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Ramsey-type results for ordered hypergraphs
Balko, Martin ; Valtr, Pavel (advisor) ; Conlon, David (referee) ; Nešetřil, Jaroslav (referee)
Ramsey-type results for ordered hypergraphs Martin Balko Abstract We introduce ordered Ramsey numbers, which are an analogue of Ramsey numbers for graphs with a linear ordering on their vertices. We study the growth rate of ordered Ramsey numbers of ordered graphs with respect to the number of vertices. We find ordered match- ings whose ordered Ramsey numbers grow superpolynomially. We show that ordered Ramsey numbers of ordered graphs with bounded degeneracy and interval chromatic number are at most polynomial. We prove that ordered Ramsey numbers are at most polynomial for ordered graphs with bounded bandwidth. We find 3-regular graphs that have superlinear ordered Ramsey numbers, regardless of the ordering. The last two results solve problems of Conlon, Fox, Lee, and Sudakov. We derive the exact formula for ordered Ramsey numbers of mono- tone cycles and use it to obtain the exact formula for geometric Ramsey numbers of cycles that were introduced by Károlyi et al. We refute a conjecture of Peters and Szekeres about a strengthening of the fa- mous Erd˝os-Szekeres conjecture to ordered hypergraphs. We obtain the exact formula for the minimum number of crossings in simple x-monotone drawings of complete graphs and provide a combinatorial characterization of these drawings in terms of colorings of ordered...
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Algoritmy pro semikoercivní úlohu s nosníkem na jednostranně pružném podloží
Sysala, Stanislav
In this article, so-called "projected" and "non-projected" algorithms for semi-coercive beam problem with a unilateral elastic subsoil of Winkler's type are presented. These algorithms are based on the minimisation of the energy functional for the considered problem. In each the iteration step of the algorithms, the linear problem with bilateral elastic springs is solved. The convergence properties of the algorithms are summarised and demonstrated on numerical examples.
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Development of methods for analysys road safety barriers in terms of dynamic effects
Koudelka, Ivan ; Krejsa,, Martin (referee) ; prof. Ing. Alois Materna, CSc., MBA (referee) ; Salajka, Vlastislav (advisor)
The presented work analyses the methodology and approach of the legislation. It presents in the press presented results of numerical modelling of the impact of vehicles crashed into barriers that are being solved in the Czech Republic and worldwide. It presents a recommendation of a methodology for assessing crash barriers. The methodology follows the basic principles used in the TP 101 and EN 1991-1-1. The kinetic energy of the vehicle at the moment of impact is replaced with substitute static force, whose effects are comparable with those of a vehicle collision. The supporting structure of crash barriers is implemented in compliance with means of statics. The calculation includes the vehicle deformation, which represents the real distribution of the energy absorbed by the deformation of the vehicle and the energy that crash barriers need to absorb. The proposed methods allow to take into account non-linear behaviour of the structure both in terms of geometry and in terms of material nonlinearity. The work also deals with the interpretation of various types of support structures in the computational model. A specific case is used for a demonstration of a way of modelling the elastic supporting column of crash barriers in the soil, or modelling the friction of a loose concrete block over the surface. To ensure the proper position of interconnected loose blocks corresponding to the reality, a method of modelling the place of a possible contact of the breakthrough is drafted. A significant contribution to the more accurate calculation is achieved by sequential increase of the load on the construction by using load increment and measurement of energy increases absorbed by the deformation in each step. The presented methodology is an effective tool to assess crash barriers. For the application of this tool, using common resources and facilities available to almost every designer dealing with statics of structures is sufficient. In conclusion, the knowledge obtained fr
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The Generalized Distribution Problem Approach
Fuksová, Lucie ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The generalized distribution problem is task from linear programming approach which belongs to the distribution problems with specific mathematical model. For solution this problems we need to use another methods than the universal simplex method. A typical example is the transportation problem. The generalized distribution problem differs from it only in a small difference in mathematical model, but compared to the traffic problem has computational difficulties. To build the model and its solution is necessary to calculate the transmission coefficients, the so-called "performance factors". This work will prepare the answers for problem formulations and mathematical model and will describe the procedures that can solve problems of similar type. Methods used in the thesis are modified distribution method and the simplex method. To calculate solutions will be used the optimization software Lingo.
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Seeming regression of economic indices
Komzáková, Magdalena ; Zvára, Karel (referee) ; Lachout, Petr (advisor)
In the time series analysis it often appears that two or more time series influence each other. When the generating stochastic processes of these series do not have stationary structure but they are stochastically non-stationary, i.e. the characteristic polynomial has a unit root, it happens that the regression modelling the dependence of some absolutely independent series gives statistically significant parameter estimations and statistics used to judge the model fitting do not indicate anything about its impropriety. This phenomenon is called seeming regression (spurious regression) and is solved with the theory of cointegration. We can say that when the series are cointegrated, their model shows their real dependence, not only the seeming one. Due to this fact, cointegration tests are also used for testing for the presence of seeming regression. These tests are based on unit root tests in generating process (or on stationarity tests), because time series can be cointegrated only if their linear combination is a stationary series.
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Eliminace harmonických složek proudu světelných zátěží pomocí aktivních filtrů
Tirmikçi, Ceyda Aksoy ; Yavuz, Cenk
Non-linear loads are an important fraction of loads in most commercial buildings. Most of these non-linear loads are lighting loads. So a small negative change in their harmonic distortion levels may affect the other loads in the building and the loads that are connected to the same bus. Shunt active power filters inject harmonic current with the same amplitude and opposite phase of the load harmonic current to eliminate the harmonic current flowing into the source. Therefore harmonic and reactive power trouble is solved simultaneously. In this study a three phase shunt active power filter based on synchronous reference frame (SRF) theory is designed and tested with an approximate linear LED model in MATLAB. A three phase current controlled voltage source inverter (VSI) and DC link capacitor is used as an active power filter. Pulses to the inverter are generated by hysteresis band current control (HBCC) technique. The THDI with the shunt active power filter is measured 2.52% which is within the allowable harmonic limits.
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Automatic hp-adaptivity on Meshes with Arbitrary-Level Hanging Nodes in 3D
Kůs, Pavel ; Vejchodský, Tomáš (advisor) ; Segeth, Karel (referee) ; Dolejší, Vít (referee)
The thesis is concerned with theoretical and practical aspects of the hp- adaptive finite element method for solving elliptic and electromagnetic prob- lems described by partial differential equations in three spatial dimensions. Besides the standard element refinements, the hp-adaptivity allows indepen- dent adaptation of degrees of the polynomial approximation as well. This leads to exponentially fast convergence even for problems with singularities. The efficiency of the hp-adaptivity is enhanced even more by the ability of the algorithm to work with meshes with arbitrary-level hanging nodes. This generality, however, leads to great complexity of the implementation. There- fore, the thesis concentrates on the mathematical analysis of algorithms that have led to successful implementation of the method. In addition, the the- sis discusses the numerical integration in 3D and the implementation of the method itself. Finally, numerical results obtained by this new implemen- tation are presented. They confirm advantages of hp-adaptivity on meshes with arbitrary-level hanging nodes. 1
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Creating conditions for evaluation of high-strength concrete characteristics using non-destructive testing methods
Procházka, David ; Horký,, Ondřej (referee) ; Kolář,, Karel (referee) ; Adámek, Jiří (referee) ; Brožovský, Jiří (advisor)
High-strength concrete (HSC) belongs in the recent years to frequently used types of concrete. It allows realization of static challenging structures and also shows due to its dense structure greater durability especially against aggressive media. Currently HSC construction realization abroad is not exceptional. It’s using in the Czech Republic is still limited. When realized, then in a small scale in civil engineering works. The realization of high-strength concrete structures is closely related with the concrete construction quality verification. Good efficiency of the quality control methods can provide non-destructive testing methods (NDT), especially when investigating strength of concrete built in structure. A lack on relevant data for non-destructive testing of HSC in technical and normative rules is to be considered as a significant deficiency. Evident for HSC generally is the lack in literature on deeper analysis of the factors affecting their non-destructive testing, as well a meaningful methodology or practically usable calibration relationships. HSC differs from ordinary concrete not only by used components, but also by more compact structure with different strength – elastic characteristics. Considering these differences, HSC strength prediction can not be performed by using calibration relationships developed for ordinary concrete. Moreover, the question is to what extent the current knowledge of the NDT results influencing factors can be considered as valid. The paper presents findings on the effects of the key factors affecting the measurement results of Schmidt hardness method and ultrasonic pulse method, including recommendations for the practical application of these methods. The problematic of static vs. dynamic modulus of elasticity was also solved. Calibration equations for predicting the compressive strength of HSC from the non-destructive testing parameter were elaborated, showing high cohesion among variables and practically usability.
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Impact of Inaccuracy in fMRI Experimental Stimulation
Mikl, Michal ; Kremláček,, Jan (referee) ; Michálek, Jiří (referee) ; Drastich, Aleš (advisor)
Aim of this work is to study the impact of inaccuracy in execution of required task (inaccuracy in subject’s behavioral response to experimental stimulation) by person who undergoes fMRI examination. The work is solved in several stages. First, theoretical analysis of inaccuracy in fMRI experiment was performed, and simulations with synthetic data were created. Several variables in general linear model and t-statistics were followed. We found that estimated effect size depends linearly on covariance between the corresponding columns of X and D matrices or their linear combination. The component of residual variance caused by inaccuracy is negligible at real-life noise levels. In such case, moreover, the dependence of t-statistics on inaccuracy becomes linear. Next, our theoretical results (dependencies/characteristics of variables) were verified using real data. All results were confirmed. Last, I focused on possible practical use of the uncovered characteristics and dependencies. Optimization of experimental design with respect to inaccuracy, correction of inaccurate results and reliability of inaccurate results are introduced and discussed. Especially, the calculation of maps of maximal tolerable inaccuracy can be useful to find robust or weak (tending to be not detected or to be significantly different from accurate value) activation in real fMRI experiments.
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Algorithms for single-fault troubleshooting with dependent actions
Lín, Václav
We study the problem of single-fault troubleshooting with dependent actions. We propose a binary integer programming formulation for the problem. This can be used to solve the problem directly or to compute lower bounds of optima using linear programming relaxation. We present an optimal dynamic programming algorithm, and three greedy algorithms for computing upper bounds of optima.
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