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The purpose of the present study was to examine the perceptual processes associated with gender differences in leadership emergence recognition. Prior research has indicated that females are less likely to be identified as an emerging leader, even when they display identical leadership behaviors as that of their male counterparts. Unlike most of the previous research performed in this area which has obtained only static snapshots of leadership recognition, the present study used a nonlinear dynamic modeling technique, called cusp catastrophe theory. It was predicted that a nonlinear model would account for more variance than a linear model. Furthermore, it was also predicted that participants would be more resistant to recognizing a female as an emerging leader, as compared to a male. This effect was expected to be greater for male participants than female participants. Participants included 19 organizational members, who watched videos of either a male or female emerging as the leader of a four-person group. Participants recorded their perceptions of leadership through a dynamic measure. In accordance with cusp catastrophe theory, results were analyzed using the program GEMCAT II (General Multivariate Methodology for Estimating Catastrophe Models). Contrary to expectations, none of the predictions were supported. It is suggested that this was primarily due to methodological issues, rather than the relevance of cusp catastrophe modeling for leadership perceptions. Recommendations for future work in this area are provided. / Master of Science

Este trabalho propõe um novo modelo de análise musical, em complementação à análise harmônica tradicional, com o estabelecimento de dois atratores - a partir da dilatação da estabilidade harmônica a partir do séc. XVIII e da resolução da dicotomia temática, condições fundamentais para a existência do modelo Sonata - definidos como catástrofe elementar com um fator de controle e dois atratores a partir da Teoria das Catástrofes de René Thom e da simultânea identificação de conflitos formais na análise estrutural, estética e harmônica da Forma Sonata, determinando seu ponto de catástrofe e definindo a mudança total em seu formato, que passa a comunicar uma nova estrutura formal diante da ultrapassagem da curva da descontinuidade. / This project proposes a new model of musical analysis, complementary to the traditional harmonic analysis. The establishment of two attractors issued from the expansion of the 18th centurys harmonic stability and from the thematic resolution of the thematic dichotomy, basic conditions for the Sonata Forms existence is its starting point, which defines an elementary catastrophe with one control factor from the René Thoms Catastrophe Theory. The simultaneous identification of formal conflicts in the structural, aesthetics and harmonic analysis of the Sonata Form is a further condition to determine its degenerate critical point and to define the total change in its format, which is to communicate a new formal structure after passing through its pitchfork bifurcation.

Este trabalho propõe um novo modelo de análise musical, em complementação à análise harmônica tradicional, com o estabelecimento de dois atratores - a partir da dilatação da estabilidade harmônica a partir do séc. XVIII e da resolução da dicotomia temática, condições fundamentais para a existência do modelo Sonata - definidos como catástrofe elementar com um fator de controle e dois atratores a partir da Teoria das Catástrofes de René Thom e da simultânea identificação de conflitos formais na análise estrutural, estética e harmônica da Forma Sonata, determinando seu ponto de catástrofe e definindo a mudança total em seu formato, que passa a comunicar uma nova estrutura formal diante da ultrapassagem da curva da descontinuidade. / This project proposes a new model of musical analysis, complementary to the traditional harmonic analysis. The establishment of two attractors issued from the expansion of the 18th centurys harmonic stability and from the thematic resolution of the thematic dichotomy, basic conditions for the Sonata Forms existence is its starting point, which defines an elementary catastrophe with one control factor from the René Thoms Catastrophe Theory. The simultaneous identification of formal conflicts in the structural, aesthetics and harmonic analysis of the Sonata Form is a further condition to determine its degenerate critical point and to define the total change in its format, which is to communicate a new formal structure after passing through its pitchfork bifurcation.

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Knowledge of motivation factors can assist conductors and music educators at all levels in planning and implementation of musical goals. The purpose of this study was to identify motivational factors to join the choir and maintain membership in the choir as well as the role of stress/anxiety in maintaining choral membership. In addition, the role of musicianship was evaluated in terms of music aptitude and vocal ability. Participants (N=135) from four adult, auditioned community choirs participated in this study. Data was collected using Advanced Measures of Music Audiation, Singing Coach, measure of vocal ability and a questionnaire relating to topics of motivation, retention and stress and anxiety contained within the sub-constructs of Cusp Catastrophe Theory. The results of this study identified aesthetic motivation as the primary construct as to why members elect to join the choir. In direct relationship to this motivation, lack of aesthetic beauty and truth was identified as why members would not retain their membership in the choir. Members did not experience stress and anxiety while learning or performing choral music. However, they did agree that some level of stress is beneficial to singing. In this study, no participant suggested that stress and anxiety related to vocal ability would prevent them from achieving their performance goal. Implications from this research may include determining program literature to be presented that is perceived as having aesthetic qualities which will be beneficial for membership and retention of choir members.

This thesis explores the effects singularities have on stationary and dynamical properties of many-body quantum systems. In papers I and II we find that the ground state suffers a Z2 symmetry breaking phase transition (PT) when a single impurity is added to a Bose-Einstein condensate (BEC) in a double well (bosonic Josephson junction). The PT occurs for a certain value of the BEC-impurity interaction energy, Λc . A result of the PT is the mean-field dynamics undergo chaotic motion in phase space once the symmetry is broken. We determine the critical scaling exponents that characterize the divergence of the correlation length and fidelity susceptibility at the PT, finding that the BEC-impurity system belongs to the same universality class as the Dicke and Lipkin-Meshkov-Glick models (which also describe symmetry breaking PTs in systems of bosons). In paper III we study the dynamics of a generic two-mode quantum field following a quench where one of the terms in the Hamiltonian is flashed on and off. This model is relevant to BECs in double wells as well as other simple many-particle systems found in quantum optics and optomechanics. We find that when plotted in Fock-space plus time, the semiclassical wave function develops prominent cusp-shaped structures after the quench. These structures are singular in the classical limit and we identify them as catastrophes (as described by the Thom-Arnold catastrophe theory) and show that they arise from the coalescence of classical (mean-field) trajectories in a path integral description. Furthermore, close to the cusp the wave function obeys a remarkable set of scaling relations signifying these structures as examples of universality in quantum dynamics. Within the cusp we find a network of vortex-antivortex pairs which are phase singularities caused by interference. When the mean-field Hamiltonian displays a Z2 symmetry breaking PT modelled by the Landau theory of PTs we calculate scaling exponents describing how the separation distance between the members of each pair diverges as the PT is approached. We also find that the cusp becomes infinitely stretched out at the PT due to critical slowing down. In paper IV we investigate in greater detail the morphology of the vortex network found within cusp catastrophes in many-body wave functions following a quench. In contrast to the cusp catastrophes studied so far in the literature, these structures live in Fock space which is fundamentally granular. As such, these cusps represent a new iii type of catastrophe, which we term a ‘quantum catastrophe’. The granularity of Fock space introduces a new length scale, the quantum length lq = N −1 which effectively removes the vortex cores. Nevertheless, a subset of the vortices persist as phase singularities as can be shown by integrating the phase of the wave function around circuits in Fock-space plus time. Whether or not the vortices survive in a quantum catastrophe is governed by the separation of the vortex-antivortex pairs lv ∝ N −3/4 in comparison to lq , i.e. they survive if lv lq . When particle numbers are reached such that lq ≈ lv the vortices annihilate in pairs. / Thesis / Doctor of Philosophy (PhD)

Catastrophe theory (CT) is a relatively new mathematical theory that comprehensively describes a system exhibiting discontinuous behavior when subjected to continuous stimuli. This study tests the theory using capital-market data. The data is a time series of stock returns on firms that filed for Chapter 11 reorganization during 1980-1985. The CT model used is based on a corporate failure model suggested by Francis, Hastings and Fabozzi (1983). The model predicts 1) as the filing date approaches, there will be a structural shift in the underlying stock-return generating process of the filing firm, and 2) firms with lower operating risk will have a smaller jump than firms with higher operating risk, corresponding to their relative positions within the bifurcation set of the catastrophe cusp.

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