This thesis investigates the area of preference learning and recommender systems. We concentrated recommending on small e-commerce vendors and efficient usage of implicit feedback. In contrast to the most published studies, we focused on investigating multiple diverse implicit indicators of user preference and substantial part of the thesis aims on defining implicit feedback, models of its combination and aggregation and also algorithms employing them in preference learning and recommending tasks. Furthermore, a part of the thesis focuses on other challenges of deploying recommender systems on small e-commerce vendors such as which recommending algorithms should be used or how to employ third party data in order to improve recommendations. The proposed models, methods and algorithms were evaluated in both off-line and on-line experiments on real world datasets and on real e-commerce vendors respectively. Datasets are included to the thesis for the sake of validation and further research. Powered by TCPDF (www.tcpdf.org)

In the present thesis we deal with dependence among extremal values within time series. Concerning this type of relations the commonly used autocorrelation function does not provide sufficient information. Moreover, autocorrelation function is suitable for Gaussian processes while nowadays we often work with heavy-tailed time series. In this thesis we cover two measures of extremal dependence that are used for this type of data. We introduce the coefficient of tail dependence, measure of extremal dependence based on tail characteristics of joint survival function. The second measure is called extremogram, which depends only on the extreme values in the sequence. In addition to the theoretical part, simulation study and application to real data of both described measures including their comparison are performed. Results are stated together with tables and graphical output.

The aim of the diploma thesis is to provide a comprehensive overview regarding survey of income and living conditions of households in the Czech Republic and propose a feasible approach to the exploitation of the collected data. The diploma thesis describes the framework of the EU-SILC survey and presents its practical implementation in the Czech Republic. A technique utilizing contingency table analysis is proposed for studying asymmetric relationships between selected housing characteristics and amenities in the dwelling with respect to different household types. The analysis is based on the relative frequencies of housing characteristics observed for particular types of households. The frequencies stem from the sample survey of income and living conditions of households carried out in the Czech Republic under the official title of Living Conditions 2008. Asymmetric measures of association for nominal and ordinal variables were used for the description of the relationships as the examined housing characteristics and household types have the character of alternative, nominal or ordinal variables. The analyses show significant relationship of the selected housing characteristics and the amenities in the dwelling on the monitored types of households.

This diploma thesis describes the intervention of the Czech National Bank in November 2013 in terms of current economic theory and practice as well as its justification. In the first theoretical part is presented actual literature dealing with the zero lower bound (ZLB). This part is divided to general description of ZLB, its prevention and possibilities of monetary policy. Further are described experiences from Japan and other countries which achieved ZLB. In this context is also presented intervention made by the Czech National Bank. Hypothesis whether the intervention was justified is tested by linear and nonlinear Taylor rule. Estimate is made by the least squares method using quarterly data from the CSO and CNB. The results of model confirm the hypothesis, which means that the optimal monetary policy interest rate would fall below zero.

Warrants are modern investment gear product. They are emitted by famous financial institution and dedicated for small investors. The main object of this diploma thesis is to analyse warrants. In first part of the thesis is theoretical background of warrants, pricing models, etc. Second part is mainly focused on investment strategies and stockjobbing. In the last part is comparsion to other financial products and also practical investment introduction are included.

The theoretical section includes basis of consolidation, procedures and methods of preparation of consolidated financial statements under Czech accounting legislation. The second part shows how to prepare consolidated financial statements of real companies.

This thesis deals with selecting the optimal portfolio for a risk averse investor. Firstly, we present the risk measures, specifically spectral risk me- asures which consider an individual risk aversion of the investor. Then we propose a diversification-consistent data envelopment analysis model. The model is searching for an efficient portfolio with respect to second-order sto- chastic dominance. The crux of the thesis is a model based on the theory of multi-criteria optimization and spectral risk measures. The presented mo- del is searching for an optimal portfolio suitable for the investor with a given risk aversion. In addition, the optimal portfolio is also consistent with second- order stochastic dominance efficiency. The topic of the practical part is a nu- merical study in which both models are implemented in MATLAB. Models are applied to a dataset from real financial markets. Personal contribution lies in comparing the diversification-consistent data envelopment analysis model and model based on multi-criteria optimization, both with respect to second order stochastic dominance efficiency.

This dissertation thesis is concerned with developing a mesoscopic model for sin- gle crystalline shape-memory alloys including thermo-dynamically consistent thermo- mechanical coupling - here the term "mesoscopic" refers to the ability of the model to capture fine spatial oscillations of the deformation gradient by means of gradient Young measures. Existence of solutions to the devised model is proved in a "phase-field-like approach" by a scale transition from a microscopic model that features a term related to the interfacial energy; this scale transition from a physically relevant model justifies the mesoscopic relaxation. Further, existence of solutions is also proved by backward- Euler time discretization which forms a conceptual numerical algorithm. Based on this conceptual algorithm a computer implementation of the model has been developed and further optimized in the rate-independent isothermal setting; some calculations using this implementation are also presented. Finally, refinements s of the analysis in the convex case as well as a limit of the phase-field-like approach in this case are exposed, too.

The aim of the thesis is the mathematical and computer modelling of thin films of martensitic materials. We derive a thermodynamic thin-film model on the meso-scale that is capable of capturing the evolutionary process of the shape-memory effect through a two-step procedure. First, we apply dimension reduction techniques in a microscopic bulk model, then enlarge gauge by neglecting microscopic interfacial effects. Computer modelling of thin films is conducted for the static case that accounts for a modified Hadamard jump condition which allows for austenite--martensite interfaces that do not exist in the bulk. Further, we characterize $L^p$-Young measures generated by invertible matrices, that have possibly positive determinant as well. The gradient case is covered for mappings the gradients and inverted gradients of which belong to $L^\infty$, a non-trivial problem is the manipulation with boundary conditions on generating sequences, as standard cut-off methods are inapplicable due to the determinant constraint. Lastly, we present new results concerning weak lower semicontinuity of integral functionals along (asymptotically) $\mathcal{A}$-free sequences that are possibly negative and non-coercive. Powered by TCPDF (www.tcpdf.org)

Název práce: Geometrické lineární a nelineární problémy prostor· funkcí Autor: Petr Petráček Katedra: Katedra matematické analýzy 'kolitel: prof. RNDr. Jaroslav Lukeš, DrSc., Katedra matematické analýzy Abstrakt: Tato práce sestává ze čtyř vědeckých článk·. lánky prezentované v prvních dvou kapitolách se věnují teorii reálných a komplexních L1-preduál·. lánky prezentované v třetí a čtvrté kapitole jsou věnovány problematice line- ability a algebrability podmnožin reálných funkcí a měr. V Kapitole 1 předsta- vujeme charakterizaci komplexních L1-preduál· pomocí komplexního barycent- rického zobrazení. Tato charakterizace je přirozeným rozšířením charakterizace reálných L1 preduál· pocházející od Bednara a Laceyho. V Kapitole 2 odpoví- dáme na otázku položenou Laceym v roce 1973. Dokazujeme přitom existenci kompaktního prostoru K a uzavřeného podprostoru H ⊂ C(K) obsahujícího kon- stantní funkce, pro který platí ∂HK = K, H je maximální vzhledem k ∂HK a H není L1-preduál. V Kapitole 3 se věnujeme lineabilitě množin nikde mono- tonních znaménkových Radonových měr na Rd . Konkrétně dokazujeme existence vektorového prostoru dimenze c jehož každý nenulový prvek je nikde monotonní míra absolutně spojitá vzhledem k d-rozměrné Lebesgueově míře. Nadto dokazu- jeme, že existuje takový lineární prostor, který je hustý...