Filtering for Stochastic Evolution Equations Vít Kubelka Doctoral thesis Abstract Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to linear SPDEs driven by Gauss-Volterra process observed at finitely many points of the domain and to delayed SPDEs driven by white noise. Subsequently, the continuous dependence of the filter and observation error on parameters which may be present both in the signal and the obser- vation process is proved. These results are applied to signals governed by stochastic heat equations driven by distributed or pointwise fractional noise. The observation process may be a noisy observation of the signal at given points in the domain, the position of which may depend on the parameter. 1

This thesis presents an investigation of the possibility of using the fixed-point arithmetic in the inertial navigation systems, which use the local level navigation frame mechanization equations. Two square root filtering methods, the Potter's square root Kalman filter and UD factorized Kalman filter, are compared with respect to the conventional Kalman filter and its Joseph's stabilized form. The effect of rounding errors to the Kalman filter optimality and the covariance matrix or its factors conditioning is evaluated for a various lengths of the fractional part of the fixed-point computational word. Main contribution of this research lies in an evaluation of the minimal fixed-point arithmetic word length for the Phi-angle error model with noise statistics which correspond to the tactical grade inertial measurements units.

title: Surface Wave Analysis and Inversion Application to the Bohemian Massif author: Mgr. Petr Kolínský, DiS. author's e-mail address: kolinsky@irsm.cas.cz departments: Department of Geophysics Faculty of Mathematics and Physics Charles University Prague V Holešovičkách 2, Praha 8 - 180 00, Czech Republic and Department of Seismology Institute of Rock Structure and Mechanics, v.v.i. Academy of Sciences of the Czech Republic V Holešovičkách 41, Praha 8 - 182 09, Czech Republic supervisor: RNDr. Johana Brokešová, CSc. supervisor's e-mail address: johana.brokesova@mff.cuni.cz consultant: RNDr. Jiří Málek, PhD. consultant's e-mail address: malek@irsm.cas.cz keywords: surface waves, group velocity, phase velocity, frequency-time analysis, multiple filtering, tomography, inversion problems, Earth crust structure, Bohemian Massif An overview of surface wave analysis methods as well as of inversion techniques is given. Special attention is paid to the multiple filtering method for dispersion curve estimation, which is described by two different ways in detail. The isometric method is used for dispersion curve inversion and its description and tests are presented. Described methods are further used in applications. The applications show examples of surface wave analysis and inversion for 1D and 2D...

The aim of this dissertation thesis was to study the factors affecting drug distribution and elimination and to use these factors to individualize dosing. The work consists of three thematic areas: estimation of the volume of distribution and subsequent dosing of selected drugs (vancomycin, amikacin, phenobarbital) using body size descriptors; estimation of clearance and subsequent dosing of selected drugs (vancomycin, amikacin, phenobarbital, perindopril) using renal function status markers; and the impact of drug interactions on the distribution and elimination of phenobarbital. The thesis summarizes original papers on these topics. Individual pharmacokinetic parameters were calculated for each patient based on their demographic and clinical characteristics, dosing records and measured serum drug levels. The relationships between distribution volume/drug clearance and body size descriptors/renal functional status markers were examined by regression analysis. Vancomycin volume of distribution was best predicted by the total body weight. Loading dose of 10.7 mg/kg of total body weight was optimal in patients taking continuous vancomycin and would lead to reducing of median time to reach target concentrations from 17 to 1 hour. On the contrary, amikacin volume of distribution was most associated...

The first part of the thesis is focused on the problems related to sludge and evaluates sludge disposal from waste treatment plants. The thesis mentions factors influencing method selection of sludge disposal as well as it compares sludge disposal in the Czech Republic and in the other states of the EU. It describes a complete waste treatment line and sludge disposal in the area of sludge treatment and disposal. It deals with sludge disintegration and describes the most effective methods of disintegration. The second part of the thesis describes an experimental part of disintegration of waste treatment sludge. An experiment was conducted in the school laboratory in a way of thermal disintegration in the double-surface pressure tank. The disintegration was conducted to temperatures of 60 °C, 90 °C, 120 °C, 150 °C, and 180 °C. We monitored dependence of the sludge dry residue content on disintegration temperature as well as content of suspended solids in liquid fraction (FUGAT). It was possible to choose optimal temperature of disintegration in accordance with processed results.

Recent breakthrough studies by Gali and Gertler (1999), Sbordone (2002) and Roberts (2001) argue that the New Keynesian Phillips curve (based on Calvo pricing model) is empirically valid concept and they conclude that the real marginal costs are preferred driving force to output gap in inflation dynamics for open economies. Neiss and Nelson (2002) and Gali, Gertler and Salido (2001), in turn, contradict that to date, there has been only little empirical evidence to support this statement. Neiss and Nelson (2002) add that "once output gap is defined consistently with economic theory, the gap-based New Keynesian Phillips curve has a fit with data which is at least as good as the real marginal costs-based one". For this purpose, my study investigates relationship between output gap and inflation described in the hybrid New Keynesian Phillips curve. Study estimates key coefficients of the hybrid gap-based New Keynesian Phillips curve, with both forward- and backward-looking inflation components, in the Czech Republic for periods 2000Q1 - 2012Q4 using Kalman filtration. My findings suggest that (i) output gap has a significant impact on Czech inflation dynamics (ii) share of forward-looking agents predominates to backward-looking agents in the Czech Republic and (iii) Czech inflation seems to be significantly driven by change in import prices.

Dissertation offers a plan for air – conditioning equipment of library building in Brno and it involves air filter experimental measurement. The proposal is divided into three parts. The first part explains air filter theory with detailed description of atmospheric air filters for separation of particles for general ventilation - filter parameter determination. Theory part ends specifically with pocket air filters and their construction. The second part focuses on experimental pocket air filter measurement execution, which calculates with variable filter cartridges and pocket count. Measurement also evaluates pressure drop and their efficiency. The last part of the dissertation looks at air – conditioning equipment design for specified building, concretely library building. The project solves fresh air traffic into interior of selected library rooms and it counts with thermal heat gain in summer season, heat loss in winter season and air humidity modification.

Final thesis is focusing on possibilities hidden in the potential of wastewaters in sewers. The goal of this thesis is to present technologies and experiences with water reclamation and with heat recovery systems using wastewaters as a source of heat energy. The theoretical part is divided in two main topics. The first topic is focused on bringing important knowledge and experiences with designing and operating decentralized sewer mining systems, which are, due to less favourable environmental conditions, largely applicated and developed in countries such as Australia, California, etc. The second topic is focusing on heat recovery from sewage water and possibilities of heating and cooling buildings. A possibility of using heat energy from sewage for heating and cooling a swimming pool building located in Brno, Czech Republic was assessed in the last part of this thesis. As a source of wastewater was considered a sewer main located near the pool building. Payback periods and economical effectivity of investing into wastewater heat recovery system was compared with centralized heat supply system, which is a very common source of heat energy in Czech Republic.

This thesis deals with methods for optimization in image processing. There is described some of optimization techniques and some applications in image processing. There is also described detailed procedure and realization of bee algorithm, genetic algorithm, PSO algorithm and their realization in image registration, matched filtering, image segmentation and image reconstruction. Algorithms and their efficiencies are compared in the particular application for image processing.

This thesis deals with classification of different types of time courses of ECG signals. Main objective was to recognize the normal cycles and several forms of arrhythmia and to classify the exact types of them. Classification has been done with usage of algorithms of Neural Networks in Matlab program, with its add-on (Neural Network Toolbox). The result of this thesis is application, which makes possible to load an ECG signal, pre-process it and classify its each cycle into five classes. Percentage results of this classification are in the conclusion of this thesis.