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Regularization methods for discrete inverse problems in single particle analysis
Havelková, Eva ; Hnětynková, Iveta (advisor) ; Plešinger, Martin (referee)
The aim of this thesis is to investigate applicability of regulariza- tion by Krylov subspace methods to discrete inverse problems arising in single particle analysis (SPA). We start with a smooth model formulation and describe its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a lin- ear operator and b represents the measured noisy data. We provide theoretical background and overview of selected methods for the solution of general linear inverse problems. Then we focus on specific properties of inverse problems from SPA, and provide experimental analysis based on synthetically generated SPA datasets (experiments are performed in the Matlab enviroment). Turning to the solution of our inverse problem, we investigate in particular an approach based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable stopping criterion for the iterative part as well as parameter-choice method for the inner regularization are discussed. Providing a complete implementation of the proposed solver (in Matlab and in C++), its performance is evaluated on various SPA model datasets, considering high levels of noise and realistic distri- bution of orientations of scanning angles. Comparison to other regularization methods, including the ART method traditionally used in SPA,...
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Modern separation and spectrometric techniques for biological sample lipidom investigation
Havelková, Eva ; Bosáková, Zuzana (advisor) ; Sýkora, David (referee)
Modern separation and spectrometric techniques for biological sample lipidom investigation Due recent progress in field of mass spectrometry the lipidomics, part of metabolomics, is increasing its importance for broad fields of biological study. The aim of this study is to test the lipid extraction techniques and to optimize the preseparation and separation of lipids suitable for mass spectrometry detection. The fragmentation patterns of four, the most abundant lipid classes of glycerolipids (PC, PE, TG, DG), were acquired for the proposed system. These patterns were compared with literature. The most appropriate method for extraction was declared technique according Folch based on methanol and chloroform solution. The preseparation due SPE method is very useful tool for lipid determination. The optimized were focused to reach higher recovery especially in polar lipid fraction. Proposed HPLC system is based on methanol with ammonium buffer, water and isopropanol. The testing was done on three columns with different type of sorbents (Gemini, Syncronis and Kinetex). The separation was evaluated according mass spectrometer response, shape and wide of particular analytes peaks. Composition contains 20% of water was determinate as the best and also the best separation was achieved by Kinetex column. The proposed...
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Regularization methods for discrete inverse problems in single particle analysis
Havelková, Eva ; Hnětynková, Iveta (advisor)
The aim of this thesis is to investigate applicability of regulariza- tion by Krylov subspace methods to discrete inverse problems arising in single particle analysis (SPA). We start with a smooth model formulation and describe its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a lin- ear operator and b represents the measured noisy data. We provide theoretical background and overview of selected methods for the solution of general linear inverse problems. Then we focus on specific properties of inverse problems from SPA, and provide experimental analysis based on synthetically generated SPA datasets (experiments are performed in the Matlab enviroment). Turning to the solution of our inverse problem, we investigate in particular an approach based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable stopping criterion for the iterative part as well as parameter-choice method for the inner regularization are discussed. Providing a complete implementation of the proposed solver (in Matlab and in C++), its performance is evaluated on various SPA model datasets, considering high levels of noise and realistic distri- bution of orientations of scanning angles. Comparison to other regularization methods, including the ART method traditionally used in SPA,...
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Regularization methods for discrete inverse problems in single particle analysis
Havelková, Eva ; Hnětynková, Iveta (advisor) ; Plešinger, Martin (referee)
The aim of this thesis is to investigate applicability of regulariza- tion by Krylov subspace methods to discrete inverse problems arising in single particle analysis (SPA). We start with a smooth model formulation and describe its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a lin- ear operator and b represents the measured noisy data. We provide theoretical background and overview of selected methods for the solution of general linear inverse problems. Then we focus on specific properties of inverse problems from SPA, and provide experimental analysis based on synthetically generated SPA datasets (experiments are performed in the Matlab enviroment). Turning to the solution of our inverse problem, we investigate in particular an approach based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable stopping criterion for the iterative part as well as parameter-choice method for the inner regularization are discussed. Providing a complete implementation of the proposed solver (in Matlab and in C++), its performance is evaluated on various SPA model datasets, considering high levels of noise and realistic distri- bution of orientations of scanning angles. Comparison to other regularization methods, including the ART method traditionally used in SPA,...
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Methods for the solution of nonlinear equations
Havelková, Eva ; Kučera, Václav (advisor) ; Tichý, Petr (referee)
The aim of this bachelor thesis is to present an overview of elementary numerical methods for solving nonlinear algebraic equations in one variable. Firstly, related concepts from numerical mathematics and mathematical analysis are explained. The main part of the thesis provides a detailed description of chosen iterative methods as well as the proofs of their orders of convergence. The methods covered are namely the bisection method, fixed-point iteration, regula falsi method, Newton's method, secant method and methods that are based on quadratic interpolation. The practical part of the thesis presents results of numerical experiments that were carried out with Matlab software on various types of nonlinear equations. These results are compared with the theory introduced in the preceding parts. The contribution of this thesis is to provide a comprehensive overview and comparison of the characteristics of basic methods for solving nonlinear equations based on a variety of literature. Powered by TCPDF (www.tcpdf.org)
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Modern separation and spectrometric techniques for biological sample lipidom investigation
Havelková, Eva ; Bosáková, Zuzana (advisor) ; Sýkora, David (referee)
Modern separation and spectrometric techniques for biological sample lipidom investigation Due recent progress in field of mass spectrometry the lipidomics, part of metabolomics, is increasing its importance for broad fields of biological study. The aim of this study is to test the lipid extraction techniques and to optimize the preseparation and separation of lipids suitable for mass spectrometry detection. The fragmentation patterns of four, the most abundant lipid classes of glycerolipids (PC, PE, TG, DG), were acquired for the proposed system. These patterns were compared with literature. The most appropriate method for extraction was declared technique according Folch based on methanol and chloroform solution. The preseparation due SPE method is very useful tool for lipid determination. The optimized were focused to reach higher recovery especially in polar lipid fraction. Proposed HPLC system is based on methanol with ammonium buffer, water and isopropanol. The testing was done on three columns with different type of sorbents (Gemini, Syncronis and Kinetex). The separation was evaluated according mass spectrometer response, shape and wide of particular analytes peaks. Composition contains 20% of water was determinate as the best and also the best separation was achieved by Kinetex column. The proposed...
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Different Points of View on Children Born with Mental Disabilities
Havelková, Eva ; Šiška, Jan (advisor) ; Zemková, Jaroslava (referee)
My diploma work called "Various aspects on a birth of mental disabled child" ties together with my bachelor work, which I wrote at Evangelic Theological Faculty at Charles Univerzity. In this bachelor work I was interested in the basical rights of mental disabled people. I taught the topic of a right to live. The meaning of this question grows with the developement of new biotechnology as an artificial insemination, an antenatal diagnostics, a miscarriage and a gene therapy. The other important question talks about the mother rights. These questions traditonally pronounce physicians, philosophers, theologians and sociologists of medicine. However special pedagogues should as well think about and participate in discussions about this topic. Special education comes to the new period with currently knowledges of not only human genome. That is why I target the bioethic sphere, different opinions and possibilities of special pedagogue's treating. in my diploma work, because bioethic spere touch the special education. I come out from historical point of view, from attitudes formulated in our history and from society attitudes to disabled individuals. The work of special pedagogues in this area should focus at disabled people and their parents who decided to take care of the child and at people who are just...
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