
Vlastnosti síťových centralit
Pokorná, Aneta ; Hartman, David (advisor) ; Balko, Martin (referee)
The need to understand the structure of complex networks increases as both their complexity and the dependency of human society on them grows. Network centralities help to recognize the key elements of these networks. Betweenness centrality is a network centrality measure based on shortest paths. More precisely, the contribution of a pair of vertices u, v to a vertex w ̸= u, v is the fraction of the shortest uvpaths which lead through w. Betweenness centrality is then given by the sum of contributions of all pairs of vertices u, v ̸= w to w. In this work, we have summarized known results regarding both exact values and bounds on betweenness. Additionally, we have improved an existing bound and obtained more exact formulation for rregular graphs. We have made two major contributions about betweenness uniform graphs, whose vertices have uniform betweenness value. The first is that all betweenness uniform graphs of order n with maximal degree n − k have diameter at most k, by which we have solved a conjecture posed in the literature. The second major result is that betweenness uniform graphs nonisomorphic to a cycle that are either vertex or edgetransitive are 3connected, by which we have partially solved another conjecture. 1


MAT TRIAD 2019: Book of Abstracts
Bok, J. ; Hartman, David ; Hladík, M. ; Rozložník, Miroslav
This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers in a variety of aspects of matrix analysis and its interdisciplinary applications to meet and share interests and ideas. The conference topics include matrix and operator theory and computation, spectral problems, applications of linear algebra in statistics, statistical models, matrices and graphs as well as combinatorial matrix theory and others. The goal of this event is to encourage further growth of matrix analysis research including its possible extension to other fields and domains.


Speed of sound prediction
Řežábková, Jana ; Hartman, David (advisor) ; Brabec, Marek (referee)
This bachelor thesis presents a novel approach for speed of sound pre diction in aqueous electrolytic solutions using machine learning techniques. A single model capable of accurately predicting the speed of sound in se lected electrolytic aqueous solutions at different temperatures and molalities is trained. The machine learning experiment is designed to exploit the dis sociation of electrolytes in water. Electrolytes are viewed as cation/anion pairs. Therefore, electrolyte description is based purely on its constituting ions. This approach allows to view the available data as a matrix in which rows represent cations, columns anions and each cell a full electrolyte. The idea of being able to fill cells for which no speed of sound data is yet avail able is tested within the thesis. The final model's accuracy is compared to existent research on speed of sound prediction. However, some of the model approaches are novel and have no existing comparable settings. 1


Powers of interval matrices
Říha, David ; Hartman, David (advisor) ; Matonoha, Ctirad (referee)
The aim of this thesis is to analyse methods of how to calculate the interval enclosure of interval matrix powers, investigate special cases where exponentiation is easier than in the general case and those methods implement to software MATLAB. In the thesis will be introduced two algorithms for calculations of interval enclosure of general interval matrix. First uses spectral decomposition, thus the decomposition based on eigenvalues and eigenvectors and the second one is based on well known binary exponentiation. Special cases include for example nonnegative interval matrices or cube power of diagonally interval matrices. For researched methods, the theory on which they are built, are explained and the methods themselves are described both verbally and by code. At the end is done the testing of quality for the interval enclosures and time complexity of calculations.


Evaluation of interval polynomials
Firment, Roman ; Hladík, Milan (advisor) ; Hartman, David (referee)
In this thesis, we deal with the finding of an enclosure of the range of the real and interval polynomials in one variable. There are presented functional forms of the real polynomials which we implemented in the Matlab environment that is using interval arithmetic of the toolbox INTLAB. These forms can be used to effectively evaluate an enclosure of a polynomial. In the theoretical part there is introduced a reduction that makes possible to use an arbitrary functional form computing an enclosure of a real polynomial to evaluate an enclosure of interval polynomial. A numerical comparison is also the part of this thesis. Based on its results we designed two global functions solving our problem that apply one of the forms. A user has a possibility to indirectly influence the choice of the form by nonmandatory parameter that is specifying the strategy of computation. This parameter defines speed of evaluation and the amount of overestimation of the computed interval.


Solving interval systems by the least squares method
Tomandl, David ; Hladík, Milan (advisor) ; Hartman, David (referee)
This thesis is describing, comparing and implementing enclosure methods for solving overdetermined system of interval linear equations by the least squares method. Input data of the methods are within given intervals. We describe the structure of the solution set, which is the basis of algorithms for computing interval hull of the solution set. Although computation of the interval hull is NPhard problem, there exist algorithms which encloses the solution set with less than exponential steps. We are heavily focusing on these algorithms. The solution set can be alternatively characterized as a solution to the symmetric interval system. Therefore the work includes solvers of the symmetric interval system. This thesis contains numerical experiments for comparing the methods. All methods are implemented in Matlab with utilisation of the interval toolbox Intlab. Powered by TCPDF (www.tcpdf.org)


Legal issues of commercial and investment banking
Hartman, David ; Kotáb, Petr (advisor) ; Kohajda, Michael (referee)
This thesis is dedicated to the Financial Law, namely to a special part of this branch of law  Banking Law, with a special focus on legal aspects of commercial and investment banking. Its concentrates on the specifics of the universal banking system in related to system of the Czech Republic. Chapter 1 deals with the general terms and concepts of the bank regulation, namely on model of universal banking model, segmented banking model and hybrid banking model, presentation of different types of banks and/or other financial institutions, variety types of bank systems a shows difference concept of banking systems, and description of basic parts of commercial and investment banking and its models of regulations. Chapter 2 describes the banking system of the Czech Republic, its history, situation on the market, types of banking institutions on the markets and detail description of bank regulations on European and national level. Chapter 3 is connected with commercial banking systems. Describes main categories of services or products provided by the commercial banks in the Czech Republic and its legal regulation. This services or products consist in a form of Banking transactions. Chapter 4 looks in detail on a model of investment banking in the market of the Czech Republic, its history and regulations...


Extension property of structures
Hartman, David ; Nešetřil, Jaroslav (advisor) ; Pultr, Aleš (referee) ; Woodrow, Robert (referee)
This work analyses properties of relational structures that imply a high degree of symmetry. A structure is called homogeneous if every mapping from any finite substructure can be extended to a mapping over the whole structure. The various types of these mappings determine corresponding types of homogeneity. A prominent position belongs to ultrahomogeneity, for which every local isomorphism can be extended to an automorphism. In contrast to graphs, the classification of ultrahomogeneous relational struc tures is still an open problem. The task of this work is to characterize "the distance" to homogeneity using two approaches. Firstly, the classification of homogeneous structures is studied when the "complexity" of a structure is increased by introducing more relations. This leads to various classifications of homomorphismhomogeneous Lcolored graphs for different L, where L colored graphs are graphs having sets of colors from a partially ordered set L assigned to vertices and edges. Moreover a hierarchy of classes of ho mogeneous structures defined via types of homogeneity is studied from the viewpoint of classes coincidence. The second approach analyses for fixed classes of structures the least way to extend their language so as to achieve homogeneity. We obtain results about relational complexity for finite...


Legal issues of commercial and investment banking
Hartman, David ; Kotáb, Petr (advisor) ; Kohajda, Michael (referee)
This thesis is dedicated to the Financial Law, namely to a special part of this branch of law  Banking Law, with a special focus on legal aspects of commercial and investment banking. Its concentrates on the specifics of the universal banking system in related to system of the Czech republic. Chapter 1 deals with the general terms and concepts of the bank regulation, namely on model of universal banking model, segmented banking model and hybrid banking model, presentation of different types of banks and/or other financial institutions, variety types of bank systems a shows difference concept of banking systems, and description of basic parts of commercial and investment banking and its models of regulations. Chapter 2 describes the banking system of the Czech Republic, its history, situation on the market, types of banking institutions on the markets and detail description of bank regulations on European and national level. Chapter 3 looks in detail on a model of investment banking in the market of the Czech Republic, its history and regulations on European level, namely MiFID I. and MiFID II. Regulations and description of legal framework of providing investing services in the Czech Republic. Chapter 4 describes the actually legal problems of bank regulations after Financial crisis which brings a...


Eigenvalues of symmetric interval matrices
Kaleyski, Nikolay Stoyanov ; Hladík, Milan (advisor) ; Hartman, David (referee)
The goal of the thesis is to describe and possibly improve some algorithms for finding inner and outer approximations of the borders of eigenvalue intervals of real symmetric interval matrices, to modify them so that they perform verified computations and to implement them in the Matlab programming language. The main principles of verification and interval arithmetic are described, as well as the used theoretical foundations and the problems which occur when attempting to verify the individual algorithms, including possibilities of overcoming them. Experiments illustrating some empirical properties of the algorithms are described. The practical result of the thesis is a software package for computing approximations of the sets of eigenvalues of symmetric interval matrices. Powered by TCPDF (www.tcpdf.org)
