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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Convex Analysis And Flows In Infinite Networks

Wattanataweekul, Hathaikarn 13 May 2006 (has links)
We study the existence of flows in infinite networks and extend basic theorems due to Gale and Hoffman and to Ford and Fulkerson. The classical approach to finite networks uses a constructive combinatorical algorithm that has become known as the labelling algorithm. Our approach to infinite networks involves Hahn--Banach type theorems on the existence of certain linear functionals. Thus the main tools are from the theory of functional and convex analysis. In Chapter II, we discuss sublinear and linear functionals on real vector spaces in the spirit of the work of K"{o}nig. In particular, a generalization of K"{o}nig's minimum theorem is established. Our theory leads to some useful interpolation results. We also establish a variant of the main interpolation theorem in the context of convex cones. We reformulate the results of Ford--Fulkerson and Gale--Hoffman in terms of certain additive and biadditive set functions. In Chapter III, we show that the space of all additive set functions may be canonically identified with the dual space of a space of certain step functions and that the space of all biadditive set functions may be identified with the dual space of a space of certain step functions in two variables. Our work an additive set functions is in the spirit of classical measure theory, while the case of biadditive set functions resembles the theory of product measures. In Chapter IV, we develop an extended version of the Gale--Hoffman theorem on the existence of flows in infinite networks in a setting of measure-theoretic flavor. This general flow theorem is one of our central results. We discuss, as an application of our flow theorem, a Ford--Fulkerson type result on maximal flows and minimal cuts in infinite networks containing sources and sinks. In addition, we present applications to flows in locally finite networks and to the existence of antisymmetric flows under certain natural conditions. We conclude with a discussion of the case of triadditive set functions. In the appendix, we review briefly the classical theory of maximal flows and minimal cuts in networks with finitely many nodes.
2

Sobre medidas unicamente maximizantes e outras questões em otimização ergódica

Spier, Thomás Jung January 2016 (has links)
Nessa dissertação estudamos Sistemas Dinâmicos do ponto de vista da Otimização Ergódica. Analizamos o problema da maximização da integral de potenciais com respeito a probabilidades invariantes pela dinâmica. Mostramos que toda medida ergódica e unicamente maximizante para algum potencial. Verificamos que o conjunto de potenciais com exatamente uma medida maximizadora e residual. Esses resultados são obtidos atrav es de técnicas da Teoria Ergódica e Análise Convexa. / In this thesis we study dynamical systems trough the viewpoint of ergodic optimization. We analyze the problem of maximizing integrals of potentials with respect to invariant probabilities. We show that every ergodic measure is uniquely maximizing for some potential. We also verify that the set of potentials with exactly one maximizing measure is residual. This results are obtained through techniques of ergodic theory and convex analysis.
3

Sobre medidas unicamente maximizantes e outras questões em otimização ergódica

Spier, Thomás Jung January 2016 (has links)
Nessa dissertação estudamos Sistemas Dinâmicos do ponto de vista da Otimização Ergódica. Analizamos o problema da maximização da integral de potenciais com respeito a probabilidades invariantes pela dinâmica. Mostramos que toda medida ergódica e unicamente maximizante para algum potencial. Verificamos que o conjunto de potenciais com exatamente uma medida maximizadora e residual. Esses resultados são obtidos atrav es de técnicas da Teoria Ergódica e Análise Convexa. / In this thesis we study dynamical systems trough the viewpoint of ergodic optimization. We analyze the problem of maximizing integrals of potentials with respect to invariant probabilities. We show that every ergodic measure is uniquely maximizing for some potential. We also verify that the set of potentials with exactly one maximizing measure is residual. This results are obtained through techniques of ergodic theory and convex analysis.
4

Sobre medidas unicamente maximizantes e outras questões em otimização ergódica

Spier, Thomás Jung January 2016 (has links)
Nessa dissertação estudamos Sistemas Dinâmicos do ponto de vista da Otimização Ergódica. Analizamos o problema da maximização da integral de potenciais com respeito a probabilidades invariantes pela dinâmica. Mostramos que toda medida ergódica e unicamente maximizante para algum potencial. Verificamos que o conjunto de potenciais com exatamente uma medida maximizadora e residual. Esses resultados são obtidos atrav es de técnicas da Teoria Ergódica e Análise Convexa. / In this thesis we study dynamical systems trough the viewpoint of ergodic optimization. We analyze the problem of maximizing integrals of potentials with respect to invariant probabilities. We show that every ergodic measure is uniquely maximizing for some potential. We also verify that the set of potentials with exactly one maximizing measure is residual. This results are obtained through techniques of ergodic theory and convex analysis.
5

A Study of Machine Learning Approaches for Biomedical Signal Processing

Shen, Minjie 10 June 2021 (has links)
The introduction of high-throughput molecular profiling technologies provides the capability of studying diverse biological systems at molecular level. However, due to various limitations of measurement instruments, data preprocessing is often required in biomedical research. Improper preprocessing will have negative impact on the downstream analytics tasks. This thesis studies two important preprocessing topics: missing value imputation and between-sample normalization. Missing data is a major issue in quantitative proteomics data analysis. While many methods have been developed for imputing missing values in high-throughput proteomics data, comparative assessment on the accuracy of existing methods remains inconclusive, mainly because the true missing mechanisms are complex and the existing evaluation methodologies are imperfect. Moreover, few studies have provided an outlook of current and future development. We first report an assessment of eight representative methods collectively targeting three typical missing mechanisms. The selected methods are compared on both realistic simulation and real proteomics datasets, and the performance is evaluated using three quantitative measures. We then discuss fused regularization matrix factorization, a popular low-rank matrix factorization framework with similarity and/or biological regularization, which is extendable to integrating multi-omics data such as gene expressions or clinical variables. We further explore the potential application of convex analysis of mixtures, a biologically inspired latent variable modeling strategy, to missing value imputation. The preliminary results on proteomics data are provided together with an outlook into future development directions. While a few winners emerged from our comparative assessment, data-driven evaluation of imputation methods is imperfect because performance is evaluated indirectly on artificial missing or masked values not authentic missing values. Imputation accuracy may vary with signal intensity. Fused regularization matrix factorization provides a possibility of incorporating external information. Convex analysis of mixtures presents a biologically plausible new approach. Data normalization is essential to ensure accurate inference and comparability of gene expressions across samples or conditions. Ideally, gene expressions should be rescaled based on consistently expressed reference genes. However, for normalizing biologically diverse samples, the most commonly used reference genes have exhibited striking expression variability, and distribution-based approaches can be problematic when differentially expressed genes are significantly asymmetric. We introduce a Cosine score based iterative normalization (Cosbin) strategy to normalize biologically diverse samples. The between-sample normalization is based on iteratively identified consistently expressed genes, where differentially expressed genes are sequentially eliminated according to scale-invariant Cosine scores. We evaluate the performance of Cosbin and four other representative normalization methods (Total count, TMM/edgeR, DESeq2, DEGES/TCC) on both idealistic and realistic simulation data sets. Cosbin consistently outperforms the other methods across various performance criteria. Implemented in open-source R scripts and applicable to grouped or individual samples, the Cosbin tool will allow biologists to detect subtle yet important molecular signals across known or novel phenotypic groups. / Master of Science / Data preprocessing is often required due to various limitations of measurement instruments in biomedical research. This thesis studies two important preprocessing topics: missing value imputation and between-sample normalization. Missing data is a major issue in quantitative proteomics data analysis. Imputation is the process of substituting for missing values. We propose a more realistic assessment workflow which can preserve the original data distribution, and then assess eight representative general-purpose imputation strategies. We explore two biologically inspired imputation approaches: fused regularization matrix factorization (FRMF) and convex analysis of mixtures (CAM) imputation. FRMF integrates external information such as clinical variables and multi-omics data into imputation, while CAM imputation incorporates biological assumptions. We show that the integration of biological information improves the imputation performance. Data normalization is required to ensure correct comparison. For gene expression data, between sample normalization is needed. We propose a Cosine score based iterative normalization (Cosbin) strategy to normalize biologically diverse samples. We show that Cosbin significantly outperform other methods in both ideal simulation and realistic simulation. Implemented in open-source R scripts and applicable to grouped or individual samples, the Cosbin tool will allow biologists to detect subtle yet important molecular signals across known or novel cell types.
6

Design and Implementation of Convex Analysis of Mixtures Software Suite

Meng, Fan 10 September 2012 (has links)
Various convex analysis of mixtures (CAM) based algorithms have been developed to address real world blind source separation (BSS) problems and proven to have good performances in previous papers. This thesis reported the implementation of a comprehensive software CAM-Java, which contains three different CAM based algorithms, CAM compartment modeling (CAM-CM), CAM non-negative independent component analysis (CAM-nICA), and CAM non-negative well-grounded component analysis (CAM-nWCA). The implementation works include: translation of MATLAB coded algorithms to open-sourced R alternatives. As well as building a user friendly graphic user interface (GUI) to integrate three algorithms together, which is accomplished by adopting Java Swing API. In order to combine R and Java coded modules, an open-sourced project RCaller is used to handle the establishment of low level connection between R and Java environment. In addition, specific R scripts and Java classes are also implemented to accomplish the tasks of passing parameters and input data from Java to R, run R scripts in Java environment, read R results back to Java, display R generated figures, and so on. Furthermore, system stream redirection and multi-threads techniques are used to build a simple R messages displaying window in Java built GUI. The final version of the software runs smoothly and stable, and the CAM-CM results on both simulated and real DCE-MRI data are quite close to the original MATLAB version algorithms. The whole GUI based open-sourced software is easy to use, and can be freely distributed among the communities. Technical details in both R and Java modules implementation are also discussed, which presents some good examples of how to develop software with both complicate and up to date algorithms, as well as decent and user friendly GUI in the scientific or engineering research fields. / Master of Science
7

On the Generalizations of Gershgorin's Theorem

Lee, Sang-Gu 01 May 1986 (has links)
This paper deals with generalization fo Gershgorin's theorem. This theorem is investigated and generalized in terms of contour integrals, directed graphs, convex analysis, and clock matrices. These results are shown to apply to some specified matrices such as stable and stochastic matrices and some examples will show the relationship of eigenvalue inclusion regions among them.
8

Metabolic design of dynamic bioreaction models

Provost, Agnès 06 November 2006 (has links)
This thesis is concerned with the derivation of bioprocess models intended for engineering purposes. In contrast with other techniques, the methodology used to derive a macroscopic model is based on available intracellular information. This information is extracted from the metabolic network describing the intracellular metabolism. The aspects of metabolic regulation are modeled by representing the metabolism of cultured cells with several metabolic networks. Here we present a systematic methodology for deriving macroscopic models when such metabolic networks are known. A separate model is derived for each “phase” of the culture. Each of these models relies upon a set of macroscopic bioreactions that resumes the information contained in the corresponding metabolic network. Such a set of macroscopic bioreactions is obtained by translating the set of Elementary Flux Modes which are well-known tools in the System Biology community. The Elementary Flux Modes are described in the theory of Convex Analysis. They represent pathways across metabolic networks. Once the set of Elementary Flux Modes is computed and translated into macroscopic bioreactions, a general model could be obtained for the type of culture under investigation. However, depending on the size and the complexity of the metabolic network, such a model could contain hundreds, and even thousands, of bioreactions. Since the reaction kinetics of such bioreactions are parametrized with at least one parameter that needs to be identified, the reduction of the general model to a more manageable size is desirable. Convex Analysis provides further results that allow for the selection of a macroscopic bioreaction subset. This selection is based on the data collected from the available experiments. The selected bioreactions then allow for the construction of a model for the experiments at hand.
9

Mathematical Modeling and Deconvolution for Molecular Characterization of Tissue Heterogeneity

Chen, Lulu 22 January 2020 (has links)
Tissue heterogeneity, arising from intermingled cellular or tissue subtypes, significantly obscures the analyses of molecular expression data derived from complex tissues. Existing computational methods performing data deconvolution from mixed subtype signals almost exclusively rely on supervising information, requiring subtype-specific markers, the number of subtypes, or subtype compositions in individual samples. We develop a fully unsupervised deconvolution method to dissect complex tissues into molecularly distinctive tissue or cell subtypes directly from mixture expression profiles. We implement an R package, deconvolution by Convex Analysis of Mixtures (debCAM) that can automatically detect tissue or cell-specific markers, determine the number of constituent sub-types, calculate subtype proportions in individual samples, and estimate tissue/cell-specific expression profiles. We demonstrate the performance and biomedical utility of debCAM on gene expression, methylation, and proteomics data. With enhanced data preprocessing and prior knowledge incorporation, debCAM software tool will allow biologists to perform a deep and unbiased characterization of tissue remodeling in many biomedical contexts. Purified expression profiles from physical experiments provide both ground truth and a priori information that can be used to validate unsupervised deconvolution results or improve supervision for various deconvolution methods. Detecting tissue or cell-specific expressed markers from purified expression profiles plays a critical role in molecularly characterizing and determining tissue or cell subtypes. Unfortunately, classic differential analysis assumes a convenient test statistic and associated null distribution that is inconsistent with the definition of markers and thus results in a high false positive rate or lower detection power. We describe a statistically-principled marker detection method, One Versus Everyone Subtype Exclusively-expressed Genes (OVESEG) test, that estimates a mixture null distribution model by applying novel permutation schemes. Validated with realistic synthetic data sets on both type 1 error and detection power, OVESEG-test applied to benchmark gene expression data sets detects many known and de novo subtype-specific expressed markers. Subsequent supervised deconvolution results, obtained using markers detected by the OVESEG-test, showed superior performance when compared with popular peer methods. While the current debCAM approach can dissect mixed signals from multiple samples into the 'averaged' expression profiles of subtypes, many subsequent molecular analyses of complex tissues require sample-specific deconvolution where each sample is a mixture of 'individualized' subtype expression profiles. The between-sample variation embedded in sample-specific subtype signals provides critical information for detecting subtype-specific molecular networks and uncovering hidden crosstalk. However, sample-specific deconvolution is an underdetermined and challenging problem because there are more variables than observations. We propose and develop debCAM2.0 to estimate sample-specific subtype signals by nuclear norm regularization, where the hyperparameter value is determined by random entry exclusion based cross-validation scheme. We also derive an efficient optimization approach based on ADMM to enable debCAM2.0 application in large-scale biological data analyses. Experimental results on realistic simulation data sets show that debCAM2.0 can successfully recover subtype-specific correlation networks that is unobtainable otherwise using existing deconvolution methods. / Doctor of Philosophy / Tissue samples are essentially mixtures of tissue or cellular subtypes where the proportions of individual subtypes vary across different tissue samples. Data deconvolution aims to dissect tissue heterogeneity into biologically important subtypes, their proportions, and their marker genes. The physical solution to mitigate tissue heterogeneity is to isolate pure tissue components prior to molecular profiling. However, these experimental methods are time-consuming, expensive and may alter the expression values during isolation. Existing literature primarily focuses on supervised deconvolution methods which require a priori information. This approach has an inherent problem as it relies on the quality and accuracy of the a priori information. In this dissertation, we propose and develop a fully unsupervised deconvolution method - deconvolution by Convex Analysis of Mixtures (debCAM) that can estimate the mixing proportions and 'averaged' expression profiles of individual subtypes present in heterogeneous tissue samples. Furthermore, we also propose and develop debCAM2.0 that can estimate 'individualized' expression profiles of participating subtypes in complex tissue samples. Subtype-specific expressed markers, or marker genes (MGs), serves as critical a priori information for supervised deconvolution. MGs are exclusively and consistently expressed in a particular tissue or cell subtype while detecting such unique MGs involving many subtypes constitutes a challenging task. We propose and develop a statistically-principled method - One Versus Everyone Subtype Exclusively-expressed Genes (OVESEG-test) for robust detection of MGs from purified profiles of many subtypes.
10

Learning Statistical and Geometric Models from Microarray Gene Expression Data

Zhu, Yitan 01 October 2009 (has links)
In this dissertation, we propose and develop innovative data modeling and analysis methods for extracting meaningful and specific information about disease mechanisms from microarray gene expression data. To provide a high-level overview of gene expression data for easy and insightful understanding of data structure, we propose a novel statistical data clustering and visualization algorithm that is comprehensively effective for multiple clustering tasks and that overcomes some major limitations of existing clustering methods. The proposed clustering and visualization algorithm performs progressive, divisive hierarchical clustering and visualization, supported by hierarchical statistical modeling, supervised/unsupervised informative gene/feature selection, supervised/unsupervised data visualization, and user/prior knowledge guidance through human-data interactions, to discover cluster structure within complex, high-dimensional gene expression data. For the purpose of selecting suitable clustering algorithm(s) for gene expression data analysis, we design an objective and reliable clustering evaluation scheme to assess the performance of clustering algorithms by comparing their sample clustering outcome to phenotype categories. Using the proposed evaluation scheme, we compared the performance of our newly developed clustering algorithm with those of several benchmark clustering methods, and demonstrated the superior and stable performance of the proposed clustering algorithm. To identify the underlying active biological processes that jointly form the observed biological event, we propose a latent linear mixture model that quantitatively describes how the observed gene expressions are generated by a process of mixing the latent active biological processes. We prove a series of theorems to show the identifiability of the noise-free model. Based on relevant geometric concepts, convex analysis and optimization, gene clustering, and model stability analysis, we develop a robust blind source separation method that fits the model to the gene expression data and subsequently identify the underlying biological processes and their activity levels under different biological conditions. Based on the experimental results obtained on cancer, muscle regeneration, and muscular dystrophy gene expression data, we believe that the research work presented in this dissertation not only contributes to the engineering research areas of machine learning and pattern recognition, but also provides novel and effective solutions to potentially solve many biomedical research problems, for improving the understanding about disease mechanisms. / Ph. D.

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