The majority of this thesis is concerned with the development of efficient and robust numerical methods based on adaptive algebraic multigrid to compute the stationary distribution of Markov chains. It is shown that classical algebraic multigrid techniques can be applied in an exact interpolation scheme framework to compute the stationary distribution of irreducible, homogeneous Markov chains. A quantitative analysis shows that algebraically smooth multiplicative error is locally constant along strong connections in a scaled system operator, which suggests that classical algebraic multigrid coarsening and interpolation can be applied to the class of nonsymmetric irreducible singular M-matrices with zero column sums. Acceleration schemes based on fine-level iterant recombination, and over-correction of the coarse-grid correction are developed to improve the rate of convergence and scalability of simple adaptive aggregation multigrid methods for Markov chains. Numerical tests over a wide range of challenging nonsymmetric test problems demonstrate the effectiveness of the proposed multilevel method and the acceleration schemes. This thesis also investigates the application of adaptive algebraic multigrid techniques for computing the canonical decomposition of higher-order tensors. The canonical decomposition is formulated as a least squares optimization problem, for which local minimizers are computed by solving the first-order optimality equations. The proposed multilevel method consists of two phases: an adaptive setup phase that uses a multiplicative correction scheme in conjunction with bootstrap algebraic multigrid interpolation to build the necessary operators on each level, and a solve phase that uses additive correction cycles based on the full approximation scheme to efficiently obtain an accurate solution. The alternating least squares method, which is a standard one-level iterative method for computing the canonical decomposition, is used as the relaxation scheme. Numerical tests show that for certain test problems arising from the discretization of high-dimensional partial differential equations on regular lattices the proposed multilevel method significantly outperforms the standard alternating least squares method when a high level of accuracy is required.

The majority of this thesis is concerned with the development of efficient and robust numerical methods based on adaptive algebraic multigrid to compute the stationary distribution of Markov chains. It is shown that classical algebraic multigrid techniques can be applied in an exact interpolation scheme framework to compute the stationary distribution of irreducible, homogeneous Markov chains. A quantitative analysis shows that algebraically smooth multiplicative error is locally constant along strong connections in a scaled system operator, which suggests that classical algebraic multigrid coarsening and interpolation can be applied to the class of nonsymmetric irreducible singular M-matrices with zero column sums. Acceleration schemes based on fine-level iterant recombination, and over-correction of the coarse-grid correction are developed to improve the rate of convergence and scalability of simple adaptive aggregation multigrid methods for Markov chains. Numerical tests over a wide range of challenging nonsymmetric test problems demonstrate the effectiveness of the proposed multilevel method and the acceleration schemes. This thesis also investigates the application of adaptive algebraic multigrid techniques for computing the canonical decomposition of higher-order tensors. The canonical decomposition is formulated as a least squares optimization problem, for which local minimizers are computed by solving the first-order optimality equations. The proposed multilevel method consists of two phases: an adaptive setup phase that uses a multiplicative correction scheme in conjunction with bootstrap algebraic multigrid interpolation to build the necessary operators on each level, and a solve phase that uses additive correction cycles based on the full approximation scheme to efficiently obtain an accurate solution. The alternating least squares method, which is a standard one-level iterative method for computing the canonical decomposition, is used as the relaxation scheme. Numerical tests show that for certain test problems arising from the discretization of high-dimensional partial differential equations on regular lattices the proposed multilevel method significantly outperforms the standard alternating least squares method when a high level of accuracy is required.

Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2004. / Ajay Misra, Committee Member ; James Craig, Committee Member ; Richard Neu, Committee Member ; Daniel Schrage, Committee Member ; Dimitri Mavris, Committee Chair. Vita. Includes bibliographical references.

Title from title page of PDF (University of Missouri--St. Louis, viewed March 23, 2010). Includes bibliographical references (p. 352-361).

abstract: Multi-label learning, which deals with data associated with multiple labels simultaneously, is ubiquitous in real-world applications. To overcome the curse of dimensionality in multi-label learning, in this thesis I study multi-label dimensionality reduction, which extracts a small number of features by removing the irrelevant, redundant, and noisy information while considering the correlation among different labels in multi-label learning. Specifically, I propose Hypergraph Spectral Learning (HSL) to perform dimensionality reduction for multi-label data by exploiting correlations among different labels using a hypergraph. The regularization effect on the classical dimensionality reduction algorithm known as Canonical Correlation Analysis (CCA) is elucidated in this thesis. The relationship between CCA and Orthonormalized Partial Least Squares (OPLS) is also investigated. To perform dimensionality reduction efficiently for large-scale problems, two efficient implementations are proposed for a class of dimensionality reduction algorithms, including canonical correlation analysis, orthonormalized partial least squares, linear discriminant analysis, and hypergraph spectral learning. The first approach is a direct least squares approach which allows the use of different regularization penalties, but is applicable under a certain assumption; the second one is a two-stage approach which can be applied in the regularization setting without any assumption. Furthermore, an online implementation for the same class of dimensionality reduction algorithms is proposed when the data comes sequentially. A Matlab toolbox for multi-label dimensionality reduction has been developed and released. The proposed algorithms have been applied successfully in the Drosophila gene expression pattern image annotation. The experimental results on some benchmark data sets in multi-label learning also demonstrate the effectiveness and efficiency of the proposed algorithms. / Dissertation/Thesis / Ph.D. Computer Science 2011

Wolbachia are widely spread, maternally transmitted insect endosymbiotic intracellular bacteria. They have been implicated in the control of several insect transmitted diseases, including dengue, yellow fever, Zika and malaria. Effective pathogen suppression in the insect host is shown to be proportional to the intracellular levels of bacteria. Therefore, understanding the molecular mechanisms underlying Wolbachia accumulation within organisms is extremely important for future epidemic control and research. Using Drosophila as a model insect, our lab has previously observed Wolbachia tropism to stem cell niches. Current work has identified polar cells as an additional site of Wolbachia tropism and demonstrated that Wg/Wnt signaling is important for Wolbachia intracellular accumulation in these somatic cells. In this thesis, we first observed that the Wg/Wnt pathway protein Armadillo also controls Wolbachia levels in the germline cells, indicating the possibility of having a conserved molecular mechanism controlling Wolbachia. Using RNAi and small molecule inhibitors of Shaggy, another component of the canonical Wg/Wnt pathway, we demonstrate that the canonical Wg/Wnt signaling is essential for Wolbachia intracellular accumulation. Our investigation provides fundamental insights into the mechanisms of Wolbachia intracellular accumulation. Furthermore, it offers novel strategies to modulate Wolbachia in non-model insect species, including various disease transmitting Anopheles, Culex, and Aedes. These findings potentially will increase the effectiveness of a Wolbachia-based vector transmitted disease suppression. / 2017-02-28

One of the central themes of modern Number Theory is to study properties of Galois and automorphic representations and connections between them. In our dissertation, we describe two different projects that study properties of these objects. In our first project, which is analytic in nature, we consider Artin representations of Q of dimension 3 that are self-dual. We show that these occur with density 0 when counted using the conductor. This provides evidence that self-dual representations should be rare in all dimensions. Our second project, which is more algebraic in nature, is related to automorphic representations. We show the existence of canonical models for certain unitary Shimura varieties. This should help us in computing certain cohomology groups of these varieties, in which regular algebraic automorphic representations having useful properties should be found.

viii, 57 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We introduce a new finite-complexity knot theory, the theory of plumbers' knots, as a model for classical knot theory. The spaces of plumbers' curves admit a combinatorial cell structure, which we exploit to algorithmically solve the classification problem for plumbers' knots of a fixed complexity. We describe cellular subdivision maps on the spaces of plumbers' curves which consistently make the spaces of plumbers' knots and their discriminants into directed systems. In this context, we revisit the construction of the Vassiliev spectral sequence. We construct homotopical resolutions of the discriminants of the spaces of plumbers knots and describe how their cell structures lift to these resolutions. Next, we introduce an inverse system of unstable Vassiliev spectral sequences whose limit includes, on its E ∞ - page, the classical finite-type invariants. Finally, we extend the definition of the Vassiliev derivative to all singularity types of plumbers' curves and use it to construct canonical chain representatives of the resolution of the Alexander dual for any invariant of plumbers' knots. / Committee in charge: Dev Sinha, Chairperson, Mathematics; Hal Sadofsky, Member, Mathematics; Arkady Berenstein, Member, Mathematics; Daniel Dugger, Member, Mathematics; Andrzej Proskurowski, Outside Member, Computer & Information Science

MACEDO, Diego Ximenes. Osciladores harmônicos acoplados dependentes do tempo. 2012. 65 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2012. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-16T21:48:15Z No. of bitstreams: 1 2012_dis_dxmacedo.pdf: 1228459 bytes, checksum: 6d71730075dc0a642cfe80de6f3c9b6d (MD5) / Approved for entry into archive by Fabíola Bezerra(fabbezerra@yahoo.com.br) on 2016-01-20T14:38:07Z (GMT) No. of bitstreams: 1 2012_dis_dxmacedo.pdf: 1228459 bytes, checksum: 6d71730075dc0a642cfe80de6f3c9b6d (MD5) / Made available in DSpace on 2016-01-20T14:38:07Z (GMT). No. of bitstreams: 1 2012_dis_dxmacedo.pdf: 1228459 bytes, checksum: 6d71730075dc0a642cfe80de6f3c9b6d (MD5) Previous issue date: 2012 / In this work we present the classical and quantum solutions of time-dependent coupled harmonic oscillators. In these systems the masses, frequencies and coupling parameter (k) are functions of time. Four systems are investigated. To obtain the classical solutions we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. We find the analytical expression for position and velocity of each oscillator of the systems. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld invariant method. The wave functions obtained are written in terms of a c-number quantity () which is solution of the Milne-Pinney equation. For each system we solve the respective Milne-Pinney equation and discuss how the quantum fluctuations and the uncertainty product evolve with time. / Neste trabalho apresentamos soluções clássicas e quânticas de osciladores harmônicos acoplados dependentes do tempo. Nesses sistemas as massas, frequências e o parâmetro de acoplamento são funções do tempo. Quatro sistemas são investigados. Para obter as soluções clássicas usamos uma transformação de coordenada e momento juntamente com uma transformação canônica para escrever o Hamiltoniano original como a soma de dois Hamiltonianos de osciladores harmônicos desacoplados dependentes do tempo com frequências modificadas dependentes do tempo e massas unitárias. Encontramos soluções analíticas para a posição e a velocidade para cada oscilador de todos os sistemas. Para obter as soluções quânticas exatas usamos uma transformação unitária e o método invariante de Lewis e Riesenfeld. As funções de onda são escritas em termos de uma quantidade escalar a qual é solução da equação de Milne-Pinney. Para cada sistema resolvemos a respectiva equação de Milne-Pinney e discutimos como as flutuações quânticas e o produto de incerteza evoluem no tempo.

Made available in DSpace on 2014-06-11T19:31:33Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-05-12Bitstream added on 2014-06-13T20:02:18Z : No. of bitstreams: 1 oliveira_jrt_dr_botfca.pdf: 1336973 bytes, checksum: 44cf547c7955ffc9a72eb93ed415128f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A necessidade de entender o relacionamento entre variáveis biológicas faz da análise multivariada uma metodologia com grande potencial de aplicação em várias áreas do conhecimento. Na agricultura, sua utilização vem auxiliando a compreensão e a obtenção de respostas altamente interessantes e práticas, que permitem optar pelo seu emprego, tanto pela eficiência como pela acurácia do método na interpretação dos resultados. A partir da utilização de técnicas multivariadas pautadas em procedimentos quantitativos mais robustos e sensíveis, buscou-se caracterizar o perfil produtivo e climático das microrregiões do Sudeste do estado de Mato Grosso e construir modelos para quantificar e aprofundar a interrelação entre produtividade e variáveis climáticas nas respectivas regiões. Para classificar microrregiões semelhantes segundo suas características, quando nenhuma suposição foi feita concernente ao número de grupos ou a estrutura do grupo, utilizou-se a análise de agrupamento. Buscando variáveis agrícolas e de produtividade e a incorporação de novos procedimentos multivariados na interrelação desses indicadores, utilizou-se a análise de correlação canônica. Para a operacionalização desses procedimentos multivariados foram estabelecidas técnicas para estimar os componentes climáticos não disponíveis em algumas das microrregiões estudadas. A análise de agrupamento permitiu desenhar um mosaico de heterogeneidade espacial e estabelecer diferentes perfis na composição dos grupos de microrregião, reunindo as mais tradicionais no cultivo de uma espécie, ou mais produtivas, ou aquelas mais propícias ao desenvolvimento de determinada cultura. A análise fatorial estabeleceu dois eixos canônicos para as interrelações entre as culturas, sendo o primeiro fator explicando 42,22% da variância total correlacionado com as culturas anuais, podendo... / The knowledge of the relationship between biological variables makes the multivariate analysis a potential tool for applications in several science fields. In agriculture, this technique has enabled the understanding and obtaining responses very real, which show the possibility of use by both the efficiency and the accuracy of the method in the interpretation of results. The purpose of this research is to use of multivariate techniques based on quantitative procedures to improve the knowledge about the climatic variables of the southeast of Mato Grosso state, which helps to solve problems in the agricultural sector. Also, the grouping analysis classified the micro regions in similar groups. The factorial analysis showed the dimensions of the variation structure of data, enabling the determination of the extent of each variable in each dimension. The smaller regions were defined from interpreting of the interrelationship between the products grown in the region. The correlation canonic analysis was used to describe the association between the number of variables and agricultural productivity. Thus, new procedures were incorporated in multivariate interrelationship of these indicators. Some climatic components, not available in a few micro regions, were estimated through multivariate techniques. Cluster analysis allowed the design of a mosaic of spatial heterogeneity regions. It established different profiles in the composition of groups, joining the more traditional in the culture of a species, or more productive, or those for the development of a particular culture. The factorial analysis established two canonical axes for the interrelationships between cultures. The first factor explaining 42.22% of total variance associated with annual crops (called annual crops factor ). The second factor explained 16, 11% (semi perennial crop factor)... (Complete abstract click electronic access below)