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A digest of solved problems offunction for lower secondary school
KARLOVSKÁ, Tamara
The aim of the bachelor thesis is to create an exercise book for primary schools in the field of mathematical functions. The paper serves for understanding of the whole topic of functions of a real variable at upper primary education including assignment of functions, graphs of functions and theoretical properties. Moreover, the thesis deals with single types of taught mathematical functions including linear functions, direct proportion, quadratic functions and indirect proportion. Furthermore, the paper is focused on graphical solutions of systems of equations using the mathematics software Geogebra.
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On Heteroscedasticity in Robust Regression
Kalina, Jan
This work studies the phenomenon of heteroscedasticity and its consequences for various methods of linear regression, including the least squares, least weighted squares and regression quantiles. We focus on hypothesis tests for these regression methods. The new approach consists in deriving asymptotic heteroscedasticity tests for robust regression, which are asymptotically equivalent to standard tests computed for the least squares regression. One approach to modeling heteroscedasticity assumes a prior knowledge or specific model for the variability of random regression errors. Another (and more general) approach does not assume a specific form of heteroscedasticity. The paper also describes heteroscedastic regression, which is a tool to incorporate heteroscedasticity to the model. This allows us to define the heteroscedastic least weighted squares regression.
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Programy a algoritmy numerické matematiky 12
This book contains more than 30 papers presented at the seminar Programs and Algorithms of Numerical Mathematics held in Dolní Maxov, Czech Republic, June 6-11, 2004. The contributions deal mostly with the finite element method and its applications. Other subjects, as spline construction, numerical linear algebra algorithms, or optimization, for example, are also covered.
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Viral hepatitis E
ANDĚLOVÁ, Šárka
The thesis contains basic information regarding Viral hepatitis E, particularly the causative agents, human and animal strains, the clinical picture and occurrence in the Czech Republic as well as abroad. The practical part is focused on analysis of trends of occurrence of the viral hepatitis E in the Czech Republic from the very earliest, up until the present time. The research further looks at morbidity in the different regions of the Czech Republic, which is compared to the morbidity in Plzen region. The practical part further focuses on the specific source, route of transmission and possible preventive measures against viral hepatitis E. In this work, both quantitative and qualitative types of research were used. In quantitative research, secondary analysis of data was used from various sources like EPIDAT. In the qualitative research, semi standardised interviews with doc. MUDr. Petr Pazdiora CSc, and with MVDR. Vaclav Polacek. Based on the interviews, an educational material in form of a leaflet was created. From the year 1996 to the year 2012, a total of 894 cases of HEV where recorded. In 1996, there was only one case of Viral hepatitis E which was recorded. From 1997 to 2005, the occurrence was sporadic and negligible. From 2006, there was a linear increase in viral hepatitis E. The incidence significantly increased in the year 2009 and 2011. In the Czech Republic, Viral Hepatitis E has an upward trend of occurrence. Viral hepatitis E cannot be prevented by active immunization, possibility of a vaccine is still being investigated. Basic preventive measures include maintaining principles of hygiene like avoiding drinking water from unknown sources, food should be prepared using drinking water and fruit should be properly washed and then peeled before consumption. It is important to find out about the occurrence of viral hepatitis E, before travelling to any foreign country. During meat processing, it is important to avoid cross contamination between clean and unclean operations. Before consuming foods like black pudding, sausages, steaks and pies, it is important to ensure that this food is properly cooked using adequate heat and for a period of time. From the research, it can be concluded that, there is need to devote adequate attention to viral hepatitis E. It may seem that the incidence in the Czech Republic is not serious, but it is important to focus on public awareness of this disease, especially the preventive measures so as to stop it from spreading.
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Extensions to Probabilistic Linear Discriminant Analysis for Speaker Recognition
Plchot, Oldřich ; Fousek, Petr (referee) ; McCree,, Alan (referee) ; Burget, Lukáš (advisor)
Tato práce se zabývá pravděpodobnostními modely pro automatické rozpoznávání řečníka. Podrobně analyzuje zejména pravděpodobnostní lineární diskriminační analýzu (PLDA), která modeluje nízkodimenzionální reprezentace promluv ve formě \acronym{i--vektorů}. Práce navrhuje dvě rozšíření v současnosti požívaného PLDA modelu. Nově navržený PLDA model s plným posteriorním rozložením modeluje neurčitost při generování i--vektorů. Práce také navrhuje nový diskriminativní přístup k trénování systému pro verifikaci řečníka, který je založený na PLDA. Pokud srovnáváme původní PLDA s modelem rozšířeným o modelování neurčitosti i--vektorů, výsledky dosažené s rozšířeným modelem dosahují až 20% relativního zlepšení při testech s krátkými nahrávkami. Pro delší testovací segmenty (více než jedna minuta) je zisk v přesnosti menší, nicméně přesnost nového modelu není nikdy menší než přesnost výchozího systému. Trénovací data jsou ale obvykle dostupná ve formě dostatečně dlouhých segmentů, proto v těchto případech použití nového modelu neposkytuje žádné výhody při trénování. Při trénování může být použit původní PLDA model a jeho rozšířená verze může být využita pro získání skóre v případě, kdy se bude provádět testování na krátkých segmentech řeči. Diskriminativní model je založen na klasifikaci dvojic i--vektorů do dvou tříd představujících oprávněný a neoprávněný soud (target a non-target trial). Funkcionální forma pro získání skóre pro každý pár je odvozena z PLDA a trénování je založeno na logistické regresi, která minimalizuje vzájemnou entropii mezi správným označením všech soudů a pravděpodobnostním označením soudů, které navrhuje systém. Výsledky dosažené s diskriminativně trénovaným klasifikátorem jsou podobné výsledkům generativního PLDA, ale diskriminativní systém prokazuje schopnost produkovat lépe kalibrované skóre. Tato schopnost vede k lepší skutečné přesnosti na neviděné evaluační sadě, což je důležitá vlastnost pro reálné použití.
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Linear relation in stock time series
Nemčíková, Lucia ; Bašta, Milan (advisor) ; Helman, Karel (referee)
The aim of this Bachelor's Thesis is to verify the hypothesis of absence of linear relations between logarithmic returns in the stock time series, determined from the efficient markets hypothesis and the existence of linear relations between the squares of returns. I used regression analysis and conditional heteroskedasticity ARCH test of linear type, to achieve the results. My own analysis proved that even if there is a linear relation between logarithmic returns, the relation is not significant. On the other hand the linear relation between squares of returns is significant with tendency to be strong, what is a necessary condition for the use of a linear model of volatility.
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