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Dose-response curves
Hezoučký, Martin ; Hlávka, Zdeněk (advisor) ; Maciak, Matúš (referee)
Title: Dose-response curves Author: Martin Hezoučký Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we deal with the process of research and development of new medical substances with a focus on statistical methods used to determine appropriate doses. For this purpose, we examine the dose-response relationship. First, we describe a typical procedure for the development of a new drug. Second, we focus in detail on the MCP-Mod method. Third, we propose a new method based on the theory of gradual change models. This approach tests whether the administration of the drug has a significant effect. If so, the dose with desired effect is estimated using an appropriate model. Specifically, we provide an esti- mate using linear, quadratic and Emax gradual change models. We also describe a construction of a confidence interval for the point of change and also for the dose with the desired effect. The advantage of the proposed method over the MCP-Mod is the determination of the confidence intervals. Finally, we apply the above mentioned methods to data from the U.S. Tox21 research program and compare the results based on several tested substances and clearly demonstrate the...
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Interactive web applications supporting education of 3D graphics
Morávek, Jan ; Mokrý, Ondřej (referee) ; Rajmic, Pavel (advisor)
This diploma thesis is focused on computer 3D graphics and the implementation of educational applications in JavaScript language. Discussed topics of computer graphics include object transformations, Bezier patches and the role of the camera in the scene. The thesis describes the basic theory of these areas and educational applications. The thesis also includes the detailed description of the features and the implementation of the created applications. In the end of the thesis possible extensions are discussed.
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Generalized ordinary differential equations in metric spaces
Skovajsa, Břetislav ; Malý, Jan (advisor)
The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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Dose-response curves
Hezoučký, Martin ; Hlávka, Zdeněk (advisor) ; Maciak, Matúš (referee)
Title: Dose-response curves Author: Martin Hezoučký Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we deal with the process of research and development of new medical substances with a focus on statistical methods used to determine appropriate doses. For this purpose, we examine the dose-response relationship. First, we describe a typical procedure for the development of a new drug. Second, we focus in detail on the MCP-Mod method. Third, we propose a new method based on the theory of gradual change models. This approach tests whether the administration of the drug has a significant effect. If so, the dose with desired effect is estimated using an appropriate model. Specifically, we provide an esti- mate using linear, quadratic and Emax gradual change models. We also describe a construction of a confidence interval for the point of change and also for the dose with the desired effect. The advantage of the proposed method over the MCP-Mod is the determination of the confidence intervals. Finally, we apply the above mentioned methods to data from the U.S. Tox21 research program and compare the results based on several tested substances and clearly demonstrate the...
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Functions and curves hidden in pictures
STRATULAT, Elena
This bachelor thesis named Functions and curves hidden in pictures is a collection of interesting tasks divided into six work sheets, which are focused on the graphical representation of different functions and curves into the coordinate system Oxy. The results of these tasks are pictures formed in the mathematical program GeoGebra, shown at the end of each work sheet. Part of bachelor thesis is also illustrative, solved exercise in mathematical program GeoGebra.
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Generalized ordinary differential equations in metric spaces
Skovajsa, Břetislav ; Malý, Jan (advisor)
The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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Zobecněné obyčejné diferenciální rovnice v metrických prostorech
Skovajsa, Břetislav ; Malý, Jan (advisor) ; Pražák, Dalibor (referee)
The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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Computer modeling of curves
Chudáčková, Eliška ; Surynková, Petra (advisor) ; Karger, Adolf (referee)
Title: Computer modeling of curves Author: Eliška Chudáčková Department: Department of Mathematics Education Vedoucí bakalářské práce: RNDr. Petra Surynková, Ph.D. Abstract: Bachelor thesis Computer modeling of curves deals with important curves of computer graphics and their applications in programs. It is especially devoted to Ferguson cubic, Bezier curve and Coons cubic. The work is outlined as a teaching text. First for high school students of informatics seminar, second for students of geometry. It is also useful as an overview of the theory of curves or a collection of examples relating to study of curves. An important contribution of this work are programs that allow experimental verification of properties of the studied curves. There is also a picture attached to most of curves and examples. Part of this work is an enclosed CD, where you can find all the programs and the picture supplement in the electronic form. Keywords: curves, modeling, interpolation, approximation, control polygon
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Metrics for eye movements comparisons
Kocián, Matěj ; Děchtěrenko, Filip (advisor) ; Vodrážka, Jindřich (referee)
Measurement of eye movements is becoming a well established part of expe- rimental research in many areas (such as human-computer interaction, cognitive psychology and others). Then usually a need arises to mutually compare the eye movements. Many different metrics have been suggested for this purpose, but what is missing is a comparison of these metrics and consequently an agreement on the ones that should be used in specific cases. In this thesis we describe some commonly used metrics and then create a model of smooth pursuit eye move- ments. We subsequently use this model to compare the ability of Levenshtein metric, Normalized Scanpath Saliency for dynamic scenes and discrete Fréchet distance to recognise similarity between the original eye movement trajectory and its modified copy. 1
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Application for 2D Curves Demonstration
Opletal, Pavel ; Švub, Miroslav (referee) ; Venera, Jiří (advisor)
This Bachelor's Thesis deals with planar curves used in computer graphics. It sums up general ideas of these curves and deals with particular methods for computing planar curves. It describes methods used for computing Ferguson cubic curves, Kochanek-Bartels spline, Cardinal spline, Catmull-Rom spline, Bézier curves and their modifications, Coons cubic curves, Coons cubic B-spline curves and NURBS. Practical part of this project deals with concept and impementation of tutorial, which demonstrates chosen curves.
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