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Theoretical description and simulation of polymer network formation
Premus, Jan ; Šomvársky, Ján (advisor) ; Dušek, Karel (referee)
One of methods for description of formation and structure of polymer ne- tworks is used in the work - combination of chemical kinetics and theory of branching processes (TVP) with correlations to neighbors. Main output of this work is computer program, whose purpose is setting up of rooted fragments of given size, differential equations for their concentrations and calculation of se- lected structural parameters using TVP. Gel points for systems formed by three and fourfunctional monomer and combination of two and threefunctional mono- mer were computated in this way. Chemical simulation of molecules was used as reference value. Larger correlation distance (larger size of fragments) led to more accurate results. Calculation of system parameters using TVP allowed study of gel parameters, concentrations of elastically active chains for all studied systems is shown in the work. 1
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The effect of introduction of Cloud Computing: The case of Venture Capital
Šomvársky, Jan ; Mejstřík, Michal (advisor) ; Čech, František (referee)
The thesis aims to examine the impact of introduction of Cloud Computing on Venture Capital (VC) financing in the United States. In the first part we review features of Cloud Computing and their impact on startup costs in context of VC. In this thesis we consider Amazon Web Services (AWS), introduced in 2006, a pioneer of widely accessible Cloud Computing. In the second part we quantify the cost reduction associated with utilization of AWS against owning IT infrastructure. Results show 529 fold decrease in startup costs in 3- month time frame. In the third part we analyze the impact of introduction of AWS on seed and later-stage investments in context of selected macroeconomic and technological factors. We perform analysis on a comprehensive dataset from National Venture Capital Association using Autoregressive Distributed Lag (ARDL) model to account for a change in lagged values of dependent and independent variables. Main finding of our analysis suggests that seed investments are significantly influenced by the introduction of AWS and subsequent drop in startup costs. Specifically, the decline in cost of startup induced 29.67% increase in seed investments. Further findings indicate insignificant relationship between seed investments and macroeconomic factors. Moreover, according to our results,...
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Study of the relaxation into a stochastic limit cycle
Hrubovský, Martin ; Holubec, Viktor (advisor) ; Šomvársky, Ján (referee)
We consider a microscopic two-level system in contact with a heat reservoir. We assume a time-periodic difference between the energies of the two levels. The system dynamics is assumed to be Markovian. From the correspond- ing master equation we calculate the dynamics of such a system in the form of a propagator matrix. Under the assumption of the detailed balance we further calculate the limit cycle probability distribution (which the system will attain after a long time) as an eigenvector of the propagator. We also find a transcen- dental equation for the initial condition that minimizes the entropy production over the first driving period. These two distributions are then expanded in an irreversibility parameter and compared. We discover that up to the first term in the irreversibility parameter (for a slow driving), the Boltzmann equilibrium probability distribution is the average of the limit cycle and entropy minimizing distribution. 1
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Noise-induced transitions in nonlinear dynamics of stochastic systems.
Humplík, Jan ; Chvosta, Petr (advisor) ; Šomvársky, Ján (referee)
In this thesis we focuse on one-dimensional diffusion in a random potential given by the general Markov dichotomous process. It was shown in [5] that this problem is closely related to the study of the stochastic Riccati equation. Using Kolmogorov forward equation we have a solution in the case of a semi-infinite interval. In order to overcome the restriction of a semi- infinite interval we present an approach to solution based on the method of Carleman embedding. We give an expression for the moments in the Laplace domain in terms of an infinite-dimensional matrix element and we try to evaluate it in the limit of infinite time and semi-infinite interval. However we find a discrepancy between our result, numerical simulation and different theoretical approach to the same problem. We also develop Monte Carlo simulations of the Riccati equations and we compare them to analytical results.
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