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Balanced and almost balanced group presentations from algorithmic viewpoint
Skotnica, Michael ; Tancer, Martin (advisor) ; Paták, Pavel (referee)
In this thesis we study algorithmic aspects of balanced group presentations which are finite presentations with the same number of generators and relations. The main motivation is that the decidability of some problems, such as the triviality problem, is open for balanced presentations. First, we summarize known results on decision problems for general finite presen- tations and we show two group properties which are undecidable even for balanced presentations - the property of "being a free group"' and the property of "having a finite presentation with 12 generators". We also show reductions of some graph problems to the triviality problem for group presentations, such as determining whether a graph is connected, k-connected or connected including an odd cycle. Then we show a reduction of the determining whether a graph with the same number of vertices and edges is a cycle to the triviality problem for balanced presentations. On the other hand, there is also a limitation of reduction to balanced presentations. We prove that there is no balanced presentation with two generators a, b|ap(m) bq(m) , ar(m) bs(m) for p(m), q(m), r(m), s(m) ∈ Z[m] which describes the trivial group if and only if m is odd. In the last part of this thesis, we describe a relation between group presentations and topology. In addition,...
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Algorithms for the computation of Galois groups
Kubát, David ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
This thesis covers the topic of the computation of Galois groups over the rationals. Beginning with the classic algorithm by R. Stauduhar, we then review the theory necessary to explain the modular algorithm by K. Yokoyama. More precisely, we discuss the notion of the universal splitting ring of a polynomial. For a separable polynomial, we then study idempotents in the universal splitting ring. The modular algorithm involves computations in the ring of p-adic integers. Examples are given for polynomials of degree 3 and 4.
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Automated Trading on Cryptocurrency Exchanges
Křesťan, Zdeněk ; Zbořil, František (referee) ; Kočí, Radek (advisor)
This thesis focuses on automated trading on cryptocurrency exchanges. Cryptos are now widespread. The possibility of hier automated buying and selling is an interesting topic, which is more and more mentioned. The main part of the thesis is the design of an algorithm for processing data from stock exchanges, their evaluation and subsequent execution of cryptocurrency trades. It also describes its implementation, testing and possible further extensions.
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Coordination of operation of PST transformers in the interconnected region
Tesař, Jan ; Topolánek, David (referee) ; Bátora, Branislav (advisor)
This master’s thesis deals with phase-shifting transformers (PST) and coordination of electrically close devices in an interconnected region. Theoretical research is performed in the work, describing methods of power control, function and design of PST, as well as actual methods of PST coordination in the rest of the world. Based on the research there is an optimalisation algorithm designed in MATLAB, which computes recommended tap petting of PST based on the network configuration. In the second part of this thesis there are described components of this algorithm and also presented the results of three demonstrative scenarios. Algorithm is able to solve minor problems in the network; more complex problems are beyond its solving ability. For an improved functionality there is a necessity to further expand this algorithm by a network redispatch solving algorithm.
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Software Guitar Looper with Remote Control
Kalník, Jan ; Říha, Kamil (referee) ; Schimmel, Jiří (advisor)
This thesis deals with creating a software guitar looper in a visual programming language called Pure Data and also building a specific remote controller for it. The remote cont- roller will be based on a MIDI protocol. As a part of the software, there will be a special aligning algorithm, that will take care of precise alignment of the created loop on beat in the way that no other intrusive rhythmical or tempo related elements are present.
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Internet library of methods and algorithms used for medical image registration
Koňařík, Jakub ; Jiřík, Radovan (referee) ; Peter, Roman (advisor)
Image registration is a procedure which is heading to search for a geometric transformation, which ensures same position, orientation and size of coresponding objects in pictures. How does these methods work? These methods and principies are explained in first part of this work. Second part of this work is aimed to explain theory about information systems and practical creation of the internet databaze. These practical part was realized in editorial system called Drupal.
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Movement Tracking in Public Transport
Paulovčák, Ján ; Rychlý, Marek (referee) ; Burget, Radek (advisor)
This master’s thesis is dedicated to user’s movement tracking in public transport, as well as to optimize route planning. In the first part, author presents information related to graph theory and graph theory algorithms, including Breadth-First Search, Djikstra’s algorithm and A*. In the second part of this thesis, author describes the design of server and mobile application including description of routing process and how individual parts works.
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