We present a system that estimates the motion of a robot relying solely on images from onboard omnidirectional camera (visual odometry). Compared to other visual odometry hardware, ours is unusual in utilizing high resolution, low frame-rate (1 to 3 Hz) omnidirectional camera mounted on a robot that is propelled using continuous tracks. We focus on high precision estimates in scenes, where objects are far away from the camera. This is achieved by utilizing omnidirectional camera that is able to stabilize the motion estimates between camera frames that are known to be ill-conditioned for narrow field of view cameras. We employ feature based-approach for estimation camera motion. Given our hardware, possibly high ammounts of camera rotation between frames can occur. Thus we use techniques of feature matching rather than feature tracking.

Title: Ray-based Born approximation Author: Libor Šachl Department: Department of Geophysics Supervisor: RNDr. Luděk Klimeš, DrSc. Supervisor's e-mail address: klimes@seis.karlov.mff.cuni.cz Abstract: One of the aims of this thesis was coding of program grdborn.for for computing the 2D and 3D ray-based Born approximation of the first order in an inhomoge- nous isotropic medium without attenuation. The computation of 3D amplitudes using the 2D Born approximation is based on the correction term, which is de- rived. The program is further used in computing the Born approximation in various models. We test its performance in three simple models. We study the effect of the discretization, the spurious waves introduced by the finite size of the grid etc. In the next step, we focus on the computations in more compli- cated models. We compute the Born seismograms in 2D heterogenous models. We study the diffracted waves, the effects of caustics etc. Keywords: Born approximation, ray theory, velocity model, perturbation 1

This thesis extends the methodology for extracting evaluations of players from samples of Go game records originally presented in (Baudiš - Moudřík, 2012). Firstly, this work adds more features and lays out a methodology for their comparison. Secondly, we develop a robust machine-learning framework, which is able to capture dependencies between the evaluations and general target variable using ensemble meta-learning with a genetic algorithm. We apply this framework to two domains, estimation of strength and styles. The results show that the inference of the target variables in both cases is viable and reasonably precise. Finally, we present a web application, which realizes the methodology, while presenting a prototype teaching aid for the Go players and gathering more data. Powered by TCPDF (www.tcpdf.org)

We present a system that estimates the motion of a robot relying solely on images from onboard omnidirectional camera (visual odometry). Compared to other visual odometry hardware, ours is unusual in utilizing high resolution, low frame-rate (1 to 3 Hz) omnidirectional camera mounted on a robot that is propelled using continuous tracks. We focus on high precision estimates in scenes, where objects are far away from the camera. This is achieved by utilizing omnidirectional camera that is able to stabilize the motion estimates between camera frames that are known to be ill-conditioned for narrow field of view cameras. We employ feature based-approach for estimation camera motion. Given our hardware, possibly high ammounts of camera rotation between frames can occur. Thus we use techniques of feature matching rather than feature tracking.

Title: A construction of minimum DNF representations of 2-interval functions Author: Jakub Dubovský Department: Dep. of Theoretical Computer Science and Mathematical Logic Supervisor: doc.RNDr.Ondřej Čepek, Ph.D. Abstract: The thesis is devoted to interval boolean functions. It is focused on construction of their representation by disjunctive normal forms with minimum number of terms. Summary of known results in this field for 1-interval functions is presented. It shows that method used to prove those results cannot be in general used for two or more interval functions. It tries to extend those results to 2-interval functions. An optimization algorithm for special subclass of them is constructed. Exact error estimation for approximation algorithm is proven. A command line software for experimentation with interval function is part of the thesis. Keywords: boolean function, interval function, representation construction, ap- proximation 1

We present a system that estimates the motion of a robot relying solely on images from onboard omnidirectional camera (visual odometry). Compared to other visual odometry hardware, ours is unusual in utilizing high resolution, low frame-rate (1 to 3 Hz) omnidirectional camera mounted on a robot that is propelled using continuous tracks. We focus on high precision estimates in scenes, where objects are far away from the camera. This is achieved by utilizing omnidirectional camera that is able to stabilize the motion estimates between camera frames that are known to be ill-conditioned for narrow field of view cameras and the fact that low frame-rate of the imaging system allows us to focus computational resources on utilizing high resolution images. We employ feature based-approach for estimation camera motion. Given our hardware, possibly high ammounts of camera rotation between frames can occur. Thus we use techniques of feature matching rather than feature tracking.

The non-increasing rearrangement of a measurable real function defined on an appropriate measure space is of the enormous significance in disciplines such as theory of function spaces or interpolation theory and their applications in PDEs. Unfortunately, while it has good and widely applicable mapping properties, it is virtually impossible to calculate the non-increasing rearrangement of a concrete given function precisely. Numerical algorithms for approximation are desirable for this reason. Such method of approximation, based on interpolation by a linear spline, is presented in this thesis. In the first half of this thesis, the developed method is described, while the error estimates of the method are subject to the second part.

The thesis is divided into two parts. The first part deals with radiative cor- rections in muonic hydrogen. The effect of vacuum polarization is studied, and the simplified derivation of the Wichmann-Kroll potential is presented. The en- ergy shift caused by vacuum polarization to the Lamb shift in muonic hydrogen is calculated and it agrees with results in literature. Further, the concept of the extended Bethe logarithm is introduced and its advantages are shown and used to calculate the combined self-energy vacuum polarization contribution to the Lamb shift in muonic hydrogen. The results given here are more accurate and somewhat different from others given in literature. In the second part, the ground-state en- ergy splitting due to the tunneling in a two-dimensional double-well potential is calculated. A systematic WKB expansion of the energy splitting is given. An in- terplay between curvature of the classical tunneling path and quantum nature of motion is observed. A series is found that describes systems with strong coupling like the proton transfer in malonaldehyde. The results show a strong sensitivity of the splitting on slight variations of the parameters entering the Hamiltonian linearly. This indicates a presence of quantum chaos in this problem. 1

In this work, we study the backreaction of high-frequency gravitational waves on cosmological backgrounds. To describe the wave, we use the Isa- acson formalism, specifically the WKB approximation, which allows us to express the backreaction through an effective stress-energy tensor of the gra- vitational wave. First, we consider the inhomogeneous cosmological model of Charach and Malin, which contains gravitational waves and a massless scalar field mini- mally coupled to gravity. We show that although this is a spatially compacti- fied solution, it is possible to add a high-frequency perturbation and solve Einstein's equations with the effective stress-energy tensor in a consistent way. The bacreaction is of the same order as the influence of the scalar field. Second, we add multiple incoherent high-frequency waves to the homoge- neous Kasner background, and discuss the relation to the late-time limit of the Gowdy (vacuum Charach and Malin) model. 1

This thesis describes the design and implementation of genetic algorithm for approximation of non-linear mathematical functions using the least squares method. One objective of this work is to theoretically describe the basics of genetic algorithms. The second objective is to create a program that would be potentially used to approximate empirically measured data by the scientific institutions. Besides the theoretical description of the given subject, the text part of the work mainly deals with the design of the genetic algorithm and the whole application solving the given problem. Specific part of the assignment is that the developed application has to support approximation of points by various mathematical non-linear functions in several different intervals, and then it has to insure, that resulting functions are continuous throughout all the intervals. Described functionality is not offered by any available software.