A system has been implemented which is able to detect symmetrical groupings in edge images. The initial stages of the algorithm consist of edge detection, curve smoothing, and the extension of the perceptual grouping phase of the SCERPO [Low87] vision system to enable detection of instances of endpoint proximity and curvilinearity among curved segments. The symmetry detection stage begins by first locating points along object boundaries which are significant in terms of curvature. These key points are then tested against each other in order to detect locally symmetric pairs. An iterative grouping procedure is then applied which matches these pairs together using a more global definition of symmetry. The end result of this process is a set of pairs of key points along the boundary of an object which are bilaterally symmetric, along with the axis of symmetry for the object or sub-object. This paper describes the implementation of this system and presents several examples of the results obtained using real images. The output of the system is intended for use as indexing features in a model-based object recognition system, such as SCERPO, which requires as input a set of spatial correspondences between image features and model features. / Science, Faculty of / Computer Science, Department of / Graduate

<p>Polarization is important for the function and morphology of many different cell types. The keys regulators of polarity in eukaryotes are the Rho-family GTPases. In the budding yeast Saccharomyces cerevisiae, which must polarize in order to bud and to mate, the master regulator is the highly conserved Rho GTPase, Cdc42. During polarity establishment, active Cdc42 accumulates at a site on the plasma membrane characterizing the “front” of the cell where the bud will emerge. The orientation of polarization is guided by upstream cues that dictate the site of Cdc42 clustering. However, in the absence of upstream cues, yeast can still polarize in a random direction during symmetry breaking. Symmetry breaking suggests cells possess an autocatalytic polarization mechanism that can amplify stochastic fluctuations of polarity proteins through a positive feedback mechanism.</p><p> Two different positive feedback mechanisms have been proposed to polarize Cdc42 in budding yeast. One model posits that Cdc42 activation must be localized to a site at the plasma membrane. Another model posits that Cdc42 delivery must be localized to a particular site at the plasma membrane. Although both mechanisms could work in parallel to polarize Cdc42, it is unclear which mechanism is critical to polarity establishment. We directly tested the predictions of the two positive feedback models using genetics and live microscopy. We found that localized Cdc42 activation is necessary for polarity establishment.</p><p> While this explains how active Cdc42 localizes to a particular site at the plasma membrane, it does not address how Cdc42 concentrates at that site. Several different mechanisms have been proposed to concentrate Cdc42. The GDI can extract Cdc42 from membranes and selective mobilize GDP-Cdc42 in the cytoplasm. It was proposed that selectively mobilizing GDP-Cdc42 in combination with local activation could locally concentrate total Cdc42 at the polarity site. Although the GDI is important for rapid Cdc42 accumulation at the polarity site, it is not essential to Cdc42 concentration. It was proposed that delivery of Cdc42 by actin-mediated vesicle can act as a backup pathway to concentrate Cdc42. However, we found no evidence for an actin-dependent concentrating pathway. Live microscopy experiments reveal that prenylated proteins are not restricted to membranes, and can enter the cytoplasm. We found that the GDI-independent concentrating pathway still requires Cdc42 to exchange between the plasma membrane and the cytoplasm, which is supported by computational modeling. In the absence of the GDI, we found that Cdc42 GAP became essential for polarization. We propose that the GAP limits GTP-Cdc42 leak into the cytoplasm, which would be prohibitive to Cdc42 polarization.</p> / Dissertation

The physical behavior of crystalline solids is very closely related to the internal symmetry of the crystal structure. For this reason it is desirable to represent mathematically this symmetry in such a way that the actual physical problems can be handled as they arise. In the case of this thesis the research has been guided by a list of desired properties for such a representation. No claim is made that the list is complete.

The objective of this thesis is to evaluate the readiness of SADC economies to complete the process of monetary integration in the region and to form a monetary union and adopt a common currency. This is done against the backdrop of optimal currency area (OCA) theory. Given this objective, the study hypothesizes that the majority of SADC economies in the region are potential candidates to bring the proposed monetary union into existence sometime in the future, if not in 2018 as proposed by SADC secretariat. The study uses a mix of different methodologies ranging from developing a conceptual framework to empirical investigation in order to answer the research questions and to test the hypotheses. In addition to theoretical reviews and discussions, four findings emerge as fundamental from the four essays. First, from the Triples test the study has not found significant evidence to reject the null hypothesis of „structural symmetry‟ among ten SADC member countries. 10 out of 15 members (i.e.66.67 percent) have exhibited structural symmetry in their real business cycles over the study period. However, close to 50 percent of the member states have weak cyclical co-movements with a low relative intensity. Taking the experience of the EMU where just five countries are able to create havoc in the entire union, we can safely say that the findings from the combined three tests from the first essay confirm that there is still work that needs to be done to coordinate economic policies in the region to improve real economic integration before entry into the proposed monetary union in 2018. In Essay 2, the study finds that the generalised purchasing power parity (GPPP) hypothesis holds for SADC economies given the stationary panel of RER series with one cointegrating relationship as exhibited by trace statistics and the existence of a long run co-integrating relationship amongst the system of real exchange rates. This implies that there is potential for relative prices to converge in the region in the long run, hence SADC is a potential OCA, based on the criteria of price convergence. However, the slow speed of adjustment towards GPPP long run equilibrium should be a warning for the possible ineffectiveness of policy to defend these countries against external shocks. In Essay 3, the Brock, Dechert, and Scheinkman (BDS) test and Fourier approximation confirm the non linear nature of real exchange series in SADC economies. This finding further supports an OCA in the region comprising those countries included in the study. The findings in this essay further strengthen the findings from the previous two essays that claim that member states could constitute a monetary union in the region at some future date. Lastly, the fourth essay, using a long run dynamic panel model finds that there are common policy variables determining the real exchange rate (RER)/ the real effective exchange rate (REER) series of SADC economies. The RER/REER equilibrium analysis reveals that SADC economies are characterised by persistent misalignment. This calls for further policy coordination and policy harmonisation in the region. By considering findings from all the four essays the study finds that nine SADC countries can potentially constitute SADC-OCA namely; Botswana, Madagascar, Malawi, Mozambique, Seychelles, South Africa, Swaziland, Tanzania and Zambia. Angola and Mauritius disqualified from a SADC-OCA at least for the sample period considered in this study. Lesotho, DRC, and Zimbabwe are not included due to data limitations, otherwise Lesotho could join the qualifying group of countries given long experience with the Common Monetary Area (CMA). To reap benefits SADC economic integration initiatives, it requires realistic time span, political will, common understandings and awareness, commitment and self-disciplined policy actions from member states and their fellow citizens. / Thesis (PhD)--University of Pretoria, 2014. / tm2015 / Economics / PhD / Unrestricted

Mean Field Games (MFG) are the infinite-population analogue of symmetric stochastic differential games with interacting players. By considering a limiting model with a continuum of players, the theory of MFG provides a more tractable representation and can effectively approximate a broad class of perfectly symmetric stochastic dynamic games. This thesis studies games with heterogeneous players, the heterogeneity being expressed either through a type parameter or through asymmetric interactions among players, and aims at understanding under which condition the MFG approximation remains valid for such games and, if it fails, to find a substitute model. In many real-life settings, players do not view themselves as exchangeable and accurate models should incorporate this heterogeneity. We first adapt the MFG paradigm to model more heterogeneous agents by introducing a type parameter in a financial problem that has gained huge interest in the recent years: the competitive Merton problem under relative performance criteria. By deriving a closed-form solution for the finitely many player investment-consumption problem, we show how the risk tolerance and competitivity of the investors influence their optimal strategy in equilibrium. Moreover, this thesis contributes to a very recent line of work bridging MFG theory and network games by studying n-player stochastic dynamic games in which interactions are governed by a graph. For games with perfectly symmetric players, the MFG approximation can be rigorously justified under suitable assumptions for two main reasons: On the one hand, the equilibria of n-player games can be shown to converge to the MFG limit. On the other hand, a solution of the continuum model may be used to construct approximate equilibria for the corresponding n-player model. This thesis extends these results in two cases: first, for games on general graph sequences in the setting of a specific yet rich linear-quadratic model and second, for general games on dense graph sequences. For linear-quadratic games, we show that the MFG is the correct limit only in the dense graph case, i.e., when the degrees diverge in a suitable sense. Even though equilibrium strategies are nonlocal, depending on the behavior of all players, we use a correlation decay estimate to prove a propagation of chaos result in both the dense and sparse regimes, with the sparse case owing to the large distances between typical vertices. We show also that the mean field game solution can be used to construct decentralized approximate equilibria on any sufficiently dense graph sequence. Finally, since graphons have been shown to be the correct limit object for converging dense graph sequences, we develop the theory of graphon-based analogues of MFG. We propose a new formulation of graphon games based on a single typical player's label-state distribution. We show how our notion of graphon equilibrium can be used to construct approximate equilibria for large finite games set on any (weighted, directed) graph which converges in cut norm. The lack of players' exchangeability necessitates a careful definition of approximate equilibrium, allowing heterogeneity among the players' approximation errors, and we show how various regularity properties of the model inputs and underlying graphon lead naturally to different strengths of approximation.

This master thesis is the documented work of the construction process and testing of a three hour laboratory session in mathematics aimed at high school level students. The purpose of the thesis was to create an interesting laboratory session for the science education center ”The House of Science” that could be used as a part of their regular program directed to schools. The thesis explores the possibilities for how one can construct a laboratory session on the topic ”molecular symmetry” as well as the underlying pedagogical theories used to describe learning processes in creative contexts. A model for such a session is proposed, an evaluation is conducted and its results and implications are appropriately discussed. An important review of the mathematical background of symmetries, group theory and linear representations of finite groups was written and can be found in the appendices.

Title: Dynamical symmetry breaking in models with strong Yukawa in- teractions Author: Petr Beneš Department: Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University Supervisor: Ing. Jiří Hošek, DrSc., Department of Theoretical Physics, Nu- clear Physics Institute, Academy of Sciences of the Czech Repub- lic Abstract: The primary aim of the thesis is to explore the possibility of spon- taneous symmetry breaking by strong Yukawa dynamics. Tech- nically, the symmetry is assumed to be broken by formation of symmetry-breaking parts of both the scalar and the fermion prop- agators, rather than by the scalar vacuum expectation values. The idea is first introduced on an example of a toy model with the underlying symmetry being an Abelian one and later applied to a realistic model of electroweak interaction. In addition, the thesis also deals with some more general, model-independent is- sues, applicable not only to the discussed model of strong Yukawa dynamics, but to a wider class of models with dynamical mass generation. First of these issues is the problem of fermion flavor mixing in the presence of fermion self-energies with a general mo- mentum dependence. It is in particular shown how to define the CKM matrix in such models and argued that it can come out in principle...

No description available.

Since Schwarzschild found the first solution of the Einstein’s equations, more than 800 solutions were found. Solutions of Einstein’s equations are classified according to their Lie algebras of isometries and their isotropy subalgebras. Solutions were taken from the USU electronic library of solutions of Einstein’s field equations and the classification used Maple code developed at USU. This classification adds to the data contained in the library of solutions and provides additional tools for addressing the equivalence problem for solutions to the Einstein field equations. In this thesis, homogeneous spacetimes, hypersurface-homogeneous spacetimes, Robinson-Trautman solutions, and some famous black hole solutions have been classified.

Indiana University-Purdue University Indianapolis (IUPUI) / Over the last two decades a new theory has been developed and intensively investigated in quantum physics. The theory stipulates that a non-Hermitian Hamiltonian can also represents a physical system as long as its energy spectra can be purely real in certain regime depending on the parameters of the Hamiltonian. It was demonstrated that the reality of the eigenenergy was conditioned by a certain kind of symmetry embedded in the actual non-Hermitian system. Indeed, such systems have a combined reflection (parity) symmetry (P) and time-reversal symmetry (T), PT-symmetry. The theory opens the door to new features particularly in open systems in which there could be gain and/or loss of particle or energy from and/or to the environment. A key property of the theory is the PT-symmetry breaking transition which occurs at the exceptional point (EP). The exceptional points are special degeneracies characterized by a coalescence of not only the eigenvalues but also of the corresponding eigenvectors of the system; and the coalescence happens when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. In recent years, quantum walks with PT-symmetric non-unitary time evolution have been realized in systems with balanced gain and loss. These systems fall in two categories namely continuous time quantum walks (CTQW) that are characterized by a unitary or non-unitary time evolution Hamiltonian, and discrete-time quantum walks (DTQW) whose dynamic is described by a unitary or non-unitary time evolution operator consisting of a product of shift, coin, and gain-loss operations. In this thesis, we investigate the PT-symmetric phase of CTQW and DTQW in a variety of non-Hermitian lattice systems with both position-dependent and position independent, parity-symmetric tunneling functions in the presence of PT-symmetric impurities located at arbitrary parity-symmetric site on the lattice. Moreover, we explore the topological phase diagram and its novel features in non-Hermitian, homogeneous and non-homogeneous, PT-symmetric DTQW with closed and open boundary conditions. We conduct our study using analytical and numerical approaches that are directly and easily implementable in physical experiments. Among others, we found that, despite their non-unitary evolution, open systems governed by parity-time symmetric Hamiltonian support conserved quantities and that the PT-symmetry breaking threshold depends on the physical structure of the Hamiltonian and its underlying symmetries.