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Compressive sampling and simulation of one-pixel camera
Hrbáček, Radek ; Špiřík, Jan (referee) ; Rajmic, Pavel (advisor)
The Nyquist theorem is the main pillar of the traditional digital signal processing approach. It states that the sampling rate must be at least twice the maximum frequency present in the signal to guarantee perfect signal reconstruction from the sequence of its samples. In practice, we often compress the signal right after the sampling process to reduce the data size. The compressive sampling approach is not limited to the frequency domain, it provides a new look at the signal by using an arbitrary basis. If we find a basis in which the signal is sparse, it is possible to take a small number of samples and reconstruct the signal successfully. One-pixel camera is one of real applications, it's formed by digital micromirror array reflexing the light into single sensor. Mathematical methods are then used to reconstruct the signal. This thesis deals with the simulation of the camera.
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Stochastic optimization in AIMMS
Kůdela, Jakub ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
Tato diplomová práce uvádí základní poznatky matematického a především stochastického programování. Navíc se zabývá použitím softwaru AIMMS při vytváření a řešení optimalizačních problémů. Naším hlavním cílem je naprogramovat v softwaru AIMMS několik metod řešení problémů stochastického programování a ukázat jejich použití a užitečnost na vybraných problémech. Jedním z problémů, který jsme si zvolili, je model spalovny. Všechny AIMMS programy, které v našem textu použijeme a popíšeme, a jejich zdrojové kódy budou přiloženy v dodatcích.
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Object Speed Measuring Using The Fourier Transform
Zikmund, Tomáš ; Martišek, Karel (referee) ; Štarha, Pavel (advisor)
This work deals with object speed measuring using image analysis method. The reader will become familiar with a mathematical theory upon which the method is based. The mathematical algorithm for obtaining the speed of a given object is illustrated. Furthermore, an original computer program has been developed and the results of real measuring are shown.
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Advanced methods for cardiac cells contour detection
Spíchalová, Barbora ; Čmiel, Vratislav (referee) ; Odstrčilík, Jan (advisor)
This thesis focuses on advanced methods of detecting contours of the cardiac cells and measuring their contraction. The theoretical section describes the types of confocal microscopes, which are used for capturing biological samples. The following chapter is devoted to the methods of cardiac cells segmentation, where we are introduced to the generally applied approaches. The most widely spread methods of segmentation are active contours and mathematical morphology, which are the crucial topics of this thesis. Thanks to the those methods we are able in the visual data to accurately detect required elements and measure their surface chnage in time. Acquired theoretical knowledge leads us to the practical realization of the methods in MATLAB.
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Modelling in Engineering
Holec, Tomáš ; Rozehnalová, Petra (referee) ; Popela, Pavel (advisor)
The aim of this bachelor thesis is to determine the optimal parameters of pump impeller in order to minimize friction loss and disc loss. The proposal has been implemented by a mathematical model in Matlab. The thesis consists of theoretical and practical part. The first four chapters summarize the theroretical background that is necessary for creating the mathematical model for the losses of an impeller. In the fifth chapter the implementation of the mathematical model in Matlab is presented and results for particular types of pumps are discussed.
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Study of factors influencing the function of MntH, membrane transport protein of E. coli
Jurková, Ingrid ; Urbánková, Eva (advisor) ; Krůšek, Jan (referee)
MntH belongs to the Nramp family of transport proteins, and plays an important role not only in homeostasis of iron and manganese, but also in bacterial defence against the immunity response of an infected host cell. MntH co-transports divalent metal ions into the cell together with protons with a stoichiometry dependent on the membrane potential and extracellular pH. Using the redistribution potential dye diS-C3(3), we measured the effects of MNTH expression and MntH-mediated metal transport on the cell membrane potential and intracellular pH. Cells expressing MNTH were found to be hyperpolarised and their membrane potential was depolarised upon the addition of metal ions. In the theoretical part of our work, we explored general four-, six-, and eight-state carrier models that were modified by introducing the voltage dependence of all rate constants. Using mathematical modelling, we simulated the effect of various model parameters (including membrane potential, substrate concentration, and carrier or substrate charge) on substrate influx. We observed some of the transport characteristics described for MntH proteins such as variable symport stoichiometry that is influenced by the membrane potential and pH. However, for a more detailed simulation of the eight-state carrier model, more information about...
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Principles of trading on betting exchanges
Karásek, Michal ; Málek, Jiří (advisor) ; Moravec, Lukáš (referee)
Unlike traditional stock exchanges, where bonds, shares and financial derivatives are traded, on the betting exchanges there are traded probabilistic estimates of the results of sporting or social events. The market price of bets, namely the market implied probability is influenced by estimate of the outcome. The specificity of betting exchanges is also a short period to maturity of contracts, and the possibility to trade with the estimated result of one real world event in several sub-markets simultaneously. In theoretical analysis, we have defined the bet, the underlying asset, and the binary betting contract, which is traded on betting exchanges. We have described some practical aspects of trading. Properties of the probabilistic contracts are demonstrated on several examples. Finally, we constructed the mathematical model of a tennis match, which is based on a binomial valuation model. This allows us to compare the market price of a contract with the price recommended by the model.
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Raymond Queneau and his novel Blue Flowers. Translation of one type of French experimental prose
Sauerová, Klaudia ; Belisová, Šárka (advisor) ; Šotolová, Jovanka (referee)
Raymond Queneau's novel s ha ve been translated in to Czech since the 60's of the 20th century. This work focuses on two of hi s novels, typical of their experimentalism: Zazie in the Metro and The Blue Flowers. A stylistic analysis of the original text showed different aspects of Queneau's poetics and also difficulties faced by a translator. Unusually rich means of expression, such as puns and neologisms at the lexical level, changing of stylistic layers or new French - handwriting created by the author to draw nearer spoken and written language, intertextuality and mathematical structures incorporated into the composition of the novel s are typ i cal features of Queneau' s work. We examined possibilities of Czech while translating Queneau's language experiments by comparing translations of two Queneau's novels, do ne by two different translators. Our work concentrates mainly on problems with translating puns, neologisms, phraseology, and new French. Jiri Pelikan 's trans lati on of the novel The Blue Flowers proved that in spite of some divergences between the original and the target text (archaization of verba dicendi, compensation), it is, on the whole, possible to keep to the author' s complex poetics, and to create, within the given scope, a work of translation that can compare with the original. The...
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Edukometrie - Item response theory
Voňková, Hana
Title: Measurement of Education - Item Response Theory Author: Hana Křížovská Department: Department of Probability and Mathematical Statistics Supervisor: Prof. Ing. František Fabian, CSc. Supervisors' e-mail address: he has not Abstract If we want to study abilities of certain pupils or other people in a given area, we can give them a didactial test, which would consist of items testing the abilities in question. The goal is then to determine the qualities of the people (ability parameter) and the relative difficulty of the questions (parameters of the questions) on the basis of the answers. Further we estimate how would a pupil, who have passed just one part of the test (assuming we have the item parameters of the whole test), would perform in the rest of the test. This is the research area of the Item Reponse Theory (IRT). In the introductory section the reasons are given for why we should use the IRT rather than the classical test theory for evaluating didactical test results, althought it's not regulary done in our country. The dichotomous Rasch model, which is one of the main IRT models, is described in detail. First the model is derived and then its main features presented. For the case of Rasch models we also demonstrate the most used methods of estimation of the ability and difficulty parameters....
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