Title: Models of Marked Point Processes Author: Ivan Héda Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zbyněk Pawlas, Ph.D. Abstract: In the first part of the thesis, we present necessary theoretical basics as well as the definition of functional characteristics used for examination of marked point patterns. Second part is dedicated to review some known marking strategies. The core of the thesis lays in the study of intensity-marked point processes. General formula for the characteristics is proven for this marking strategy and general class of the models with analytically computable characteristics is introduced. This class generalizes some known models. Theoretical results are used for real data analysis in the last part of the thesis. Keywords: marked point process, marked log-Gaussian Cox process, intensity-marked point process 1

The paper deals with the channel coding and modulation in DVB-H and DVB-SH and with the simulation of the components in MATLAB. In the case of DVB-H the document also discuss the influence of different types of transmission channels on the transmission process. The first part of this work describes the channel coding and inner modulation in DVB-H and DVB-SH. The next part describes applications created in MATLAB for settings and simulation of the transmission in the standards DVB-H and DVB-SH. The last part of this document graphically presents selected results of the simulation of the transmission and discuss them.

This work is focused on the study of the intensity profile of optical beams. In the first part problematics of optical beams from theoretical point of view is discussed, Model of realistically circular symmetric beam in an ideal lossless, stationary, homogeneous and isotropic medium is formed in Matlab®. The next part of the thesis deals with implementation of automatic workplace for measuring intensity profile of optical beams. Within the thesis - PCB desing of photodetector in Eagle®, is discussed. Custom application for controlling the motorized linear stage M – IMS 400 and communication with photodetector in the Microsoft Visual Studio 2010® was created.

In the Thesis, linear stochastic differential equations in a Hilbert space driven by a cylindrical fractional Brownian motion with the Hurst parameter in the interval H < 1/2 are considered. Under the conditions on the range of the diffusion coefficient, existence of the mild solution is proved together with measurability and continuity. Existence of a limiting distribution is shown for exponentially stable semigroups. The theory is modified for the case of analytical semigroups. In this case, the conditions for the diffusion coefficient are weakened. The scope of the theory is illustrated on the Heath-Jarrow-Morton model, the wave equation, and the heat equation. 1

The topic of this thesis is an audio recording classification with 15 different acoustic scene classes that represent common scenes and places where people are situated on a regular basis. The thesis describes 2 approaches based on GMM and i-vectors and a fusion of the both approaches. The score of the best GMM system which was evaluated on the evaluation dataset of the DCASE Challenge is 60.4%. The best i-vector system's score is 68.4%. The fusion of the GMM system and the best i-vector system achieves score of 69.3%, which would lead to the 20th place in the all systems ranking of the DCASE 2017 Challenge (among 98 submitted systems from all over the world).

This work deals with questions of space assembling of several optics beams. There are mentioned the base features and values of space distribution of beam intensity in laser beam. The forms of diffusion of space localized light that is described by beam optics. There is a characterization of Gaussian beam, and diffraction of several beams. There is mentioned a simulation an assembling of two and more beams. It contains model of assembling incoherent beams. The work also includes suggestion of final layout of laser beams, which form optical transmitter with radiating characteristics, resistant to defects evoked by atmosphere.

Dizertačná práca je zameraná na štúdium a analýzu rozloženia optickej intenzity v laserovom zväzku v rovine vysielacej (TXA) a prijímacej apertúry (RXA), ktorý podlieha zmenám ako pri šírení voľným priestorom, tak pri šírení atmosférou. Cieľom práce je nájsť optimálne rozloženie optickej intezity v rovine vysielacej apertúry, ktoré bude minimálne ovplyvnené apertúrou vysielača a atmosférickými turbulenciami. Za účelom analýzy šírenia optickej vlny atmosférou bola využitá simulácia založená na metóde Split-Step. Šírenie Flattened Gaussian zväzku bolo analyzované pre režim slabých a stredných turbulencií. Práca sa zaoberá použitím multimódového vlákna s veľkým priemerom jadra ako tvarujúceho elementu a obsahuje návrh refrakčného tvarovača, pomocou ktorého je možno konvertovať Gaussovský zväzok na zväzok s uniformným rozložením optickej intenzity. Nakoniec je pomocou získaných poznatkov zostavený plne fotonický vysielač a prijímač, ktorých použitie spočíva v generovaní a príjmaní optickej koherentnej vlny prenášajúcej presnú fázu.