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Groebner bases
Mašková, Kristýna ; Trlifaj, Jan (advisor) ; Příhoda, Pavel (referee)
Gröbner basis is a particular kind of a generating set of an ideal in the polynomial ring S = K[x1, . . . , xn]. This notion is based upon the concept of a monomial order. We define these concepts and present Buchberger's criterion, that enables us to effectively verify whether a generating set is a Gröbner basis. We introduce Buchberger's algorithm, that produces a Gröbner basis from a finite set of generators. We consider a special case of linear homogeneous ideals, where Gröbner basis can be computed simply by the Gaussian elimination. Finally, we extend this theory to submodules of free modules and briefly indicate how to use Gröbner bases to prove Hilbert's syzygy theorem. 1
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Searching for the common function of the BBSome across the evolution and development
Mašková, Kristýna ; Štěpánek, Ondřej (advisor) ; Čajánek, Lukáš (referee)
The BBSome is a protein complex whose function is associated with ciliary trafficking. It has been found that the BBSome is evolutionarily conserved among ciliated organisms. The disruption of the BBSome leads to cilia dysfunctions and affects many signalling pathways. In humans, genetic defects in the BBSome are the cause of Bardet-Biedl Syndrome, which is a pleiotropic disease. The BBSome is studied separately in various model organisms and cell lines to understand the molecular functions of the BBSome. These studies have not been compared to see if there is a common BBSome function, which could be why the BBSome is evolutionarily conserved among ciliated organisms. In this bachelor's thesis, the knowledge about the BBSome was summarized and compared to identify a putative common function of the BBSome among various model organisms or cell types. It seems that there has not been found any BBSome function that could be identified as the common function because the BBSome has many specialized functions in different organisms and tissues. The only distant similarity is BBSome-dependent ciliary retrograde transport, which has been described in most of the studied model organisms and cell types.
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Thematic and purpose maps
MAŠKOVÁ, Kristýna
This bachelor thesis describes thematic and purpose maps. The introductory section presents basic definitions of cartography. Afterwards the work characterizes the thematic and purpose maps and the differences between these types. The following section deals with the division of maps. The work also includes a chapter on content and purpose of thematic maps and analyzes their composition. Particular attention is paid to the cartographic means of expression. The final section provides examples of maps and reviews.
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