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Random measurable sets
Fojtík, Vít ; Rataj, Jan (advisor) ; Pawlas, Zbyněk (referee)
The aim of this thesis is to compare two major models of random sets, the well established random closed sets (RACS) and the more recent and more general random measurable sets (RAMS). First, we study the topologies underlying the models, showing they are very different. Thereafter, we introduce RAMS and RACS and reformulate prior findings about their relationship. The main result of this thesis is a characterization of those RAMS that do not induce a corresponding RACS. We conclude by some examples of such RAMS, including a construction of a translation invariant RAMS. 1
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A case study on the methodological measurability of integrational project's success
Walser, Michael ; Hájek, Martin (advisor) ; Čada, Karel (referee)
ii Abstract The topic of his thesis, "Social Sustainability", arising from the social sciences, specifically sociology, has naturally its core focus on society and its functioning. To be more exact, the functioning of society in context of integration, which is an ever more growing topic in the globalised world we live in. In relation to this thesis, an integrational project/workshop has been carried out at a folk high school, Brandbjerg, in Denmark, with the purpose to practically test, the methodological measurability of change in subjectivity. Worth mentioning, that the hosting community, in terms of immigration, was in focus and its perception on variation of habitus. Hereto, Q-Methodology from William Stephenson functioned as the foundation for the development of the workshop, as well as it aided the analysis of the therefrom taken data, to determine a change in the participants subjectivity. The aim of this practical implementation, was to put the findings into perspective of the theoretical framework of sustainability, specifically social sustainability. The findings served in combination with face to face interaction as part of social integration, to underline the need for sustainable integration and an alteration of social sustainability upon further research. A tendency was determined as being the...
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Statistical Depth for Functional Data
Nagy, Stanislav ; Hlubinka, Daniel (advisor) ; Claeskens, Gerda (referee) ; Hušková, Marie (referee)
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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