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Hamiltonovské kružnice v hyperkrychlích s odstraněnými vrcholy
Pěgřímek, David ; Gregor, Petr (advisor) ; Dvořák, Tomáš (referee)
In 2001 Stephen Locke conjectured that for every balanced set F of 2k faulty vertices in the n-di- mensional hypercube Qn where n ≥ k + 2 and k ≥ 1 the graph Qn − F is hamiltonian. So far the conjecture remains open although partial results are known; some of them with additional conditions on the set F. We explore hamiltonicity of Qn − F if the set of faulty vertices F forms certain isometric subgraph in Qn. For an odd (even) isometric path P in Qn the graph Qn − V (P) is Hamiltonian laceable for every n ≥ 4 (resp. n ≥ 5). Although a stronger result is known, the method we use in proving the theorem allows us to obtain following results. Let C be an isometric cycle in Qn of length divisible by four for n ≥ 6. Then the graph Qn −V (C) is Hamiltonian laceable. Let T be an isometric tree in Qn with odd number of edges and let S be an isometric tree in Qm with even number of edges. For every n ≥ 4, m ≥ 5 the graphs Qn −T and Qm −S are Hamiltonian laceable. A part of the proof is verified by a computer. 1
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Decision trees
Jahoda, Miroslav ; Mrázová, Iveta (advisor) ; Gregor, Petr (referee)
Among the known methods of data mining are neural networks, ILP, associative rules, Bayes networks, clustering, decision trees and others. This thesis is about decision trees, their implementation, visualization, extraction rules and the comparison of different decision trees and models of classification data in general. An integral part of the data mining process is preprocessing of data, which plays an important role and is also discussed in this thesis. Part of this thesis also concerns the comparison of different decision tree models such as CART, CHAID, C5.0 (See5) and others on a set of 3 data kinds. Finally, this model's results are compared to its results when data preprocessed by PCA analysis is used.
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Třídy Booleovských funkcí umožňující efektivní hledání minimálních reprezentací.
Kuřík, Stanislav ; Čepek, Ondřej (advisor) ; Gregor, Petr (referee)
This thesis deals with the Boolean minimization problem. We discuss its time complexity in the general case for various representations of the input. Since this problem is known to be NP-complete, a survey of some of important classes for which it is polynomially solvable follows. The main part of this thesis presents a definition of a new class of Boolean functions, along with an algorithm for finding a minimal representation of a given function from this class in polynomial time. Finally, a generalization of this class is obtained and its minimization-related properties are discussed.
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Software for Modeling Car Driving Properties
Malý, Ondřej ; Surynek, Pavel (advisor) ; Gregor, Petr (referee)
This work is intended for all interested in physical modelling, discrete computer simulations and motorism. Text part describes mathematical model of a car, description of forces and effects which occurs within car motion. Model is focused especially on the engine, trasferring the torque, braking and turning. Furthermore the thesis deals with electronic systems like ABS or ESP, which improves the steering control. The most important part of this work is a computer application for simulating and visualising the model. The program supports batch input and become a useful tool for experimenting with different settings of the car. Text part of the work includes screenshots taken during the tests and along with mathematical interpretation provides an insight into a physical principle of the car behaviour.
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Boolean methods in knowledge compilation
Kaleyski, Nikolay Stoyanov ; Čepek, Ondřej (advisor) ; Gregor, Petr (referee)
The open problem in knowledge compilation of whether the language PI is at least as succinct as MODS is answered in the negative. For this purpose a class of Boolean functions with a number of prime implicants that is superpolynomial in their number of false points is constructed. A lower bound (proving that PI is not at least as succinct as MODS), an upper bound (proving that the counterexample cannot yield an exponential separation of PI and MODS) and the precise number of the prime implicants of these functions is computed. Powered by TCPDF (www.tcpdf.org)
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Rozklady propojovacích sítí na dlouhé cesty
Měkuta, Kryštof ; Gregor, Petr (advisor) ; Dvořák, Tomáš (referee)
❚✐t❧❡✿ P❛rt✐t✐♦♥s ♦❢ ✐♥t❡r❝♦♥♥❡❝t✐♦♥ ♥❡t✇♦r❦s ✐♥t♦ ❧♦♥❣ ♣❛t❤s ❆✉t❤♦r✿ ❑r②➨t♦❢ ▼➙❦✉t❛ ❉❡♣❛rt♠❡♥t✿ ❉❡♣❛rt♠❡♥t ♦❢ ❚❤❡♦r❡t✐❝❛❧ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡ ❛♥❞ ▼❛t❤❡♠❛t✐❝❛❧ ▲♦❣✐❝ ❙✉♣❡r✈✐s♦r✿ ▼❣r✳ P❡tr ●r❡❣♦r✱ P❤✳❉✳✱ ❑❚■▼▲ ❆❜str❛❝t✿ ❲❡ s✉r✈❡② s♦♠❡ ❜❛s✐❝ ♣r♦♣❡rt✐❡s ♦❢ s❡❧❡❝t❡❞ ✐♥t❡r❝♦♥♥❡❝t✐♦♥ ♥❡t✇♦r❦s✱ ♠♦r❡ ♣r❡❝✐s❡❧② ♠♦❞✐✜❝❛t✐♦♥s ♦❢ ❤②♣❡r❝✉❜❡s✳ ■♥ ♣❛rt✐❝✉❧❛r✱ ✇❡ st✉❞② ❢❛✉❧t✲t♦❧❡r❛♥❝❡ ♦❢ ❛✉❣♠❡♥t❡❞ ❝✉❜❡s ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ❡①✐st❡♥❝❡ ♦❢ ❍❛♠✐❧t♦♥✐❛♥ ❝②❝❧❡s✳ ❲❡ ❛❧✲ s♦ ♣r❡s❡♥t ❛ ♠❡t❤♦❞ t♦ ❝♦♥str✉❝t ♠❛♥② s♣❛♥♥✐♥❣ s✉❜❣r❛♣❤s ♦❢ AQn ✐s♦♠♦r♣❤✐❝ t♦ Qn ✉s✐♥❣ ❡❧❡♠❡♥t❛r② ❢❛❝ts ❢r♦♠ ❧✐♥❡❛r ❛❧❣❡❜r❛✳ ❲❡ ♣r♦✈❡ t❤❛t n✲❞✐♠❡♥s✐♦♥❛❧ ❛✉❣♠❡♥t❡❞ ❝✉❜❡ AQn ✇✐t❤ f ❢❛✉❧t② ❡❞❣❡s ❝♦♥t❛✐♥s ❛ ❝♦♣② ♦❢ n✲❞✐♠❡♥s✐♦♥❛❧ ❤②♣❡r✲ ❝✉❜❡ Qn ✇✐t❤ ❛t ♠♦st n 2n−1 f ❢❛✉❧t② ❡❞❣❡s✳ ❯s✐♥❣ t❤✐s r❡s✉❧t ✇❡ ❛r❡ ❛❜❧❡ t♦ ❡❛s✐❧② tr❛♥s❢❡r s❡✈❡r❛❧ ♣r♦♣❡rt✐❡s ♦❢ Qn ✇✐t❤ ❢❛✉❧t② ❡❞❣❡s t♦ AQn ✇✐t❤ ✭♠♦r❡✮ ❢❛✉❧t② ❡❞❣❡s✳ ❆♣♣❧②✐♥❣ s✐♠✐❧❛r ♠❡t❤♦❞✱ ✇❡ ❛❧s♦ s❤♦✇ t❤❛t ✐❢ f ≤ 3n−7 ❛♥❞ ❡✈❡r② ✈❡rt❡① ♦❢ AQn ✐s ✐♥❝✐❞❡♥t t♦ ❛t ❧❡❛st t✇♦ ♥♦♥✲❢❛✉❧t② ❡❞❣❡s✱ t❤❡♥ AQn ❤❛s ❛ ♥♦♥✲❢❛✉❧t② ❤❛♠✐❧t♦♥✐❛♥ ❝②❝❧❡✳ ▼♦r❡♦✈❡r✱ ✇❡ s❤♦✇ t❤❛t ❡✈❡r② t✇♦ ♠♦♥♦♠♦r♣❤✐s♠s ♦❢ G1 t♦ AQn ❛♥❞ G2 t♦ AQm ❝❛♥ ❜❡ ❝♦♠♣♦s❡❞ ✐♥t♦ ❛ ♠♦♥♦♠♦r♣❤✐s♠ ♦❢ t❤❡ ❈❛rt❡s✐❛♥ ♣r♦❞✉❝t G1 G2 t♦ AQn+m✳ ❑❡②✇♦r❞s✿ ❤②♣❡r❝✉❜❡✱ ❛✉❣♠❡♥t❡❞ ❝✉❜❡✱ ❤❛♠✐❧t♦♥✐❝✐t②✱ ❢❛✉❧t② ❡❞❣❡s
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Electronic Textbook in Mathematical Methods of Physics - Line and Surface Integral of a Vector Field, Differential Operators
Gregor, Pavel ; Kolář, Petr (advisor) ; Snětinová, Marie (referee)
The main objective of this thesis is to supplement already created teaching materials for the subject Mathematical Methods of Physics with chapters dealing with line and surface integral of a vector field and differential operators. The resulting text, as well as the existing texts, should serve full-time students of physics teaching, students of Lifelong Learning and others interested in the processed issues. The bachelor's thesis is based on the preparations of Doctor A. Hladík, Professor J. Podolský and Associate Professor V. Žák. The experience of both the author of this work and the author of the teaching texts created so far were taken into account. The bachelor thesis also contains a search of existing resources on the topics covered in this work. 1
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The contribution of myocardial contrast echocardiography in patients with coronary heart disease
Toušek, Petr ; Gregor, Pavel (advisor) ; Chaloupka, Václav (referee) ; Hradec, Jaromír (referee) ; Kittnar, Otomar (referee)
Contrast echocardiography is a new myocardial echocardiographic method that extends the capabilities of conventional echocardiography. In our first two works, we focused on determining the size of infarction in patients after AMI and compared this method with today's most commonly used diagnostic methods. We found good agreement between KEM and SPECT in the evaluation of infarction size and correlation between the extent of oscillations Q on ECG and impaired microvascular perfusion of the myocardium - or the size of infarction. In patients with chronic forms of CHD, we found that the KEM can fairly well predict the kinetics porevaskularizační improvement segments with severely impaired kinetics and in this clinical situation is comparable with Contrast-magnetic resonance imaging. In addition, low variability and low number of investigative areas nehodnotitelných infarction KEM show that it is a simple, easily reproducible and teachable method. Finally, the relatively low cost and wide availability KEM indicate great potential usefulness of this method in clinical practice.
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Genetic and clinical correlates in hypertrophic cardiomyopathy
Čurila, Karol ; Gregor, Pavel (advisor) ; Málek, Ivan (referee) ; Krejčí, Jan (referee)
Hypertrophic cardiomyopathy (HCM) is a hereditary disease, which is caused by mutations in genech coding for proteins of carcomere of heart muscle. Disease is characterised by wide genotypic and fenotypic heterogeneity. Since the 90-th of 20-th century, when the first mutation responsible for HCM was identified, many research was done in detecting the correlation between mutant gene and clinical picture of the affected patient. As the first in Czech republic, we determined the frequencies of 4 most common genes in HCM in czech patients. We figured out, that spectrum of mutations is somehow different from another populations. We didn't find any correlation between specific gene mutation and morfologic and clinical characteristics of affected subjects. In our study with AT-1 receptor blocker - candesartan, we demostrated positive effect of candesartan on level of hypertrophy and function of the left heart ventricle and clinical symptoms of the patients with HCM.
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