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Mixed Precision in Uncertainty Quantification Methods
Martínek, Josef ; Carson, Erin Claire (advisor) ; Hnětynková, Iveta (referee)
This work is concerned with analysing and exploiting mixed precision arithmetic in un- certainty quantification methods with emphasis on the multilevel Monte Carlo (MLMC) method. Although mixed precision can improve performance, it should be used carefully to avoid unwanted effects on the solution accuracy. We provide a rigorous analysis of uncertainty quantification methods in finite precision arithmetic. Based on this analysis, we exploit mixed precision arithmetic in uncertainty quantification methods to improve runtime while preserving the overall error. We begin by stating the model problem, an elliptic PDE with random coefficients and a random right-hand side. Such a problem arises, for example, in uncertainty quantification for groundwater flow. Our focus is on approximating a quantity of interest given as the expected value of a functional of the solution of the PDE problem. To this end, we use the conforming finite element method for approximation in the spatial variable and the MLMC method for approximation of the expected value. We provide a novel rigorous analysis of the MLMC method in finite precision arithmetic and based on this we formulate an adaptive algorithm which determines the optimal precision value on each level of discretisation. To our knowledge, this is a new approach. Our...
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The reflective effect of manipulative therapy on blood pressure.
Martínek, Josef ; Bitnar, Petr (advisor) ; Slabý, Kryštof (referee)
The topic of the thesis is The reflective effect of manipulative therapy on blood pressure. The aim of the thesis is to summarize current knowledge, which talk about the relationship between the ma-nipulative therapy and the changes of blood pressure. One of the purpose of the thesis is to clarify the using of manipulative therapy in the treatment of arterial hypertension. In the thesis another methods of manipulative therapy are discussed to give broad overwiev and to have a posibble to comparison. Powered by TCPDF (www.tcpdf.org)
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Parameter optimization in COVID-19 epidemiological models
Martínek, Josef ; Kučera, Václav (advisor) ; Kopfová, Jana (referee)
This work is concerned with modelling of the spread of infectious diseases with em- phasis on the current COVID-19 pandemic. Our goal is to estimate unknown parameters in epidemiological models from real data on the spread of the disease in the Czech Repub- lic. To model the evolution of the epidemic, we consider compartmental models, which lead to a system of ordinary differential equations. We then formulate a non-linear least squares problem for the optimization of the model parameters to fit the model outcome to the observed data. We numerically optimize by the Levenberg-Marquardt method, which requires the Jacobian of the vector of residuals. This is obtained by deriving and solving the sensitivity equations corresponding to the considered model. We test the method on noisy artificial data and on a well documented English boarding school in- fluenza epidemic. Finally, we apply the method to Czech COVID-19 data and discuss the results. One of the conclusions of this work is the introduction of the concept of effective population size, to overcome the unrealistic assumption of complete homogeneity of the population. Thus the population size is not apriori given, but is an unknown parameter to be optimized. This leads to much better agreement of the models and real data. This appears to be a new concept. 1
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Quality of sensorimotor control on lower limbs in relation to lateral preference in young athletes (soccer players).
Martínek, Josef ; Opálková, Michaela (advisor) ; Janečková, Alexandra (referee)
Objectives: Our thesis is focused on correlation of lateral (side) preferencies of lower limbs and quality of sensorimotor control. Our aim is to figure out whether there is difference in laterality of sensorimotor control of lower limbs and if so, whether there is correlation with side preferency. Methods: Study is made on 18 volunteers. We tested somatosenzoric system, specifically two-point discrimination, graphesthesia, pallesthesia, statesthesia, kinesthesia. We used a questionnare to determine side preferency of lower limbs. We used paired sample t- tests, with level of importance p=0,05. Results: According to t-tests, there are no differencies in sensorimotor control in lower limbs. According to those results, it is not possible to determine the difference in sensorimotor control due to lower limb preferency. Summary: There is no difference in sides in sensorimotor control of lower limbs.
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The reflective effect of manipulative therapy on blood pressure.
Martínek, Josef ; Bitnar, Petr (advisor) ; Slabý, Kryštof (referee)
The topic of the thesis is The reflective effect of manipulative therapy on blood pressure. The aim of the thesis is to summarize current knowledge, which talk about the relationship between the ma-nipulative therapy and the changes of blood pressure. One of the purpose of the thesis is to clarify the using of manipulative therapy in the treatment of arterial hypertension. In the thesis another methods of manipulative therapy are discussed to give broad overwiev and to have a posibble to comparison. Powered by TCPDF (www.tcpdf.org)
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