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Segmentace mikroskopických snímků pomocí level-set metod
Bílková, Zuzana ; Kučera, Václav (advisor)
Název práce: Segmentace mikroskopických snímků pomocí level-set metod Autor: Zuzana Bílková Katedra: Katedra numerické matematiky Vedoucí diplomové práce: RNDr. Václav Kučera, Ph.D., KNM, MFF UK Konzultant: RNDr. Jindřich Soukup, ÚTIA, AV ČR Abstrakt: Tato diplomová práce představuje novou metodu pro segmentaci snímků pořízených mikroskopem s fázovým konrastem. Cílem je oddělit buňky od pozadí. Algoritmus je založen na variační formulaci level set metod, tedy na minimalizaci funkcionálu popisujícího level set funkci. Funkcionál je minimalizován gradientním tokem popsaným evoluční parciální diferenciální rovnicí. Nejdůležitější nové myšlenky jsou inicializace pomocí prahování a nové členy ve funkcionálu, které zrychlují konvergenci a zpřesňují výsledky. Také jsme použili nové funkce napsané v jazyce C k počítání gradientu a Laplaceova operátoru. Tato implementace je třikrát rychlejší než standardní funkce v MATLABu. Dosáhli jsme lepších výsledků než algoritmy, se kterými jsme metodu porovnávali. Klíčová slova: Segmentace, level set metody, aktivní kontury Title: Segmentation of microscopic images using level set methods Author: Zuzana Bílková Department: Department of Numerical Mathematics Supervisor: RNDr....
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Solving flows with very low Mach numbers
Kučera, Václav
Nazev prace: Reseni stlacitelneho proudeni s malymi Machovymi cisly. Autor: Vaclav Kucera Katedra (listav): Katedra numericke matematiky Vedouci diplomove prace: Prof. RNDr. Miloslav Feistauer, DrSc. Abstrakt: Tato prace se zabyva numerickym resenim nestacionarniho nevazkeho stlacitelneho proudeni pomoci nespojite Galerkinovy metody. Experimentalni rad presnosti metody je ovefen v pfipade skalarni rovnice konvekce-difuze. Pro Eulerovy rovmce vyzaduje explicitni casova diskretizace vyrazne omezeni casoveho kroku, umerne Machovu cislu. K odstraneni teto nevyhody je na Eulerovy rovnice aplikovana semiimplicitni linearizace z prace citovane jako [4]. Numericke experimenty ukazuji, ze tento algoritmus nedava dostatecne dobre vysledky v pfipade malych Machovych cisel. Ukazeme., ze to je zpusobeno volbou okrajove podminky. Navrzeny jsou dve techniky vedouci ke zlepseni: jednoducha heuristicka modifikace standardnich okrajovych podminek a odvozeni novych okrajovych podminek zalozenych na metode charakteristik. Ty druhe jsou testovany pro Machova cisla 0.7 az 10"6. Na zaver je navrzena semiimplicitni linearizaci vazkych clenii jako rozsifeni schematu pfevzateho z citovane prace, pro nedostatek casu neni implementovana. Puvodnim pfinosem autora je hlavne aplikovani jiz existujici prace na pfipad malych Machovych...
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Numerical solution of traffic flow models
Vacek, Lukáš ; Kučera, Václav (advisor)
Our work describes the simulation of traffic flows on networks. These are described by partial differential equations. For the numerical solution of our models, we use the discontinuous Galerkin method in space and a multistep method in time. This combination of the two methods on networks is unique and leads to a robust numerical scheme. We use several different approaches to model the traffic flow. Thus, our program must solve both scalar problems as well as systems of equations described by first and second order partial differential equations. The output of our programs is, among other things, the evolution of traffic density in time and 1D space. Since this is a physical quantity, we introduce limiters which keep the density in an admissible interval. Moreover, limiters prevent spurious oscillations in the numerical solution. All the above is performed on networks. Thus, we must deal with the situation at the junctions, which is not standard. The main task is to ensure that the law of conservation of the total amount of cars passing through the junction is still satisfied. This is achieved by modifying the numerical flux for junctions. The result of this work is the comparison of all the models, the demonstration of the benefits of the discontinuous Galerkin method and the influence of limiters.
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Numerical solution of equations describing the dynamics of flocking
Živčáková, Andrea ; Kučera, Václav (advisor)
This work is devoted to the numerical solution of equations describing the dynamics of flocks of birds. Specifically, we pay attention to the Euler equati- ons for compressible flow with a right-hand side correction. This model is based on the work Fornasier et al. (2010). Due to the complexity of the model, we focus only on the one-dimensional case. For the numerical solution we use a semi- implicit discontinuous Galerkin method. Discretization of the right-hand side is chosen so that we preserve the structure of the semi-implicit scheme for the Euler equations presented in the work Feistauer, Kučera (2007). The proposed numeri- cal scheme was implemented and numerical experiments showing the robustness of the scheme were carried out. 1
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The Crime of Trafficking in human beings
Kučera, Václav ; Bohuslav, Lukáš (referee)
The aim of the thesis is to investigate the crime of Trafficking in human beings from the point of view of substantive criminal law in the Czech Republic, to analyze its weaknesses and propose their solution. The investigation should include an assessment of whether the Czech Republic's regulation is in line with international law obligations to criminalize this crime. In this work, compilation, legal-historical, analytical and general and legal interpretation methods are used. The first part is an introduction to the issue of human trafficking. This part introduces the subject of the social deviant phenomenon and points out the necessity of its perception in various, not only legal, fields. The following is a historical outline of the development of looking at human trafficking. In the second, fundamental part of the thesis, there is an analysis of the valid substantive criminal law, which deals with human trafficking. This hermeneutic-critical analysis serves to determine the problems that are proposed in the third part of the thesis. The work for quality analysis explores the historical basis of the legal regulation of the crime of trafficking in human beings. It also sets out the three most important sources of international law, which affect the current regulation and compares whether they are...
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The Crime of Trafficking in human beings
Kučera, Václav ; Bohuslav, Lukáš (referee)
The aim of the thesis is to investigate the crime of Trafficking in human beings from the point of view of substantive criminal law in the Czech Republic, to analyze its weaknesses and propose their solution. The investigation should include an assessment of whether the Czech Republic's regulation is in line with international law obligations to criminalize this crime. In this work, compilation, legal-historical, analytical and general and legal interpretation methods are used. The first part is an introduction to the issue of human trafficking. This part introduces the subject of the social deviant phenomenon and points out the necessity of its perception in various, not only legal, fields. The following is a historical outline of the development of looking at human trafficking. In the second, fundamental part of the thesis, there is an analysis of the valid substantive criminal law, which deals with human trafficking. This hermeneutic-critical analysis serves to determine the problems that are proposed in the third part of the thesis. The work for quality analysis explores the historical basis of the legal regulation of the crime of trafficking in human beings. It also sets out the three most important sources of international law, which affect the current regulation and compares whether they are...
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Numerical solution of traffic flow models
Vacek, Lukáš ; Kučera, Václav (advisor)
Our work describes the simulation of traffic flows on networks. These are described by partial differential equations. For the numerical solution of our models, we use the discontinuous Galerkin method in space and a multistep method in time. This combination of the two methods on networks is unique and leads to a robust numerical scheme. We use several different approaches to model the traffic flow. Thus, our program must solve both scalar problems as well as systems of equations described by first and second order partial differential equations. The output of our programs is, among other things, the evolution of traffic density in time and 1D space. Since this is a physical quantity, we introduce limiters which keep the density in an admissible interval. Moreover, limiters prevent spurious oscillations in the numerical solution. All the above is performed on networks. Thus, we must deal with the situation at the junctions, which is not standard. The main task is to ensure that the law of conservation of the total amount of cars passing through the junction is still satisfied. This is achieved by modifying the numerical flux for junctions. The result of this work is the comparison of all the models, the demonstration of the benefits of the discontinuous Galerkin method and the influence of limiters.
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Numerical modelling of compressible flow using spectral element method
Jurček, Martin ; Dolejší, Vít (advisor) ; Kučera, Václav (referee)
The development of computational fluid dynamics has given us a very powerful tool for investigation of fluid dynamics. However, in order to maintain the progress, it is necessary to improve the numerical algorithms. Nowadays, the high-order methods based on the discontinuous projection seem to have the largest potential for the future. In the work, we used open-source framework Nektar++, which provides the high-order discretization method. We tested the abilities of the framework for computing the compressible sonic and transonic flow. We successfully obtained simulations of the viscous and inviscid flow. We computed the lift and the drag coefficients and showed that for a higher polynomial order we can obtain the same accuracy with less degrees of freedom and lower computational time. Also, we tested the shock capturing method for the computation of the inviscid transonic flow and confirmed the potential of the high order methods. 1
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The Crime of Trafficking in human beings
Kučera, Václav ; Tejnská, Katarína (advisor) ; Beranová, Andrea (referee)
The aim of the thesis is to investigate the crime of Trafficking in human beings from the point of view of substantive criminal law in the Czech Republic, to analyze its weaknesses and propose their solution. The investigation should include an assessment of whether the Czech Republic's regulation is in line with international law obligations to criminalize this crime. In this work, compilation, legal-historical, analytical and general and legal interpretation methods are used. The first part is an introduction to the issue of human trafficking. This part introduces the subject of the social deviant phenomenon and points out the necessity of its perception in various, not only legal, fields. The following is a historical outline of the development of looking at human trafficking. In the second, fundamental part of the thesis, there is an analysis of the valid substantive criminal law, which deals with human trafficking. This hermeneutic-critical analysis serves to determine the problems that are proposed in the third part of the thesis. The work for quality analysis explores the historical basis of the legal regulation of the crime of trafficking in human beings. It also sets out the three most important sources of international law, which affect the current regulation and compares whether they are...
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Regularization properties of Krylov subspace methods
Kučerová, Andrea ; Hnětynková, Iveta (advisor) ; Kučera, Václav (referee)
The aim of this thesis is to study and describe regularizing properties of iterative Krylov subspace methods for finding a solution of linear algebraic ill- posed problems contaminated by white noise. First we explain properties of this kind of problems, especially their sensitivity to small perturbations in data. It is shown that classical methods for solving approximation problems (such as the least squares method) fail here. Thus we turn to explanation of regularizing pro- perties of projections onto Krylov subspaces. Basic Krylov regularizing methods are considered, namely RRGMRES, CGLS, and LSQR. The results are illustrated on model problems from Regularization toolbox in MATLAB. 1
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