Learning is a mechanism intrinsic to all sentient biological systems. Despite the diverse range of paradigms that exist, it appears that an artificial system has yet to be developed that can emulate learning with a comparable degree of accuracy or efficiency to the human brain. With the development of new approaches comes the opportunity to reduce this disparity in performance. A model presented by Janson and Marsden [arXiv:1107.0674 (2011)] (Memory foam model) redefines the critical features that an intelligent system should demonstrate. Rather than focussing on the topological constraints of the rigid neuron structure, the emphasis is placed on the on-line, unsupervised, classification, retention and recognition of stimuli. In contrast to traditional AI approaches, the system s memory is not plagued by spurious attractors or the curse of dimensionality. The ability to continuously learn, whilst simultaneously recognising aspects of a stimuli ensures that this model more closely embodies the operations occurring in the brain than many other AI approaches. Here we consider the pertinent deficiencies of classical artificial learning models before introducing and developing this memory foam self-shaping system. As this model is relatively new, its limitations are not yet apparent. These must be established by testing the model in various complex environments. Here we consider its ability to learn and recognize the RGB colours composing cartoons as observed via a web-camera. The self-shaping vector field of the system is shown to adjust its composition to reflect the distribution of three-dimensional inputs. The model builds a memory of its experiences and is shown to recognize unfamiliar colours by locating the most appropriate class with which to associate a stimuli. In addition, we discuss a method to map a three-dimensional RGB input onto a line spectrum of colours. The corresponding reduction of the models dimensions is shown to dramatically improve computational speed, however, the model is then restricted to a much smaller set of representable colours. This models prototype offers a gradient description of recognition, it is evident that a more complex, non-linear alternative may be used to better characterize the classes of the system. It is postulated that non-linear attractors may be utilized to convey the concept of hierarchy that relates the different classes of the system. We relate the dynamics of the van der Pol oscillator to this plastic self-shaping system, first demonstrating the recognition of stimuli with limit cycle trajectories. The location and frequency of each cycle is dependent on the topology of the systems energy potential. For a one-dimensional stimuli the dynamics are restricted to the cycle, the extension of the model to an N dimensional stimuli is approached via the coupling of N oscillators. Here we study systems of up to three mutually coupled oscillators and relate limit cycles, fixed points and quasi-periodic orbits to the recognition of stimuli.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19475号 / 理博第4135号 / 新制||理||1595(附属図書館) / 32511 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)講師 市川 正敏, 教授 佐々 真一, 教授 山本 潤 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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No description available.

Thesis (PhD (Biochemistry))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: With the recent advances in the field of molecular biology, there is an increased need to integrate data on the various constituents of the cell in kinetic models that can predict and describe cellular behavior. When working towards a description of the entire cell using such kinetic models, the question arises: How do we compare different models for a given biological network? This is the central question addressed in my thesis and I developed and applied mathematical and computational methods for comparing dozens of existing models of erythrocyte and yeast glycolysis. To compare the steady-state behavior in models of erythrocyte glycolysis, I focussed on the function of the pathway, which is to supply the cell with Gibbs-free energy (γ- phosphate of ATP). I used supply-demand analysis in the framework of metabolic control analysis to make this comparison, which revealed that the ATP concentrations were homeostatically buffered at varying supply rates. I also applied this approach to compare steady-state behavior in models of yeast glycolysis, finding that they were not necessarily optimized for homeostatic maintenance of the ATP concentration and that in models for this organism the rate of ATP production is often determined by the supply reactions of glycolysis. In addition, I tested whether a kinetic model can describe novel behavior if it is adjusted to conditions different from those for which the model was originally constructed. More specifically, using a model of steady-state yeast glycolysis, I showed that small adjustments to the original enzyme concentrations are enough to obtain an oscillating model, which shows a remarkable resemblance to the experimentally observed oscillations. Importantly, some of these enzyme concentrations changes are known to occur during the pre-treatment of the cells which is necessary to obtain oscillatory behavior. To the best of my knowledge, the resulting model is the first detailed kinetic model that describes the experimentally observed strong synchronization of glycolytic oscillations in yeast populations. To analyze the dynamic behavior of yeast glycolytic models and to compare different models in terms of dynamics, I introduced a framework used in physics and engineering to create a vector based, two dimensional graphical representation of the oscillating metabolites and reactions of glycolysis. Not only was it possible to make a concise comparison of the set of models, but with the method I could also quantify the contribution of the interactions in the network to the transduction of the oscillations. Furthermore I could distinguish between different mechanisms of oscillation for each of the models, and demonstrated how the framework can be used to create such representations for experimental data sets. / AFRIKAANSE OPSOMMING: Met die onlangse vooruitgang in die veld van molekulere biologie, is daar ?n toenemende behoefte om data rakende die verskeie komponente van die sel in kinetiese modelle te integreer, om sodanig selgedrag te voorspel en te beskryf. As daar gepoog word om ’n beskrywing van die sel as geheel te verkry d.m.v. sulke kinetiese modelle, onstaan die vraag: Hoe vergelyk ons verskillende modelle van ’n gegewe biologiese netwerk? Dit is die sentrale vraag wat my tesis aanspreek en ek het wiskundige en numeriese metodes ontwikkel en toegepas om talle bestaande modelle van gis- en eritrosietglikolise te vergelyk. Om die bestendige-toestand gedrag in modelle van eritrosietglikolise te vergelyk, het ek gefokus op die funksie van die padweg, naamlik om die sel met Gibbs-vrye energie (γ-fosfaat van ATP) te voorsien. Ek het vraag-aanbod analiese in die raamwerk van metaboliese kontrole analiese gebruik om hierdie vergelyking te maak, wat getoon het dat die ATP konsentrasies homeostaties gebuffer was by verskillende aanbod tempos. Ek het ook hierdie aanpak gebruik om die bestendige-toestand gedrag in modelle van gisglikolise te vergelyk, en het bevind dat hulle nie noodwendig geoptimiseer is om ?n homeostatiese balans in die ATP konsentrasie te handhaaf nie, en dat in modelle vir hierdie organisme, die tempo van ATP produksie dikwels bepaal word deur die aanbod reaksies van glikoliese. Ek het verder ook bepaal of so ?n kinetiese model nuwe soorte gedrag kan beskryf, as dit aangepas word aan omstandighede wat verskil van dié waarvoor die model oorspronklik gekonstrueer was. Meer spesifiek, deur ?n model van bestendige-toestand gisglikolise te gebruik, kon ek wys dat klein veranderinge aan die oorspronkline ensiem konsentrasies genoeg was om ?n ossilerende model te verkry, wat opmerklik ooreenstem met die eksperimenteel waargenome ossilasies. Let ook daarop dat sommige van hierdie ensiem konsentrasie veranderinge plaasvind tydens die voorafbehandeling van die selle, wat essensieel is om die ossilasies waar te neem. Tot die beste van my kennis is die model wat ek met hierdie prosedures verkry het, die eerste gedetaileerde kinetiese model wat die eksperimenteel waargenome sterk sinkronisasie in ossilerende gis populasies voorspel. Om gis glikolitiese modelle te vergelyk in terme van hul dinamiese gedrag, het ek ?n raamwerk wat in fisika en ingeneurswese gebruik word, ingespan om ?n vektor-gebasseerde, twee dimensionele grafiese voorstelling van die ossilerende metaboliete en reaksies te maak. Hierdie raamwerk het dit nie net moontlik gemaak om ?n kompakte vergelyking van ?n stel modelle te maak nie, maar ek kon ook die bydrae van interaksies in die netwerk tot transduksie van die ossilasies kwantifiseer. Ek kon verder onderskeid tref tussen die verskillende ossilasiemeganismes vir elk van die modelle, en het ook gedemonstreer hoe die raamwerk gebruik kan word om sulke voorstellings vir eksperimentele datastelle te skep.

Nonlinear limit cycle oscillators are common in nature and man-made equipments, for example, they occur in electronics, robotics, lasers, chemical reactions, biological systems and economical models. Such oscillators demonstrate periodic behavior with fixed frequency and amplitude independently of the system’s initial conditions. The goal of the doctoral thesis is the development and application of phase reduction and averaging methods to analyze particular nonlinear problems in self-oscillatory systems. The phase reduction method allows us to reduce the dynamic of a weakly perturbed limit cycle oscillator to a single scalar equation that defines the dynamics of the phase. This method is usually applied to the systems described by ordinary differential equations. Here this method is extended for the systems with time delay. The phase reduction method is applied to analyze the delayed feedback control (DFC) algorithm. Such an approach allows us to obtain analytical results for slightly mismatched DFC scheme and to stabilize unstable periodic orbits with topological restriction. The averaging method is applied to self-oscillatory systems driven by high-frequency periodic force. The method allows to derive the equations for the slow motion, averaged over high-frequency oscillations. Using this method the mechanism of suppression of sustained neuronal spiking under high frequency electrical stimulation is investigated. / Netiesiniai ribinio ciklo osciliatoriai dažnai sutinkami gamtoje bei žmogaus sukonstruotose sistemose, pavyzdžiui elektronikoje, robototechnikoje, lazeriuose, cheminėse reakcijose, biologinėse sistemose bei ekonominiuose modeliuose. Tokie osciliatoriai vaizduoja periodinį elgesį su fiksuotu dažniu ir amplitude nepriklausomai nuo sistemos pradinių sąlygų. Šios disertacijos tikslas yra išplėtoti ir pritaikyti fazinės redukcijos ir vidurkinimo metodus konkretiems uždaviniams spręsti. Fazinės redukcijos metodas leidžia silpnai perturbuoto ribinio ciklo osciliatoriaus dinamiką redukuoti iki vieno skaliarinio kintamojo dinamikos. Darbe fazinės redukcijos metodas išplėtotas ribinio ciklo osciliatoriams su delsa. Plačiai išnagrinėtas fazinės redukcijos taikymas chaotinėms sistemoms, kurių nestabili periodinė orbita (NPO) yra stabilizuojama uždelstuoju grįžtamuoju ryšiu (UGR). Toks priėjimas leidžia gauti analizinius rezultatus silpnai išderintai URG valdomai sistemai bei stabilizuoti NPO su topologiniu ribojimu. Vidurkinimo metodas leidžia gauti sistemos dinamiką, suvidurkintą per aukšto dažnio periodą, kai sistema yra veikiama aukšto dažnio periodine jėga. Darbe yra išnagrinėtas neuronų savųjų osciliacijų nuslopinimo mechanizmas, stimuliuojant juos aukšto dažnio elektriniu signalu.

Netiesiniai ribinio ciklo osciliatoriai dažnai sutinkami gamtoje bei žmogaus sukonstruotose sistemose, pavyzdžiui elektronikoje, robototechnikoje, lazeriuose, cheminėse reakcijose, biologinėse sistemose bei ekonominiuose modeliuose. Tokie osciliatoriai vaizduoja periodinį elgesį su fiksuotu dažniu ir amplitude nepriklausomai nuo sistemos pradinių sąlygų. Šios disertacijos tikslas yra išplėtoti ir pritaikyti fazinės redukcijos ir vidurkinimo metodus konkretiems uždaviniams spręsti. Fazinės redukcijos metodas leidžia silpnai perturbuoto ribinio ciklo osciliatoriaus dinamiką redukuoti iki vieno skaliarinio kintamojo dinamikos. Darbe fazinės redukcijos metodas išplėtotas ribinio ciklo osciliatoriams su delsa. Plačiai išnagrinėtas fazinės redukcijos taikymas chaotinėms sistemoms, kurių nestabili periodinė orbita (NPO) yra stabilizuojama uždelstuoju grįžtamuoju ryšiu (UGR). Toks priėjimas leidžia gauti analizinius rezultatus silpnai išderintai URG valdomai sistemai bei stabilizuoti NPO su topologiniu ribojimu. Vidurkinimo metodas leidžia gauti sistemos dinamiką, suvidurkintą per aukšto dažnio periodą, kai sistema yra veikiama aukšto dažnio periodine jėga. Darbe yra išnagrinėtas neuronų savųjų osciliacijų nuslopinimo mechanizmas, stimuliuojant juos aukšto dažnio elektriniu signalu. / Nonlinear limit cycle oscillators are common in nature and man-made equipments, for example, they occur in electronics, robotics, lasers, chemical reactions, biological systems and economical models. Such oscillators demonstrate periodic behavior with fixed frequency and amplitude independently of the system’s initial conditions. The goal of the doctoral thesis is the development and application of phase reduction and averaging methods to analyze particular nonlinear problems in self-oscillatory systems. The phase reduction method allows us to reduce the dynamic of a weakly perturbed limit cycle oscillator to a single scalar equation that defines the dynamics of the phase. This method is usually applied to the systems described by ordinary differential equations. Here this method is extended for the systems with time delay. The phase reduction method is applied to analyze the delayed feedback control (DFC) algorithm. Such an approach allows us to obtain analytical results for slightly mismatched DFC scheme and to stabilize unstable periodic orbits with topological restriction. The averaging method is applied to self-oscillatory systems driven by high-frequency periodic force. The method allows to derive the equations for the slow motion, averaged over high-frequency oscillations. Using this method the mechanism of suppression of sustained neuronal spiking under high frequency electrical stimulation is investigated.

A conversão de vibração em energia elétrica tem sido investigada por diversos grupos de pesquisa na última década. A principal motivação é a prospecção de fontes alternativas de energia elétrica para sistemas eletroeletrônicos remotamente operados e com fontes limitadas de energia. Diferentes mecanismos de transdução são investigados na literatura para a coleta de energia, entretanto, o piezelétrico tem se destacado devido à densidade de energia que proporciona e também facilidade de uso. Uma alternativa promissora que começa a ser estudada por alguns grupos de pesquisas é a conversão de energia de oscilações aeroelásticas em energia elétrica. Apesar da natureza destrutiva da maioria dos fenômenos aeroelásticos, eles apresentam um grande potencial para o estudo de novos mecanismos e sistemas para coleta de energia. A conversão piezelétrica de energia a partir de oscilações aeroelásticas lineares tem sido investigada. Entretanto, a geração piezoaeroelástica de energia pode se tornar mais atrativa e prática se realizada a partir sistemas aeroelásticos não lineares. A conversão se daria a partir de oscilações persistentes e com amplitude limitada (oscilações em ciclo limite – LCO) ocorrendo em um amplo intervalo de velocidades de escoamento. Define-se o objetivo deste projeto como a investigação numérica da conversão piezelétrica de energia a partir de oscilações aeroelásticas não lineares. Um modelo por elementos finitos para placa plana com piezocerâmicas é desenvolvido, respeitando-se as hipóteses de uma placa de von Kàrmàn. O carregamento aerodinâmico não estacionário é determinado a partir do método de malha de dipolos e uma aproximação do domínio do tempo obtida a partir da formulação apresentada por Roger. Os resultados eletroaeroelásticos são apresentados para asas com diferentes razões de aspecto investigadas em uma ampla faixa de velocidades e considerando-se diversos valores de resistores no domínio elétrico. / The converting of vibration into usable electrical energy has been investigated by several researches groups in the last decade. The main motivation is the possibility of obtaining alternatives electrical energy sources to power electronic system remotely operated and with limited energy sources. Different transduction mechanism has been presented in the energy harvesting literature. However the piezoelectric has been gained more attention because not only of its power density but also its ease of use. A promissory alternative that is becoming studied is the converting of aeroelastic oscillation into electrical energy. Despite of the destructive nature of unstable aeroelastic phenomena (such as, flutter), they present a great potential to the study of innovative mechanism to harvest energy. Although the piezoelectric energy conversion using linear aeroelastic has been investigated in the literature, the use of non linear aeroelastic system can be more practical and attractive. The non linear aeorelastic harvesting occurs by persistent oscillation and with limited amplitudes (Limited Cycle Oscillation – LCO) and can be performed by considerable velocity interval greater than the linear flutter speed. The objective of this work is to investigate the energy harvesting by non linear aeroelastic oscillation. A finite element model of a thin plate (with piezoceramics) is developed), using the non linear hypothesis of von Karman. The unstable aerodynamic loading is obtained by a doublet-lattice method (DLM) and with its time domain conversion using the Roger approximation. The eletroaeroelastic results are presented for several wings with different aspect ratios, and with different resistance values in the electrical domain. The eletroaeroelastic results of the generator wing are investigated for several airspeed greater than its linear flutter speed.

Os dispositivos robóticos bípedes tem um grande potencial de aplicações tanto comerciais como para pesquisa. Dentre as presentes lacunas existentes que limitam a sua aplicabilidade prática tem um destaque especial a incapacidade de realizar uma marcha estável, robusta, versátil e eficiente no ponto de vista energético. No presente estado da arte, existem três principais estratégias de abordagem para o problema e algumas de suas implementações obtiveram sucesso em satisfazer pelo menos um dos requisitos listados, porém nunca todos eles de forma simultânea. Dentro deste cenário, este trabalho se propôs desenvolver um novo critério de estabilidade para marcha bípede que possibilite marchas versáteis, robustas e eficientes. Inicialmente foi realizada uma avaliação de diversos simuladores de código aberto e o Simbody foi definido como o mais apropriado para ser utilizado no desenvolvimento das simulações dinâmicas realizadas nesta Tese. Uma toolbox de MATLAB para auxiliar nos cálculos cinemáticos e dinâmicos foi desenvolvida em conjunto com um módulo de Inter Process Communication para realizar a comunicação entre o MATLAB e o simulador. Foi realizado um estudo da marcha bípede, implementando e avaliando as estratégias do Zero Moment Point e do Limit CycleWalking. Este estudo resultou numa proposta de controlador não linear comutado para robôs em Ciclo Limite. Na procura de um novo critério de estabilidade foi abordado o estudo da marcha humana. Um procedimento para identificar os mecanismos que controlam a estabilidade da marcha humana é analisar a mesma sob perturbações, como tropeços, ou na ultrapassagem de obstáculos. Na literatura existiam bastantes referências sobre este tema, porém, faltou uma comparação da marcha humana sob diferentes condições de visão com a marcha de robôs que utilizam o ZMP. Foi descoberto que os seres humanos privados de visão têm uma estratégia de ultrapassagem de obstáculos semelhante a um robô com ZMP. A partir do conhecimento adquirido deste estudo é proposto e formulado um novo critério de estabilidade, o Step Viability, inspirado na marcha humana e no conceito de N-Step Capturability. O Step Viability baseia-se na definição de restrições que garantem a viabilidade de realizar passos futuros que garantam a convergência para um ponto fixo em tempo finito. O critério foi implementado utilizando-se uma otimização de trajetória multi-fase. Múltiplos testes foram realizados utilizando-se o modelo Compass Gait com diferentes parâmetros (distribuição de massa, torque máximo disponível), com diferentes inclinações e com vários padrões de marcha desejados (periódico, aumento uniforme e até aleatório não periódico). Adicionalmente o critério foi testado em um modelo de 5 segmentos, sintetizando uma marcha com variação tanto linear quanto aleatória. O critério foi bem-sucedido na geração de uma marcha estável em todos os testes e os resultados foram consistentes. A marcha pode ser sintetizada completamente desacoplada do critério de estabilidade, e o modelo renunciou automaticamente do padrão desenhado em favor da estabilidade. / Bipedal robots present a great potential for both commercial and research applications. However, there are some drawbacks that limit their applicability in the real world. The most prominent is the inability to perform a stable, robust, versatile and efficient gait. There are three main state of the art strategies to approach this problem. However, none of them has been successful in satisfying all the listed requirements simultaneously. In this context, this work conducted a study of bipedal gait, both in humans and robots, in order to implement and evaluate existing stability strategies. As a first step, an evaluation of several open source simulators was performed and Simbody was chosen as the most adequate for the dynamic simulations carried out in this Thesis. A MATLAB toolbox to help in the kinematic and dynamic calculations was developed in conjunction with a module of an Inter Process Communication to perform the communication between MATLAB and the simulator. A bipedal gait study was carried out, implementing and evaluating Zero Moment Point and Limit Cycle Walking strategies. This study resulted in a proposed nonlinear switched controller for Limit Cycle robots. In the search for a new stability criterion, human gait was analyzed. A procedure to identify the mechanisms controlling human gait stability is to analyze gait under disturbances such as stumbling or overcoming obstacles. In the literature, there were many references on this subject, however, there was a lack of comparison of the human gait under different vision conditions with the gait of robots that use the ZMP. It was found that vision-deprived humans have an obstacle crossing strategy similar to robots with ZMP. From the knowledge acquired from this study, it is proposed a novel stability criterion, the Step Viability, inspired on human gait and the N-Step Capturability concept. The Step Viability is based on the definition of constraints that ensure the viability of performing future steps that guarantee convergence to a fixed point in finite time. The criterion was implemented using a multi-phase trajectory optimization. Multiple tests were performed using the Compass Gait model with different parameters (mass distribution, maximum available torque), with different slopes and with several desired gait patterns (periodic, uniform increase and even random non-periodic). Additionally, the criterion was tested in a 5-links model, synthesizing a gait with both linear and random velocity variation. The criterion was successful on generating a stable gait in all the tests and the results presented consistent data. The gait could be designed completely uncoupled from the stability criterion, yet the model automatically renounced to follow the desired pattern in favor of maintaining stability.

Nesta tese estudamos um dos principais problemas na teoria qualitativa das equações diferenciais planares: o problema de determinar a bacia de atração de um ponto de equilíbrio. Damos uma prova rigorosa de que para sistemas lineares por partes de costura com duas zonas no plano, definidas por matrizes Hurwitz o único ponto de equilíbrio na reta de separação é globalmente assintoticamente estável. Por outro lado, provamos que nesta classe de sistemas, podemos ter um ponto de equilíbrio instável na origem quando uma curva poligonal separa as zonas, levando a um resultado contra-intuitivo do comportamento dinâmico de sistemas lineares por partes no plano. Além disso, estudamos os ciclos limites em perturbações suaves por partes de centros Hamiltonianos. Neste cenário, é comum adaptar resultados clássicos de sistemas suaves, como funções de Melnikov, para sistemas não-suaves. No entanto, existe pouca justificativa para este procedimento na literatura. Ao utilizar o método de regularização damos uma prova que suporta o uso de funções de Melnikov diretamente do problema não-suave original. / In this thesis we study one of the main problems in the qualitative theory of planar differential equations: the problem of determining the basin of attraction of an equilibrium point. We give a rigorous proof that for planar sewing piecewise linear systems with two zones, defined by Hurwitz matrices the unique equilibrium point in the separation straight line is globally asymptotically stable. On the other hand, we prove that sewing piecewise linear systems with two zones in the plane, defined by Hurwitz matrices can have one unstable equilibrium point at the origin allowing a broken line to separate the zones, leading to counterintuitive dynamical behaviors of simple piecewise linear systems in the plane. Furthermore, we study limit cycles in piecewise smooth perturbations of Hamiltonians centers. In this setting it is common to adapt classical results for smooth systems, like Melnikov functions, to non-smooth ones. However, there is little justification for this procedure in the literature. By using the regularization method we give a proof that supports the use of Melnikov functions directly from the original non-smooth problem.