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State space formulations of dynamical problems
Kozánek, Jan
The 3n and 4n state space formulations of system of n linear second-order ordinary differential equations with special right side are proposed. The paper is concerned to an other than common understanding of resonant phenomena of dynamical systems
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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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Analysis, design and implementation of CRM solutions for selected company
Ilavský, Dávid ; Pour, Jan (advisor) ; Šedivá, Zuzana (referee)
Bachelor thesis focuses on the area of information systems, which are used to support customer relationship management in companies. The main objective of this work is to provide a sample of solution for CRM system implementation for real customer from the banking sector. The first part defines basic functional areas of any CRM application. Each of these areas is described in more detail in terms of its primary use and tasks that within the CRM as a whole performs. Further is described the analytical area of CRM application (or Customer Intelligence), which is gradually playing a key role in the entire CRM system in past few years. It includes its potential uses in various fields. At the end of the theoretical part, the author compares the fundamental differences between cloud model of deployment and traditional on-premise solution. The practical part focuses on the main objective of the thesis and description of the supplied solution in the form of a module, which extends the existing CRM application with the option for business partners registration of Hypoteční banka, a. s. and ČSOB Pojišťovna, centralized in one system. The requirement is build in Microsoft Dynamics CRM 2011 and as the source system it is used CRM system of Hypoteční banka, a. s..
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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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Methodology of highly reliable systems design
Straka, Martin ; Gramatová, Elena (referee) ; Racek, Stanislav (referee) ; Kotásek, Zdeněk (advisor)
In the thesis, a methodology alternative to existing methods of digital systems design with increased dependability implemented into FPGA is presented, new features which can be used in the implementation and testing of these systems are demonstrated. The research is based on the use of FPGA partial dynamic reconfiguration for the design of fault tolerant systems. In these applications, the partial dynamic reconfiguration can be used as a mechanism to correct the fault and recover the system after the fault occurrence. First, the general principles of diagnostics, testing and digital systems dependability are presented including a brief description of FPGA components and their architectures. Next, a survey of currently used methods and techniques used for the design and implementation of fault tolerant systems into FPGA is described, especially the methods used for fault detection and localization, their correction, together with the principles of evaluating fault tolerant systems design quality. The most important part of the thesis is seen in the description of the design methodology, implementation and testing of fault tolerant systems implemented into FPGAs which uses SRAMs as the configuration memory. First, the methodology of developing and automated checker components design for digital systems and communication protocols is presented. Then, a reference architecture of a dependable system implemented into FPGA is demonstrated including several fault tolerant architectures based on the use of partial dynamic reconfiguration as the mechanism of fault correction and the recovery from it. The principles of controlling the reconfiguration process are described together with the description of the test platform which allows to test and verify the design of fault tolerant systems based on the methodology presented in the thesis. The experimental results and the contribution of the thesis are discussed in the conclusions.
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Methodology of highly reliable systems design
Straka, Martin ; Kotásek, Zdeněk (advisor)
In the thesis, a methodology alternative to existing methods of digital systems design with increased dependability implemented into FPGA is presented, new features which can be used in the implementation and testing of these systems are demonstrated. The research is based on the use of FPGA partial dynamic reconfiguration for the design of fault tolerant systems. In these applications, the partial dynamic reconfiguration can be used as a mechanism to correct the fault and recover the system after the fault occurrence. First, the general principles of diagnostics, testing and digital systems dependability are presented including a brief description of FPGA components and their architectures. Next, a survey of currently used methods and techniques used for the design and implementation of fault tolerant systems into FPGA is described, especially the methods used for fault detection and localization, their correction, together with the principles of evaluating fault tolerant systems design quality. The most important part of the thesis is seen in the description of the design methodology, implementation and testing of fault tolerant systems implemented into FPGAs which uses SRAMs as the configuration memory. First, the methodology of developing and automated checker components design for digital systems and communication protocols is presented. Then, a reference architecture of a dependable system implemented into FPGA is demonstrated including several fault tolerant architectures based on the use of partial dynamic reconfiguration as the mechanism of fault correction and the recovery from it. The principles of controlling the reconfiguration process are described together with the description of the test platform which allows to test and verify the design of fault tolerant systems based on the methodology presented in the thesis. The experimental results and the contribution of the thesis are discussed in the conclusions.
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Dynamics of mouse sperm capacitation and acrosome reaction
Dvořáková-Hortová, Kateřina ; Frolíková, Michaela ; Děd, Lukáš ; Šebková, Nataša
Capacitation followed by the acrosome reaction (AR), is a very complex event of molecular changes, including acrosome matrix rearrangement and actin polymerization, which mammalian sperm must undergo in the female reproductive tract in order to obtain the ability to penetrate and fertilize the egg. CD46 and β1-integrin belong to specific proteins, which are predicted to interact during molecular reorganization of capacitating sperm. The IZUMO1 as the primary fusion protein of the mammalian sperm is also involved in this dynamic network. We investigated the relationship between the Izumo, CD46 and β1 integrin relocation in the sperm head during the capacitation and AR in vitro. We have already successfully monitored by immunofluorescent labelling the dynamics of proteins CD46 and β1-integrin. The changes in the localization of these proteins associated with the AR and their mutual co-localization was observed. The original β1-integrin location in the freshly released epididymal sperm is in the acrosome and it relocates during the AR further through the sperm head compartments into the equatorial segment and over the whole sperm head. Its density over the equatorial segment is decreasing with the extended time of the AR. Also its presence in the perforatorium of the mouse sperm head is very prominent. The pattern for protein CD46 is extremely similar if not identical in both aspects such as compartment localization and time progress during capacitation and AR in vitro. The molecular interaction of CD46 and β1-integrin was investigated using the Proximity Ligation Assay and Super resolution microscopy STED. The data were statistically analysed. The newly obtained results from CD46 and β1-integrin relocation are in correlation with IZUMO1 dynamics and giving a substantial knowledge on the studied protein network rearrangement during capacitation and AR in mouse spermatozoa.
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Modelling Scenarios of Development of Small Agriculture Businesses
Koláčková, Gabriela ; Tichá, Ivana (advisor) ; Stanislava, Stanislava (referee)
The paper deals with the dynamic simulation of possible development scenarios of small farmers. The model is based on the official data sources but also on the qualitative research of small farmers. The modelling structure reflects the specifics of the examined field and personal and social specifics of small farmers. For the purposes of the analysis, the business model describes the value creation in the small farms, thereafter the model is extended into dynamic simulation model and the selected scenarios of development are simulated.
The analysis shows the impact of the current setup in the field. Despite the paper contains the optimistic scenarios, simple change of parameters leads to unsustainable situation. The pessimistic scenarios grow from realistic conditions when parameters reflects the recent period settings. This clearly depicts the influence of weak market position of the farmers and advocates the diversification tendencies.
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Simulation of infrastructure building impact on wine bar and candy store economic performance
Škoda, Dominik ; Krejčí, Igor (advisor) ; Horáková, Tereza (referee)
The bachelor thesis deals with the application of system dynamics to a small business, which has been affected by a sewage system construction in the past few years. The theoretical part of this thesis describes to a general description of system dynamics, including its history and development. It focuses on the definition of some of the basic terms used in system dynamics and specifies the difference between system and linear thinking. It also provides a description of tools used in system dynamics and a characterization of structures frequently used in practice and often used in complex models. The practical part gives information about the activity field and the conduct of the modelled business. It introduces modelled structures, created using Vensim PLE software, which helped to achieve the final aim of this Bachelor thesis. The stock and flow diagram scripts and the following result interpretation are included.
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Application of system dynamics in selected municipality
Těžký, Vojtěch ; Krejčí, Igor (advisor) ; Horáková, Tereza (referee)
This work is focused on the application of the system dynamic in the selected municipal. In the first theoretical part is explained history, principles of the system dynamics. Furthermore, it is approached, its relation to systemic thinking, how it is necessary to change the view of the world and its functioning for the use of system dynamics. In the last section dedicated to system dynamics explains the basic archetypes of behavior. In the section that deals with municipal budgets are explained the principles on which it is based budgeting and also from which the components are made.
The practical part is devoted to the assembly of the model and then evaluating the results of simulations of several scenarios. Two scenarios used for simulation were: Reducing expenditures for the proper repayment of debt, then the possibility of completing the pipeline network.
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