The goal of this thesis was to implement a practical tool for optimizing hy- perparameters of neural networks using Bayesian optimization. We show the theoretical foundations of Bayesian optimization, including the necessary math- ematical background for Gaussian Process regression, and some extensions to Bayesian optimization. In order to evaluate the performance of Bayesian op- timization, we performed multiple real-world experiments with different neural network architectures. In our comparison to a random search, Bayesian opti- mization usually obtained a higher objective function value, and achieved lower variance in repeated experiments. Furthermore, in three out of four experi- ments, the hyperparameters discovered by Bayesian optimization outperformed the manually designed ones. We also show how the underlying Gaussian Process regression can be a useful tool for visualizing the effects of each hyperparameter, as well as possible relationships between multiple hyperparameters. 1

Master theses of Automatic Shift Control of the Digital Data Recorder is primarily concerned to design and construction of equipment used for measuring the half-width of the laser beam. The introductory part is devoted to the related theoretical basics and serves for better orientation in the following chapters. The second part is devoted to construction, completion and basic setting of product.

The objective of this thesis is to create Gaussian 1D filters with rotating kernel theory which enables to program algorithm for noise reduction and beam structure highlighting in a digital picture of the solar corona. A fragment of original picture of solar corona and of pictures filtred by this algorithm is in the enclosure.

Diplomová práce se zabývá návrhem a sestavením nového spektrometru opticky detekované magnetické rezonance (ODMR) modifikací stávajícího spektrometru magnetického kruhového dichroismu (MCD) přivedením mikrovlnného ozařování. Je navrhnut nový držák vzorku umožnující osvětlení jak viditelným světlem, tak mikrovlnným zářením. Pro přivedení vlnění o nižších frekvencích je navržena anténa, určená k umístění pod vzorkem. Schopnosti celého systému jsou demonstrovány na sloučenínách kovových komplexů.

This thesis focuses on comparing methods of denoising by deep learning and their implementation. In the last few years, it has become clear that it is not necessary to have paired data, as for noisy and clean pictures, to train convolution neural networks but it is sufficient to have only noisy pictures for denoising in particular cases. By using methods described in this thesis it is possible to effectively remove i.e. additive Gaussian noise and what more, it is possible to achieve better results than by using statistic methods, which are being used for denoising these days.

In the first part of the thesis discusses the function of the laser design and construction of its class. Here is an explanation of coherence and other properties of laser radiation. Listed below are the possibilities of energy distribution in the laser beam. Described in particular Gaussian beam. The paper explains the phenomena of bending and Young's experiment. The paper examines the influence of atmospheric environment in the transmission of electromagnetic waves, defined as light. Particular attention is devoted to atmospheric turbulence. In the second part are first discussed the possibility of measuring atmospheric turbulence and coherence of laser beam parameters. The following is designed to measure workplace coherence width and coherence length in a turbulent environment. At these workplaces were measured. The results of these measurements are also listed in the job. The following comparison of results with theoretical values.

The objective of this thesis is to create Gaussian 1D filters with rotating kernel theory which enables to program algorithm for noise reduction and beam structure highlighting in a digital picture of the solar corona.

Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possible definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive understanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. 1

Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possi- ble definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive un- derstanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. Method for Hurst index estimation for fractional Gaussian noise and it's application on logarithmic returns of shares of selected produ- cers of beer are included in this work. 1

Stochastic Integrals Driven by Isonormal Gaussian Processes and Applications Master Thesis - Petr Čoupek Abstract In this thesis, we introduce a stochastic integral of deterministic Hilbert space valued functions driven by a Gaussian process of the Volterra form βt = t 0 K(t, s)dWs, where W is a Brownian motion and K is a square integrable kernel. Such processes generalize the fractional Brownian motion BH of Hurst parameter H ∈ (0, 1). Two sets of conditions on the kernel K are introduced, the singular case and the regular case, and, in particular, the regular case is studied. The main result is that the space H of β-integrable functions can be, in the strictly regular case, embedded in L 2 1+2α ([0, T]; V ) which corresponds to the space L 1 H ([0, T]) for the fractional Brownian mo- tion. Further, the cylindrical Gaussian Volterra process is introduced and a stochastic integral of deterministic operator-valued functions, driven by this process, is defined. These results are used in the theory of stochastic differential equations (SDE), in particular, measurability of a mild solution of a given SDE is proven.