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The theoretical part of the diploma thesis introduces the issue of gradebooks and school information systems. Finally, it describes the selected school information system Bakaláři, which is the subject of research. The research part deals with the view of teachers on online record books in education, on their evaluation and use of the Bachelors system. To collect research data, it was conducted through a questionnaire survey.

Implied volatility obtained from market option prices is widely regarded as an efficient predictor of future realised volatility. Implied volatility can be thought of as market's expectation of future realised volatility. We distinguish between volatility-changing events with respect to expectations - scheduled events (such as information releases) and unscheduled events. We propose a method of testing the information content of option-implied risk-neutral moments prior to volatility-changing events. Using the method introduced by Bakshi, Kapadia & Madan (2003) we extract implied volatility, skewness and kurtosis from S&P 500 options market prices and apply the proposed method in four case studies. Two are concerned with scheduled events - United Kingdom European Union membership referendum, 2016 and United States presidential election, 2016, two are concerned with unscheduled events - flash crash of August 24, 2015 and flash crash of October 15, 2014. Implied volatility indicates a rise in future realised volatility prior to both scheduled events. We find a significant rise in implied kurtosis during the last three days prior to the presidential election of 2016. Prior to unscheduled events, we find no evidence of implied moments indicating a rise in future realised volatility.

When the Czech Republic joined the European Union in 2004, the number of foreign nationals working in the Czech Republic quickly grew, along with their impact on the national economy. The aim of this thesis is to analyse and compare the effects of foreign and native labour on the gross domestic product (GDP) of the Czech Republic. Then we shall compare the effects of immigrant labour originating from the EU with other foreign nationals. Using the ordinary least squares method to analyse time series data, it is shown that labour migration has a positive effect on the GDP growth and the results are statistically significant. It seems that labour from the EU is the most productive group, followed by the foreign labour from other countries.

This work deals with Newton method of interior point which is applied on finding estimation of polynomial L_1 regression. The aim of this thesis is to find new modifications of long step choice in Newton method in order to find faster solution of L_1 estimations for large data sets. Designed modifications are based on full-Newton step algorithm for the self-dual model. According to reasults, the best are algorithms AF-L, F-LP1, AF-LP1 a AF-L-mixed, which modify the barrier update parameter in adaptive way. Algorithms and obtained results were implemented end visualized in MatLab.

The thesis is focused on application of econometric methods in the area of sport statistics, specifically in the area of ice hockey. Datasets were extracted from the National Hockey League (NHL) website, from the RTSS (Real Time Scoring System) from seasons 2002/2003 to 2014/15 by using the R package nhlscrapr. The Analysis of these datasets is based on previous work by Brian Macdonald [1]. The result is an adjusted +/- statistics (plus - minus), which describes the individual performance of each player. These statistics were later used for an estimation of probability of advance of selected teams to the playoffs, assuming the selected team uses anticipated players. These estimations were obtained by usage of logistic regression. It was found out, that the predictive ability of these models is weak.

Aim of this application-oriented master's thesis is to prove a benefits from using data analysis techniques connected with geodata processing to support business decisions. As a conclusion two solutions are given which are more attractive then starting situation. Since the first solution proposed is oriented on giving maximum success ratio while considering transactions, the second one is oriented on business value of each transaction. In this thesis R programming language is widely used together with ArcGIS Online in its final part.

This thesis deals with the calculation of the upper limit of the sample variance when the exact data are not known but intervals which certainly contain them are available. Generally, finding the upper limit of the sample variance knowing only interval data is an NP-hard problem, but under certain conditions imposed on the input data an appropriate efficient algorithm can be used. In this work algorithms were modified so that, even at the cost of exponential complexity, one can always find the optimal solution. The goal of this thesis is to compare selected algorithms for calculating the upper limit of sample variance over interval data from the perspective of the average computational complexity on the generated data. Using simulations it is shown that if the data meets certain conditions, the complexity of the average case is polynomial.

Companies dependent on commodities for their production have to deal with volatile commodity prices and should employ measures for risk reduction as unfavourable spot price development may cause significant losses. A useful tool for diminishing the risk is hedging on futures market; however, this approach faces a crucial question of optimal hedge ratio determination (ratio between spot and futures units). Our thesis examines nine different ways of optimal hedge ratio estimation (naive, Sharpe, mean extended Gini coefficient, generalized semivariance, value at risk, and minimum variance through OLS, error correction, GARCH, and bivariate GARCH models) and evaluates their efficiency using the data on eight different commodities. The results differ across the respective commodities and cannot be generalized. Two conclusions resulting from the analysis refer to performance of naive and OLS hedge ratios and constant vs time varying hedge ratios. We find that complex hedge ratios, such as bivariate GARCH or VaR hedge ratios, do not outperform naive and OLS hedge ratios and that the results of constant hedge ratios are mostly as good as results of time-varying hedge ratios.

The diploma thesis focuses on the topic of the future regulatory regime of the insurance and reinsurance market of the European Union called Solvency II. Currently the most discussed issue without a final structure is an extensive set of legislative and technical changes not only in the area of solvency treatment. Primarily, the work focuses on the standard formula calculation of capital requirements that reflect the solvency position of companies on the market. The first part deals with the theoretical description of the calculating methods of the required capital levels under current and future rules on the basis of available official documents. Further the general overview of the Solvency II is presented, a more detailed description of the valuation techniques of balance sheet items for the purposes of Solvency II, dealing with company's own funds and possible ways to optimize the asset portfolio are also included. Some theoretical descriptions of computational procedures applied on a fictitious life insurance company are presented in the second, more practical part of the diploma thesis.

This diploma thesis describes problem of change-points in volatility of the time-series and their impact on price of nancial assets. Those change-points are estimated by using statistical methods and tests. Change-point estimation was tested on simulated datas and real world driven datas. Simulation helped to discover signi cant characteristics of change-point test, those data were simulated with using stochastic calculus. Google share prices and prices of call options were chosen to analyse impact of volatility change on those prices. Also implied volatility and its impact to call option price was analysed.

This paper deals with optimization in systems of biological populations adjusted to harvesting. First, a description, behavior and evolution over time in basic models of Malthus, Verhulst and Gompertz, is solved in case of not harvesting and then harvesting. There are two options for harvesting, continuous and discrete harvesting. In case of continuous harvesting we have two ways how to harvest,with constant yield and constant effort. With simplifying assumptions it is possible to combine continuous and discrete model in the form of profit function for the harvesting and also gives us ability to implement harvesting costs. For profit-seeking function is best solved using numerical methods with model examples with help of the Maple solver. The last chapter is devoted to the introduction of interest to the harvesting models.

Application of constraint programming (CP) is one of the possible ways of solving discrete problems. It can be used for both search for feasible solution and optimization. CP offers a whole range of approaches for either a solution search or for acceleration of the process of its search -- from search algorithms or consistency techniques to propagation algorithms, which are basically only a combination of the two preceding methods. For optimization we most often use branch and bound approach, which differs in some aspects from a method of the same name used in mathematical programming (MP). Comparison of CP and MP is interesting in many other aspects. With CP the formulation of problems is more flexible, which allows for creation of often simpler and smaller models. On the other hand, its disadvantage is a limited use: Constraint satisfaction (optimisation) problem, as we call the constraint programming problem, cannot contain any discrete variables. CP is suitable especially for problems with a lot of constraints and only few variables, ideally only two. In the beginning, the paper introduces the basic terms of constraint programming, then it describes algorithms and techniques used for solving discrete problems and compares CP with mathematical programming.

The thesis deals with the task of refining the constructional and operational parameters of a tubular photobioreactor in order to maximise the growth rate of algae contained in the cultivation suspension. It builds on a basic growth model of the Porhydrium sp. alga, and focuses on the optimization of external irradiance, which is one of the key determinants of algae growth. Two distinct methodological approaches are applied: analytic approach, which employs Markov Chains, and simulation approach, which relies on agent-based simulations. In the analytic part, we introduce the construction of state transition matrix for a Markov Chain that accounts for varying irradiance inside the photobioreactor (in contrast to constant-irradiance methods that have been published so far). In the simulation part, we devised an agent-based model of algae population that enables us to analyze the system behaviour while interactively changing the model parameters. In the context of the results from both the analytic and simulation part, we conclude by suggesting the optimal level of external irradiance.

In the present work we study Interior Point Algorithm used for solving linear problems

Anywhere we see a prognostication system; we can run up against the need of evaluating it. For the evaluation is frequently used unsuitable methods. There are such cases where is need to correctly take effects of mistakes into consideration. And here we can use statistic based on information measure either entropy. The first part deals with this point of issue. In the second part I am trying to show possible areas of use, for example betting. I enclose practical remarks from this issue and the methods making these estimators, which are dependent on nature of issued events.

The bankruptcy problem involves the distribution of perfectly divisible goods. Particular attention is paid to the situations, where the amount of goods available is not enough to cover the demand. An example of real life situations that can be solved using various bankruptcy rules may be a division of a heritage or when a company goes bankrupt and its estates are sold to satisfy interested parties' claims. This paper introduces to the problem a linear structure of the participants, meaning that participants are now satisfied one after another in a preset order. It applies the equal awards (CEA) and the equal losses (CEL) solutions on the revised problem. Since their axiomatization is no longer valid, both solutions are extended and new characterizations are given in the thesis. The thesis contains a series of original proofs for both extended solutions and whole problem is examined in the setting of the well-known river sharing problem.

The thesis unifies the most important author's results in the field of algorithms concerning zonotopes and their applications in optimization and statistics. The computational-geometric results consist of a new compact output-sensitive algorithm for enumerating vertices of a zonotope, which outperforms the rival algorithm with the same complexity-theoretic properties both theoretically and empirically, and a polynomial algorithm for arbitrarily precise approximation of a zonotope with the Löwner-John ellipsoid. In the application area, the thesis presents a result, which connects linear regression model with interval outputs with the zonotope matters. The usage of presented geometric algorithms for solving a nonconvex optimisation problem is also discussed.

Práce se zabývá použitím vybrané metody lineárního programování. Aplikace metody včetně dvojrozměrné vizualizace výsledku jejího řešení probíhá v~prostředí JAVA. Tím je zajištěno, že uživatelé mohou využívat výsledky této práce bez vazby na jeden konkrétní operační systém. Během zpracovávání této bakalářské práce byly využity znalosti získané na Katedře informačních technologií.

Tato bakalářská práce popisuje vývoj metod Interior-point od roku 1984, kdy Karmarkar představil svůj revoluční algoritmus pro lineární programování. Je zde stručně popsáno použití těchto metod v oblastech jako např. lineárního programování, konvexní kvadratické programování, semidefinitní programování, nekonvexní a nelineární úlohy. Dále je zde naznačeno použití těchto metod v oblasti celočíselného programování a její srovnání se simplexovou metodou.

Práce se zabývá charakterizací flowshop problému ? problému optimálního řazení dávek u dvou procesorů a měla by posloužit jako zdroj informací o této problematice. Jsou zde zavedeny jednotlivé teorémy, obnoveny některé základní pojmy, používané při definování částečného uspořádání a vztahující se k analýze intervalové struktury. Dále jsou zde náhledy na dvě konkrétní intervalové struktury pro F2|prmu|Cmax problém a vyloženo několik postačujících podmínek optimality, začínající u částečné intervalové struktury a končící u obecných, celých případů.