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Topological Properties of Generalized Context Structures
Chernikava, Alena ; Chvalina, Jan (oponent) ; Beránek,, Jaroslav (oponent) ; Kovár, Martin (vedoucí práce)
This work is focused on the interaction of several branches of mathematics. The main idea was to nd dependencies, relationships and analogies between them. First part of the work is concerned to the relationship between Formal Concept Analysis, General Topology and Partial Metrics. A formal context is a very general mathematical structure that can represent other mathematical structures in a unied form. In a natural way, we could represent an information in a cross-table-like view of a formal context (fully respecting all set-theoretical limitations) and generate a topology on an attribute and object sets. In the second part the we study especially the pretopological systems as a special case of the formal contexts. They dier from topological systems especially by a more general poset structure of the set of attributes, representing the generalized open sets. Since the properties of this order structure are essential for the behavior of the whole structure, we pay them a special attention at the end of the chapter. Among others, we construct and study an analogue of the de Groot dual for posets, including its iteration properties. The third part is devoted to a mathematical structure called framework that has a contextual nature. A framework consists of two sets, rst one is a set of places, and the second one is a family of some its subsets, without the necessity of any external axioms to be fullled. The structure is equipped with a simple duality construction, allowing to switch between the classical point-set representation (like in topological spaces) and the point-less representation of topological relationships. At the end of the chapter, we suggest and study how a framework could be approximated by a directed family of nite frameworks from the point of view of the generated topology. In the last part the general topology methods were used to correct and improve one of the fundamental theorems in the game theory. It was showed that in a normal form game if i-th player has a continuous utility function and if the set of his strategies is almost-compact then he has an undominated strategy. In addition to this result, in the last two chapters we show that game theory naturally generates very general, for instance non-Hausdor topological and context structures, which shifts the traditional perception of reality in unexpected direction.
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Mining texts at the discourse level
Van de Moosdijk, Sara Francisca ; Pecina, Pavel (vedoucí práce) ; Novák, Michal (oponent)
Lingvistický diskurz se zabývá významem delších kusů textu, od vět po celé dokumenty, mohl by se však uplatnit i v úlohách získávání informací z textu, např. vyhledávání dokumentů či jejich sumarizace. Cílem této práce je uplatnění informací o stavbě diskurzu psaného textu pro potřeby získávání znalostí. Jedná se o prvnípokus, který se snaží skloubit tyto dva velice odlišné obory, a jeho ambicí je tak připravit základ pro tento způsob získávání znalostí. Náš postup spočívá v použití metod neřízeného strojového učení k analýze diskurzních vztahů a jejich následovném modelování pomocí vzorových struktur z formální konceptuální analýzy. Naši metodu jsme aplikovali na korpus lékařských článků z databáze PubMed. Tyto lékařské texty potom obohacujeme o koncepty z metathesauru UMLS, které jsou kombinovány s daty ze sémantické sítě UMLS, která fungují jako ontologie ve vzorových strukturách. Naše výsledky ukazují, že i přes vysokou úroveň šumu je naše metoda slibná a bylo by možné ji aplikovat i na jiné domény. Powered by TCPDF (www.tcpdf.org)
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Mining texts at the discourse level
Van de Moosdijk, Sara Francisca ; Pecina, Pavel (vedoucí práce) ; Novák, Michal (oponent)
Lingvistický diskurz se zabývá významem delších kusů textu, od vět po celé dokumenty, mohl by se však uplatnit i v úlohách získávání informací z textu, např. vyhledávání dokumentů či jejich sumarizace. Cílem této práce je uplatnění informací o stavbě diskurzu psaného textu pro potřeby získávání znalostí. Jedná se o prvnípokus, který se snaží skloubit tyto dva velice odlišné obory, a jeho ambicí je tak připravit základ pro tento způsob získávání znalostí. Náš postup spočívá v použití metod neřízeného strojového učení k analýze diskurzních vztahů a jejich následovném modelování pomocí vzorových struktur z formální konceptuální analýzy. Naši metodu jsme aplikovali na korpus lékařských článků z databáze PubMed. Tyto lékařské texty potom obohacujeme o koncepty z metathesauru UMLS, které jsou kombinovány s daty ze sémantické sítě UMLS, která fungují jako ontologie ve vzorových strukturách. Naše výsledky ukazují, že i přes vysokou úroveň šumu je naše metoda slibná a bylo by možné ji aplikovat i na jiné domény. Powered by TCPDF (www.tcpdf.org)
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Topological Properties of Generalized Context Structures
Chernikava, Alena ; Chvalina, Jan (oponent) ; Beránek,, Jaroslav (oponent) ; Kovár, Martin (vedoucí práce)
This work is focused on the interaction of several branches of mathematics. The main idea was to nd dependencies, relationships and analogies between them. First part of the work is concerned to the relationship between Formal Concept Analysis, General Topology and Partial Metrics. A formal context is a very general mathematical structure that can represent other mathematical structures in a unied form. In a natural way, we could represent an information in a cross-table-like view of a formal context (fully respecting all set-theoretical limitations) and generate a topology on an attribute and object sets. In the second part the we study especially the pretopological systems as a special case of the formal contexts. They dier from topological systems especially by a more general poset structure of the set of attributes, representing the generalized open sets. Since the properties of this order structure are essential for the behavior of the whole structure, we pay them a special attention at the end of the chapter. Among others, we construct and study an analogue of the de Groot dual for posets, including its iteration properties. The third part is devoted to a mathematical structure called framework that has a contextual nature. A framework consists of two sets, rst one is a set of places, and the second one is a family of some its subsets, without the necessity of any external axioms to be fullled. The structure is equipped with a simple duality construction, allowing to switch between the classical point-set representation (like in topological spaces) and the point-less representation of topological relationships. At the end of the chapter, we suggest and study how a framework could be approximated by a directed family of nite frameworks from the point of view of the generated topology. In the last part the general topology methods were used to correct and improve one of the fundamental theorems in the game theory. It was showed that in a normal form game if i-th player has a continuous utility function and if the set of his strategies is almost-compact then he has an undominated strategy. In addition to this result, in the last two chapters we show that game theory naturally generates very general, for instance non-Hausdor topological and context structures, which shifts the traditional perception of reality in unexpected direction.
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