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Statistical Physics of Hard Optimization Problems
Zdeborová, Lenka ; Janiš, Václav (advisor) ; Mertens, Stephan (referee) ; Zecchina, Riccardo (referee)
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly dicult, it is believed that the number of operations required to minimize the cost function is in the most dicult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this thesis is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint...
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The use of multichannel flow cytometry in biomedicine and experimental biology
Kideryová, Linda
Linda Kideryová USE OF MULTICHANNEL FLOW-CYTOMETRY IN BIOMEDICINE AND EXPERIMENTAL BIOLOGY SUMMARY Flow-cytometry is a process on which large numbers of single cells are quantitatively and qualitatively analyzed. This method gives information about size, granularity surface or intracellular markers of every single cell in suspension. In modern biology is worthy to perform quick, objective multiparametric analyses of cell phenotype. This project was focused on cells, which analyses are complicated by extreme rareness or lack of clearly identifying specific markers. Analysis of stromal cells of the investigated tumors (histiocytoma and tumor fibroblasts originating in squamous epithelium: basalioma (BCCF) and spinalioma (SCCF) elucidated alteration of gene expression induced by tumor cells. Tumor-derived stromal fibroblasts acquire distinct properties to shape a microenvironment conducive to altering the phenotypic characteristics of normal epithelial cells in vitro. Reproducible, quick and highly sensitive method of detection extremely rare non-haematopoetic cells (EPC, CEC) was established. Numbers of CFU-En correlate neither with circulating endothelial progenitors nor with matured endothelial cells detected by flow-cytometry. These colonies are formed in cooperation of CD14 + and CD4+ cells. Numbers of...
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The Graphic Production of Albrecht Altdorfer after 1520 in the Collections of the National Gallery in Prague
Kadlecová, Žaneta ; Nespěšná Hamsíková, Magdaléna (advisor) ; Royt, Jan (referee)
12 Summary The Graphic Production of Albrecht Altdorfer after 1520 in Collections of the National Gallery in Prague Thesis deals with the graphic works of Albrecht Altdorfer after 1520 in collections of the National Gallery in Prague. The aim of this paper is to outline the situation in the Danube region at the turn of 15 to 16 century and the creation of so-called Danube school. It presents celebrity of Danube artist Albrecht Altdorfer versatile talents as a master and a man of high social status. Creation of the artist remains somewhat neglected in Bohemia and is thus largely outside the interest of art historians. Even most German works that deal with work of this artist is aimed at producing a master painter and graphic works are therefore in his life's work a little taken a back seat. Particular attention is placed on the graphic art of miniatures in 1520 after the National Gallery in Prague with the aim to clarify the way graphics suggestions are displayed and to point out to changes in the development of miniatures style. Fundamental chapter is part of the catalogue with the newly developed the catalogue headwords, which will present a series of graphic works, which are reported by the National Gallery in Prague only with basic information on size and current condition. Bachelor thesis is...
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Physical properties of ultrafine-grained polycrystals of magnesium based alloys
Vrátná, Jitka ; Janeček, Miloš (advisor) ; Kužel, Radomír (referee)
The objective of the thesis is the study of microstructure evolution, mechanical properties, defect structure and corrosion resistance of ultra-ne grained magnesium alloy AZ31 prepared by a combined two-step process: the extrusion and the equal-channel angular pressing (ECAP). The microstructure development was studied using light and transmission electron microscopy and electron backscatter diffraction (EBSD). Mechanical properties were studied by microhardness measurement and tensile tests and the defect structure by positron annihilation spectroscopy (PAS). The results of tensile tests indicates that the characteristic stress 0.2 increases slightly with increasing number of ECAP passes only to the second pass and then decreases signicantly with additional ECAP straining. This behaviour is in accordance with the results of PAS. EBSD measurements show that the microstructure of extruded and ECAPed material has a bimodal distribution of grain sizes. The bimodal distribution becomes homogeneous with increasing number of ECAP passes and no remaining large grains are observed after 8 passes. The average grain size in the specimen after 8 passes is in the submicrometer range and the fraction of high-angle grain boundary (HAGB) is approximately 80%. The extruded specimens after 8 ECAP passes show the best...
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Technologies for storing and processing of extremely large volumes of data in the ORACLE
Spurný, Petr ; Macák, Petr (advisor) ; Krch, David (referee)
The aim of the Bachelor's thesis is to provide an overview and description of such technologies in the Oracle database, which can be used for work with extremely large volumes of data and to verify the benefits of some of these technologies in practice. At the beginning, the work deals with problems of large amounts of data in general and seeks to define the size of data in the database systems. In the theoretical part, several different technologies will be introduced. The greatest emphasis is placed on various forms of partitioning. The practical part contains a proposal for the implementation of tests, building automated test procedures, and for the execution of these tests. The work can be used as a quick guide in case of dealing with performance issues with large volumes of data. Making any changes for the particular case is easy according to examples given in the text. Last, but not least, the work may help with automatic testing procedures, which can be used with a slight adjustment for a wide range of test cases.
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Parameter Optimization of Multi-Level Diffraction Gratings
Matějka, Milan ; Kolařík, Vladimír ; Horáček, Miroslav ; Král, Stanislav
Originally, the e-beam lithography (EBL) is a technique for creating high-resolution black and white masks for the optical lithography. Multi-level relief structures can be also prepared using EBL patterning. Their preparation is based on the image patterning with a gradient of exposure doses. Large-area multi-level structures can be effectively prepared using the electron beam pattern generator with a variable shaped beam. We present several writing strategies. Basically, the main writing strategy uses one stamp (i.e. one elementary exposure of the shaped electron beam) per one elementary area with the same exposure dose. This simple approach is fast and flexible, however it does not guarantee optimal results. The main problem is an imperfection of the stamps (size, shape, and homogeneity). Advanced algorithms are based on multiple\nexposure of the same elementary area, the total local exposure dose is a sum of several different elementary exposures (stamps). Using these algorithms, a smoother surface of the structure can be achieved. On the other hand, the writing speed is considerably decreased. Tradeoff between the achieved parameters and the writing speed is discussed for selected set of writing strategy algorithms.
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Statistical tests power analysis
Kubrycht, Pavel ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This Thesis deals with the power of a statistical test and the associated problem of determining the appropriate sample size. It should be large enough to meet the requirements of the probabilities of errors of both the first and second kind. The aim of this Thesis is to demonstrate theoretical methods that result in derivation of formulas for minimum sample size determination. For this Thesis, three important probability distributions have been chosen: Normal, Bernoulli, and Exponential.
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Hodnocení Výsledků Fuzzy Shlukování
Říhová, Elena ; Pecáková, Iva (advisor) ; Řezanková, Hana (referee) ; Žambochová, Marta (referee)
Cluster analysis is a multivariate statistical classification method, implying different methods and procedures. Clustering methods can be divided into hard and fuzzy; the latter one provides a more precise picture of the information by clustering objects than hard clustering. But in practice, the optimal number of clusters is not known a priori, and therefore it is necessary to determine the optimal number of clusters. To solve this problem, the validity indices help us. However, there are many different validity indices to choose from. One of the goals of this work is to create a structured overview of existing validity indices and techniques for evaluating fuzzy clustering results in order to find the optimal number of clusters. The main aim was to propose a new index for evaluating the fuzzy clustering results, especially in cases with a large number of clusters (defined as more than five). The newly designed coefficient is based on the degrees of membership and on the distance (Euclidean distance) between the objects, i.e. based on principles from both fuzzy and hard clustering. The suitability of selected validity indices was applied on real and generated data sets with known optimal number of clusters a priory. These data sets have different sizes, different numbers of variables, and different numbers of clusters. The aim of the current work is regarded as fulfilled. A key contribution of this work was a new coefficient (E), which is appropriate for evaluating situations with both large and small numbers of clusters. Because the new validity index is based on the principles of both fuzzy clustering and hard clustering, it is able to correctly determine the optimal number of clusters on both small and large data sets. A second contribution of this research was a structured overview of existing validity indices and techniques for evaluating the fuzzy clustering results.
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THE INVESTIGATION OF AN Al7075 ALLOY PREPARED BY SPARK PLASMA SINTERING OF MILLED POWDERS
Molnárová, O. ; Málek, P. ; Nemeth, G. ; Kozlík, J. ; Lukáč, František ; Chráska, Tomáš ; Cinert, Jakub
Atomized powder of an Al7075 alloy was high energy ball milled at room and cryogenic temperatures and compacted by spark plasma sintering (SPS) method. The influence of processing parameters on phase composition and microstructure was studied by X-ray diffraction, light and scanning electron microscopy. The mechanical properties were characterized by microhardness measurements. The atomized powder contained a large volume fraction of intermetallic phases located predominantly in continuous layers separating cells or dendrites in the interior of individual powder particles. Consolidation by SPS destroyed partially this morphology and replaced it by individual particles located at boundaries of original powder particles, at cell boundaries or arranged in chains in previous dendritic regions. High energy milling destroyed most intermetallic particles and enriched the matrix by solute atoms. The high deformation energy introduced into the powder during milling enhanced microhardness up to 220 HV. Consolidation of milled powders by SPS led to the formation of very fine-grained structure with the grain size even below 1 μm and with the fraction of high-angle boundaries about 0.9. Two main types of heterogeneously distributed precipitates were found. The irregularly shaped precipitates with a size about 1 μm seemed to encompass areas with rod like nano-precipitates in most samples. A drop in microhardness to 118HV was observed after SPS, predominantly due to a release of introduced deformation energy.
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