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Data Mining
Slezák, Milan ; Hynčica, Ondřej (referee) ; Honzík, Petr (advisor)
The thesis is focused on an introduction of data mining. Data mining is focused on finding of a hidden data correlation. Interest in this area is dated back to the 60th the 20th century. Data analysis was first used in marketing. However, later it expanded to more areas, and some of its options are still unused. One of methodologies is useful used for creating of this process. Methodology offers a concise guide on how you can create a data mining procedure. The data mining analysis contains a wide range of algorithms for data modification. The interest in data mining causes that number of data mining software is increasing. This thesis contains overviews some of this programs, some examples and assessment.
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Operators related to Fourier transform
Buriánková, Eva ; Honzík, Petr (advisor) ; Ryabogin, Dmitry (referee) ; Slavíková, Lenka (referee)
This manuscript provides an overview of known results in the theory of singular integral operators and multilinear multipliers as well as new results in this context. The first such result we describe is boundedness of rough maximal bilinear singular integrals on Lp spaces which is a part of the first attached paper. The same problem is discussed for a special kind of bilinear operator consisting of smooth bumps, this result is a part of the attached paper number two. Finally we attack the multilinear case of the same type of operator and present a result which is a part of an upcoming paper.
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Differentiability of the inverse mapping
Konopecký, František ; Hencl, Stanislav (advisor) ; Honzík, Petr (referee)
Primary objective of the thesis is proof of the statement that if for ∈ ℕ a ≥ 1 a bilipschitz mapping belongs to +1, loc ∩ ,∞ loc then also its inverse −1 belongs to +1, loc . We prove a similar statement also for spaces loc . For this purpose we construct a new ordering of -th partial derivatives to generalized Jacobian matrix. Thanks to this matrix we are able to differentiate matrices in an applicable way. Generalized Jacobian matrix is projected so that there still holds the Chain rule and, in some way, also rules for matrices product differentiation. 1
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Control of linear systems
Cesneková, Ivana ; Milota, Jaroslav (advisor) ; Honzík, Petr (referee)
The aim of this work is to look into the theory of linear systems via population model represented by partial differential equations with boundary and initial condition. Special attention is devoted to the strongly continuous semig- roups on a complex Banach space. For this purpose, the notion of a homogeneous and inhomogeneous Cauchy problem is introduced and we solve our model in this abstract formulation. The system behaviour is based on properties of the resolvent set and spectrum. Controllability question limits to solve the uniformly exponen- tially stability and the exponentially stabilizability. The point of this problem is in the case of the unstability to show exponencially stability of the system by using feedback. Keywords: control, differential equations, stability, controllability 1
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Sobolev embedding theorem on domains without Lipschitz boundary
Roskovec, Tomáš ; Hencl, Stanislav (advisor) ; Honzík, Petr (referee)
We study the Sobolev embeddings theorem and formulate modified theorems on domains with nonlipschitz boundary. The Sobolev embeddings the- orem on a domain with Lipschitz boundary claims f ∈ W1,p ⇒ f ∈ Lp∗ (p) , kde p∗ (p) = np n − p . The function p∗ (p) is continuous and even smooth. We construct a domain with nonlipschitz boundary and function of the optimal embedding i.e. analogy of p∗ (p) is not continous. In the first part, according to [1], we construct the domain with the point of discontinuity for p = n = 2. Though we used known construction of domain, we prove this by using more simple and elegant methods. In the second part of thesis we suggest the way how to generalize this model domain and shift the point of discontinuity to other point than p = n = 2.
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Modelování spotových cen elektrické energie
Šmíd, Vítězslav ; Honzík, Petr (advisor) ; Hencl, Stanislav (referee)
We describe a single-period vector autoregressive model with parameter restrictions and find a consistent estimator of the parameters. We apply several restricted models to electricity prices in two markets. The datasets are comprised of the settlement prices of day-ahead auctions in which market participants bid on next day's electricity deliveries in 24 separate hourly blocks. We therefore model the data as a time series in R^24. To avoid overfitting we crossvalidate all models using sliding windows of training and testing data. We find that simple models perform better because they are more resilient in volatile periods than more comprehensive models. We suggest that model performance could be improved by incorporating exogenous data, such as weather conditions. Powered by TCPDF (www.tcpdf.org)
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Small-Size Microphone Array for Estimation of Direction of Arrival of Sound
Kubišta, Ladislav ; Honzík, Petr (referee) ; Schimmel, Jiří (advisor)
This thesis describe detection of direction receiving sound with small–size microphone array. Work is based on analyzing methods of time delay estimation, energy decay or phase difference signal. Work focus mainly on finding of angle of arrival in small time difference. Results of measuring, as programming sound, so sound recorded in laboratory conditions and real enviroment, are mentioned in conclusion. All calculations were done by platform Matlab
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