Quantum chemistry is plagued by the presence of high-rank quantities, stemming from the N-body nature of the electronic Schrödinger equation. These high-rank quantities present a significant mathematical and computational barrier to the computation of chemical observables, and also drastically complicate the pedagogical understanding of important interactions between particles in a molecular system. The application of physically-motivated rank reduction approaches can help address these to problems. This thesis details recent efforts to apply rank reduction techniques in both of these arenas. With regards to computational tractability, the representation of the 1/r Coulomb repulsion between electrons is a critical stage in the solution of the electronic Schrödinger equation. Typically, this interaction is encapsulated via the order-4 electron repulsion integral (ERI) tensor, which is a major bottleneck in terms of generation, manipulation, and storage. Many rank reduction techniques for the ERI tensor have been proposed to ameliorate this bottleneck, most notably including the order-3 density fitting (DF) and pseudospectral (PS) representations. Here we detail a new and uniquely powerful factorization - tensor hypercontraction (THC). THC decomposes the ERI tensor as a product of five order-2 matrices (the first wholly order-2 compression proposed for the ERI) and offers great flexibility for low-scaling algorithms for the manipulations of the ERI tensor underlying electronic structure theory. THC is shown to be physically-motivated, markedly accurate, and uniquely efficient for some of the most difficult operations encountered in modern quantum chemistry. On the front of chemical understanding of electronic structure theory, we present our recent work in developing robust two-body partitions for ab initio computations of intermolecular interactions. Noncovalent interactions are the critical and delicate forces which govern such important processes as drug-protein docking, enzyme function, crystal packing, and zeolite adsorption. These forces arise as weak residual interactions leftover after the binding of electrons and nuclei into molecule, and, as such, are extremely difficult to accurately quantify or systematically understand. Symmetry-adapted perturbation theory (SAPT) provides an excellent approach to rigorously compute the interaction energy in terms of the physically-motivated components of electrostatics, exchange, induction, and dispersion. For small intermolecular dimers, this breakdown provides great insight into the nature of noncovalent interactions. However, SAPT abstracts away considerable details about the N-body interactions between particles on the two monomers which give rise to the interaction energy components. In the work presented herein, we step back slightly and extract an effective 2-body interaction for each of the N-body SAPT terms, rather than immediately tracing all the way down to the order-0 interaction energy. This effective order-2 representation of the order-N SAPT interaction allows for the robust assignment of interaction energy contributions to pairs of atoms or functional groups (the A-SAPT or F-SAPT partitions), allowing one to discuss the interaction in terms of atom- or functional-group-pairwise interactions. These A-SAPT and F-SAPT partitions can provide deep insight into the origins of complicated noncovalent interactions, e.g., by clearly shedding light on the long-contested question of the nature of the substituent effect in substituted sandwich benzene dimers.

How to properly aggregate indirect information is more and more important. In this dissertation, we will present two aspects of the issue: indirect comparison of treatment effects and aggregation of ordered-based rank data. / Statistics

Purpose: Explain how consumer engagement affects consumers motivation to rank and review on price-comparison sites. Hypotheses raised:H1 - There is a positive relationship between affective consumer engagement and theconsumer's motivation to rank products online.H2 - There is a positive relationship between affective consumer engagement and theconsumer's motivation to review products online.H3 - There is a positive relationship between cognitive consumer engagement and theconsumer's motivation to rank products online.H4 - There is a positive relationship between cognitive consumer engagement and theconsumer's motivation to review products online.H5 - There is a positive relationship between behavioral consumer engagement and theconsumer's motivation to rank products online.H6 - There is a positive relationship between behavioral consumer engagement and theconsumer's motivation to review products online. Methodology: Cross-sectional social survey design with a self-completion questionnaire. Conclusion: Based on this research all hypothesis tied to each individual dimension has been accepted, thus it can be concluded that consumer engagement does have a positive relationship with consumer’s motivation to engage online.

This dissertation investigates the problem of estimating a kernel over a large graph based on a sample of noisy observations of linear measurements of the kernel. We are interested in solving this estimation problem in the case when the sample size is much smaller than the ambient dimension of the kernel. As is typical in high-dimensional statistics, we are able to design a suitable estimator based on a small number of samples only when the target kernel belongs to a subset of restricted complexity. In our study, we restrict the complexity by considering scenarios where the target kernel is both low-rank and smooth over a graph. Using standard tools of non-parametric estimation, we derive a minimax lower bound on the least squares error in terms of the rank and the degree of smoothness of the target kernel. To prove the optimality of our lower-bound, we proceed to develop upper bounds on the error for a least-square estimator based on a non-convex penalty. The proof of these upper bounds depends on bounds for estimators over uniformly bounded function classes in terms of Rademacher complexities. We also propose a computationally tractable estimator based on least-squares with convex penalty. We derive an upper bound for the computationally tractable estimator in terms of a coherence function introduced in this work. Finally, we present some scenarios wherein this upper bound achieves a near-optimal rate. The motivations for studying such problems come from various real-world applications like recommender systems and social network analysis.

This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.

SOKAL, B. Semi-blind receivers for multi-relaying mimo systems using rank-one tensor factorizations. 2017. 85 f. Dissertação (Mestrado em Engenharia de Teleinformática)-Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Renato Vasconcelos (ppgeti@ufc.br) on 2017-09-15T20:38:29Z No. of bitstreams: 1 2017_dis_bsokal.pdf: 1689224 bytes, checksum: f0e2e9424de721f23bf0629ba55330c1 (MD5) / Rejected by Marlene Sousa (mmarlene@ufc.br), reason: Prezado Bruno: Existe uma orientação para que normalizemos as dissertações e teses da UFC, em suas paginas pré-textuais e lista de referencias, pelas regras da ABNT. Por esse motivo, sugerimos consultar o modelo de template, para ajudá-lo nesta tarefa, disponível em: http://www.biblioteca.ufc.br/educacao-de-usuarios/templates/ Vamos agora as correções sempre de acordo com o template: 1. As informações da capa, folha de rosto (que segue a capa) e ficha catalográfica devem ser em língua portuguesa, mesmo que sua dissertação esteja em língua inglesa. A partir da folha de aprovação, devem ser em língua inglesa. 2. Exemplificando a capa, as informações que devem aparecer são pela ordem (Toadas em Maiúsculo e negrito): Nome da universidade, do centro, do departamento e nome do programa; Nome do aluno; Título; Cidade e data. 2. A folha de rosto também tem informações que não são necessárias. Consulte o template para ver uso de maiúsculas, negrito e ordem de apresentação das informações. 3. A ficha catalográfica deve vir antes da folha de aprovação e não depois desta. 4. A folha de aprovação não deve ter as informações do quadro no alto da folha, nem deve ser em negrito. Veja modelo no template. 5. De acordo com a ABNT mesmo escrita em outro idioma, primeiro coloca-se o resumo na língua portuguesa e depois o Abstract. As palavras RESUMO e ABSTRCT vem ser em caixa alta, negrito e no centro da folha. Não devem iniciar com paragrafo. Essa folhas são contadas mas não numeradas. Só a partir da introdução é que são numeradas. 6. Veja no template a ordem das folhas a partir dos agradecimentos e como devem ser apresentadas. 7. Na lista de figuras mantenha o mesmo espaço entre as linhas. 8. O sumário não deve conter as informações anteriores a INTRODUÇÃO, deve ser em negrito e sem recuo de paragrafo. Observe o uso de Caixa alta, itálico nas seções. Após a conclusão devem vir os APÊNDICES e as REFERENCIAS. 9. Na lista de referencias, pela ABNT, deve-se iniciar pelo sobrenome do autor, seguido do prenome. Elaboramos ferramentas para ajuda-lo a gerar as referencias e gerenciadores bibliográficos disponivel em: http://www.biblioteca.ufc.br/ferramentas-de-pesquisa/ Em artigos de revistas usa-se a seguinte nomenclatura para volume, numero e páginas: v. , n. , p. Não se destacam subtítulos e nos artigos de revistas se destaca-se apenas o ´nome da revista. Att. Marlene Rocha 3366-9620 mmarlene@ufc.br on 2017-09-18T11:38:11Z (GMT) / Submitted by Renato Vasconcelos (ppgeti@ufc.br) on 2017-09-20T14:04:25Z No. of bitstreams: 1 2017_dis_bsokal.pdf: 1481998 bytes, checksum: bdf4f504f50622f6b0e2084361272481 (MD5) / Approved for entry into archive by Marlene Sousa (mmarlene@ufc.br) on 2017-09-21T17:44:15Z (GMT) No. of bitstreams: 1 2017_dis_bsokal.pdf: 1481998 bytes, checksum: bdf4f504f50622f6b0e2084361272481 (MD5) / Made available in DSpace on 2017-09-21T17:44:15Z (GMT). No. of bitstreams: 1 2017_dis_bsokal.pdf: 1481998 bytes, checksum: bdf4f504f50622f6b0e2084361272481 (MD5) Previous issue date: 2017-07-27 / Cooperative communications have shown to be an alternative to combat the impairments of signal propagation in wireless communications, such as path loss and shadowing, creating a virtual array of antennas for the source. In this work, we start with a two-hop MIMO system using a a single relay. By adding a space-time filtering step at the receiver, we propose a rank-one tensor factorization model for the resulting signal. Exploiting this model, two semi-blind receivers for joint symbol and channel estimation are derived: i) an iterative receiver based on the trilinear alternating least squares (Tri-ALS) algorithm and ii) a closed-form receiver based on the truncated higher order SVD (T-HOSVD). For this system, we also propose a space-time coding tensor having a PARAFAC decomposition structure, which gives more flexibility to system design, while allowing an orthogonal coding. In the second part of this work, we present an extension of the rank-one factorization approach to a multi-relaying scenario and a closed-form semi-blind receiver based on coupled SVDs (C-SVD) is derived. The C-SVD receiver efficiently combines all the available cooperative links to enhance channel and symbol estimation performance, while enjoying a parallel implementation. / Comunicações cooperativas têm mostrado ser uma alternativa para combater os efeitos de propagação do sinal em comunicações sem-fio, como, por exemplo, a perda por percurso e sombreamento, criando um array virtual de antenas para a fonte transmissora. Neste trabalho, toma-se como ponto de partida um modelo de sistema MIMO de dois saltos com um único relay. Adicionando um estágio de filtragem no receptor, é proposta uma fatoração de rank-um para o sinal resultante. A partir deste modelo, dois receptores semi-cegos para estimação conjunta de símbolo e canal são propostos: i) um receptor iterativo baseado no algoritmo trilinear de mínimos quadrados alternados (Tri-ALS) e ii) um receptor de solução fechada baseado na SVD de ordem superior truncada (T-HOSVD). Para este sistema, é também proposto um tensor de codificação espacial-temporal com uma estrutura PARAFAC, o que permite maior flexibilidade de design do sistema, além de uma codificação ortogonal. Na segunda parte deste trabalho, é apresentada uma extensão da fatoração de rank-um para o cenário multi-relay e um receptor semi-cego de solução fechada baseado em SVD's acopladas (C-SVD) é desenvolvido. O receptor C-SVD combina de modo eficiente todos os links cooperativos disponíveis, melhorando o desempenho da estimação de símbolos e de canal, além de oferecer uma implementação paralelizável.

abstract: The ability to identify unoccupied resources in the radio spectrum is a key capability for opportunistic users in a cognitive radio environment. This paper draws upon and extends geometrically based ideas in statistical signal processing to develop estimators for the rank and the occupied subspace in a multi-user environment from multiple temporal samples of the signal received at a single antenna. These estimators enable identification of resources, such as the orthogonal complement of the occupied subspace, that may be exploitable by an opportunistic user. This concept is supported by simulations showing the estimation of the number of users in a simple CDMA system using a maximum a posteriori (MAP) estimate for the rank. It was found that with suitable parameters, such as high SNR, sufficient number of time epochs and codes of appropriate length, the number of users could be correctly estimated using the MAP estimator even when the noise variance is unknown. Additionally, the process of identifying the maximum likelihood estimate of the orthogonal projector onto the unoccupied subspace is discussed. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2014

abstract: Higher-rank graphs, or k-graphs, are higher-dimensional analogues of directed graphs, and as with ordinary directed graphs, there are various C*-algebraic objects that can be associated with them. This thesis adopts a functorial approach to study the relationship between k-graphs and their associated C*-algebras. In particular, two functors are given between appropriate categories of higher-rank graphs and the category of C*-algebras, one for Toeplitz algebras and one for Cuntz-Krieger algebras. Additionally, the Cayley graphs of finitely generated groups are used to define a class of k-graphs, and a functor is then given from a category of finitely generated groups to the category of C*-algebras. Finally, functoriality is investigated for product systems of C*-correspondences associated to k-graphs. Additional results concerning the structural consequences of functoriality, properties of the functors, and combinatorial aspects of k-graphs are also included throughout. / Dissertation/Thesis / Masters Thesis Mathematics 2016

Made available in DSpace on 2014-06-11T19:23:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-12-19Bitstream added on 2014-06-13T18:19:49Z : No. of bitstreams: 1 coutinho_ccc_me_araca.pdf: 114919 bytes, checksum: 49f558e8cba145ffdabb2e45dc62ada3 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Na dinâmica da reparação óssea os fenômenos de reabsorção e neoformação são dependentes e acoplados. Proteínas efetivamente envolvidas na diferenciação celular determinam ativação ou inibição das atividades que regulam o ganho ou perda de massa óssea. Dentre as proteínas ósseas identificadas e envolvidas na dinâmica óssea podemos destacar a OPG, a RANK e RANKL como marcadores de atividades celulares. O presente trabalho tem como objetivo identificar, nos diferentes períodos da cronologia do processo de reparo alveolar através de técnica imunoistoquímica, a presença das proteínas OPG, RANK e RANKL. Para tanto foram utilizados 60 ratos machos submetidos à exodontia do incisivo superior direito e perfundidos aos 14, 21 e 28 dias pós-operatórios. As hemi-maxilas contendo o alvéolo dental em reparação foram removidas, pósfixadas, descalcificadas em EDTA, crioprotegidas e obtidos cortes longitudinais com 14æm em criostato. Os cortes foram submetidos à reação imunoistoquímica mediante a utilização de anticorpos primários para OPG, RANK e RANKL, como amplificador foi utilizado o sistema avidina-biotina e a diaminobenzidina (DAB) como cromógeno. Os resultados mostram que qualitativamente ocorre um balanço na expressão das proteínas que caracterizam reabsorção e neoformação óssea nos diferentes períodos estudados, onde aos 14 e 21 dias ocorre maior expressão de RANK. Com relação às proteínas OPG e RANKL, observa-se que elas apresentam-se expressas nas células da linhagem osteoblástica de forma similar, sendo que 28 dias é o período de maior expressão destas proteínas. / In the bone healing dynamics, the resorption and neoformation processes are dependent. Proteins involved in the cellular differentiation determinate the activation or inhibition of the activities that regulate the gain or loss of bone mass. From all of the identified bone proteins, it may be distinguished the OPG, RANK and RANKL. The present study has the aim to identify, in the different periods of alveolar bone healing chronology, the expression of OPG, RANK and RANKL proteins using the immunohistochemistry methodology. To perform this study, 60 male rats had the right upper incisive extracted and they were perfused at 14, 21 and 28 pos-operative days. The hemimaxilla with the rat extraction socket was removed, pos fixed and decalcified in EDTA. Then, they were cryoprotected and longitudinal slices with 14 ìm thickness were obtained in cryostat. The slices were submitted to immunohistochemistry reaction and the primary antibodies used were against OPG, RANK and RANKL proteins. It was used the avidinbiotin system to amplify the sign and diaminobenzidine was the cromogen. The results show that there is a balance in the expression of the proteins, showing that there is an increase in the expression of RANK at 14 and 21 pos-operative periods. In relation to OPG and RANKL, these proteins presents a similar expression in all of the pos-extraction periods analysed in this study and at 28 days after the extraction there is the greater expression of both proteins.

Resumo: O objetivo deste estudo foi avaliar histológica, histometrica e imunoistoquimicamente os efeitos do laser (LLLT) e da terapia fotodinâmica (PDT) no tratamento periodontal de ratas ovariectomizadas com ou sem reposição hormonal. Duzentas e setenta ratas foram divididas em 3 grupos de 90 animais: (A) SHAM; (B) Ovariectomizadas; (C) Ovariectomizadas tratadas com reposição hormonal. Nos primeiros molares inferiores esquerdos, de todos os animais, a doença periodontal foi induzida por ligadura. Após 7 dias, esta foi removida e nestes dentes procedeu-se a raspagem e alisamento corono-radicular (RAR). A seguir foram dividos em subgrupos de acordo com os tratamentos locais: I (n = 90) - Irrigação com 1 ml de soro fisiológico (RAR); II (n = 90) - Irrigação com 1 ml de soro fisiológico associado a aplicação de laser de baixa intensidade (LLLT) e III (n = 90) - Irrigação com 1 ml de azul de toluidina-O e, após 1 minuto, aplicação de laser em baixa intensidade (PDT). Dez animais de cada subgrupo foram sacrificados aos 7, 15 e 30 dias. Os animais do grupo A apresentaram perda óssea (PO) significativamente maior (p<0,01) no tratamento com RAR (1.11±0.26; 0.84±0.47) comparado à PDT (0.70±0.30; 0.42±0.20) nos períodos de 7 e 15 dias respectivamente. Os espécimes tratados com LLLT aos 30 dias demonstraram PO significativamente menor (p<0,01) no grupo A (0.35±0.18) comparado aos grupos B (0.82±0.21) e C (0.83±0.19). No tratamento com PDT, observou-se PO significativamente menor (p<0,01) no grupo A (0.42±0.20) comparado aos grupos B (0.95±0.20) e C (0.81±0.32) aos 15 dias. No entanto, no grupo C aos 30 dias a PDT demonstrou PO (0.52±0.23) em nível próximo ao observado nos espécimes do grupo A, no mesmo período (0.50±0.26). Na análise entre períodos, no mesmo grupo e tratamento, observou-se no grupo A, que o tratamento I apresentou PO significativamente maior... (Resumo completo clicar acesso eletrônico abaixo) / Abstract: The aim of this study was to evaluate histological, histometrically and immunohistochemistry the influence of laser and photodynamic therapy (PDT) as an adjuvant treatment on the experimentally induced periodontitis in ovariectomy rats with or without replacement hormone. Two hundred and seventy females rats were divided into 3 groups of 90 animals. (A) Normal female rats; (B) Control - Ovarectomy; (C) Ovarectomy treated with replacement hormone. The periodontal disease was induced by ligation and after 7 days was removed and the animals divided into subgroups who received the treatments: I - scaling and root planing (SRP) and irrigation with saline; II - SRP and irrigation with saline solution and LLLT (Laser -AsGaAl - 685 nm); III - SRP, irrigation with 1ml of Toluidine Blue (TBO) and, after 1 minute, application of laser (685 nm), performing photodynamic therapy (PDT). Ten animals of each subgroup were sacrificed at 7, 15 and 30 days. The animals of the group A presented bony loss (BL) significantly larger (p <0,01) in the treatment with RAR (1.11±0.26; 0.84±0.47) compared to PDT (0.70±0.30; 0.42±0.20) at 7 and 15 days respectively. In the specimens treated with LLLT at 30 days showed BL significantly less (p <0,01) in the group A (0.35±0.18) compared at groups B (0.82±0.21) and C (0.83±0.19). In the treatment with PDT, it was observed BL significantly less (p <0,01) in the group A (0.42±0.20) than groups B (0.95±0.20) and C (0.81±0.32) at 15 days. However, in the group C at 30 days PDT showed BL (0.52±0.23) in close level that observed in the specimens of the group A, in the same period (0.50±0.26). In the analysis among periods, in the same group and treatment, it was observed in the group A, that the treatment I presented BL significantly larger (p <0,01) at 7 days (1.11±0.26); that the treatment II showed larger BL (p <0,01) in the period of 7 days (0.90±0.29)... (Complete abstract click electronic access below) / Orientador: Valdir Gouveia Garcia / Coorientador: Maria José Hitomi Nagata / Banca: Álvaro Francisco Bosco / Banca: Juliana Rico Pires / Mestre