If an organism is explicitly taught an A->B association, then might it also spontaneously learn the symmetrical B->A association? There is only a small amount of evidence that attests to the detection of emergent symmetry in nonhuman animals (e.g., one chimpanzee and two pigeons). This report examines the necessary and sufficient conditions for finding emergent symmetry in pigeons while attempting to control for the problems of spatial and temporal location found in previous symmetry and stimulus equivalence experiments. Using a successive go/no go matching-to-sample procedure, which showed all of the training and testing stimuli in one location, four experimental manipulations were examined. In Experiment 1 temporal location was controlled without the inclusion of identity matching intermixed with arbitrary matching; Experiment 2 contained identity matching with stimuli different from arbitrary matching; in Experiment 3 identity matching was trained to criterion and then intermixed with arbitrary matching; and in Experiment 4 two sets of arbitrary matching were trained (e.g., AB and CD) but only one of those stimulus sets was trained in identity matching (e.g., AB). No evidence of emergent symmetry was found in Experiments 1 and 2. In Experiment 3, two pigeons showed moderate evidence of emergent symmetry, one pigeon showed suggestive evidence of emergent symmetry, and one pigeon did not show any evidence of emergent symmetry. In Experiment 4, two pigeons showed moderate evidence of emergent symmetry with the AB Stimulus Set (one of those pigeons also showed suggestive evidence of emergent symmetry with the CD Stimulus Set) and one pigeon did not show any evidence of emergent symmetry with either stimulus set. These data suggest that intermixing identity matching with the same stimuli used in arbitrary matching is a necessary, but not sufficient condition to obtaining emergent symmetry in pigeons.

Quantum Chromodynamics (QCD) is believed to be the theory of strong interactions. At high energies, it has been successfully applied to explain the interactions in accelerators. At these energies, the method used to do the calculations is perturbation theory. But at low energies, since the strong coupling constant becomes large, perturbation theory is no longer applicable. Hence, one needs non-perturbative approaches. Some of these approaches are based on the fundamental QCD Lagrangian, such as the QCD sum rules or lattice calculations. Some others use an effective theory approach to relate experimental observables one to the other. Chiral Perturbation Theory (ChPT) is one of these approaches. In this thesis, we make a review of chiral perturbation theory and its applications to study the mixing phenomenon between the neutral pseudoscalar mesons eta and eta-prime.

Facial symmetry has been a central component in many studies on face perception. The relationship between bilateral symmetry and subjective judgments on faces is still arguable in the literature. In this study, a database of natural looking face images with different levels of symmetry is constructed using several digital preprocessing and morphing methods. Our aim is to investigate the correlations between quantified asymmetry, perceived symmetry and a subjective judgment: &lsquo / attractiveness&rsquo / . Images in the METU-Face Database are built to represent three levels of symmetry (original, intermediate, and symmetrical) within five classes which also represent the orientation of bilateral symmetry: left versus right. In addition, the asymmetry of original images is quantified using a landmark-based method. Based on the theory of holistic face perception, we introduce a novel method to quantify facial asymmetry wholesomely: Entropybased quantification. In Experiment 1 and 2, images were rated on attractiveness judgments and on perceived symmetry, respectively. Results indicate that landmark-based quantifications were not sufficient to account for perceived symmetry ratings (SRs), but they revealed that as the vertical deviation of the symmetry decreases, attractiveness rating (AR) collected from that face increases. Moreover, morphing classes and their relationship to both ARs and SRs were highly correlated. Consistent with the previously done research, symmetrical images were found more attractive. We found that although ARs were the same for left versus right composites, for SRs, there is a significant difference between left and right. Finally, a more elucidative quantification approach for subjective face perception is achieved through significant correlations of entropy scores with both ARs and SRs.

Many studies of the Archaic Greek kore focus exclusively on stylistic considerations in an attempt to date these statues more and more accurately. Other studies propose various meanings for the kore. Each of these approaches can be extremely subjective, with the result that the large body of extant literature about the kore tends to be repetitive and argumentative in nature, and, with several exceptions, does not advance the understanding of the kore to any appreciable degree past where it had developed by the 1980s. I use a different, more empirical methodology to study a small group of korai, found in the 1880s near the Erechtheion on the Athenian Akropolis. Symmetry analysis of the patterns painted onto these korai at the time of their creation reveals both consistency of pattern use through the period of seventy years between c560 BCE and c490 BCE, as well as some anomalous patterns. I tabulate the various patterns, as well as their frequency of occurrence, and briefly speculate that there is a correlation between the pattern consistencies and anomalies and events in the known historical record, such as the mid-6th century rule by the Peisistratids and the democratic reforms of Kleisthenes. I also propose other directions in which the study of the kore could be taken using symmetry analysis. / Thesis (Master, Classics) -- Queen's University, 2008-01-31 13:25:56.567

Orientador: Claudemir Murari / Banca: Marcelo José Saia / Banca: Miriam Godoy Penteado / Resumo: Este trabalho teve o objetivo de produzir um conjunto de atividades para analisar como o uso do caleidoscópio associado ao estudo dos ornamentos planos pode contribuir no ensino de grupos de simetria e transformações geométricas em um curso de graduação em Matemática. Esta pesquisa tem caráter qualitativo e foi desenvolvida segundo a proposta metodológica de Romberg. Elaborou-se uma proposta de ensino baseada na metodologia de Resolução de Problemas que foi aplicada a um grupo de professores (alguns em fase de formação) de matemática. As atividades tiveram a finalidade de fazer com que os alunos usassem o caleidoscópio para reproduzir ornamentos planos e, a partir de então, discutissem, com base em argumentos geométricos e algébricos, quais as possibilidades (e impossibilidades) que esse instrumento oferece para obtenção desses ornamentos e suas respectivas justificativas. A coleta de dados ocorreu, essencialmente, por observação participante em sala de aula por meio do uso de questionários, anotações e registros fotográficos. Após a coleta de dados, foi feita uma análise das possibilidades e limitações do material desenvolvido para o ensino de grupos de simetria e transformações geométricas, bem como o uso do caleidoscópio enquanto recurso didático / Abstract: The purpose of this work was to develop a set of activities to analyze how the use of kaleidoscope associated to the study of ornaments can contribute to the teaching of symmetry groups and geometric transformations on a undergraduate course in Mathematics. This is a qualitative research and it was developed according to the methodological proposal of Romberg. A teaching proposal was drafted and was applied to a group of mathematics teachers. Activities were designed following the methodology of problem-solving and intended to make students to use the kaleidoscope to reproduce some ornaments and thereafter, discuss, based on geometric and algebraic arguments, the possibilities and impossibilities that this tool provides to obtain ornaments and their respective justifications. Data collection occurred primarily by participant observation in the classroom through the use of questionnaires, notes and photographic records. After the end of the course a viability analysis of the activities was done (possibilities and limitations) for teaching symmetry groups and geometric transformations as well as the use of Kaleidoscope as a didactic tool / Mestre

Neste trabalho estudamos três diferentes aspectos envolvendo a supersimetria no contexto da teoria de campos em $(2+1)$ dimensões do espaço-tempo. Consideramos primeiramente a possibilidade da quebra dinâmica de supersimetria no modelo de Wess-Zumino, calculando o potencial efetivo até a aproximação de dois laços. Verificamos que o estado de vácuo permanece supersimétrico e que indução de massa e a correspondente quebra de simetria discreta não são perturbativamente consistentes. Em seguida, voltamos nossa atenção para a análise das identidades de Slavnov-Taylor na eletrodinâmica não comutativa supersimétrica. A transversalidade da polarização do vácuo é verificada explicitamente na aproximação de um laço e com a conclusão de que nenhuma anomalia é introduzida pela não comutatividade ou pelo esquema de regularização adotado no formalismo de supercampos. Por fim, o comportamento ultravioleta para a teoria de Yang-Mills-Chern-Simons supersimétrica acoplada minimamente com supercampos de matéria é investigado. Verificamos que o modelo é superenormalizável e que os termos divergentes persistem somente nas funções 1PI de dois pontos para o supercampo de calibre até a ordem de dois laços. / In this work we study three different aspects involving supersymmetry in the context of quantum field theory in $(2+1)$ space-time dimensions. We consider first the possibility of dynamical supersymmetry breaking in the Wess-Zumino model, calculating the effective potential up to two loops. We found that the vacuum state remains supersymmetric and the dynamical generation of mass together with the discrete symmetry breaking are not perturbatively consistent. Next, we turn our attention to the analysis of the Slavnov-Taylor identities in the noncommutative supersymmetric electrodynamics. The transversality of the vacuum polarization is verified explicitly in the one loop approximation with the conclusion that no anomaly is introduced by the noncommutativity or the regularization scheme adopted in the superfields formalism. Finally, the ultraviolet behavior for supersymmetric Yang-Mills-Chern-Simons theory minimally coupled to matter superfields is investigated. We verify that the model is superenormalizable and that the divergent terms persist only in the gauge superfield self-energy diagrams up to two-loop.

Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22233号 / 理博第4547号 / 新制||理||1653(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 河合 俊哉, 教授 大槻 知忠, 教授 入谷 寛 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Indiana University-Purdue University Indianapolis (IUPUI) / This research investigates characteristics of PT (parity-time) symmetry breaking in a system of two optically-coupled, time-delayed semiconductor lasers. A theoretical rate equation model for the lasers' electric fields is presented and then reduced to a 2x2 Hamiltonian model, which, in the absence of time-delay, is PT-symmetric. The important parameters we control are the temporal separation of the lasers, the frequency detuning, and the coupling strength. The detuning is experimentally controlled by varying the lasers' temperatures, and intensity vs. detuning behavior are examined, specifically how the PT-transition and the period and amplitude of sideband intensity oscillations change with coupling and delay. Experiments are compared to analytic predictions and numerical results, and all are found to be in good agreement. Eigenvalues, eigenvectors, and exceptional points of the reduced Hamiltonian model are numerically and analytically investigated, specifically how nonzero delay affects existing exceptional points.

Title: Algebraic Approaches to Elementary Excitations in Media with Broken Spatial or Time-reversal Symmetry Author: Kay Condie Erb Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: Ing. Jiří Hlinka, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Structural phase transitions with macroscopic symmetry breaking can be divided into 212 non-magnetic species according to the mutual spatial orien- tation of the point groups of both phases. Classification into the given species implies a set of universal transition properties such as the number of macroscopic domain states of the low-symmetry phase and their distinguishability by order parameter. In this work, the distinguishability of macroscopic domain states by all order pa- rameters which transform as vectors or vectorlike quantities (called bidirectors) was studied. For solving this task, a computer algorithm was designed which enabled an explicit listing of all vector and vectorlike order parameters, not only for the 212 non-magnetic species, but even for all 1602 magnetic species which includes transitions between crystallographic gray and bicolor point groups. In addition, irreducible representations of the 122 magnetic crystallographic point groups which transform as vectors or vectorlike quantities are...