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Bond Indices in Solids. A Numerical Approach to Analytical Model
Ponec, Robert ; Kohout, M.
To overcome this problem we proposed as a feasible alternative the numerical calculations using the explicit summation over N/2 of low energy states. Such an approach gives for the index between nearest neighbour atoms the value 0.111, which well agrees with the exact value 0.12 reported in the study. This result is very important as it demonstrates that the numerical remedy of the problems with the specification of integration domains does indeed represents a feasible strategy for the calculation of bond indices in solids and examples of the applications to other types of unit cells will be discussed.
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Irrationality in the decision- making of an individual as an economic entity in the territory of the Czech Republic
Böhm, Tomáš ; Zeman, Martin (advisor) ; Babin, Jan (referee)
The main objective of this thesis is an in-depth analysis of the decision-making process on issues of economic nature for individuals in the Czech Republic. The degree of rationality occurring in consumer behavior is evaluated based on lessons learned. The theoretical section is concerned with the economic aspect of the decision-making process, which mainly includes knowledge of neoclassical theory, whose basis is the cardinal and ordinal concept of utility maximization. Subsequently there are introduced the alternative approaches to decision making, focusing on the subjective aspects of human reasoning. Using the mutual synthesis of these approaches, the author draws a term behavioral economics, specific elements of which constitute a substantive content of the whole work. The practical section verifies the hypothesis that the decision-making contradicts the theory of rational individual conduct. Data collected through the questionnaire is subjected to analytical procedures by which the stated hypothesis was verified.
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Analysis and design of intranet structure
Novák, Miroslav ; Pour, Jan (advisor) ; Šedivá, Zuzana (referee)
Nowadays, Intranet is an inseparable part of every company, notwithstanding of their size or field of activity. Both, in my work and personal life, I often come across different intranets that usually do not get a positive response. But they usually have the same source of the problem, which is based on their wrong structure. This is why is chose this topic for my thesis. The goal of my thesis is to perform an analysis of an existing intranet of a particular company and subsequently create a design of the intranet new structure using the card-sorting method. This thesis primarily represents a generalized method of how to proceed during such realization and which areas to look into. Theoretical part of this thesis covers the topics of information architecture and also the term intranet itself, where the most frequent issues I came across in the intranets are pointed out. Practical part covers the analysis itself, where I focus on the structure of the existing intranet, categorization of its content, connections with other systems, customization, permission management, surveys of contentment, and intranet usage. The analysis is performed manually by scanning through the existing intranet of the company, since other methods or approaches could not be applied due to technical limitations or insufficient permis-sions. Based on the outputs of the analysis, web categorizations and the card-sorting method, a design of a structure of the new intranet has been proposed. The design itself is a demonstration of the method how to approach the new intranet design.
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Clustering and regression analysis of micro panel data
Sobíšek, Lukáš ; Pecáková, Iva (advisor) ; Komárek, Arnošt (referee) ; Brabec, Marek (referee)
The main purpose of panel studies is to analyze changes in values of studied variables over time. In micro panel research, a large number of elements are periodically observed within the relatively short time period of just a few years. Moreover, the number of repeated measurements is small. This dissertation deals with contemporary approaches to the regression and the clustering analysis of micro panel data. One of the approaches to the micro panel analysis is to use multivariate statistical models originally designed for crosssectional data and modify them in order to take into account the within-subject correlation. The thesis summarizes available tools for the regression analysis of micro panel data. The known and currently used linear mixed effects models for a normally distributed dependent variable are recapitulated. Besides that, new approaches for analysis of a response variable with other than normal distribution are presented. These approaches include the generalized marginal linear model, the generalized linear mixed effects model and the Bayesian modelling approach. In addition to describing the aforementioned models, the paper also includes a brief overview of their implementation in the R software. The difficulty with the regression models adjusted for micro panel data is the ambiguity of their parameters estimation. This thesis proposes a way to improve the estimations through the cluster analysis. For this reason, the thesis also contains a description of methods of the cluster analysis of micro panel data. Because supply of the methods is limited, the main goal of this paper is to devise its own two-step approach for clustering micro panel data. In the first step, the panel data are transformed into a static form using a set of proposed characteristics of dynamics. These characteristics represent different features of time course of the observed variables. In the second step, the elements are clustered by conventional spatial clustering techniques (agglomerative clustering and the C-means partitioning). The clustering is based on a dissimilarity matrix of the values of clustering variables calculated in the first step. Another goal of this paper is to find out whether the suggested procedure leads to an improvement in quality of the regression models for this type of data. By means of a simulation study, the procedure drafted herein is compared to the procedure applied in the kml package of the R software, as well as to the clustering characteristics proposed by Urso (2004). The simulation study demonstrated better results of the proposed combination of clustering variables as compared to the other combinations currently used. A corresponding script written in the R-language represents another benefit of this paper. It is available on the attached CD and it can be used for analyses of readers own micro panel data.
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Míry podobnosti pro nominální data v hierarchickém shlukování
Šulc, Zdeněk ; Řezanková, Hana (advisor) ; Šimůnek, Milan (referee) ; Žambochová, Marta (referee)
This dissertation thesis deals with similarity measures for nominal data in hierarchical clustering, which can cope with variables with more than two categories, and which aspire to replace the simple matching approach standardly used in this area. These similarity measures take into account additional characteristics of a dataset, such as frequency distribution of categories or number of categories of a given variable. The thesis recognizes three main aims. The first one is an examination and clustering performance evaluation of selected similarity measures for nominal data in hierarchical clustering of objects and variables. To achieve this goal, four experiments dealing both with the object and variable clustering were performed. They examine the clustering quality of the examined similarity measures for nominal data in comparison with the commonly used similarity measures using a binary transformation, and moreover, with several alternative methods for nominal data clustering. The comparison and evaluation are performed on real and generated datasets. Outputs of these experiments lead to knowledge, which similarity measures can generally be used, which ones perform well in a particular situation, and which ones are not recommended to use for an object or variable clustering. The second aim is to propose a theory-based similarity measure, evaluate its properties, and compare it with the other examined similarity measures. Based on this aim, two novel similarity measures, Variable Entropy and Variable Mutability are proposed; especially, the former one performs very well in datasets with a lower number of variables. The third aim of this thesis is to provide a convenient software implementation based on the examined similarity measures for nominal data, which covers the whole clustering process from a computation of a proximity matrix to evaluation of resulting clusters. This goal was also achieved by creating the nomclust package for the software R, which covers this issue, and which is freely available.
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Use of Interest Rate Models for Interest Rate Risk Management in the Czech Financial Market Environment
Cíchová Králová, Dana ; Arlt, Josef (advisor) ; Cipra, Tomáš (referee) ; Witzany, Jiří (referee)
The main goal of this thesis is to suggest an appropriate approach to interest rate risk modeling in the Czech financial market environment in various situations. Three distinct periods are analyzed. These periods, which are the period before the global financial crisis, period during the financial crisis and in the aftermath of the global financial crisis and calming subsequent debt crisis in the eurozone, are characterized by different evaluation of liquidity and credit risk, different relationship between financial variables and market participants and different degree of market regulations. Within this goal, an application of the BGM model in the Czech financial market environment is crucial. Use of the BGM model for the purpose of predicting a dynamics of a yield curve is not very common. This is firstly due to the fact that primary use of this model is a valuation of interest rate derivatives while ensuring the absence of arbitrage and secondly its application is relatively difficult. Nevertheless, I apply the BGM model to obtain predictions of the probability distributions of interest rates in the Czech and eurozone market environment, because its complexity, direct modeling of a yield curve based on market rates and especially a possibility of parameter estimation based on current swaptions volatilities quotations may lead to a significant improvement of predictions. This improvement was also confirmed in this thesis. Use of swaptions volatilities market quotations is especially useful in the period of unprecedented mone- tary easing and increased number of central banks and other regulators interventions into financial markets that occur after the financial crisis, because it reflects current market expectations which also include future interventions. As a consequence of underdevelopment of the Czech financial market there are no market quotations of Czech koruna denominated swaptions volatilities. I suggest their approximations based on quotations of euro denominated swaptions volatilities and also using volatilities of koruna and euro forward rates. Use of this approach ensures that predictions of the Czech yield curve dynamics contain current market expectations. To my knowledge, any other author has not presented similar application of the BGM model in the Czech financial market environment. In this thesis I further predict a Czech and Euro area money market yield curve dynamics using the CIR and the GP models as representatives of various types of interest rates models to compare these predictions with BGM predictions. I suggest a comprehensive system of three criteria, based on comparison of predicti- ons with reality, to describe a predictive power of selected models and an appropria- teness of their use in the Czech market environment during different situations in the market. This analysis shows that predictions of the Czech money market yield curve dynamics based on the BGM model demonstrate high predictive power and the best 8 quality in comparison with other models. GP model also produces relatively good qua- lity predictions. Conversely, predictions based on the CIR model as a representative of short rate model family completely failed when describing reality. In a situation when the economy allows negative rates and there is simultaneously a significant likelihood of their implementation, I recommend to obtain predictions of Czech money market yield curve dynamics using GP model which allows existence of negative interest rates. This analysis also contains a statistical test for validating the predictive power of each model and information on other tests. Berkowitz test rejects a hypothesis of accurate predictions for each model. However, this fact is common in real data testing even when using relatively good model. This fact is especially caused by difficult fulfilment of test conditions in real world. To my knowledge, such an analysis of the predictive power of selected interest rate models moreover in the Czech financial market environment has not been published yet. The last goal of this thesis is to suggest an appropriate approach to obtaining pre- dictions of Czech government bonds risk premium dynamics. I define this risk premium as a difference between government bond yields and fixed rate of CZK IRS with the same length. I apply the GP model to describe the dynamics of this indicator of the Czech Republic credit risk. In order to obtain a time series of the risk premium which are necessary for estimation of GP model parameters I firstly estimate yield curves of Czech government bonds using Svensson model for each trading day since 2005. Resulting si- mulations of risk premium show that the GP model predicts the real development of risk premiums of all maturities relatively well. Hence, the proposed approach is suitable for modeling of Czech Republic credit risk based on the use of information extracted from financial markets. I have not registered proposed approach to risk premium modeling moreover in the Czech financial market environment in other publications.
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The theory of redistribution and its application
Mihalčinová, Hana ; Dlouhý, Martin (advisor) ; Valenčík, Radim (referee) ; Peško, Štefan (referee)
The theory of redistribution systems is a practical extension of a game theory, which deals with a redistribution within a social system of more than two players with di?erent performances and ability to create coalitions. This thesis is divided into three chapters. The ?rst chapter describes the known knowledge of a game theory. The second chapter deals with the theory of redistribution systems. Using an elementary redistribution system and its generalization group behaviour when dividing a payment, achieved by a collective performance, is described. This part introduces the extension of the redistribution system to a compound redistribution system with a fractal structure. Furthermore the theory of discriminatory equilibrium and the theory of commonly acceptable equilibrium are veri?ed using the elementary redistribution system and utility theory. The third chapter deals with an application to the allocation of funds among faculty departments. A game theory approach was used to reduce the game to a non-cooperative game of two players by using the forming of coalitions. Also the theory of redistribution systems was applied when a reduction was used to create a non-cooperative two-player game. This reduced non-cooperative game between two players was converted to a cooperative play of more than two players by changing the rules of the game and allowing a formation of coalitions. In the practical part both of these approaches are compared with real data and a current state.
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A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems
Axelsson, Owe ; Blaheta, Radim ; Hasal, Martin
The paper overviews and compares some block preconditioners for the solution of saddle point systems, especially systems arising from the Brinkman model of porous media flow. The considered preconditioners involve different Schur complements as inverse free Schur complement in HSS (Hermitian - Skew Hermitian Splitting preconditioner), Schur complement to the velocity matrix and finally Schur complement to a regularization block in the augmented matrix preconditioner. The inverses appearing in most of the considered Schur complements are approximated by simple sparse approximation techniques as element-by-element and Frobenius norm minimization approaches. A special interest is devoted to problems involving various Darcy, Stokes and Brinkman flow regions, the efficiency of preconditioners in this case is demonstrated by some numerical experiments.
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Modelling, parameter estimation, optimisation and control of transport and reaction processes in bioreactors.
ŠTUMBAUER, Václav
With the significant potential of microalgae as a major biofuel source of the future, a considerable scientific attention is attracted towards the field of biotechnology and bioprocess engineering. Nevertheless the current photobioreactor (PBR) design methods are still too empirical. With this work I would like to promote the idea of designing a production system, such as a PBR, completely \emph{in silico}, thus allowing for the in silico optimization and optimal control determination. The thesis deals with the PBR modeling and simulation. It addresses two crucial issues in the current state-of-the-art PBR modeling. The first issue relevant to the deficiency of the currently available models - the incorrect or insufficient treatment of either the transport process modeling, the reaction modeling or the coupling between these two models. A correct treatment of both the transport and the reaction phenomena is proposed in the thesis - in the form of a unified modeling framework consisting of three interconnected parts - (i) the state system, (ii) the fluid-dynamic model and (iii) optimal control determination. The proposed model structure allows prediction of the PBR performance with respect to the modelled PBR size, geometry, operating conditions or a particular microalgae strain. The proposed unified modeling approach is applied to the case of the Couette-Taylor photobioreactor (CTBR) where it is used for the optimal control solution. The PBR represents a complex multiscale problem and especially in the case of the production scale systems, the associated computational costs are paramount. This is the second crucial issue addressed in the thesis. With respect to the computational complexity, the fluid dynamics simulation is the most costly part of the PBR simulation. To model the fluid flow with the classical CFD (Computational Fluid Dynamics) methods inside a production scale PBR leads to an enormous grid size. This usually requires a parallel implementation of the solver but in the parallelization of the classical methods lies another relevant issue - that of the amount of data the individual nodes must interchange with each other. The thesis addresses the performance relevant issues by proposing and evaluation alternative approaches to the fluid flow simulation. These approaches are more suitable to the parallel implementation than the classical methods because of their rather local character in comparison to the classical methods - namely the Lattice Boltzmann Method (LBM) for fluid flow, which is the primary focus of the thesis in this regard and alternatively also the discrete random walk based method (DRW). As the outcome of the thesis I have developed and validated a new Lagrangian general modeling approach to the transport and reaction processes in PBR - a framework based on the Lattice Boltzmann method (LBM) and the model of the Photosynthetic Factory (PSF) that models correctly the transport and reaction processes and their coupling. Further I have implemented a software prototype based on the proposed modeling approach and validated this prototype on the case of the Coutte-Taylor PBR. I have also demonstrated that the modeling approach has a significant potential from the computational costs point of view by implementing and validating the software prototype on the parallel architecture of CUDA (Compute Unified Device Architecture). The current parallel implementation is approximately 20 times faster than the unparallized one and decreases thus significantly the iteration cycle of the PBR design process.
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