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Lecharlier, Loïc. "Blind inverse imaging with positivity constraints". Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209240.
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Dans les problèmes inverses en imagerie, on suppose généralement connu l’opérateur ou matrice décrivant le système de formation de l’image. De façon équivalente pour un système linéaire, on suppose connue sa réponse impulsionnelle. Toutefois, ceci n’est pas une hypothèse réaliste pour de nombreuses applications pratiques pour lesquelles cet opérateur n’est en fait pas connu (ou n’est connu qu’approximativement). On a alors affaire à un problème d’inversion dite “aveugle”. Dans le cas de systèmes invariants par translation, on parle de “déconvolution aveugle” car à la fois l’image ou objet de départ et la réponse impulsionnelle doivent être estimées à partir de la seule image observée qui résulte d’une convolution et est affectée d’erreurs de mesure. Ce problème est notoirement difficile et pour pallier les ambiguïtés et les instabilités numériques inhérentes à ce type d’inversions, il faut recourir à des informations ou contraintes supplémentaires, telles que la positivité qui s’est avérée un levier de stabilisation puissant dans les problèmes d’imagerie non aveugle. La thèse propose de nouveaux algorithmes d’inversion aveugle dans un cadre discret ou discrétisé, en supposant que l’image inconnue, la matrice à inverser et les données sont positives. Le problème est formulé comme un problème d’optimisation (non convexe) où le terme d’attache aux données à minimiser, modélisant soit le cas de données de type Poisson (divergence de Kullback-Leibler) ou affectées de bruit gaussien (moindres carrés), est augmenté par des termes de pénalité sur les inconnues du problème. La stratégie d’optimisation consiste en des ajustements alternés de l’image à reconstruire et de la matrice à inverser qui sont de type multiplicatif et résultent de la minimisation de fonctions coût “surrogées” valables dans le cas positif. Le cadre assez général permet d’utiliser plusieurs types de pénalités, y compris sur la variation totale (lissée) de l’image. Une normalisation éventuelle de la réponse impulsionnelle ou de la matrice est également prévue à chaque itération. Des résultats de convergence pour ces algorithmes sont établis dans la thèse, tant en ce qui concerne la décroissance des fonctions coût que la convergence de la suite des itérés vers un point stationnaire. La méthodologie proposée est validée avec succès par des simulations numériques relatives à différentes applications telle que la déconvolution aveugle d'images en astronomie, la factorisation en matrices positives pour l’imagerie hyperspectrale et la déconvolution de densités en statistique.Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Fortmann, Joshua. "Domestic Violence as a Risk Factor in HIV Positivity: An Analysis of Mozambican Women". Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/asrf/2021/presentations/11.
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Domestic violence has long been studied as a factor in health issues, specifically chronic illness and mental health issues. However, less research has been conducted concerning domestic violence as a risk factor for certain infectious diseases. Mozambique has alarmingly high rates of both domestic violence and human immunodeficiency virus (HIV) infections. The object of this research is to ascertain if there is link between women who suffer from domestic violence and risk of being HIV positive. The data used for this analysis was obtained from a 2018 survey conducted in Mozambique by the Department of Health Surveys (DHS). The data was cleaned to remove any observations that did not contain responses to relevant questions surrounding domestic violence and HIV positivity. The final population used for analysis was 2125 individuals. During analysis, age was identified as a possible confounder, and was included in analysis as well as in the final logistic model. A chi squared test was performed which indicated that a relationship exists between Domestic Violence and HIV Positivity (p=.0003). A second chi squared test also indicated a relationship between Age and HIV Positivity (p=
3
Chang, Xiao-Wen. "Perturbation analysis of some matrix factorizations". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0023/NQ29906.pdf.
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Chang, Xiao-Wen 1963. "Pertubation analysis of some matrix factorizations". Thesis, McGill University, 1997. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41999.
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Matrix factorizations are among the most important and basic tools in numerical linear algebra. Perturbation analyses of matrix factorizations are not only important in their own right, but also useful in many applications, e.g. in estimation, control and statistics. The aim of such analyses is to show what effects changes in the data will have on the factors. This thesis is concerned with developing new general purpose perturbation analyses, and applying them to the Cholesky, QR and LU factorizations, and the Cholesky downdating problem.We develop a new approach, the so called 'matrix-vector equation' approach, to obtain sharp results and true condition numbers for the above problems. Our perturbation bounds give significant improvements on previous results, and could not be sharper. Also we use the so called 'matrix equation' approach originated by G. W. Stewart to derive perturbation bounds that are usually weaker but easier to interpret. This approach allows efficient computation of satisfactory estimates for the true condition numbers derived by our approach. The combination of these two approaches gives a powerful understanding of these problems. Although first-order perturbation bounds are satisfactory for all but the most delicate work, we also give some rigorous perturbation bounds for some factorizations.
We show that the condition of many such factorizations is significantly improved by the standard pivoting strategies (except the L factor in the LU factorization), and provide firmly based theoretical explanations as to why this is so. This extremely important information is very useful for designing more reliable matrix algorithms.
Our approach is a powerful general tool, and appears to be applicable to the perturbation analysis of any matrix factorization.
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El, Zant Samer. "Google matrix analysis of Wikipedia networks". Thesis, Toulouse, INPT, 2018. http://www.theses.fr/2018INPT0046/document.
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Cette thèse s’intéresse à l’analyse du réseau dirigé extrait de la structure des hyperliens de Wikipédia. Notre objectif est de mesurer les interactions liant un sous-ensemble de pages du réseau Wikipédia. Par conséquent, nous proposons de tirer parti d’une nouvelle représentation matricielle appelée matrice réduite de Google ou "reduced Google Matrix". Cette matrice réduite de Google (GR) est définie pour un sous-ensemble de pages donné (c-à-d un réseau réduit).Comme pour la matrice de Google standard, un composant de GR capture la probabilité que deux noeuds du réseau réduit soient directement connectés dans le réseau complet. Une des particularités de GR est l’existence d’un autre composant qui explique la probabilité d’avoir deux noeuds indirectement connectés à travers tous les chemins possibles du réseau entier. Dans cette thèse, les résultats de notre étude de cas nous montrent que GR offre une représentation fiable des liens directs et indirects (cachés). Nous montrons que l’analyse de GR est complémentaire à l’analyse de "PageRank" et peut être exploitée pour étudier l’influence d’une variation de lien sur le reste de la structure du réseau. Les études de cas sont basées sur des réseaux Wikipédia provenant de différentes éditions linguistiques. Les interactions entre plusieurs groupes d’intérêt ont été étudiées en détail : peintres, pays et groupes terroristes. Pour chaque étude, un réseau réduit a été construit. Les interactions directes et indirectes ont été analysées et confrontées à des faits historiques, géopolitiques ou scientifiques. Une analyse de sensibilité est réalisée afin de comprendre l’influence des liens dans chaque groupe sur d’autres noeuds (ex : les pays dans notre cas). Notre analyse montre qu’il est possible d’extraire des interactions précieuses entre les peintres, les pays et les groupes terroristes. On retrouve par exemple, dans le réseau de peintre sissu de GR, un regroupement des artistes par grand mouvement de l’histoire de la peinture. Les interactions bien connues entre les grands pays de l’UE ou dans le monde entier sont également soulignées/mentionnées dans nos résultats. De même, le réseau de groupes terroristes présente des liens pertinents en ligne avec leur idéologie ou leurs relations historiques ou géopolitiques.Nous concluons cette étude en montrant que l’analyse réduite de la matrice de Google est une nouvelle méthode d’analyse puissante pour les grands réseaux dirigés. Nous affirmons que cette approche pourra aussi bien s’appliquer à des données représentées sous la forme de graphes dynamiques. Cette approche offre de nouvelles possibilités permettant une analyse efficace des interactions d’un groupe de noeuds enfoui dans un grand réseau dirigéThis thesis concentrates on the analysis of the large directed network representation of Wikipedia.Wikipedia stores valuable fine-grained dependencies among articles by linking webpages togetherfor diverse types of interactions. Our focus is to capture fine-grained and realistic interactionsbetween a subset of webpages in this Wikipedia network. Therefore, we propose to leverage anovel Google matrix representation of the network called the reduced Google matrix. This reducedGoogle matrix (GR) is derived for the subset of webpages of interest (i.e. the reduced network). Asfor the regular Google matrix, one component of GR captures the probability of two nodes of thereduced network to be directly connected in the full network. But unique to GR, anothercomponent accounts for the probability of having both nodes indirectly connected through allpossible paths in the full network. In this thesis, we demonstrate with several case studies that GRoffers a reliable and meaningful representation of direct and indirect (hidden) links of the reducednetwork. We show that GR analysis is complementary to the well-known PageRank analysis andcan be leveraged to study the influence of a link variation on the rest of the network structure.Case studies are based on Wikipedia networks originating from different language editions.Interactions between several groups of interest are studied in details: painters, countries andterrorist groups. For each study, a reduced network is built, direct and indirect interactions areanalyzed and confronted to historical, geopolitical or scientific facts. A sensitivity analysis isconducted to understand the influence of the ties in each group on other nodes (e.g. countries inour case). From our analysis, we show that it is possible to extract valuable interactions betweenpainters, countries or terrorist groups. Network of painters with GR capture art historical fact sucha painting movement classification. Well-known interactions of countries between major EUcountries or worldwide are underlined as well in our results. Similarly, networks of terrorist groupsshow relevant ties in line with their objective or their historical or geopolitical relationships. Weconclude this study by showing that the reduced Google matrix analysis is a novel powerfulanalysis method for large directed networks. We argue that this approach can find as well usefulapplication for different types of datasets constituted by the exchange of dynamic content. Thisapproach offers new possibilities to analyze effective interactions in a group of nodes embedded ina large directed network
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Diar, Fares Sonja. "All is well : An analysis of positivity through adjectives in two contemporary New Age self-help books". Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-40144.
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Self-help counselling is an important industry that not only influences its immediate users’ behavior but also society and social behaviors more generally. Since New Ageis a main branch of self-help, and since positivity is a dominant concept in (New Age) self-help discourse, it is worth analyzing how positivity might be achieved in terms of language use. The present study investigates whether the adjectives in a couple of New Age publications contribute to communicating positivity and, if yes, how. What adjectives are used and how can they be categorized in terms of positive, negative, neutral or undetermined connotations as well as semantic prosody? The findings support the hypothesis that the use of “positive adjectives” (Rozin, Berman & Royzman, 2010, p. 536) is what helps to make New Age self-help books convey a positive spirit.
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Barnett, John D. (John Derek) 1970. "Convex matrix factorization for gene expression analysis". Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30098.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 68-71).
A method is proposed for gene expression analysis relying upon convex matrix factorization (CMF). In CMF, one of the matrix factors has a convexity constraint, that is, each row is nonnegative and sums to one, and hence can be interpreted as a probability distribution. This is motivated biologically by expression data resulting from a mixture of different cell types. This thesis investigates implementing CMF with various constraints applied to the expression matrix, and applies the technique to a problem in analysis of the cell cycle and two problems in cancer classification.
by John D. Barnett.
S.M.
8
Lee, Shi-Wei. "Analysis of Composite Laminates with Matrix Cracks". Thesis, Virginia Tech, 1987. http://hdl.handle.net/10919/45539.
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Analysis of the effects of matrix cracking on composite laminates is a well-known problem which has attracted considerable attention for the past decade. An approximate analytical solution is introduced in this thesis to study this type of problem.
The subjects of primary concern are the degradation of effective laminate properties, such as axial stiffness, Poisson's ratio, shear modulus, and coefficient of thermal expansion, as a function of crack density and the axial stress redistribution due to the existence of matrix cracks. Both transverse cracks (2-D problem) and cross (transverse and longitudinal) cracks (3-D problem) are studied. Results for graphite/epoxy cross-ply laminates are presented and compared to those of other approaches. Some other materials, for instance, glass/epoxy, are also studied. The results and comparisons will appear where appropriate. In general, the agreement between the results of the present analysis and those of other approaches, in particular, the finite element method, is good for the lower crack density. The present study shows that Poisson's ratio may be a good indicator of the degree of damage for a cracked laminate.Master of Science
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Vaandrager, Paul. "Jost-matrix analysis of nuclear scattering data". Thesis, University of Pretoria, 2020. http://hdl.handle.net/2263/75605.
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The analysis of scattering data is usually done by fitting the S-matrix at real experimental energies. An analytic continuation to complex and negative energies must then be performed to locate possible resonances and bound states, which correspond to poles of the S-matrix. Difficulties in the analytic continuation arise since the S-matrix is energy dependent via the momentum, k and the Sommerfeld parameter, η, which makes it multi-valued. In order to circumvent these difficulties, in this work, the S-matrix is written in a semi-analytic form in terms of the Jost matrices, which can be given as a product of known functions dependent on k and η, and unknown functions that are entire and singled-valued in energy. The unknown functions are approximated by truncated Taylor series where the expansion coefficients serve as the data-fitting parameters. The proper analytic structure of the S-matrix is thus maintained. This method is successfully tested with data generated by a model scattering potential. It is then applied to α12C scattering, where resonances of 16O in the quantum states Jρ =0+, 1−, 2+, 3−, and 4+ are located. The parameters of these resonances are accurately determined, as well as the corresponding S-matrix residues and Asymptotic Normalisation Coefficients, relevant to astrophysics. The method is also applied to dα scattering to determine the bound and resonance state parameters, corresponding S-matrix residues and Asymptotic Normalisation Coefficients of 6Li in the 1+, 2+, 3+, 2−, and 3− states.Thesis (PhD)--University of Pretoria, 2020.
National Research Foundation (NRF)
Physics
PhD
Unrestricted
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Knox, Andrew Ramsay. "Design and analysis of the magnetic matrix display". Connect to electronic version, 2000. http://hdl.handle.net/1905/187.
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Knox, Andrew R. "Design and analysis of the magnetic matrix display". Thesis, University of Glasgow, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325450.
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Younes, Imad Sabeh. "Transfer matrix analysis of frame-shear wall systems". Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280922.
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Roberts, Jeremy Alyn. "Advanced response matrix methods for full core analysis". Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/87490.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 195-200).
Modeling full reactor cores with high fidelity transport methods is a difficult task, requiring the largest computers available today. This thesis presents work on an alternative approach using the eigenvalue response matrix method (ERMM). The basic idea of ERMM is to decompose a reactor spatially into local "nodes." Each node represents an independent fixed source transport problem, and the nodes are linked via approximate boundary conditions to reconstruct the global problem using potentially many fewer explicit unknowns than a direct fine mesh solution. This thesis addresses several outstanding issues related to the ERMM based on deterministic transport. In particular, advanced transport solvers were studied for application to the relatively small and frequently repeated problems characteristic of response function generation. This includes development of preconditioners based on diffusion for use in multigroup Krylov linear solvers. These new solver combinations are up to an order of magnitude faster than competing algorithms. Additionally, orthogonal bases for space, angle, and energy variables were investigated. For the spatial variable, a new basis set that incorporates a shape function characteristic of pin assemblies was found to reduce significantly the error in representing boundary currents. For the angular variable, it was shown that bases that conserve the partial current at a boundary perform very well, particularly for low orders. For the deterministic transport used in this work, such bases require use of specialized angular quadratures. In the energy variable, it was found that an orthogonal basis constructed using a representative energy spectrum provides an accurate alternative to few group calculations. Finally, a parallel ERMM code Serment was developed, incorporating the transport and basis development along with several new algorithms for solving the response matrix equations, including variants of Picard iteration, Steffensen's method, and Newton's method. Based on results from several benchmark models, it was found that an accelerated Picard iteration provides the best performance, but Newton's method may be more robust. Furthermore, initial scoping studies demonstrated good scaling on an [omicron](100) processor machine.
by Jeremy Alyn Roberts.
Ph. D.
14
Gong, Liyun. "Nonnegative matrix analysis for data clustering and compression". Thesis, University of Liverpool, 2015. http://livrepository.liverpool.ac.uk/2007800/.
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Nonnegative matrix factorization (NMF) has becoming an increasingly popular data processing tool these years, widely used by various communities including computer vision, text mining and bioinformatics. It is able to approximate each data sample in a data collection by a linear combination of a set of nonnegative basis vectors weighted by nonnegative weights. This often enables meaningful interpretation of the data, motivates useful insights and facilitates tasks such as data compression, clustering and classification. These subsequently lead to various active roles of NMF in data analysis, e.g., dimensionality reduction tool [11, 75], clustering tool[94, 82, 13, 39], feature engine [40], source separation tool [38], etc. Different methods based on NMF are proposed in this thesis: The modification of k- means clustering is chosen as one of the initialisation methods for NMF. Experimental results demonstrate the excellence of this method with improved compression performance. Independent principal component analysis (IPCA) which combines the advantage of both principal component analysis (PCA) and independent component analysis (ICA) has been chosen as the significant initialisation method for NMF with improved clustering accuracy. We have proposed the new evolutionary optimization strategy for NMF driven by three proposed update schemes in the solution space, saying NMF rule (or original movement), firefly rule (or beta movement) and survival of the fittest rule (or best movement). This proposed update strategy facilitates both the clustering and compression problems by using the different system objective functions that make use of the clustering and compression quality measurements. A hybrid initialisation approach is used by including the state-of-the-art NMF initialization methods as seed knowledge to increase the rate of convergence. There is no limitation for the number and the type of the initialization methods used for the proposed optimisation approach. Numerous computer experiments using the benchmark datasets verify the theoretical results, make comparisons among the techniques in measures of clustering/compression accuracy. Experimental results demonstrate the excellence of these methods with im- proved clustering/compression performance. In the application of EEG dataset, we employed several standard algorithms to provide clustering on preprocessed EEG data. We also explored ensemble clustering to obtain some tight clusters. We can make some statements based on the results we have got: firstly, normalization is necessary for this EEG brain dataset to obtain reasonable clustering; secondly, k-means, k-medoids and HC-Ward provide relatively better clustering results; thirdly, ensemble clustering enables us to tune the tightness of the clusters so that the research can be focused.
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Payseur, Scott. "Essays in realized covariance matrix estimation /". Thesis, Connect to this title online; UW restricted, 2008. http://hdl.handle.net/1773/7410.
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Kardell, Marcus. "Total positivity and oscillatory kernels : An overview, and applications to the spectral theory of the cubic string". Thesis, Linköpings universitet, Tillämpad matematik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-58005.
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In the study of the Degasperis-Procesi dierential equation, an eigenvalue problem called the cubic string occurs. This is a third order generalization of the second order problem describing the eigenmodes of a vibrating string. In this thesis we study the eigenfunctions of the cubic string for discrete and continuous mass distributions, using the theory of total positivity, via a combinatorial approach with planar networks.
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Cadima, Jorge Filipe Campinos Landerset. "Topics in descriptive Principal Component Analysis". Thesis, University of Kent, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314686.
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Neretin, Yurii A., i neretin@main mccme rssi ru. "Matrix Balls, Radial Analysis of Berezin Kernels, and Hypergeometric". ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi974.ps.
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Li, Yuemeng. "Spectral Analysis of Directed Graphs using Matrix Perturbation Theory". Thesis, The University of North Carolina at Charlotte, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10618933.
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The spectral space of the adjacency matrix contains important structural information of a given network (graph), where such information can be leveraged in developing a variety of algorithms in applications such as graph partition, structural hierarchy discovery, and anomaly detection. Although many prominent works have laid the foundation for studying the graph spectra, it is still challenging to analyze the spectral space properties for directed graphs due to possible complex valued decompositions. Matrix factorization techniques such as Laplacian and normalized Laplacian have been widely adopted to study the associated spectral spaces, but network structural properties may not be well preserved in those spectral spaces due to transformations.
In this dissertation work, we explore the adjacency eigenspace of directed graphs using matrix perturbation theory and examine the relationships between graph structures and the spectral projection patterns. We study how to detect dominant structures such as clusters or anomalous nodes by establishing a connection between the connectivity of nodes and the geometric relationships in the adjacency eigenspace. We leverage selected key results from perturbation theory, linear algebra and graph theory as our tools to derive theoretical results that help to elaborate observed graph spectral projection patterns. In order to validate our theoretical results, novel algorithms including spectral clustering for both signed and unsigned networks, asymmetry analysis for network dominance, and anomaly analysis for streaming network data are developed and tested on both synthetic and real datasets. The empirical evaluation results suggest that our algorithms performs better when compared with existing state-of-the-art methods.
20
Phelan, Thomas Joseph. "GENETIC AND MOLECULAR ANALYSIS OF PLANT NUCLEAR MATRIX PROTEINS". NCSU, 2001. http://www.lib.ncsu.edu/theses/available/etd-20011104-233111.
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PHELAN, THOMAS JOSEPH, Genetic and Molecular Analysis of Plant Nuclear Matrix Proteins. (Under the direction of Steven L. Spiker.)The eukaryotic nucleus is composed of DNA, RNA and protein, encapsulated by a nuclear envelope. DNA is compacted up to ten thousand times in order to be packaged into the nucleus. The nucleus must maintain order in the presence of a very high density and variety of protein and RNA. The nuclear matrix is a proteinaceous network thought to provide structure and organization to the nucleus. We believe that relatively stable interactions of nuclear molecules with the nuclear matrix are key to organization of the nucleus. Numerous "Matrix Attachment Region" DNA elements (MARs), have been isolated from plants, animals, and fungi. Evidence suggests that these MARs attach to the nuclear matrix, delimiting loops of chromosomal DNA. In studies of transgenic plants and animals, MARs have been shown to give important advantages to organisms transformed with genes flanked by these elements. Unlike most DNA elements, no specific sequence elements have been identified in MAR DNAs. Partly due to the insolubility of the matrix, and to the heterogeneity of MAR DNA, very few of the protein components of the nuclear matrix have been identified. This work presents analysis the proteins of the plant nuclear matrix. We have characterized a set of related proteins from the model plant Arabidopsis that associate with MAR DNA in vitro. These proteins appear to be similar to the NOP56/NOP58 family of proteins previously identified in several eukaryotic organisms. The NOP56/NOP58 proteins are thought to be involved in modifications of ribosomal RNA. Binding studies presented in this work suggest that these plant proteins may participate in RNA/DNA/protein complexes in the nucleus.
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Peterson, Anders. "The Origin-Destination Matrix Estimation Problem : Analysis and Computations". Doctoral thesis, Norrköping : Dept. of Science and Technology, Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-8859.
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Al-Mutawah, Jameela. "Using matrix isolation FTIR for trace atmospheric gas analysis". Thesis, University of Reading, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270218.
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Schutz, James Branch. "Test methods and analysis for glass-ceramic matrix composites". Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/13711.
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Sthapit, Akshay R. (Akshay Ratna) 1978. "An object oriented approach to matrix analysis of structures". Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/84810.
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Wakasa, Yuji. "Control System Analysis and Synthesis Based on Matrix Inequalities". 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/151475.
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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものであるKyoto University (京都大学)
0048
新制・論文博士
博士(情報学)
乙第10519号
論情博第6号
新制||情||4(附属図書館)
UT51-2000-P686
(主査)教授 山本 裕, 教授 磯 祐介, 教授 片山 徹
学位規則第4条第2項該当
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寛康, 阿部, i Hiroyasu Abe. "Extensions of nonnegative matrix factorization for exploratory data analysis". Thesis, https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB13001149/?lang=0, 2017. https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB13001149/?lang=0.
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非負値行列因子分解(NMF)は，全要素が非負であるデータ行列に対する行列分解法である．本論文では，実在するデータ行列に頻繁に見られる特徴や解釈容易性の向上を考慮に入れ，探索的にデータ分析を行うためのNMFの拡張について論じている．具体的には，零過剰行列や外れ値を含む行列を扱うための確率分布やダイバージェンス，さらには分解結果である因子行列の数や因子行列への直交制約について述べている．Nonnegative matrix factorization (NMF) is a matrix decomposition technique to analyze nonnegative data matrices, which are matrices of which all elements are nonnegative. In this thesis, we discuss extensions of NMF for exploratory data analysis considering common features of a real nonnegative data matrix and an easy interpretation. In particular, we discuss probability distributions and divergences for zero-inflated data matrix and data matrix with outliers, two-factor vs. three-factor, and orthogonal constraint to factor matrices.
博士(文化情報学)
Doctor of Culture and Information Science
同志社大学
Doshisha University
27
Caceres, Arsenio. "Local damage analysis of fiber reinforced polymer matrix composites". Morgantown, W. Va. : [West Virginia University Libraries], 1998. http://etd.wvu.edu/templates/showETD.cfm?recnum=328.
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Thesis (Ph. D.)--West Virginia University, 1998.Title from document title page. Document formatted into pages; contains x, 107 p. : ill. (some col.) Includes abstract. Includes bibliographical references (p. 104-107).
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Wang, Peng. "IMPEDANCE-TO-SCATTERING MATRIX METHOD FOR LARGE SILENCER ANALYSIS". UKnowledge, 2017. https://uknowledge.uky.edu/me_etds/102.
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Large silencers used in the power generation industry usually have a very large cross section at the inlet and outlet. Higher-order modes will populate the inlet and outlet even at very low frequencies. Although the silencer itself is often modeled by a three-dimensional analysis tool such as the boundary element method (BEM) or finite element method (FEM), a direct computation of the transmission loss (TL) from the BEM or FEM model can be challenging without incorporating certain forms of modal expansion.
A so-called “impedance-to-scattering matrix method” is proposed to extract the modes at the inlet and outlet from the BEM impedance matrix based on the point collocation method. The BEM impedance matrix relates the sound pressures at the inlet and outlet to the corresponding particle velocities, while the scattering matrix relates the modes at the inlet and outlet. Normally there are more boundary elements than the total number of modes at the inlet and outlet, and a least-squares procedure is used to condense the element-based impedance matrix to the mode-based scattering matrix. The TL computation will follow if a certain form of the incident wave is assumed and the outlet is non-reflective. Several commonly used inlet/outlet configurations are considered in this dissertation, which include axisymmetric, non-axisymmetric circular, and rectangular inlet/outlet shapes. In addition to the single inlet and outlet silencers, large multi-inlet and multi-outlet silencers are also investigated.
Besides the collocation-based impedance-to-scattering matrix method, an integral-based impedance-to-scattering matrix method based on the reciprocal identity is also proposed for large silencer analysis. Although it may be more time-consuming to perform the additional numerical integration, an integral-based method is free of any uncertainties associated with collocation points. The computational efficiency, accuracy and stability are compared between two proposed methods.
One bonus effect of producing the scattering matrix is that it can also be used to combine subsystems in series connection. The Redheffer’s star product is introduced to combine scattering matrices of subsystems.
In the design stage, rapid assessment of the silencer performance is always preferred. However, the existing analytical approaches are only suitable for simple dissipative silencers such as straight lined ducts. A two-dimensional first-mode semi-analytical solution is developed to quickly evaluate the performance of tuned dissipative silencers below the cut-off frequency. The semi-analytical solution can also serve as a validation tool for the BEM.
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Dong, Kai. "High-dimensional covariance matrix estimation with application to Hotelling's tests". HKBU Institutional Repository, 2015. https://repository.hkbu.edu.hk/etd_oa/191.
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In recent years, high-dimensional data sets are widely available in many scientific areas, such as gene expression study, finance and others. Estimating the covariance matrix is a significant issue in such high-dimensional data analysis. This thesis focuses on high-dimensional covariance matrix estimation and its application. First, this thesis focuses on the covariance matrix estimation. In Chapter 2, a new optimal shrinkage estimation of the covariance matrices is proposed. This method is motivated by the quadratic discriminant analysis where many covariance matrices need to be estimated simultaneously. We shrink the sample covariance matrix towards the pooled sample covariance matrix through a shrinkage parameter. Some properties of the optimal shrinkage parameter are investigated and we also provide how to estimate the optimal shrinkage parameter. Simulation studies and real data analysis are also conducted. In Chapter 4, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, a total of nine covariance matrix estimation methods will be considered for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. A few practical guidelines are also made on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this chapter also serves as a proxy to assess the performance of the covariance matrix estimation. Second, this thesis focuses on the application of high-dimensional covariance matrix estimation. In Chapter 3, we consider to estimate the high-dimensional covariance matrix based on the diagonal matrix of the sample covariance matrix and apply it to the Hotelling’s tests. In this chapter, we propose a shrinkage-based diagonal Hotelling’s test for both one-sample and two-sample cases. We also propose several different ways to derive the approximate null distribution under different scenarios of p and n for our proposed shrinkage-based test. Simulation studies show that the proposed method performs comparably to existing competitors when n is moderate or large, and it is better when n is small. In addition, we analyze four gene expression data sets and they demonstrate the advantage of our proposed shrinkage-based diagonal Hotelling’s test. Apart from the covariance matrix estimation, we also develop a new classification method for a specific type of high-dimensional data, RNA-sequencing data. In Chapter 5, we propose a negative binomial linear discriminant analysis for RNA-Seq data. By Bayes’ rule, we construct the classifier by fitting a negative binomial model, and propose some plug-in rules to estimate the unknown parameters in the classifier. The relationship between the negative binomial classifier and the Poisson classifier is explored, with a numerical investigation of the impact of dispersion on the discriminant score. Simulation results show the superiority of our proposed method. We also analyze four real RNA-Seq data sets to demonstrate the advantage of our method in real-world applications. Keywords: Covariance matrix, Discriminant analysis, High-dimensional data, Hotelling’s test, Log determinant, RNA-sequencing data.
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Islam, Md Sajedul. "Matrix Dynamic Models for Structured Populations". Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3645.
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Matrix models are formulated to study the dynamics of the structured populations. We consider closed populations, that is, without migration, and populations with migration. The effects of specific patterns of migration, whether with constant or time-dependent terms, are explored within the context of how they manifest in model output, such as population size. Time functions, commonly known as relative sensitivities, are employed to rank the parameters of the models from most to least influential in the population size or abundance of individuals per group
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Shaver, Ryan J. "Analysis of the Tapered Transition Waveguide". Wright State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=wright1431711280.
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Amadeo, Lily. "Large Scale Matrix Completion and Recommender Systems". Digital WPI, 2015. https://digitalcommons.wpi.edu/etd-theses/1021.
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"The goal of this thesis is to extend the theory and practice of matrix completion algorithms, and how they can be utilized, improved, and scaled up to handle large data sets. Matrix completion involves predicting missing entries in real-world data matrices using the modeling assumption that the fully observed matrix is low-rank. Low-rank matrices appear across a broad selection of domains, and such a modeling assumption is similar in spirit to Principal Component Analysis. Our focus is on large scale problems, where the matrices have millions of rows and columns. In this thesis we provide new analysis for the convergence rates of matrix completion techniques using convex nuclear norm relaxation. In addition, we validate these results on both synthetic data and data from two real-world domains (recommender systems and Internet tomography). The results we obtain show that with an empirical, data-inspired understanding of various parameters in the algorithm, this matrix completion problem can be solved more efficiently than some previous theory suggests, and therefore can be extended to much larger problems with greater ease. "
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Gálvez, Sánchez José-Luis. "Analysis of bidirectional switch power modules for matrix converter application". Doctoral thesis, Universitat Autònoma de Barcelona, 2017. http://hdl.handle.net/10803/457719.
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Existeix una creixent demanda en aplicacions industrials que requereixen una transferència bidireccional de potència entre la xarxa elèctrica i una càrrega i viceversa com per exemple: elevadors, escales mecàniques, energies renovables (molins de vent, fotovoltaica, cel·les de combustible, xarxes elèctriques intel·ligents), tracció elèctrica, etc. La possibilitat de dur a terme una conversió AC-AC directa sense un bus de contínua és una realitat gràcies a la topologia de convertidor matricial de potència (CM). La típica configuració d’un CM consisteix en nou interruptors bidireccionals (IBDs) que connecten directament tres fases d’entrada de la xarxa amb tres fases de sortida d’una càrrega (típicament un motor). Controlant els IBDs d’una manera adequada, es poden obtenir una amplitud i freqüència de sortida variables. Per tant, l’IBD controlable esdevé l’element clau en la implementació de CMs, el qual és capaç de conduir corrent i bloquejar tensió en ambdues polaritats (operació en quatre quadrants) i operar a elevades freqüències de commutació.
L’objectiu d’aquesta tesi és l’anàlisi dels processos de commutació en els IBDs, predir la seva potència dissipada en un CM en operació normal i el desenvolupament d’un nou mòdul interruptor bidireccional controlable que integra l’etapa de potència amb la de control en un component que millora la modularitat i la viabilitat de les aplicacions del CM.
Primer de tot és important entendre com es comporten els IBDs en un CM. Mitjançant la simulació SPICE d’un CM simplificat de dues fases d’entrada i una de sortida s’han pogut analitzar els fenòmens de commutació que es donen entre IBDs. Commutacions dures i febles són generades en els dispositius de potència depenent de la tensió i el signe del corrent en l’IBD. Entendre els detalls dels processos de commutació permet una definició òptima de les estratègies de commutació entre IBDs i modelar la potència dissipada deguda a la seva commutació.
S’han analitzat també les característiques estàtiques i dinàmiques de varis dispositius de potència de diferent tecnologies emprats per implementar IBDs. Per aquest propòsit s’ha fabricat un circuit de test dinàmic basat en el circuit simulat de dues fases d’entrada i una de sortida abans esmentat. Aquest circuit de test ha permès avaluar IBDs discrets i mòduls de potència IBD integrats amb la mateixa placa de potència i de control. La potència en conducció i commutació s’han pogut modelar d’una manera acurada gràcies a les mesures extretes del comportament dels dispositius de l’IBD.
Aquesta tesi descriu també la implementació d’un mètode de computació per avaluar la potència dissipada en conducció i commutació (dura i feble) dels dispositius de potència de l’IBD. En base als models de pèrdues en conducció i commutació, la potència dissipada dels dispositius ha estat calculada en funció de diferent condicions d’operació del CM com l’algoritme de modulació, la freqüència de sortida, el ràtio entre tensió de sortida i d’entrada, el factor de potència de la càrrega i la freqüència de commutació. Tot aquest estudi esdevé una eina pràctica per ajudar al dissenyador del convertidor alhora de seleccionar els dispositius de potència òptims donada una aplicació i de predir d’una manera precisa la potència dissipada dels dispositius de potència per dimensionar i implementar un correcte sistema d’extracció de calor.
Finalment, un prototipus de mòdul interruptor bidireccional integrat de potència i intel·ligent (IBD-IPM) s’ha dissenyat, fabricat i testejat en un CM de tres fases d’entrada i una de sortida per donar un pas endavant en l'aplicació pràctica dels CMs. El IBD-IPM és en si mateix un sistema de potència complex perquè moltes disciplines convergeixen en ell: dispositius semiconductors de potència, gestió tèrmica, control a nivell de dispositiu i control d’alt nivell.There is a wide and increasing demand in industrial applications which require bidirectional transfer of power between the AC utility and the load, and vice versa such as: rolling mills, elevators, centrifuges, escalators, renewable energies (wind turbines, photo-voltaic, fuel-cells; smart-grids), electric traction, etc. The possibility of performing a direct AC-AC conversion with the absence of a DC link is a fact thanks to the Matrix Converter (MC) topology. The typical configuration of a MC is based on nine bidirectional switches (BDSs) required to directly connect the three input phases of an AC grid with the three output phases of a load (typically, a motor). Controlling the BDSs in a suitable way, a variable amplitude and frequency can be obtained at the output. Consequently, the key element of the MC implementation is the controlled BDS which must be able to conduct current and block voltage in both polarities (four quadrant I-V operation) and to operate at relatively high switching frequencies. The aim of this thesis is the analysis of the commutation processes in BDSs, the prediction of their power dissipation in typical MC operation and the development of a new controlled bidirectional switch module which integrates the power stage functionality with the intelligence in one component to enhance the modularity and feasibility of MC applications First of all it is important to understand how behave the BDSs within a MC. A SPICE simulation work of a simplified two-phase to single-phase MC was performed in order to analyse the commutation phenomena involved between BDSs. Hard and soft commutations are undergone by the different power devices depending on the voltage across the BDS and the direction of the current through it. Understanding the details of the switching processes allow an optimum definition of the commutation strategies within BDSs and modelling of the switching power losses. The static and dynamic characteristics of several power devices of different technologies used in BDS implementations are also analysed. A switching test circuit based on the aforementioned two-phase to single-phase MC was fabricated for this purpose. This MC test circuit allowed testing discrete BDSs as well as integrated power modules sharing the same power stage and control board. Based on the extracted measured data of the BDSs devices, their conduction and their switching losses were accurately modelled. This thesis describes also the implementation of a computational method to evaluate the conduction and switching losses (hard and soft types) of the power devices within the BDS. Based on the conduction and switching losses models, the power losses of the semiconductor devices are calculated depending on different operating condition of the MC such as the modulation algorithm, the output frequency, the output to input voltage ratio, the load power factor and the switching frequency. All these studies resulted in a practical tool to help the converter designer to select the optimum power devices for a given application and to predict in an accurate way the semiconductors power losses in order to size and implement the suitable cooling system. Finally in this work, an integrated bidirectional switch intelligent power module (BDS-IPM) prototype is designed, built and tested in a three-phase to one-phase MC in order to take a step forward in the practical implementation of MCs. The BDS-IPM is itself a complex power electronics system since many disciplines converge in it: power semiconductor devices, thermal power management, device level control (i.e. gate drive circuits) and high level control (i.e. current commutation strategy implementation, active protection issues).
34
Afsari, Bijan. "Gradient flow based matrix joint diagonalization for independent component analysis". College Park, Md. : University of Maryland, 2004. http://hdl.handle.net/1903/1352.
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Thesis (M.S.) -- University of Maryland, College Park, 2004.Thesis research directed by: Electrical Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Juozapavicius, Ausrius. "Density-Matrix Renormalization-Group Analysis of Kondo and XY models". Doctoral thesis, KTH, Physics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3260.
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Peacock, Matthew James McKenzie. "Random Matrix Theory Analysis of Fixed and Adaptive Linear Receivers". University of Sydney, 2006. http://hdl.handle.net/2123/985.
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Doctor of Philosophy (PhD)This thesis considers transmission techniques for current and future wireless and mobile communications systems. Many of the results are quite general, however there is a particular focus on code-division multiple-access (CDMA) and multi-input multi-output (MIMO) systems. The thesis provides analytical techniques and results for finding key performance metrics such as signal-to-interference and noise power ratios (SINR) and capacity. This thesis considers a large-system analysis of a general linear matrix-vector communications channel, in order to determine the asymptotic performance of linear fixed and adaptive receivers. Unlike many previous large-system analyses, these results cannot be derived directly from results in the literature. This thesis considers a first-principles analytical approach. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. The approach is also used to derive the distribution of sums and products of free random matrices. Expressions for the asymptotic SINR of the MMSE receiver are derived, along with the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.
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McCutcheon, Michael Warren. "Analysis of a 2-3 exchange symmetric neutrino mass matrix". Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=79048.
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We present an analysis of the requirements of a 2--3 exchange symmetry in the neutrino mass matrix in comparison to the experimentally allowed ranges of neutrino oscillation parameters. The symmetric matrix, being defined at an energy scale appropriate to a right-handed neutrino in a See-saw scheme of mass suppression, is subject to evolution under Supersymmetric Renormalisation Group Equations, in order to interpret the matrix at experimental energies. By way of motivation we discuss the status of neutrino mass in the Standard Model and justify the context of the analysis by examining the mechanisms and evidence for oscillations. We then review the See-saw mechanism and also the process of renormalisation and its implications for bridging disparate energy scales. We present the relevant Renormalization Group Equations and demonstrate the parameterisation of pertinent Renormalization Group effects. Finally, we review previous work analysing this symmetry before updating some of these results and extending the analysis to its global behaviour in the space of both solar and atmospheric neutrino oscillation parameters.
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Müller, Axel. "Random Matrix Analysis of Future Multi Cell MU-MIMO Networks". Thesis, Supélec, 2014. http://www.theses.fr/2014SUPL0021/document.
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Les futurs systèmes de communication sans fil devront utiliser des architectures cellulaires hétérogènes composées de grandes cellules (macro) plus performantes et de petites cellules (femto, micro, ou pico) très denses, afin de soutenir la demande de débit en augmentation exponentielle au niveau de la couche physique. Ces structures provoquent un niveau d'interférence sans précèdent à l'intérieur, comme à l'extérieur des cellules, qui doit être atténué ou, idéalement, exploité afin d'améliorer l'efficacité spectrale globale du réseau. Des techniques comme le MIMO à grande échelle (dit massive MIMO), la coopération, etc., qui contribuent aussi à la gestion des interférences, vont encore augmenter la taille des grandes architectures hétérogènes, qui échappent ainsi à toute possibilité d'analyse théorique par des techniques statistiques traditionnelles.Par conséquent, dans cette thèse, nous allons appliquer et améliorer des résultats connus de la théorie des matrices aléatoires à grande échelle (RMT) afin d'analyser le problème d'interférence et de proposer de nouveaux systèmes de précodage qui s'appuient sur les résultats acquis par l'analyse du système à grande échelle. Nous allons d'abord proposer et analyser une nouvelle famille de précodeurs qui réduit la complexité de calcul de précodage pour les stations de base équipées d'un grand nombre d'antennes, tout en conservant la plupart des capacités d'atténuation d'interférence de l'approche classique et le caractère quasi-optimal du précodeur regularised zero forcing. Dans un deuxième temps, nous allons proposer une variation de la structure de précodage linéaire optimal (obtenue pour de nombreuses mesures de performance) qui permet de réduire le niveau d'interférence induit aux autres cellules. Ceci permet aux petites cellules d'atténuer efficacement les interférences induites et reçues au moyen d'une coopération minimale. Afin de faciliter l'utilisation de l'approche analytique RMT pour les futures générations de chercheurs, nous fournissons également un tutoriel exhaustif sur l'application pratique de la RMT pour les problèmes de communication en début du manuscritFuture wireless communication systems will need to feature multi cellular heterogeneous architectures consisting of improved macro cells and very dense small cells, in order to support the exponentially rising demand for physical layer throughput. Such structures cause unprecedented levels of inter and intra cell interference, which needs to be mitigated or, ideally, exploited in order to improve overall spectral efficiency of the communication network. Techniques like massive multiple input multiple output (MIMO), cooperation, etc., that also help with interference management, will increase the size of the already large heterogeneous architectures to truly enormous networks, that defy theoretical analysis via traditional statistical methods.Accordingly, in this thesis we will apply and improve the already known framework of large random matrix theory (RMT) to analyse the interference problem and propose solutions centred around new precoding schemes, which rely on large system analysis based insights. First, we will propose and analyse a new family of precoding schemes that reduce the computational precoding complexity of base stations equipped with a large number of antennas, while maintaining most of the interference mitigation capabilities of conventional close-to-optimal regularized zero forcing. Second, we will propose an interference aware linear precoder, based on an intuitive trade-off and recent results on multi cell regularized zero forcing, that allows small cells to effectively mitigate induced interference with minimal cooperation. In order to facilitate utilization of the analytic RMT approach for future generations of interested researchers, we will also provide a comprehensive tutorial on the practical application of RMT in communication problems
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Cheng, Yongming 1964. "Dynamic stiffness and transfer matrix analysis of marine riser vibration". Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/107859.
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Majundar, Pradip. "Analysis of desiccant cooling systems using advanced desiccant matrix structure". access full-text online access from Digital Dissertation Consortium, 1986. http://libweb.cityu.edu.hk/cgi-bin/er/db/ddcdiss.pl?8707884.
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Peacock, Matthew James McKenzie. "Random Matrix Theory Analysis of Fixed and Adaptive Linear Receivers". Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/985.
Pełny tekst źródłaStreszczenie:
This thesis considers transmission techniques for current and future wireless and mobile communications systems. Many of the results are quite general, however there is a particular focus on code-division multiple-access (CDMA) and multi-input multi-output (MIMO) systems. The thesis provides analytical techniques and results for finding key performance metrics such as signal-to-interference and noise power ratios (SINR) and capacity. This thesis considers a large-system analysis of a general linear matrix-vector communications channel, in order to determine the asymptotic performance of linear fixed and adaptive receivers. Unlike many previous large-system analyses, these results cannot be derived directly from results in the literature. This thesis considers a first-principles analytical approach. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. The approach is also used to derive the distribution of sums and products of free random matrices. Expressions for the asymptotic SINR of the MMSE receiver are derived, along with the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.
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ZHOU, SIYUAN. "Finite Random Matrix Theory Analysis of Multiple Antenna Communication Systems". Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2601779.
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Multiple-antenna systems are capable of providing substantial improvement to wireless communication networks, in terms of
data rate and reliability. Without utilizing extra spectrum or power resources, multiple-antenna technology has already been supported
in several wireless communication standards, such as LTE, WiFi and WiMax. The surging popularity and enormous prospect of
multiple-antenna technology require a better understanding to its fundamental performance over practical environments.
Motivated by this, this thesis provides analytical characterizations of several seminal performance measures in advanced multiple-antenna
systems. The analytical derivations are mainly based on finite dimension random matrix theory and a collection of novel random matrix theory
results are derived.
The closed-form probability density function of the output of multiple-input multiple-output (MIMO) block-fading channels is studied.
In contrast to the existing results, the proposed expressions are very general, applying for arbitrary number of antennas, arbitrary signal-to-noise
ratio and multiple classical fading models. Results are presented assuming two input structures in the system: the independent identical distributed
(i.i.d.) Gaussian input and a product form input. When the channel is fed by the i.i.d. Gaussian input, analysis is focused on the channel matrices
whose Gramian is unitarily invariant. When the channel is fed by a product form input, analysis is conducted with respect to two capacity-achieving
input structures that are dependent upon the relationship between the coherence length and the number of antennas. The mutual information
of the systems can be computed numerically from the pdf expression of the output. The computation is relatively easy to handle, avoiding the
need of the straight Monte-Carlo computation which is not feasible in large-dimensional networks.
The analytical characterization of the output pdf of a single-user MIMO block-fading channels with imperfect channel state information at the receiver
is provided. The analysis is carried out under the assumption of a product structure for the input. The model can be thought of as a perturbation
of the case where the statistics of the channel are perfectly known. Specifically, the average singular values of the channel are given, while the
channel singular vectors are assumed to be isotropically distributed on the unitary groups of dimensions given by the number of transmit and
receive antennas. The channel estimate is affected by a Gaussian distributed error, which is modeled as a matrix with i.i.d. Gaussian entries of
known covariance.
The ergodic capacity of an amplify-and-forward (AF) MIMO relay network over asymmetric channels is investigated. In particular, the source-relay
and relay-destination channels undergo Rayleigh and Rician fading, respectively. Considering arbitrary-rank means for the relay-destination channel,
the marginal distribution of an unordered eigenvalue of the cascaded AF channel is presented, thus the analytical expression of the ergodic capacity
of the system is obtained. The results indicate the impact of the signal-to-noise ratio and of the Line-of-Sight component on such asymmetric
relay network.
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Kuang, Da. "Nonnegative matrix factorization for clustering". Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/52299.
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This dissertation shows that nonnegative matrix factorization (NMF) can be extended to a general and efficient clustering method. Clustering is one of the fundamental tasks in machine learning. It is useful for unsupervised knowledge discovery in a variety of applications such as text mining and genomic analysis. NMF is a dimension reduction method that approximates a nonnegative matrix by the product of two lower rank nonnegative matrices, and has shown great promise as a clustering method when a data set is represented as a nonnegative data matrix. However, challenges in the widespread use of NMF as a clustering method lie in its correctness and efficiency: First, we need to know why and when NMF could detect the true clusters and guarantee to deliver good clustering quality; second, existing algorithms for computing NMF are expensive and often take longer time than other clustering methods. We show that the original NMF can be improved from both aspects in the context of clustering. Our new NMF-based clustering methods can achieve better clustering quality and run orders of magnitude faster than the original NMF and other clustering methods.
Like other clustering methods, NMF places an implicit assumption on the cluster structure. Thus, the success of NMF as a clustering method depends on whether the representation of data in a vector space satisfies that assumption. Our approach to extending the original NMF to a general clustering method is to switch from the vector space representation of data points to a graph representation. The new formulation, called Symmetric NMF, takes a pairwise similarity matrix as an input and can be viewed as a graph clustering method. We evaluate this method on document clustering and image segmentation problems and find that it achieves better clustering accuracy. In addition, for the original NMF, it is difficult but important to choose the right number of clusters. We show that the widely-used consensus NMF in genomic analysis for choosing the number of clusters have critical flaws and can produce misleading results. We propose a variation of the prediction strength measure arising from statistical inference to evaluate the stability of clusters and select the right number of clusters. Our measure shows promising performances in artificial simulation experiments.
Large-scale applications bring substantial efficiency challenges to existing algorithms for computing NMF. An important example is topic modeling where users want to uncover the major themes in a large text collection. Our strategy of accelerating NMF-based clustering is to design algorithms that better suit the computer architecture as well as exploit the computing power of parallel platforms such as the graphic processing units (GPUs). A key observation is that applying rank-2 NMF that partitions a data set into two clusters in a recursive manner is much faster than applying the original NMF to obtain a flat clustering. We take advantage of a special property of rank-2 NMF and design an algorithm that runs faster than existing algorithms due to continuous memory access. Combined with a criterion to stop the recursion, our hierarchical clustering algorithm runs significantly faster and achieves even better clustering quality than existing methods. Another bottleneck of NMF algorithms, which is also a common bottleneck in many other machine learning applications, is to multiply a large sparse data matrix with a tall-and-skinny dense matrix. We use the GPUs to accelerate this routine for sparse matrices with an irregular sparsity structure. Overall, our algorithm shows significant improvement over popular topic modeling methods such as latent Dirichlet allocation, and runs more than 100 times faster on data sets with millions of documents.
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Lawrence, David Peter. "Skills analysis aboard ships". Thesis, University of Plymouth, 1988. http://hdl.handle.net/10026.1/1717.
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Willison, Peter A. "Transmission line matrix modelling of underwater acoustic propagation". Thesis, University of Essex, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334426.
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Kwizera, Petero. "Matrix Singular Value Decomposition". UNF Digital Commons, 2010. http://digitalcommons.unf.edu/etd/381.
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This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is applied to image compression by using reduced rank matrix approximations to represent greyscale images. MATLAB results for approximations of JPEG and .bmp images are presented. The results indicate that images can be represented with reasonable resolution using low rank matrix SVD approximations.
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Zhou, Ke. "Extending low-rank matrix factorizations for emerging applications". Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50230.
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Low-rank matrix factorizations have become increasingly popular to project high dimensional data into latent spaces with small dimensions in order to obtain better understandings of the data and thus more accurate predictions. In particular, they have been widely applied to important applications such as collaborative filtering and social network analysis. In this thesis, I investigate the applications and extensions of the ideas of the low-rank matrix factorization to solve several practically important problems arise from collaborative filtering and social network analysis.
A key challenge in recommendation system research is how to effectively profile new users, a problem generally known as \emph{cold-start} recommendation.
In the first part of this work, we extend the low-rank matrix factorization by allowing the latent factors to have more complex structures --- decision trees to solve the problem of cold-start recommendations. In particular, we present \emph{functional matrix
factorization} (fMF), a novel cold-start recommendation method that
solves the problem of adaptive interview construction based on low-rank matrix factorizations.
The second part of this work considers the efficiency problem of making recommendations in the context of large user and item spaces.
Specifically, we address the problem through learning binary codes for collaborative filtering, which can be viewed as restricting the latent factors in low-rank matrix factorizations to be binary vectors that represent the binary codes for both users and items.
In the third part of this work, we investigate the applications of low-rank matrix factorizations in the context of social network analysis. Specifically, we propose a convex optimization approach to discover the hidden network of social influence with low-rank and sparse structure by modeling the recurrent events at different individuals as multi-dimensional Hawkes processes, emphasizing the mutual-excitation nature of the dynamics of event occurrences. The proposed framework combines the estimation of mutually exciting process and the low-rank matrix factorization in a principled manner.
In the fourth part of this work, we estimate the triggering kernels for the Hawkes process. In particular, we focus on estimating the triggering kernels from an infinite dimensional functional space with the Euler Lagrange equation, which can be viewed as applying the idea of low-rank factorizations in the functional space.
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Martin, David Royce. "Quadrature Approximation of Matrix Functions, with Applications". Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1337658656.
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He, Yihong. "Matrix-dominated constitutive laws for composite materials". Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34666.
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Accurate three-dimensional stress-strain constitutive properties are essential to understanding complex deformation and failure mechanisms for materials with highly anisotropic mechanical properties. The large number of different methods and specimen types currently required to generate three-dimensional allowables for structural design slow down the material characterization. Also, some of the material constitutive properties are never measured due to prohibitive cost of the specimens needed. A method for measurement of three-dimensional constitutive properties using short-beam specimens subject to three-point bend load has been recently developed. This method is based on the Digital Image Correlation (DIC) full-field deformation measurement and closed-form stress approximation. The purpose of this work is to improve the accuracy of the constitutive properties through accurate stress solution. A method is developed based on a combination of full-field strain measurement and nonlinear finite element stress analysis in the material characterization. The nonlinear shear stress-strain relations are the major concern in this work. An iterative procedure is applied to update the nonlinear shear properties using iterative finite element simulations. The accuracy of the numerical procedure is verified by comparing the finite element strain results with full-field measurements. The procedure is further verified using the V-notched beam test results. Excellent agreement has been achieved in the verification. Simplicity of the short-beam specimens and accuracy of the constitutive property approximations make the present method attractive for measurement of three-dimensional stress-strain relations for anisotropic materials at various load rates.
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Belton, Alexander C. R. "A matrix formulation of quantum stochastic calculus". Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301800.
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We develop the theory of chaos spaces and chaos matrices. A chaos space is a Hilbert space with a fixed, countably-infinite, direct-sum decomposition. A chaos matrix between two chaos spaces is a doubly-infinite matrix of bounded operators which respects this decomposition. We study operators represented by such matrices, particularly with respect to self-adjointness. This theory is used to re-formulate the quantum stochastic calculus of Hudson and Parthasarathy. Integrals of chaos-matrix processes are defined using the Hitsuda-Skorokhod integral and Malliavin gradient,following Lindsay and Belavkin. A new way of defining adaptedness is developed and the consequent quantum product Ito formula is used to provide a genuine functional Ito formula for polynomials in a large class of unbounded processes, which include the Poisson process and Brownian motion. A new type of adaptedness, known as $\Omega$-adaptedness, is defined. We show that quantum stochastic integrals of $\Omega$-adapted processes are well-behaved; for instance, bounded processes have bounded integrals. We solve the appropriate modification of the evolution equation of Hudson and Parthasarathy: $U(t)=I+\int_{0}^{t}E(s)\mathrm{d}\Lambda(s)+F(s)\mathrm{d} A(s)+ G(s)U(s)\mathrm{d} A^{\dagger}(s)+H(s)U(s)\mathrm{d} s, $ where the coefficients are time-dependent, bounded, $\Omega$-adapted processes acting on the whole Fock space. We show that the usual conditions on the coefficients, viz. $(E,F,G,H)=(W-I,L,-WL^{*},iK+\mbox{$\frac{1}{2}$}LL^{*})$ where $W$ is unitary and $K$ self-adjoint, are necessary and sufficient conditions for the solution to be unitary. This is a very striking result when compared to the adapted case.