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Network-wide Security Analysis
de Silva, Hidda Marakkala Gayan Ruchika ; Šafařík,, Jiří (referee) ; Šlapal, Josef (referee) ; Švéda, Miroslav (advisor)
Práce představuje model a metody analýzy vlasností komunikace v počítačových sítích. Model dosažitelnosti koncových prvků v IP sítích je vytvořen na základě konfigurace a síťové topologie a umožňuje ukázat, že vabraný koncový uzel je dosažitelný v dané síťové konfiguraci a stavu. Prezentovaná práce se skládá ze dvou částí. První část se věnuje modelování sítí, chování směrovaích protokolů a síťové konfiguraci. V rámci modelu sítě byla vytvořena modifikovaná topologická tabulka (MTT), která slouží pro agregaci síťových stavů určených pro následnou analýzu. Pro analýzu byl použit přístup založený na logickém programování, kdy model sítě je převeden do Datalog popisu a vlastnosti jsou ověřovány kladením dotazů nad logickou databází. Přínosy práce spočívají v definici grafu síťových filtrů, modifikované topologické tabulce, redukce stavového prostoru agrgací síťových stavů, modelů aktivního síťového prvku jako filter-transformace komponenty a metoda pro analýzu dosažitelnosti založena na logickém programování a databázích.
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Algebraic classification of the Weyl tensor
Pravdová, Alena
Alignment classification of tensors on Lorentzian manifolds of arbitrary dimension is summarized. This classification scheme is then applied to the case of the Weyl tensor and it is shown that in four dimensions it is equivalent to the well known Petrov classification. The approaches using Bel-Debever criteria and principal null directions of the superenergy tensor are also discussed.
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Graphical Tool for Creation and Modification of Graphs
Hynšt, Miroslav ; Navrátil, Jan (referee) ; Zuzaňák, Jiří (advisor)
This paper deals with basics of the graph theory and graph rewriting. In the first part there is described a graph, graph rewriting systems, graph grammar and algebraic approach to the graph rewriting. In the second part of this paper there is analyzed an implementation of the designed aplication for creation, modification and saving graphs and graph rewrite systems.
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Algebraický přístup k CSP
Bulín, Jakub ; Barto, Libor (advisor) ; Růžička, Pavel (referee)
For a finite relational structure A, the Constraint Satisfaction Problem with template A, or CSP(A), is the problem of deciding whether an input relational structure X admits a homomorphism to A. The CSP dichotomy conjecture of Feder and Vardi states that for any A, CSP(A) is either in P or NP-complete. In the first part we present the algebraic approach to CSP and summarize known results about CSP for digraphs, also known as the H-coloring problem. In the second part we study a class of oriented trees called special polyads. Using the algebraic approach we confirm the dichotomy conjecture for special polyads. We provide a finer description of the tractable cases and give a construction of a special polyad T such that CSP(T) is tractable, but T does not have width 1 and admits no near-unanimity polymorphisms.
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The Use of the spatial data examining methods for definition of rural areas
KROHOVÁ, Zuzana
The aim of this thesis is technical evaluation of existing approaches to defining rural areas in our country, in Europe and in the world. The main result of the work will be a comprehensive proposal for a new definition of rural areas of the Czech Republic by means of spatial data analysis in a geographic information system. The main method of the spatial analysis will be the map algebra, using it to define a new criterion for rural areas. A new proposal for the definition of rural areas of the Czech Republic will be based on a combination of commonly used criterias for defining rural (population, population density, unemployment rate, etc.) along with their processing in GIS (spatial models, overlay operations, spatial statistics and others). The result of this work should serve to further evaluate the proposals and rural areas of sustainable development.
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Mathematics in Physics
BLAŽEK, Jiří
The presented work deals with mathematical tools, which are used to describe harmonic oscillations and waves in secondary schools. Harmonic quantities are most frequently represented as projections of rotating symbolic vectors ? phasors, nevertheless most attention is paid to representation of harmonic quantities by complex numbers. It is shown that both these methods are in fact formalized methods of solution of differential-algebraic equations, describing relevant physical phenomena. All these approaches are applied simultaneously and compared to each other during solution of model examples. The work is primarily intended for teachers of physics in secondary schools and for students of physics of pedagogical faculties.
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Control of non-stable Systems
Heczko, Lukáš ; Findura, Milan (referee) ; Vavřín, Petr (advisor)
This master´s thesis deals with control of unstable processes with two unstable complex poles using algebraic control with emphasis in value of the controller output. Thesis consists of theoretical introduction, including initial conditions with analysis of basic approaches to the control design with one or two degrees of freedom regulators by solving polynomial equations. Constrained control is studied more detailed. Optimization problem of „lowest fuel consumption“ is used for design of controller and is used for both degrees of freedom regulators with additional condition of zero variance control. Thesis includes some examples of control design by described method. Small library of MatLab functions were developed also to make the design more easier. Conclusions are made at the end and achieved goals are reviewed.
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A parallel finite element solver for unsteady incompressible Navier-Stokes equations
Šístek, Jakub
A parallel solver for unsteady incompressible Navier-Stokes equations is presented. It is based on the finite element method combined with the pressure-correction approach. Semi-implicit treatment of the convective term is considered, leading to five systems of linear algebraic equations to be solved in each time step. Krylov subspace iterative methods are employed for the solution of these systems with a particular emphasis on efficient parallel preconditioners. A simulation of a benchmark problem of incompressible viscous flow around a sphere at Reynolds number 300 is presented and compared with literature.
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