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Hybrid Algorithms in Optimization
Zamazal, Petr ; Hrabec, Pavel (referee) ; Popela, Pavel (advisor)
This work deals with the solution of an integer programming task using a hybrid algorithm. Mentioned task is a minimum cost network flow problem with option of adding new edges. The hybrid algorithm is based on a genetic algorithm using the network simplex method. Implementation is in the Python programming language.
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Assessment of the strength of the lumbar spine fixator screw using stochastically entered input variables
Rapantová, Zuzana ; Hrabec, Pavel (referee) ; Vosynek, Petr (advisor)
The bachelor's thesis deals with the strength and fatigue of the spinal rod fixator. The topic is addressed by creating a computational model with two lengths of fixation screws. Simulations are performed using the Ansys software with the application of Six Sigma analysis. The strength analysis is quantified from the average load values, and the stress-strain analysis employs stochastic input variables. The results demonstrate that the modulus of elasticity of the cancellous bone significantly affects the deformation of the fixator. In the conclusion, the output data between the two lengths undergo statistical tests. Based on the acceptance of hypotheses regarding the equality of mean values, it is evaluated that a screw not passing through the entire cross-section of the cancellous bone in the vertebra is more suitable.
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Tennis match modelling using Markov chains
Walica, Roman ; Hübnerová, Zuzana (referee) ; Hrabec, Pavel (advisor)
This thesis deals with the application of Markov chains in the tennis field and their subsequent adjustment based on formulated hypotheses. The first part of thesis describes the principles of the tennis game. In the second part, we deal with concepts from the field of statistics. These concepts are mainly used for creation and subsequent branching of Markov chains. The result of this work is several Markov chains for the game, divided by tennis serve or reception or by the type of surface on which the match is played. The other chains mentioned are chains for tiebreak, set and match. In final part of thesis we introduce obtained prediction of the result and the duration of the tennis match and its modeled parts.
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Modeling of scoring probability in sport
Hilscher, Ondřej ; Bednář, Josef (referee) ; Hrabec, Pavel (advisor)
This thesis aims for modelling of scoring probability in football. It describes necessary mathematical methods used in logistic regression model building and in basic statistical hypothesis tests. Afterwards the mathematical methods are used on available data from professional football matches. Resulting model uses shooting method, pitch location and simplified match situation as predictors.
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Dimensionality reduction of statistical dataset
Sabo, Adam ; Kosová, Petra (referee) ; Hrabec, Pavel (advisor)
This thesis introduces methods which are used to reduce dimensionality and their subsequent application to selected sets of sports statistical data. The first part of the thesis deals with the theoretical apparatus of mathematical statistics, in particular with the Principal Component Analysis and its alternative - the Factor Analysis. The second part provides a brief explanation of the terms related to the selected sets of football statistics where these methods are applied. The third part introduces the results of the application of both methods to statistical files. Data obtained through calculations performed in Python programming language are organized and interpreted by means of graphs and tables.
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Sports data analysis
Horák, Patrik ; Bednář, Josef (referee) ; Hrabec, Pavel (advisor)
The main preoccupation of this thesis is analysis of ice hockey statistics. The first section describes widely used elementary and advanced ice hockey statistics. The second part contains selected comparable studies working with similar hypotheses. The third section introduces necessary mathematical tools, such as, Two-sample t-test, correlation, Two-way analysis of variance with no interaction and their nonparametric equivalents. In the last section described statistical hypotheses tests are applied to ice hockey dataset. Results interpretation is also included.
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Measurement of Human Hand Geometric Parameters
Vanžurová, Anna ; Hrabec, Pavel (referee) ; Štarha, Pavel (advisor)
In practice, there is no easy way to obtain the size of the surface of a human hand. Therefore, this work deals with the search for a mathematical model determining the approximate surface of the hand. This model uses the basic geometric parameters of the hand obtained from her photograph. Since it is necessary to obtain parameters from the image, compare the mathematical model with reality and verify its accuracy in terms of statistics, the work includes the theory of digitization of image information, 3D scanning and statistics.
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THEORETICAL PROPERTIES AND APPLICATIONS OF ADVANCED DESIGNS OF EXPERIMENT
Hrabec, Pavel ; Hlávka,, Zdeněk (referee) ; Kraus, David (referee) ; Bednář, Josef (advisor)
The methodology of the design of experimnet has become an integral part of the optimisation of manufacturing processes in recent decades. Problems regarding designs of experiments are still up to date, especially because of a variety of approaches to collecting and evaluating data. Scientists in different research and development areas often do not take into account possible shortcommings or even essential assumptions of selected design and/or its evaluation methods. This disertation thesis summarizes theoretical bases of selected designs of experiments. Describes several applications of central composite design on responses regarding wire electrical discharge machining process. And compares different designs of experiment for response surfaces of five parameters with regards to algoritmic selection of statistically signifficant parameters.
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Hybrid Algorithms in Optimization
Zamazal, Petr ; Hrabec, Pavel (referee) ; Popela, Pavel (advisor)
This work deals with the solution of an integer programming task using a hybrid algorithm. Mentioned task is a minimum cost network flow problem with option of adding new edges. The hybrid algorithm is based on a genetic algorithm using the network simplex method. Implementation is in the Python programming language.
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