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Coupling and the speed of convergence of Markov chains
Macháček, Adam ; Prokešová, Michaela (advisor) ; Honzl, Ondřej (referee)
In the present work we study two methods for estimating the rate of convergence of marginal distribution of a discrete-time irre- ducible and aperiodic Markov chain to its stationary distribution (i.e. the speed of mixing). Firstly, we concentrate on deriving an upper bound for the rate of convergence by using the coupling technique. Moreover, we will also define the total variation distance and explain its role in the es- timation of the speed of mixing. In the second part we will study the me- thod of strong uniform times. Both methods are described in detail and several basic theorems are proved. Finally we demonstrate the use of both approaches on a number of models, particularly on the random walk on a hypercube and on shuffling a deck of cards. 1
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Coupling and speed of convergence of discrete MCMC algorithms.
Kalaš, Martin ; Prokešová, Michaela (advisor) ; Dvořák, Jiří (referee)
Convergence of the marginal distribution of a Markov chain to its stationary distribution is an essential property of this model with many applications in different fields of modern mathematics. Such typical applications are for example the Markov Chain Monte Carlo algorithms, which are useful for sampling from complicated probability distributions. A crucial point for usefulness of such algorithms is the so called mixing time of corresponding Markov chain, i.e. the number of steps the chain has to make for the difference between its current marginal distribution and stationary distribution to be sufficiently small. The main goal of this thesis is to describe a method for estimation of the mixing time based on a probability technique called coupling. In the first part we collect some definitions and propositions to show how the method works. Later the method is demonstrated on several traditional examples of Markov chains including e.g. random walk on a graph. In the end we study Metropolis chain on the set of proper colorings of a graph as a specific example of MCMC algorithm and show how to estimate its mixing time.
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Coupling atmospheric chemistry/aerosols to regional climate models
Huszár, Peter ; Halenka, Tomáš (advisor) ; Macoun, Jan (referee) ; Eben, Kryštof (referee)
Title: Coupling atmospheric chemistry/aerosols to regional climate models Author: Peter Huszár Department: Department of Meteorology and Environment Protection Supervisor: doc. RNDr. Tomáš Halenka, CSc. Supervisor's e-mail address: tomas.halenka@mff.cuni.cz Abstract: In this thesis, the connections between air quality and climate are studied. For this purpose, regional climate model RegCM3 and chemistry transport model CAMx has been coupled offline with one- and two-way interaction. Our work represents a first attempt to connect RegCM3 not only with CAMx, but with any other chemistry transport model. As a first step, an offline one way couple of RegCM3 and CAMx has been developed, meaning that the climate model drives the transport, emission, chemical transformation and deposition of species while the radiative feedbacks of gases and aerosols are not considered. A meteorological interface has been developed at our department in order to convert the meteorological data generated by RegCM3 to fields required by CAMx. For those parameters that are essential for CAMx but the regional climate model does not supply them, diagnostic methods were implemented into this interface. Further, it is used to calculate biogenic emissions. Regarding anthropogenic emissions, a simple utility has been developed to...
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Analysis of Driving a Passenger Vehicle with a Trailer
Šujan, Tomáš ; Kropáč, František (referee) ; Vémola, Aleš (advisor)
The subject of this thesis is the analysis of the negative effects associated with the operation of a trailer for a personal vehicle with respect to the design speed, technical checks and analysis related legislation. Its work is drawn from the measurement, cooperation with leading Czech production plant trailers Vezeko s.r.o., an organization engaged in the implementation of engineering controls DEKRA Automobil a.s. and available literature, including electronic resources. Results of the work end with proposals for specific measures to minimize the identified adverse effects.
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Simulation of rod ejection accident byPARCS code
Matějková, J.
This paper describes reactor core model used for simulating REA. The model was designed in PARCS utilizing graphical interface SNAP. The data for model were given from benchmark NEACPR L-335. The PARCS model used integrated thermal hydraulic block for calculation. The results and solution is shown in the paper. Thermal hydraulic calculation can also be provided by external system code TRACE. The PARCS model is prepared to couple with TRACE model for giving more accurate calculation.
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Modeling of planar coupling circuits
Valošek, Josef ; Puskely, Jan (referee) ; Láčík, Jaroslav (advisor)
This master’s thesis deals with modelling of the planar coupling circuits, namely type of the wideband couplers and the ultra-wideband couplers. The purpose of this thesis is an analysis, a synthesis, a numerical modelling and a fabrication (only chosen types) of the presented couplers. All of the couplers works on medium frequency f0 = 7 GHz with coupling C = 3 dB. Types of the substrate are Arlon 25N and Arlon AD600. EM simulator IE3D and circuit simulator in program Ansoft Designer are used for the numerical modelling. The realized wideband couplers were measuring by the vector analyzer Agilent E3864B.
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Solution technology of manufacturing for part "disc of coupler"
Borek, Vít ; Osička, Karel (referee) ; Mouralová, Kateřina (advisor)
An introduction to main principles of coupling and description of basic types has been done. An analysis of the given component and a proposal for suitable intermediate was made. A selection of machines and tools for individual operations has been done. A proposition of technologic process and enumeration of machines times was proposed. Economic evaluation containing costs for tools, cooperation, workmen’s wages, intermediate and energy for operating machines has been calculated.
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Evaluating Quality of Service Design
Hejl, Daniel ; Feuerlicht, Jiří (advisor) ; Pavlíčková, Jarmila (referee)
Service Oriented Architecture is a popular choice of system architecture and many organization are moving towards it in order to closely align IT capabilities with their business goals. They are expecting that the implementation of SOA will lead to increased efficiency, the ability to rapidly respond to changing business environments, and significantly improved return on investment. In order to meet these expectations, great emphasis must be given on correct service design. However, designing services in the way that they are highly reusable and the final product is highly maintainable can be especially challenging. This bachelor thesis focuses on summarization of how metrics for measuring structural properties of service oriented software designs can be used for predicting potential problems in service design. In the practical part of this thesis, a tool for evaluating a service design based on coupling between service interfaces was implemented and practical applicability of one of the metric was demonstrated.
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Interaction of a spherical shell surrounded by an acoustical medium
Zolotarev, Igor
The interaction problem of a spherical shell with an acoustical medium is studied as some approximation of the human skull. The elastic sphere is described by using the thin shell theory and, in general, a compressible inviscid fluid that is considered on the inside of the vibrating shell. The dynamic characteristics such as the natural frequencies and the modes of vibration are analysed as functions of the geometrical and physical parameters of the studied system. The coupling of the elastic sphere and the acoustic medium are presented by use variations of the natural frequencies on the wave parameter and the influence of fluid on these variations.
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