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Cellular functions of tail-anchored proteins.
Martincová, Eva ; Zubáčová, Zuzana (referee) ; Doležal, Pavel (advisor)
This work reviews recent studies on the biogenesis of tail-anchored proteins. These proteins form a distinct class of integral membrane proteins which are intensively studied nowadays. Although this class of proteins is defined by the structure and membrane topology, individual proteins do not share any functional similarities. The basic cellular functions, structure and localisation are reviewed there. The work is focused mainly on the unique transport mechanisms and the determination of the target cellular compartments - endomembrane system and mitochondrial outer membrane. A separate part of the work also summarizes existing knowledge about VAP protein family which belongs to the class of tail-anchored proteins and which is conserved across all eukaryotic species. The last chapter presents results and goals of the research of these proteins in the human parasite Giardia intestinalis in the laboratory of organellar biogenesis.
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Non-negative linear operators and their use in econometric and statistic models
Horský, Richard ; Arlt, Josef (advisor) ; Vrabec, Michal (referee) ; Klazar, Martin (referee)
Non-negative operators, in special case non-negative matrices, are an interesting topics for many scientists and scientific teams from the beginning of the 20th century. It is not suprising because there are a lot of applications in different areas of science like economy, statistics, linear programming, computer science and others. We can give as the particular example the theory of the Markov chains in which we deal with non-negative matrices, so called transition matrices. They are of the special form and we called them stochastic matrices. Another example is given by the non-negative operator on spaces of infinite dimension which is employed in the theory of stochastic processes. It is the backward shift operator called the lag operator as well. The non-negativity in these examples is considered as the piecewise non-negativity. Another type of non-negativity is that in the sense of inner products. In the case of matrices we talk about positive-definite or positive-semidefinite matrices. A typical example is the covariance matrix of a random vector or symmetrization of any linear operator, for instance the symmetrization of the difference operator. The terms inverse problem or ill-posed problem have been gaining popularity in modern science since the middle of the last century. The subjects of the first publications in this area were related to quantum scattering theory, geophysics, astronomy and others. Thanks to powerful computers the chances for applications of the theory of inverse and ill-posed problems has extended in almost all fields of science which use mathematical methods. Ill-posed problems bear the feature of instability and there is the need of regularization if we want to get some reasonable solution. A typical example of the regularization is the differencing of stochastic process with the purpose to obtain a stationary process. Another concept of regularization used for solving e.g. integral equations with compact operators consists in application of regularization method as truncated singular value decomposition, Tichonov regularization method or Landweber iteration method. Mathematical tools employed in this work are those of the functional analysis. It is the area of mathematics in which distinct mathematical structures meet each other. They are structures built within different mathematical disciplines as mathematical analysis, topology, theory of sets, algebra (mainly linear algebra) and theory of measure (probability). The functional analysis framework enables us to obtain right formulations of definitions and problems providing the general view on the notions and problems of the theory of stochastic processes.
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Instantons and Unitarily Inequivalent Quantum Vacua
Derco, Roman ; Iorio, Alfredo (advisor) ; Novotný, Jiří (referee)
Title: Instantons and Unitarily Inequivalent Quantum Vacua Author: Roman Derco Department: Institute of Particle and Nuclear Physics Supervisor: doc. Alfredo Iorio, Ph.D., Institute of Particle and Nuclear Physics Abstract: In the presented thesis we investigate the relationship between the topologically distinct instantonic vacua and the unitarily inequivalent vacua of the quantum field theory. We focus on quantum mechanical exam- ples, where instantons appear but the complications due to quantum gauge field theory are absent. A model for quantum dissipation and the theory of one particle escaping from a metastable minimum were compared, what led to some observations. A double well system was build from harmonic oscillators and an interaction term to get closer to the quantum dissipation model, where inequivalent representations are involved. We identified the particularly simple model of a quantum particle constrained on a circle to be the ideal toy model for spotting the relation among unitarily inequivalent vacua and topologically distinct vacua we were seeking for. 1
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Dense sets in products of topological spaces
Bartoš, Adam ; Simon, Petr (advisor) ; Hušek, Miroslav (referee)
A subset of a product space is thin if every two its distinct points are distinct in at least two coordinates. A subset of a product space is very thin if every two its distinct points are distinct in all coordinates. The thesis sum- marizes the basic properties of thin-type dense sets in products of topological spaces. Sufficient and necessary conditions of their existence are given and several examples are shown. The main result of the thesis is a construction showing that under the continuum hypothesis, for every natural n ≥ 1, there exists a countable T3 dense-in-itself space X such that Xn contains an n-thin dense subset, but Xm , n < m < 2n, doesn't. Besides, Xm , n < m < ω, does not contain any (n + 1)-thin dense subset. A weaker form of the theorem is proven under Martin's axiom.
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