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Mechanical forces in asymmetric cell division
Šabata, Vojtěch ; Macůrková, Marie (advisor) ; Middelkoop, Teije Corneel (referee)
Cell division is one of the most studied topics in the field of cellular and molecular biology. In some cases, cells can exploit diverse mechanisms to alter the basic function of their division machineries to divide asymmetrically. This results in two daughter cells that differ from each other in some manner, which is an essential premise for the development and adult homeostasis of complex multicellular organisms. This work is focused on the division of Caenorhabditis elegans zygote, a classic example of asymmetric division. Using this model system, this work highlights the cellular mechanisms used to generate polarity, with emphasis on the purely mechanical aspects present. In recent years, great progress has been made in describing these fundamental pathways, which are at their core highly conserved from nematodes to humans. Deeper knowledge of processes, that are responsible for a successful cell division in general, can be beneficial for a better understanding of organismal development in health and disease.
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Mechanisms of symmetry breaking during embryogenesis
Ždímalová, Michaela ; Lánský, Zdeněk (advisor) ; Búran, Peter (referee)
Left-right symmetry breaking is crucial for correct body development of many organisms, including humans. The fact that the left-right asymmetry is established consistently in all healthy individuals of given species fascinates researchers for a long time. Although several models offering a mechanistic insight to this phenomenon were proposed or already accepted, they lack a sufficient molecular description or do not explain all cases. A model of acto-myosin flows - intracellular counter-rotating flows driven by an active torque generation in acto-myosin cortex - leading to the left-right symmetry breaking during embryogenesis is a topic of particular interest in current research. This thesis introduces the problematics of acto-myosin flows in a context of the previous research related to the left-right symmetry breaking. Since the left-right asymmetry is tightly associated with chirality at different scales, this thesis also discusses the current knowledge about possible processes of propagating chirality of molecules to the larger scale. 1
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Singular Behavior of the Hartree-Fock Equations
Uhlířová, Tereza ; Zamastil, Jaroslav (advisor) ; Čížek, Martin (referee)
The non-linear Hartree-Fock (HF) equations are usually solved via the iterative self-consistent field method. However, there is no a priori guarantee of convergence, especially in systems with strong electron correlation where symmetry breaking occurs. This work focuses on closed- shell systems in the HF approximation and the (in)stability of the found solutions, and proposes new deterministic methods for the localization of both symmetry-adapted and broken symmetry solutions. We employ a perturbative method and show how one can always obtain a symmetry-adapted solution of the HF equations. We also determine the radius of convergence, related to the existence of at least one bound state, of the perturbative series. Next, we rederive the matrix of stability and adapt it to spin and orbital symmetry. Calculation of higher energy variations follows, first in terms of spin-orbitals and then orbitals. Motivated by the investigation of the structure of a broken-symmetry solution, we propose a new deterministic method for the localization of a broken-symmetry solution. The general expressions are verified by reformulating the stability conditions for simple cases. The proposed methods are successfully applied to helium-, beryllium- and neon-like systems.
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Exploiting Structures in Automated Planning
Kuckir, Ivan ; Barták, Roman (advisor) ; Chrpa, Lukáš (referee)
This thesis focuses on improving the process of automated planing through symmetry breaking. The aim is to describe symmetries, which are often observed by human programmers, but haven't been properly theoretically formalized. After an analysis of available research, there are new definitions of symmetries proposed in context of classical planning, such as state equivalence, T1 automorphisms and more general automorphisms of constants. Several theorems are proved about new symmetries. As a result, an algorithm for detecting a special symmetry class is proposed, together with a method of exploiting such class during planning. Experimens are made to show the effect of symmetry breaking on the performance of the planner. Powered by TCPDF (www.tcpdf.org)
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