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Fylogenetická analýza peniální morfologie u novoguinejských hlodavců
KOVAŘÍK, Vojtěch
This study deals with the description of the penile and bacular morphology of New Guinean rodents. I documented and scored many qualitative and quantitative characters using the stereoscopic microscope and non-destructive microcomputer tomography machine (CT). The obtained data matrix was analyzed phylogenetically, which enabled me to reconstruct ancestral conditions for Rattini, and various subgroups of hydromyine rodents. I also identified a complex evolution of penile and bacular features, and also some perspectives for future investigations.
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Genetický monitoring vybraných populací sysla obecného v České republice
KOVAŘÍK, Vojtěch
This study deals with the description of genetic variability of current populations of the European ground squirrel (Spermophilus citellus) using 12 microsatellite loci, the analysis of which showed relatively high intrapopulation variability with high proportion of heterozygous individuals, but also negative isolation and very high differentiation between populations which prevents long-term stable existence of these populations, and which requires further design of conservation measures that are also mentioned in this study.
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Limit behavior of the Nash equlibrium
Kovařík, Vojtěch ; Spurný, Jiří (advisor) ; Bárta, Tomáš (referee)
The subject of study of game theory - games - serves as mathematical models for real-life problems. In every game there are two or more players who aim to maximize their own profit by choosing their actions. A situation where no player can benefit from changing his own action alone has got particular importance in the study of games - it is called Nash equilibrium. Games with a finite number of players have certain advantages over those with an infinite number of players. For one, problems whose model is a game with a finite number of players are quite common. Moreover, one of the classical results of game theory is that (with certain additional assumptions) in every game with a finite number of players there exists a Nash equilibrium. On the other hand, when trying to describe the properties of a game with an infinite number of players we might be able to use calculus instead of going trough all possibilities (as is common for games with a finite number of players), which tends to be computationally demanding. However, if we want to use these advantages of games with an infinite number of players, it is important first to know whether there is any relationship between games with a finite and infinite number of players at all. The goal of this thesis is to define terms and to introduce tools which would allow...
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Absolute and non-absolute F-Borel spaces
Kovařík, Vojtěch ; Kalenda, Ondřej (advisor)
We investigate F-Borel topological spaces. We focus on finding out how a complexity of a space depends on where the space is embedded. Of a particular interest is the problem of determining whether a complexity of given space X is absolute (that is, the same in every compactification of X). We show that the complexity of metrizable spaces is absolute and provide a sufficient condition for a topological space to be absolutely Fσδ. We then investigate the relation between local and global complexity. To improve our understanding of F-Borel spaces, we introduce different ways of representing an F-Borel set. We use these tools to construct a hierarchy of F-Borel spaces with non-absolute complexity, and to prove several other results. 1
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Absolute and non-absolute F-Borel spaces
Kovařík, Vojtěch ; Kalenda, Ondřej (advisor) ; Matheron, Ethienne (referee) ; Holický, Petr (referee)
We investigate F-Borel topological spaces. We focus on finding out how a complexity of a space depends on where the space is embedded. Of a particular interest is the problem of determining whether a complexity of given space X is absolute (that is, the same in every compactification of X). We show that the complexity of metrizable spaces is absolute and provide a sufficient condition for a topological space to be absolutely Fσδ. We then investigate the relation between local and global complexity. To improve our understanding of F-Borel spaces, we introduce different ways of representing an F-Borel set. We use these tools to construct a hierarchy of F-Borel spaces with non-absolute complexity, and to prove several other results. 1
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Absolute and non-absolute F-Borel spaces
Kovařík, Vojtěch ; Kalenda, Ondřej (advisor)
We investigate F-Borel topological spaces. We focus on finding out how a complexity of a space depends on where the space is embedded. Of a particular interest is the problem of determining whether a complexity of given space X is absolute (that is, the same in every compactification of X). We show that the complexity of metrizable spaces is absolute and provide a sufficient condition for a topological space to be absolutely Fσδ. We then investigate the relation between local and global complexity. To improve our understanding of F-Borel spaces, we introduce different ways of representing an F-Borel set. We use these tools to construct a hierarchy of F-Borel spaces with non-absolute complexity, and to prove several other results. 1
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Descriptive set properties of collections of exceptional sets in Harmonic analysis
Kovařík, Vojtěch ; Vlasák, Václav (advisor) ; Zelený, Miroslav (referee)
We study families of small sets which appear in Harmonic analysis. We focus on the systems H(N) , N ∈ N, U and U0. In particular we compare their sizes via comparing the polars of these classes, i.e. the families of measures annihilating all sets from given class. Lyons showed that in this sense, the family N∈N H(N) is smaller than U0. The main goal of this thesis is the study of the question whether this also holds when the system U0 is replaced by the much smaller system U. To this end we define a new system H(∞) and systems of sets of type N where N ∈ N∪{∞}. We then prove some of their properties, which might be useful in solving the studied question. 1
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Limit behavior of the Nash equlibrium
Kovařík, Vojtěch ; Spurný, Jiří (advisor) ; Bárta, Tomáš (referee)
The subject of study of game theory - games - serves as mathematical models for real-life problems. In every game there are two or more players who aim to maximize their own profit by choosing their actions. A situation where no player can benefit from changing his own action alone has got particular importance in the study of games - it is called Nash equilibrium. Games with a finite number of players have certain advantages over those with an infinite number of players. For one, problems whose model is a game with a finite number of players are quite common. Moreover, one of the classical results of game theory is that (with certain additional assumptions) in every game with a finite number of players there exists a Nash equilibrium. On the other hand, when trying to describe the properties of a game with an infinite number of players we might be able to use calculus instead of going trough all possibilities (as is common for games with a finite number of players), which tends to be computationally demanding. However, if we want to use these advantages of games with an infinite number of players, it is important first to know whether there is any relationship between games with a finite and infinite number of players at all. The goal of this thesis is to define terms and to introduce tools which would allow...
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