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Path analysis of Wiener Process
Belyaeva, Evgeniya ; Hlubinka, Daniel (advisor) ; Seidler, Jan (referee)
In this thesis we research and introduce several properties of paths of a Wiener process. At first we present a way to prove existence of a Wiener process and then we discuss its basic properties. The second chapter is devoted to analytical properties of Wiener's paths including monotonicity, differentiability, Hölder continuity and quadratic variation. In the third chapter we research the reflection principle and the distribution of maxima of paths in the case of a random walk and then also in the case of a Wiener process. The fourth chapter concentrates on the Skorohod embedding and its application in the proof of the classic central limit theorem. Finally, using the results of the first chapter we simulate a path of a Wiener process and illustrate some of the properties discussed earlier. To demonstrate the concepts, several problems were included in the relevant chapters together with an author's solution. Powered by TCPDF (www.tcpdf.org)
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Methods for the evaluation of postural stability
Nevěčná, Leona ; Janoušek, Oto (referee) ; Koťová, Markéta (advisor)
This study deals with methods for evaluation of postural stability. The main problem of posturography is lack of standardization in measurement and evaluation. There are presented some parameters affecting postural stability that are often taken into account. Those are parameters that might be changed while measuring, for example standing position, sampling duration or visual control. And others that are altered when evaluating is taking place, variability of those parameters, is much greater. Measurement protocol taking into account the most promising parameters was put together based on literary search. Changes in COP of ten subjects were measured with Wii Balance Board, according to the proposed measurement protocol. The data acquired from a particular subject were used to count values of parameters used in evaluation. After that the values were statistically analyzed. To compare each parameter, trajectory with good results according to other literature was chosen to pose as a reference. Final result is comparison firstly between importance of changes in parameters of measuring and secondly between success of detection of those changes of separate parameters.
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NoSQL: Support of Multidimensional Data Storage
Hrivnák, Jan ; Zendulka, Jaroslav (referee) ; Volf, Tomáš (advisor)
This bachelor's thesis deals with posibilities of storing multidimensional data in NoSQL databases. It compares suitability of several different databases for storing trajectories of moving 2D objects. Experiments with MongoDB were carried out to find the best way to store trajectories and create indexes over them. This thesis also provides a simple demonstration program in Python which works with MongoDB API.
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Knowledge Discovery in Spatio-Temporal Data
Pešek, Martin ; Bartík, Vladimír (referee) ; Zendulka, Jaroslav (advisor)
This thesis deals with knowledge discovery in spatio-temporal data, which is currently a rapidly evolving area of research in information technology. First, it describes the general principles of knowledge discovery, then, after a brief introduction to mining in the temporal and spatial data, it focuses on the overview and description of existing methods for mining in spatio-temporal data. It focuses, in particular, on moving objects data in the form of trajectories with an emphasis on the methods for trajectory outlier detection. The next part of the thesis deals with the process of implementation of the trajectory outlier detection algorithm called TOP-EYE. In order to testing, validation and possibility of using this algorithm is designed and implemented an application for trajectory outlier detection. The algorithm is experimentally evaluated on two different data sets.
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Path Planning of Airplane with Obstacles
Očenáš, Marek ; Zbořil, František (referee) ; Samek, Jan (advisor)
The aim of this master's thesis is the implementation of optimal trajectory planning for an airplane flying in lower altitudes, which has to avoid collision with obstacles. For the planning we assume static and fully known environment. There are described principals, optimality and complexity for some chosen methods of planning in this thesis. And based on the methods' characteristics it's chosen the best method for implementation.
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Activity Recognition from Moving Object Trajectories
Schwarz, Ivan ; Zendulka, Jaroslav (referee) ; Pešek, Martin (advisor)
The aim of this thesis is a development of a system for trajectory-based periodic pattern recognition and following GPS trajectory classification. This system is designed according to a performed analysis of techniques of data mining in moving object data and furthermore, on recent research on a subject of a trajectory-based activity recognition. This system is implemented in C++ programming language and experiments addresing its effectiveness are performed.
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Moving Objects Indexing
Vetešník, Jiří ; Chmelař, Petr (referee) ; Zendulka, Jaroslav (advisor)
This work is aimed for proposing acceptable indexing of moving objects. With the enlargement of mobile computing it is needed to manage large sets of spatiotemporal data. We introduce the problem of spatiotemporal data and basic general approaches of indexing these data. Further, we show support of spatial data in Oracle. The movement is typically represented as trajectory in two dimensional space with temporal component in third dimension. The thesis contains experiments performed in database Oracle on artificially generate data.
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Knowledge Discovery in Object Relational Databases
Chytka, Karel ; Vrážel, Dušan (referee) ; Chmelař, Petr (advisor)
The goal of this master's thesis is to acquaint with a problem of a knowledge discovery and objectrelational data classification. It summarizes problems which are connected with mining spatiotemporal data. There is described data mining kernel algorithm SVM. The second part solves classification method implementation. This method solves data mining in a Caretaker trajectory database. This thesis contains application's implementation for spatio-temporal data preprocessing, their organization in database and presentation too.
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Damage correspondence of car hit by the fragments of roofing
Prnka, Jiří ; Sedlák, Robert
The article deals with the traffic accident with supposed contact of a car with fragments of roofing, which were lost from an oncoming truck, and caused subsequent running off a car into a ditch. Based on correspondence damage, mechanism of damage and movement of fragments of roofing it was researched if the question could arise as mentioned accident plot, as it was described by the participant.
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Advanced trajectory management techniques for model station in the OPNET Modeler environmen
Ludvíček, Pavel ; Mácha, Tomáš (referee) ; Vajsar, Pavel (advisor)
The aim of this work is to study and theoretically process existing movement options of station in OPNET Modeler environment. These options are described in first part. Furthermore to design and implement function to display path obtained from real-world conditions and done to station following this route during simulation. Coordinates used to move station are obtained by GPX format, which is used to store clearly the GPS coordinates. Second part is devoted to describing creation of this function, first using PHP script, then direct implementation into OPNET Modeler environment using C++.
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