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Structural aspects of graph coloring
Pekárek, Jakub ; Dvořák, Zdeněk (advisor) ; Esperet, Louis (referee) ; Zhu, Xuding (referee)
In this thesis, we study the structural and algorithmic properties of graphs embedded or represented in surfaces and with constraints on their faces or cycles. We derive tools to quantify properties of embedded flows and use these to design an algorithm to decide the extendability of a precoloring of the boundary cycles of near- quadrangulations of the cylinder. We then develop methods to reduce 3-coloring of triangle- free graphs embedded in the torus to 3-coloring near-quadrangulations, obtaining prac- tical algorithms for deciding 3-colorability in linear time, and obtaining a 3-coloring in quadratic time. We also investigate connection between geometric graph representations and the in- duced odd cycle packing number (iocp) parameter. We show that wide variety of rep- resentable graphs exhibit limited iocp and show that graphs with limited iocp are χ- bounded. We derive an EPTAS for maximum independent set of graphs with limited iocp and linear independence number, as well as QPTAS assuming only limited iocp. 1
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Electromigration of defects in (CdZn)Te single crystals.
Pekárek, Jakub ; Belas, Eduard (advisor) ; Grill, Roman (referee)
In the present work we study effect of electromigration of defects in CdTe material in external electric field at various temperatures and biases. The aim was to verify this effect using a set of electric contacts arranged linearly along the sample. These contacts as a potential probes was used for the detection of the drift of the local resistance modulation. We try to determine under what conditions and why it happens and then decide how this effect can be used for purification of semi-conducting samples and for preparation of semi-insulating material.
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Gamma and X- ray CdTe/CdZnTe detectors
Pekárek, Jakub
In the present work we studied an influence of different types of surface etching and surface passivation of high resistivity CdZnTe-based semiconductor detector material. The aim was to find the optimal conditions to improve the properties of metal-semiconductor contact. The main effort was to reduce the leakage current and thus get better X-ray and gamma-ray spectrum, ie to create a detector operating at room temperature based on this semiconductor material with sufficient energy resolution and the maximum charge collection efficiency. Individual surface treatments were characterized by volt-ampere characteristics, spectral analysis and by determination of the profile of the internal electric field.
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Room-temperature semiconducting detectors
Pekárek, Jakub ; Belas, Eduard (advisor) ; Oswald, Jiří (referee) ; Štekl, Ivan (referee)
Semiconducting material CdTe/CdZnTe has a huge application potential in spectroscopic room temperature radiation detection due to its properties. Such detectors can be used in medical applications, homeland security and for monitoring of nuclear facilities. However, the final device quality is influenced by many parameters. One crucial stage in detector fabrication is the proper surface treatment. The detailed study of surface treatments and their effect on final detector device is reported. Another crucial fact is the polarization of the detector caused by high radiation fluxes which negatively affects the use of such devices. The polarization occurs by capturing the photogenerated holes at the deep levels inside the semiconductor. The possible detector depolarization by infrared illumination during the detector operation has been experimentally verified and the obtained results are shown in this thesis. For optimal technology of preparation, it is also necessary to develop the fast characterization method for prepared detectors. The last aim of the thesis is to study the resulting quality of prepared planar and co-planar detectors by transient-current-technique (TCT). TCT is an electro-optical method allowing to determine variety of transport properties of radiation detectors, such as internal electric...
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3-Coloring Graphs on Torus
Pekárek, Jakub ; Dvořák, Zdeněk (advisor) ; Šámal, Robert (referee)
The theory of Dvořák et al. shows that a 4-critical triangle-free graph embedded in the torus has only a bounded number of faces of length greater than 4 and that the size of these faces is also bounded. We study the natural reduction in such embedded graphs-identification of opposite vertices in 4-faces. We give a computer-assisted argument showing that there are exactly four 4-critical triangle-free irreducible toroidal graphs in which this reduction cannot be applied without creating a triangle. Using this result we demonstrate several properties that are necessary for every triangle-free graph embedded in the torus to be 4-critical. Most importantly we demonstrate that every such graph has at most four 5-faces, or a 6-face and two 5-faces, or a 7-face and a 5-face, in addition to at least seven 4-faces.
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Gamma and X- ray CdTe/CdZnTe detectors
Pekárek, Jakub
In the present work we studied an influence of different types of surface etching and surface passivation of high resistivity CdZnTe-based semiconductor detector material. The aim was to find the optimal conditions to improve the properties of metal-semiconductor contact. The main effort was to reduce the leakage current and thus get better X-ray and gamma-ray spectrum, ie to create a detector operating at room temperature based on this semiconductor material with sufficient energy resolution and the maximum charge collection efficiency. Individual surface treatments were characterized by volt-ampere characteristics, spectral analysis and by determination of the profile of the internal electric field.
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Citadels AI
Pekárek, Jakub ; Holan, Tomáš (advisor) ; Gemrot, Jakub (referee)
The aim of this thesis is to implement a playable version of the game Citadels with console interface, and to use it for analysis of the game's properties and development of artificial intelligence. This thesis includes an analysis of strategies, a scheme for their design, an organization of turn processing, a model of intelligence implementation and testing tools. A number of approaches to specific moves have been developed, all of which achieved positive impact on overall intelligence performance. Game analysis showed a variety of game situations that need to be approached in different ways. Consequently, inappropriateness of usage of general approaches has been demonstrated; while showing benefits of the suggested inteligence design, based on a composition of separate strategies. A strong influence of player earnings on the overall performance has also been demonstrated, while other factors only show very low influence in general case. Powered by TCPDF (www.tcpdf.org)
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Gamma and X- ray CdTe/CdZnTe detectors
Pekárek, Jakub ; Belas, Eduard (advisor) ; Doležal, Zdeněk (referee)
In the present work we studied an influence of different types of surface etching and surface passivation of high resistivity CdZnTe-based semiconductor detector material. The aim was to find the optimal conditions to improve the properties of metal-semiconductor contact. The main effort was to reduce the leakage current and thus get better X-ray and gamma-ray spectrum, ie to create a detector operating at room temperature based on this semiconductor material with sufficient energy resolution and the maximum charge collection efficiency. Individual surface treatments were characterized by volt-ampere characteristics, spectral analysis and by determination of the profile of the internal electric field.
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Electromigration of defects in (CdZn)Te single crystals.
Pekárek, Jakub ; Belas, Eduard (advisor) ; Grill, Roman (referee)
In the present work we study effect of electromigration of defects in CdTe material in external electric field at various temperatures and biases. The aim was to verify this effect using a set of electric contacts arranged linearly along the sample. These contacts as a potential probes was used for the detection of the drift of the local resistance modulation. We try to determine under what conditions and why it happens and then decide how this effect can be used for purification of semi-conducting samples and for preparation of semi-insulating material.
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