledge of the problem.

The dielectric tensor of Ga2O3 in the monoclinic (β) phasewas determined by generalized spectroscopic ellipsometry in a wide spectral range from 0.5 eV to 8.5 eV as well as by density functional theory calculations combined with many-body perturbation theory including quasiparticle and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are assigned to the corresponding valence bands. It is shown that the off-diagonal element of the dielectric tensor reaches values up to |εxz| ≈ 0.30 and cannot be neglected. Even in the transparent spectral range where it is quite small (|εxz| < 0.02) it causes a rotation of the dielectric axes around the symmetry axis of up to 20◦.