Classification is a very common task in information processing and important problem in many sectors of science and industry. In the case of data measured as a function of a dependent variable such as time, the most used algorithms may not pattern each of the individual shapes properly, because they are interested only in the choiced measurements. For the reason, the presented paper focuses on the specific techniques that directly address the curve clustering problem and classifying new individuals. The main goal of this work is to develop alternative methodologies through the extension to various statistical approaches, consolidate already established algorithms, expose their modified forms fitted to demands of clustering issue and compare some efficient curve clustering methods thanks to reported extensive simulated data experiments. Last but not least is made, for the sake of executed experiments, comprehensive confrontation of effectual utility. Proposed clustering algorithms are based on two principles. Firstly, it is presumed that the set of trajectories may be probabilistic modelled as sequences of points generated from a finite mixture model consisting of regression components and hence the density-based clustering methods using the Maximum Likehood Estimation are investigated to recognize the most homogenous partitioning. Attention is paid to both the Maximum Likehood Approach, which assumes the cluster memberships to be some of the model parameters, and the probabilistic model with the iterative Expectation-Maximization algorithm, that assumes them to be random variables. To deal with the hidden data problem both Gaussian and less conventional gamma mixtures are comprehended with arranging for use in two dimensions. To cope with data with high variability within each subpopulation it is introduced two-level random effects regression mixture with the ability to let an individual vary from the template for its group. Secondly, it is taken advantage of well known K-Means algorithm applied to the estimated regression coefficients, though. The task of the optimal data fitting is devoted, because K-Means is not invariant to linear transformations. In order to overcome this problem it is suggested integrating clustering issue with the Markov Chain Monte Carlo approaches. What is more, this paper is concerned in functional discriminant analysis including linear and quadratic scores and their modified probabilistic forms by using random mixtures. Alike in K-Means it is shown how to apply Fisher's method of canonical scores to the regression coefficients. Experiments of simulated datasets are made that demonstrate the performance of all mentioned methods and enable to choose those with the most result and time efficiency. Considerable boon is the facture of new advisable application advances. Implementation is processed in Mathematica 4.0. Finally, the possibilities offered by the development of curve clustering algorithms in vast research areas of modern science are examined, like neurology, genome studies, speech and image recognition systems, and future investigation with incorporation with ubiquitous computing is not forbidden. Utility in economy is illustrated with executed application in claims analysis of some life insurance products. The goals of the thesis have been achieved.

Cells are the basic units of life. Studying complex tissues and whole organs requires an understanding of cell heterogeneity and responses to stimuli at the single-cell level. Even the cells, which belong to the same cell type, behave differently at a specific moment and contain different amount of mRNA. Quantitative polymerase chain reaction (qPCR) is one the most sensitive methods for the detection of mRNA, however, gene expression profiling in single cells leads to a large amount of missing data due to the fact that the transcript is missing, or is below the level of detection. Therefore, it is necessary to establish a new statistical approach for analysis of single cells. In this thesis the potential of single-cell gene expression profiling using the high throughput instrument Biomark, focusing on data analysis and biological interpretation, is discussed. Data normalization and handling of missing data are two important steps in data analysis that are performed differently at the single-cell level. Single cells are not normalized by reference genes but the number of cells as a normalizer is applied. Missing data are replaced by value, which is equaled one quarter of transcript amount in the cell. Furthermore it is shown how single-cell gene expression data can be viewed and how subpopulations...

This thesis deals with the evaluating efficiency of Czech banks using data envelopment analysis (DEA), which is a method based on mathematical programming. Each bank is then evauluated with the relative efficiency coefficient that indicates the efficiency or inefficiency of the particular bank. The work is further developed the classical approach of bank performance measuring in comparison to DEA, researches that have applied DEA models to evaluate banks in the past in different countries and detailed analysis of the results of the precessed model.

Title: Analysis of Point Clouds Representing Surfaces of Engineering Practice Author: Petra Surynková Department: Department of Mathematics Education Supervisor: Mgr. Šárka Voráčová, Ph.D., Faculty of Transportation Sciences, Czech Technical University in Prague Abstract: The doctoral dissertation Analysis of Point Clouds Representing Surfaces of Engineering Practice addresses the development and application of methods of digital reconstruction of surfaces of engineering and construction practice from point clouds. The main outcome of the dissertation is a presentation of new procedures and methods that contribute to each of the stages of the reconstruction process from the input point clouds. The work is mainly focused on the analysis of input clouds that describe special types of surfaces. Several completely new algorithms and improvements of existing algorithms that contribute to individual steps of surface reconstruction are presented. New procedures are based on geometrical characteristics of the reconstructed object. An important result of the dissertation is an analysis of not only synthetically generated point clouds but above all an analysis of real point clouds that have been obtained from measurements of real objects. The significant contribution of the dissertation is also an...

Statistical data depth is a nonparametric tool applicable to multivariate datasets in an attempt to generalize quantiles to complex data such as random vectors, random functions, or distributions on manifolds and graphs. The main idea is, for a general multivariate space M, to assign to a point x ∈ M and a probability distribution P on M a number D(x; P) ∈ [0, 1] characterizing how "centrally located" x is with respect to P. A point maximizing D(·; P) is then a generalization of the median to M-valued data, and the locus of points whose depth value is greater than a certain threshold constitutes the inner depth-quantile region corresponding to P. In this work, we focus on data depth designed for infinite-dimensional spaces M and functional data. Initially, a review of depth functionals available in the literature is given. The emphasis of the exposition is put on the unification of these diverse concepts from the theoretical point of view. It is shown that most of the established depths fall into the general framework of projection-driven functionals of either integrated, or infimal type. Based on the proposed methodology, characteristics and theoretical properties of all these depths can be evaluated simultaneously. The first part of the work is devoted to the investigation of these theoretical properties,...

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This thesis deals with the issue of fiscal imbalance in 8 selected postcommunist countries within the European Union (the Czech Republic, Estonia, Latvia, Lithuania, Hungary, Poland, Slovakia and Slovenia). These countries together with Cyprus and Malta represented the largest expansion of the European Union in 2004. In the empirical analysis the determinants affecting the size of the public debt in these countries for the period 1995-2012 are examined. The thesis also deals with the causality between the public debt and economic activity in these countries in order to determine whether the public debt leads to a decline in GDP or not. Within the sub-analysis, the attention is paid to the development of the indebtedness of these countries in order to assess its sustainability.

This thesis analyzes the issue of fiscal imbalance in selected member states of European Union, namely, the first 12 states which officially introduced the Euro banknotes and coins in 2002. Empirical part of thesis analyzes the development of indebtedness in selected countries. The thesis also deals with the existence of causal relationship between public debt and economic growth in these countries via regression analysis of data panel for period 1995-2014 and 2008-2014. Sub-analysis of the thesis aims also at research of determinants of public debt in these countries.

The aim of the thesis is to assess the quality of outputs accounting agenda processing in specific programs to handle the needs of accounting entities. On the market there are countless different accounting software, although to some extent differ in several criteria. Here are two selected published accounting software, which is very different from each other. Accounting software for each entity and a necessary part of the tool for processing of accounting and the right choice is very difficult.

In the Master’s thesis were described privacy protection problems while using cloud technologies. Some of the problems can be solved with help of homomorphic encryption, data splitting or searchable encryption. These techniques were described and compared by provided security, privacy protection and efficiency. The data splitting technique was chosen and implemented in the C language. Afterwards a performance of the implemented solution was compared to AES encryption/decryption performance. An application for secured data storing in cloud was designed and implemented. This application is using the implemented data splitting technique and third-party application CloudCross. The designed application provides command line interface (CLI) and graphical user interface (GUI). GUI extends the capabilities of CLI with an ability to register cloud and with an autodetection of registered clouds. The process of uploading/downloading the data to/from cloud storage is transparent and it does not overload the user with technical details of used data splitting technique.