This dissertation is dedicated to the rigorous study of discontinuous transitions in star graphs of coupled phase oscillators. A star graph consists of a central node, called hub, connected to peripheral nodes called leaves. We consider the setting where the frequency of the leaves is identical and the hub has a higher frequency when isolated. This captures the effect of positive correlation between the hub high number of connections and its high natural frequency. Hub higher frequency turns out to be the key feature for discontinuity in the transition from incoherent to synchronous behavior. This transition has been observed numerically and explained via a non-rigorous analytical treatment in the thermodynamic limit. Using Möbius group reduction and the theory of persistence of normally hyperbolic invariant manifold, we prove that this transition is indeed discontinuous for a certain set of initial conditions. / Esta dissertação dedica-se em estudar rigorosamente transições descontínuas de osciladores de fase acoplados em grafos estrelas. Um grafo estrela é composto de um nó central, chamado hub, conectado a nós periféricos chamados folhas. Consideramos a situação na qual a frequência das folhas é igual e o hub tem frequência mais elevada, o efeito de correlação positiva entre o grande número de conexões do hub e sua frequência. A elevada frequência do hub resulta por ser o aspecto crucial na descontinuidade da transição do comportamento incoerente para o síncrono. Esta transição foi observada numericamente e estudada por meio de tratamento analítico não rigoroso no limite termodinâmico. Usando técnica de redução a partir do grupo de Möbius e a teoria de variedades invariantes normalmente hiperbólicias, provamos que esta transição é de fato descontínua para certo conjunto de condições iniciais.

Os sistemas de automação se tornam cada vez mais abrangentes e complexos, criando a necessidade de uma estruturação básica durante o seu desenvolvimento de forma a permitir melhor visualização, organização e entendimento destes sistemas. Este trabalho propõe o desenvolvimento de uma metodologia para análise, implementação e verificação da sincronização das bases de tempo dos equipamentos organizados conforme a estruturação hierárquica CIM (Computer Integrated Manufacturing). Esta metodologia é uma ferramenta útil para o desenvolvimento de sistemas de automação integrados e sincronizados. Inicialmente são apresentadas e analisadas as funções, especificações e utilidade da estruturação hierárquica dos sistemas de automação industrial. Os principais componentes de um sistema moderno de automação são apresentados e para cada um dos equipamentos principais é definido o nível a qual este pertence na pirâmide da automação baseada no modelo CIM. Na etapa seguinte é realizado o levantamento e a análise da necessidade de sincronização dos diversos sistemas automatizados e proposta uma metodologia que auxilie na análise e implementação da sincronização das bases de tempos nestes sistemas de automação integrados. No final do trabalho, esta metodologia é aplicada num caso prático para a comprovação da sua validade. / The automation systems are becoming more and more wide-ranging and complex creating the necessity of using some kind of structuring for their development in order to allow better visualization, organization and understanding of these systems. This research proposes the development of a method for analysis, implementation and check of synchronization of the equipments timebases in a hierarchical structuring of CIM (Computer Integrated Manufacturing). This procedure is useful for development of integrated and syncronized automation systems. Initially are presented and analysed the functions, specifications and uses of hierarchical structuring in industrial automation systems. The main components of a modern automation system are presented and for each equipment is defined the level that it belongs in the automation?s piramid based on CIM model. In the next stage are surveyed and analysed the needs of synchronization of automated systems and proposed a helpful method for analysis and implementation of timebases` synchronization in integrated automation systems. At the end of this research, this method is applied in a practical case for its validation.

Foram realizados cinco experimentos com o objetivo de sincronização do estro e indução da ovulação em tempo fixo em éguas. Experimento I: avaliou a eficácia de um novo protocolo hormonal para a sincronização do estro, sendo realizado durante o período transicional em éguas cujo status reprodutivo era desconhecido. Experimento II: foi delineado para determinar o momento ideal para retirada dispositivo intravaginal de progesterona (DIP), sendo o dispositivo retirado no dia 7, 8 ou 9 do protocolo de tratamento hormonal. Experimento III: testou se a eficiência do protocolo é dependente da fase do ciclo estral da égua e definiu o melhor momento para indução da ovulação. Experimentos IV e V: as éguas foram submetidas ao protocolo completo de sincronização da onda folicular e indução da ovulação em diferentes fases do ciclo estral ou com status reprodutivo conhecido. A hipótese testada foi de que a sincronização do estro e indução da ovulação, com o uso do DIP de 1,44g provoca a supressão do crescimento folicular e através da indução da ovulação, com hCG e GnRH, promove a ovulação dentro de 42 ± 6 horas de no mínimo 75% dos animais. Para isso, os efeitos das prostaglandinas e progestágenos foram avaliados quanto à capacidade de sincronizar a onda de crescimento folicular. Um novo tratamento para induzir a ovulação em tempo fixo foi testado com uma combinação de GnRH e hCG em dois momentos estratégicos (D10 e D12) visando maximizar o número de éguas ovuladas. O protocolo com administração de prostaglandina no D0, D6 e D8 juntamente com a colocação do DIP mantido durante 8 dias (D0 ao D7) demonstrou ser eficaz para suprimir a taxa de crescimento folicular em éguas cíclicas. Nas éguas submetidas a este protocolo as ovulações que ocorreram naturalmente se concentraram entre os dias 10 e 13 do tratamento. Foi testada a eficiência da indução da ovulação no D10 e D12. Na maioria dos animais tratados, o folículo pré-ovulatório foi responsivo à combinação de GnRH e hCG promovendo o sucesso da indução da ovulação. A eficiência do protocolo hormonal testado para sincronização do estro e da ovulação foi de 76,73%, sustentando a hipótese deste estudo. Novos estudos devem ser realizados em um maior número de animais para possíveis adequações na terapia hormonal e verificação do resultado em um grande número experimental de animais. / Five experiments were conducted with the objective of estrus synchronization and fixed time ovulation induction in mares. Experiment I: evaluated the efficacy of a new hormonal protocol for estrus synchronization in mares whose reproductive status was unknown during the transitional period. Experiment II: was designed to determine the best time to remove the P4 intravaginal device (PID). The device was removed on day 7, 8 or 9 of the hormonal treatment protocol. Experiment III: tested if protocol efficiency depends on the stage of mares estrus cycle and indicated the best time for hormonal induction of ovulation. Experiments IV and V: mares were submitted to the full protocol of follicular wave synchronization and ovulation induction at different stages of estrus cycle or at known reproductive status. The tested hypothesis was that the estrus synchronization and induction of ovulation, using an PID of 1.44g, causes suppression of follicular growth, and ovulation induction using hCG and GnRH promote ovulation within 42 ± 6 hours of at least 75% of treated animals. The effect of prostaglandin and progestagens at specific times were evaluated for the ability to synchronize follicular wave. A new treatment to induce fixed time ovulation was tested with GnRH and hCG combination in two strategic moments (D10 and D12) to maximize the number of ovulated mares. Administration of prostaglandin at D0, D6 and D8 together with PID maintained for 8 days (D0 to D7) proved to be effective to suppress follicular growth during reproductive period. In mares submitted to this protocol, ovulation occurred naturally and concentrated between D10 and D13. The ovulation induction efficiency was tested at D10 and D12. Most of the animals had preovulatory follicle responsiveness to GnRH and hCG, promoting the success of ovulation induction. The efficiency of the tested synchronization of estrus and ovulation induction protocol was 76.73% and supported the hypothesis of this study. Further studies should be performed on a larger number of animals for possible adjustments in hormonal therapy and verification of the result in a large number of animals.

This dissertation is dedicated to the rigorous study of discontinuous transitions in star graphs of coupled phase oscillators. A star graph consists of a central node, called hub, connected to peripheral nodes called leaves. We consider the setting where the frequency of the leaves is identical and the hub has a higher frequency when isolated. This captures the effect of positive correlation between the hub high number of connections and its high natural frequency. Hub higher frequency turns out to be the key feature for discontinuity in the transition from incoherent to synchronous behavior. This transition has been observed numerically and explained via a non-rigorous analytical treatment in the thermodynamic limit. Using Möbius group reduction and the theory of persistence of normally hyperbolic invariant manifold, we prove that this transition is indeed discontinuous for a certain set of initial conditions. / Esta dissertação dedica-se em estudar rigorosamente transições descontínuas de osciladores de fase acoplados em grafos estrelas. Um grafo estrela é composto de um nó central, chamado hub, conectado a nós periféricos chamados folhas. Consideramos a situação na qual a frequência das folhas é igual e o hub tem frequência mais elevada, o efeito de correlação positiva entre o grande número de conexões do hub e sua frequência. A elevada frequência do hub resulta por ser o aspecto crucial na descontinuidade da transição do comportamento incoerente para o síncrono. Esta transição foi observada numericamente e estudada por meio de tratamento analítico não rigoroso no limite termodinâmico. Usando técnica de redução a partir do grupo de Möbius e a teoria de variedades invariantes normalmente hiperbólicias, provamos que esta transição é de fato descontínua para certo conjunto de condições iniciais.

The most important and most common channels on cell membrane are voltage-gated Na+ and K+ channels. In so-called "excitable cells" like neurons and muscle cells, these channels open or close in response to changes in potential across the membrane in order to accomplish muscle contraction and transmit signals. By controlling the membrane potential, we observe extraordinary inactivation behaviors of the voltage-gated Na+ channels and the voltage-gated delayed rectifier K+ channels, which shows that electric stimulation pulses can temporarily close the Na+ and K+ channels, just as drugs, like tetrodotoxin (TTX) and tetraethylammonium (ETA), do. The Na/K pump is essential for living system and is expressed in virtually all cell membranes. The ionic transport conducted by Na/K pumps creates both an electrical and a chemical gradient across the plasma membrane, which are required for maintaining membrane potentials, cell volume, and secondary active transport of other solutes, etc. We use a pulsed, symmetric, oscillating membrane potential with a frequency close to the mean physiological turnover rate across the cell membrane to synchronize Na/K pump molecules. The pump molecules can work as a group, pumping at a synchronized pace after a long train of pulses. As a result, the pump functions can be significantly increased. After the pump molecules are synchronized, the applied electric-field frequency can gradually increase in order to resynchronize the molecules to a new, higher frequency. Modulating the pump molecules to a higher frequency leads to a significant increase of pump current. Synchronization and modulation of pump molecules can become a new method to study the function of Na/K pump molecules. This method has huge potential applications in clinic medical treatment. After single-fiber-level study, the final project is on organ level, the rat kidney, by using synchronization and modulation of Na/K pump molecules on the proximal tubule membrane. Because Na+ re-absorption is directly related to the function of the Na/K pump, the more active Na/K pumps are, the more Na+ ions can be absorbed, which results in an increased potential inside the renal proximal tubule. This project is the first step of synchronization and modulation applied on the level of an organ.

The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific analysis of each model individually. In this thesis, we propose a potential classification method for time-dependent dynamical systems, namely comparing the possible deformations of the original problem, and identifying dynamical systems which share the same deformation space. The specific model on which this procedure is developed is the Kuramoto model for interacting, disordered oscillators. Studied in the mean-field limit by a variety of methods, its associated synchronization phase transition appears as an appropriate model for cooperative phenomena ranging from coupled Josephson junctions to self-ordering patterns in biological and social systems. We investigate the geometric deformation of the dynamical system into the space of univalent maps of the unit disk, related to the Douady-Earle extension and the Denjoy-Wolff theory, and separately the algebraic deformation into the space of nonlinear sigma models for unitary operators. The results indicate that the Kuramoto model is representative for a large class of non-equilibrium synchronization models, with a rich phase-space diagram.

The rapid evolution of current and upcoming high speed and complex communications networks often necessitates flawless time synchronization among the network nodes in order to guarantee performance. GPS based synchronizers have long been used for synchronizing telecommunications equipment, currently providing an accuracy of up to 10ns. Such high accuracy demands excellent operation from GPS timing receivers. Interference is an important threat to GPS performance. Any degradation in performance, due to the introduction of interference, can cause these receivers to provide a low quality timing solution, or to lose lock with incoming GPS signals altogether. This consideration motivates the study of the performance of GPS timing receivers in the presence of harmful interference. This work is devoted to the theoretical and practical investigations of the effects of RF interference on GPS-based synchronizers and their impacts on communications networks. Contributions made during this work include: a) Identification of the processes and the parameters involved in producing a timing solution which are vulnerable to interference; b) experimentbased confirmation of a hypothesis about the effects of interference on GPS timing receivers; c) identification of the effects of degraded synchronization on the performance of communications networks, especially CDMA and GSM cellular networks, which rely upon GPS based synchronizers; and d) proposal of a method to predict and avoid communications network performance degradation.

Computer vision is concerned with the recovery of useful scene or camera information from a set of images. One classical problem is the estimation of the 3D scene structure depicted in multiple photographs. Such estimation fundamentally requires determining how the cameras are related in space. For a dynamic event recorded by multiple video cameras, finding the temporal relationship between cameras has a similar importance. Estimating such synchrony is key to a further analysis of the dynamic scene components. Existing approaches to synchronisation involve using visual cues common to both videos, and consider a discrete uniform range of synchronisation hypotheses. These prior methods exploit known constraints which hold in the presence of synchrony, from which both a temporal relationship, and an unchanging spatial relationship between the cameras can be recovered. This thesis presents methods that synchronise a pair of independently moving cameras. The spatial configuration of cameras is assumed to be known, and a cost function is developed to measure the quality of synchrony even for accuracies within a fraction of a frame. A Histogram method is developed which changes the approach from a consideration of multiple synchronisation hypotheses, to searching for seemingly synchronous frame pairs independently. Such a strategy has increased efficiency in the case of unknown frame rates. Further savings can be achieved by reducing the sampling rate of the search, by only testing for synchrony across a small subset of frames. Two robust algorithms are devised, using Bayesian inference to adaptively seek the sampling rate that minimises total execution time. These algorithms have a general underlying premise, and should be applicable to a wider class of robust estimation problems. A method is also devised to robustly synchronise two moving cameras when their spatial relationship is unknown. It is assumed that the motion of each camera has been estimated independently, so that these motion estimates are unregistered. The algorithm recovers both a synchronisation estimate, and a 3D transformation that spatially registers the two cameras. / Thesis (Ph.D.) - University of Adelaide, School of Computer Science, 2008

Pour une exploitation technologique possible en ingénierie électromécanique, nous considérons dans cette thèse l'étude dynamique et la synchronisation des dispositifs électromécaniques non-linéaires décrits par le système couplé constitué de l'oscillateur électrique de Duffing couplé magnétiquement et paramètriquement aux oscillateurs mécaniques linéaires en série et en parallèle. L'intérêt porté sur ces dispositifs électromécaniques revêt un caractère technologique indéniable, dû à sa présence dans plusieurs branches de l'ingénierie électromécanique. Nous étudions le comportement de ces dispositifs à travers les études analytique et numérique, et montrons que les phénomènes non-linéaires tels que: les phénomènes de résonances, d'anti-résonances, d'hystérésis et de multi-stabilité, les oscillations sous et super harmoniques, et le chaos peuvent être utilisé pour améliorer les perfectionnements à des taches industrielles. Le problème de synchronisation des états régulier et chaotique de ces dispositifs est aussi d'un grand intérêt pour des applications en ingénierie électromécanique.

<p>All large-scale digital Integrated Circuits need an appropriate strategy for clocking and synchronization. In large-scale and high-speed System-on-Chips (SoC), the traditional"Globally Synchronous"(GS) approach is not longer viable, due to severe wire delays. Instead new solutions as"Globally Synchronous, Locally Asynchronous"(GALS) approaches have been proposed. We propose to replace the GALS approach with a mesochronous clocking principle. In this work, such an approach together with a circuit solution in 0.18mm CMOS process has been presented. This solution allows clocking frequencies up to 4 GHz.</p>