Mathematical methods and models for radiation carcinogenesis studies

Research on radiation carcinogenesis requires a twofold approach. Studies of primary molecular lesions and subsequent cytogenetic changes are essential, but they cannot at present provide numerical estimates of the risk of small doses of ionizing radiations. Such estimates require extrapolations from dose, time, and age dependences of tumor rates observed in animal studies and epidemiological investigations, and they necessitate the use of statistical methods that correct for competing risks. A brief survey is given of the historical roots of such methods, of the basic concepts and quantities which are required, and of the maximum likelihood estimates which can be derived for right censored and double censored data. Non-parametric and parametric models for the analysis of tumor rates and their time and dose dependences are explained

Mathematical programming methods of pattern classification

Mathematical programming methods of pattern classificatio

Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.Comment: 10 pages, 4 figure

Mathematical methods of optimal control theory and their applications

Tato diplomová práce se zabývá problematikou spojitého optimálního řízení, což je jedna z nejvýznamnějších aplikací teorie diferenciálních rovnic. Cílem této práce bylo jak nastudování matematické teorie optimálního řízení, tak především ukázat užití Pontrjaginova principu maxima a Bellmanova principu optimality při řešení vybraných úloh optimálního řízení. Důraz byl kladen především na problematiku časově a energeticky optimálního řízení elektrického vlaku, při zahrnutí kvadratické odporové funkce.This master's thesis deals with the continuous optimal control problem, which is one of the most important applications of the dierential equations theory. The aim of this work was to study the mathematical theory of the optimal control and the signicant part was to show how Pontryagin's maximum principle and Bellman's principle of optimality can be used in the particular optimal control problems. The emphasis was mainly put on the time and energy ecient electrically powered train control problem, where the quadratic resistant function has been involved.

Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century

Mathematical Methods in Economics

Diplomová práce se zabývá hodnocením a výběrem dodavatelů výrobků a služeb pro společnost Momedica, s.r.o. pomocí fuzzy logiky. Výsledný fuzzy systém bude sloužit jako nástroj pro podporu rozhodování v podniku.Master’s thesis deals with the evaluation and selection of suppliers of products and services for the company Momedica, s.r.o. using fuzzy logic. The resulting fuzzy system will serve as a decision support instrument of company.