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Approximation of a non-increasing rearrangement of a function
Franců, Martin ; Pick, Luboš (advisor) ; Felcman, Jiří (referee)
The non-increasing rearrangement of a measurable real function defined on an appropriate measure space is of the enormous significance in disciplines such as theory of function spaces or interpolation theory and their applications in PDEs. Unfortunately, while it has good and widely applicable mapping properties, it is virtually impossible to calculate the non-increasing rearrangement of a concrete given function precisely. Numerical algorithms for approximation are desirable for this reason. Such method of approximation, based on interpolation by a linear spline, is presented in this thesis. In the first half of this thesis, the developed method is described, while the error estimates of the method are subject to the second part.
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Interpolace hladkých funkcí pomocí kvadratických a kubických splinů
Eckstein, Jiří ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
In this thesis, we study properties of cubic and quadratic spline interpolation. First, we define the notions of spline and interpolation. We then merge them to study cubic and quadratic spline interpolations. We go through the individual spline interpolation types, show an algorithm for constructing selected types and sum up their basic properties. We then present a computer program based on the provided algorithms. We use it to construct spline interpolations of some sample functions and we calculate errors of these interpolation and compare them with theoretical estimates.
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Prediction error in non-life claims reserves
Divišová, Kateřina ; Justová, Iva (advisor) ; Mandl, Petr (referee)
This thesis deals with a description of three claims reserving methods - with stochastic models for Chain ladder, Bornhuetter/Ferguson and multiplicative method. There are mentioned their assumptions, parameter estimates, their properties and formulas for loss reserves in the first part. The second part of the text is devoted to formulas for the mean squared error of prediction and its estimate. Finally, a numerical example shows comparison of these methods.
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Nonstationary particle processes
Jirsák, Čeněk ; Rataj, Jan (advisor) ; Beneš, Viktor (referee)
Title: Nonstacionary particle processes Author: Čeněk Jirsák Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Jan Rataj, CSc., Mathematical Institute, Charles University Supervisor's e-mail address: rataj@karlin.mff.cuni.cz Abstract: Many real phenomena can be modeled as random closed sets of different Hausdorff dimension in Rd . One of the main characteristics of such random set is its expected Hausdorff measure. In case that this measure has a density, the density is called intensity function. In present paper we define a nonparametric kernel estimation of the intensity function. The concept of Hk -rectifiable set has a key role here. Properties of kernel estimation such as unbiasness or convergence behavior are studied. As the esti- mation may be difficult to compute precisely numerical approximations are derived for practical use. Parametric models are also briefly mentioned and the kernel estimation is used with the minimum contrast method to estimate the parameters of the model. At last the suggested methods are tested on simulated data. Keywords: stochastic geometry, intensity measure, random closed set, kernel estimation 1
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Geometry and stability study of nucleic acids distinctive single-strand motifs
Říhová, Martina ; Štěpánek, Josef (advisor) ; Mašek, Vlastimil (referee)
Subject of this thesis is the regulatory DNA segment, the so-called Serum Response Element (SRE), which possesses highly specific structural characteristics and its structural flexibility plays probably a key role in its physiological activity. Structural properties of 16-mer SRE segments capable to form hairpin structures were studied by means of accurate measurements of temperature dependent Raman spectra. Due to the close connection of oligonucleotide chain structural stability with the stacking interaction, temperature dependent Raman and UV absorption spectra were measured on dinucleotides serving as a simple model system for the stacking investigation. The measurements results processed by factor analysis provided characteristic spectral patterns and confirmed that stacking interaction depends on the base order. By fitting the thermodynamic equilibrium equations to the factor analysis outputs, the thermodynamic characteristics of the thermally induces structural changes in hairpinforming complexes were estimated and difference spectra characterizing opened and closed hairpins, which enable the further specification of the geometry of these complexes, were obtained.
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Asymptotic properties of the weighted least squares estimate
Gajdošík, Vladislav ; Zvára, Karel (referee) ; Víšek, Jan Ámos (advisor)
This diploma thesis dissertate about consistency and asymptotic representation of the least weighted squares estimator (LWS). In preface we mention reasons for data processing with robust statistical methods and differencies between LWS estimator and other methods (the least squares estimator, the least trimmed squares estimator). In the following sections we show proofs of lemmas about consistency and assymptotic representation of the least weighted squares estimator. Compared to the similar results published before we have concluded ours based on different conditions. Impulse for this thesis were new results about uniform convergence of empirical function mentioned in work from prof. Jan Ámos Víšek - Kolmogorov-Smirnov statistics in multiple regression from year 2006 (see Víšek (2006a)).
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Social aspects of facial appearance
Rubešová, Anna ; Havlíček, Jan (advisor) ; Smékal, Vladimír (referee) ; Blažek, Vladimír (referee)
The dissertation thesis consists of an introductory analysis of literature and further of manuscripts, both published and submitted for publication. The analysis of literature firstly describes the theme of facial perception from the view of neuropsychology. It also discusses the question of stereotypical judgment of others according to the facial appearance and the theme of halo effect, as well as the possibility of accuracy in judging others according to their face. Further, it deals with the influence of facial appearance in a numerous social contexts (e.g. in one's career, at school, in politics). The second part of the thesis includes two reviews concerning mainly the accuracy of personality judgment on the basis of facial appearance and various aspects of facial attractiveness. Next, there are four research studies included in the thesis, which were aimed at finding the level of accuracy in judgments of Cattell's personality factors on the basis of facial appearance of an unknown individual. The results suggest that a mere facial appearance contains some relevant information regarding personality of an individual and that the perceiver is able to estimate some personality traits (mainly Social boldness, Liveliness and Warmth) relatively accurately on the basis of both, an individual picture and a...
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Mobile Banking in the Czech Republic and in the World and its Development
Matoušek, Dominik ; Matuštík, Ondřej (advisor) ; Exnarová, Anna (referee)
This bachelor thesis tries to provide the compact and actual insight to the issue of mobile banking. A reader is acquainted with current offered services which are consequently analysed. The conclusion of this thesis will be treatise on an estimation of the future evolution. The thesis consists of five sections. The first part specifies the issue of the mobile banking and makes the reader acquainted with the history of this banking service. This part is followed by listing a general characteristics which are divided into two groups - positives and negatives. The reader is further acquainted with the functionality and its structure in the next chapter. The third part than analyses a particular forms of mobile banking which are subsequently followed by the issue of security and possible threats. The last part deals with the analysis of the current offered services with the evaluation.
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Acoustic properties of road markings
Drnovský, Ondřej ; Caudr, Michal (referee) ; Radimský, Michal (advisor)
The thesis deals with verifying the acoustic properties of road markings in real conditions the vehicle travels. It contains basic information about the acoustics of the sources of traffic noise and methods of measuring noise. Below are the main information about the horizontal signposts and its impact on safety. The practical part contains descriptions of results, estimation of measurement and subsequently implemented economic assessment.
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