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Numerické optimalizační metody
Lukšan, Ladislav
Tato zpráva popisuje teoretické i praktické vlastnosti numerických metod pro nepodmíněnou optimalizaci. Studují se metody pro obecné i speciální optimalizační úlohy, mezi které patří minimalizace součtu čtverců, součtu absolutních hodnot, maximní hodnoty a dalších nehladkých funkcí. Kromě metod pro standardní úlohy středních rozměrů jsou studovány i metody pro rozsáhlé řídké a strukturované úlohy. Velká pozornost je věnována soustavám nelineárních rovnic.\n
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Computational methods in single molecule localization microscopy
Ovesný, Martin ; Hagen, Guy Michael (advisor) ; Plášek, Jaromír (referee) ; Fliegel, Karel (referee)
Computational methods in single molecule localization microscopy Abstract Fluorescence microscopy is one of the chief tools used in biomedical research as it is a non invasive, non destructive, and highly specific imaging method. Unfortunately, an optical microscope is a diffraction limited system. Maximum achievable spatial resolution is approximately 250 nm laterally and 500 nm axially. Since most of the structures in cells researchers are interested in are smaller than that, increasing resolution is of prime importance. In recent years, several methods for imaging beyond the diffraction barrier have been developed. One of them is single molecule localization microscopy, a powerful method reported to resolve details as small as 5 nm. This approach to fluorescence microscopy is very computationally intensive. Developing methods to analyze single molecule data and to obtain super-resolution images are the topics of this thesis. In localization microscopy, a super-resolution image is reconstructed from a long sequence of conventional images of sparsely distributed single photoswitchable molecules that need to be sys- tematically localized with sub-diffraction precision. We designed, implemented, and experimentally verified a set of methods for automated processing, analysis and visualization of data acquired...
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Numerical Optimization Methods for the Falsification of Hybrid Dynamical Systems
Kuřátko, Jan ; Ratschan, Stefan (advisor) ; Bergamaschi, Luca (referee) ; Lukšan, Ladislav (referee)
Title: Numerical Optimization Methods for the Falsification of Hybrid Dynamical Systems Author: Jan Kuřátko Department: Department of Numerical Mathematics Supervisor: Stefan Ratschan, Institute of Computer Science, The Czech Academy of Sciences Abstract: This thesis consists of three published papers that contribute to the finding of error trajectories of hybrid dynamical systems. A hybrid dynamical system is a dynamical system that has both discrete and continuous state. For example, one can use it as a model for a thermostat in a room: Such a thermostat may have two discrete states, one where the heating is off, and another one, where the heating is on. Its continuous state is the temperature in the room. For such a model one may be interested in finding an error trajectory, that is, an evolution of the system that reaches an unsafe state that is to be avoided. Industry is in need of methods for automatized testing and verification of safety conditions in order to identify flaws in the design of systems. The thesis contains several contributions to finding error trajectories that are based on numerical optimization. Keywords: optimization, dynamical systems, saddle-point matrix
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Computational methods in single molecule localization microscopy
Ovesný, Martin ; Hagen, Guy Michael (advisor) ; Plášek, Jaromír (referee) ; Fliegel, Karel (referee)
Computational methods in single molecule localization microscopy Abstract Fluorescence microscopy is one of the chief tools used in biomedical research as it is a non invasive, non destructive, and highly specific imaging method. Unfortunately, an optical microscope is a diffraction limited system. Maximum achievable spatial resolution is approximately 250 nm laterally and 500 nm axially. Since most of the structures in cells researchers are interested in are smaller than that, increasing resolution is of prime importance. In recent years, several methods for imaging beyond the diffraction barrier have been developed. One of them is single molecule localization microscopy, a powerful method reported to resolve details as small as 5 nm. This approach to fluorescence microscopy is very computationally intensive. Developing methods to analyze single molecule data and to obtain super-resolution images are the topics of this thesis. In localization microscopy, a super-resolution image is reconstructed from a long sequence of conventional images of sparsely distributed single photoswitchable molecules that need to be sys- tematically localized with sub-diffraction precision. We designed, implemented, and experimentally verified a set of methods for automated processing, analysis and visualization of data acquired...
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