Tesi: "Self-organized criticality"

1

Hasty, Jeff. "A renormalization group study of self-organized criticality." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/29887.

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Neuß, Marius [Verfasser]. "Stochastic partial differential equations arising in self-organized criticality / Marius Neuß." Bielefeld : Universitätsbibliothek Bielefeld, 2021. http://d-nb.info/1231994762/34.

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Харченко, Дмитро Олегович, Дмитрий Олегович Харченко, Dmytro Olehovych Kharchenko, and I. R. Vernyhora. "Simulation of self-organized criticality within the framework of sandpile model." Thesis, Видавництво СумДУ, 2005. http://essuir.sumdu.edu.ua/handle/123456789/17177.

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4

Marsili, Matteo. "From Interface Growth to Dynamics in Disordered Media and Self Organized Criticality." Doctoral thesis, SISSA, 1994. http://hdl.handle.net/20.500.11767/4536.

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5

Warren, Keith Leverett. "Scaling, self-organized criticality and trend persistence in state psychiatric hospital admissions and discharges /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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6

Westrin, Pontus. "External Conditions Effects on the Self-Organised Criticality of the Calving Glacier Front of Tunabreen, Svalbard." Thesis, Uppsala universitet, Institutionen för geovetenskaper, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-255867.

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Mass balance processes in glaciers are important for determining the growth or retreat of ice. Calving, the mechanical breakage of ice bergs from a glacier front, is a poorly understood phenomenon. This process has great importance to the mass balance of many glaciers, for example on Antarctica and in the Arctic. A recent paper by Åström et al. (2014) compare calving fronts to Self-Organized Critical (SOC) systems, especially the Abelian sand pile model, meaning that the calving front will stay at a critical state at all times. Fluctuations in external conditions will cause the glacier front to either retreat or advance. The calving frequency and size distribution of Tunabreen, a tidewater glacier in Svalbard, was studied during August and September, 2014, with the use of a time-lapse camera set up in front of the calving front. An 11-day period is studied in detail and compared to certain external factors, i.e. tide, air temperature, humidity, atmospheric pressure, wind speed and wind direction. The results are also compared to the relationships found by Åström et al. (2014). The results vary: tide relationships are found as the amplitude reaches above 1 meter, but seize to correlate as the tide falls off. Temperature trends are found for certain periods, but are of low credibility. Humidity, atmospheric pressure, wind speed and wind direction show low to no correlation with the calving size distribution. Fragment size distribution and calving rates show good correlation with the results from Åström et al. (2014). This helps to confirm the theory of SOC applied to calving fronts. Time-lapse photography is deemed as a good way to observe calving fronts, but have certain problems which are mostly related to the weather. Longer time periods would be needed to find better long term relationships between external conditions and calving frequencies, but data is hard to acquire and time consuming to process. The theory of SOC applied to calving fronts is promising and opens up new discussions for the research community. Massbalansprocesser för glaciärer är viktiga för att bestämma om isen drar sig tillbaka eller avancerar. Den mekaniska brytningen av isberg från glaciärer kallas kalvning. Kalvning är väldigt viktig för ett flertal glaciärers massbalans, exempelvis för landisen på Antarktis och glaciärer i Arktis. Ny forskning visar att kalvande glaciärfronter alltid försöker befinna sig i ett kritiskt läge, liknande ett så kallat Self-Organized Critical (SOC) system. Detta kan liknas vid hur en sandhög försöker befinna sig vid sin kritiska sluttningsvinkel när ett konstant flöde av sandkorn adderas. Adderandet av sandkorn kan jämföras med hur externa förhållanden, så som temperatur och tidvatten, ändras. När dessa värden ändras med tid så kommer fronten kalva, mycket likt hur sandhögen rasar när sandkorn tillförs. Externa förhållanden kommer alltså styra om glaciären kalvar eller inte, och när.En time-lapse-kamera installerades framför Tunabreen, en tidvatten glaciär på Svalbard, under Augusti-September, 2014. Bilderna över Tunabreens kalvningsfront, som varade över en 11-dagars period, användes för att ta ut varje enskild kalvingshändelse. Denna data jämfördes sedan med tidvatten, temperatur, luftfuktighet, atmosfäriskt tryck, vindhastighet och vindriktning. Resultaten jämfördes även med de förhållanden som visades i den nya studien som beskrevs tidigare.Resultaten är blandade. När tidvattnets amplitud var större än 1 meter så följer kalvningen tidvattnets mönster, men detta avtar när amplituden är mindre. Temperaturen visar viss korrelation, men endast för kortare perioder. Då temperaturens förhållande till kalvningen inte följer under de högsta och lägsta värden som fanns så bedöms temperaturen ha låg trovärdighet som kontrollerande faktor. Luftfuktighet, atmosfäriskt tryck, vindhastighet och vindriktning visar låg, till ingen, korrelation med kalvning. Storleksfördelningen av fragment och kalvningshastigheten har god korrelation med forskningen kring SOC, resultaten hjälper till att bekräfta denna teori. Time-lapse-fotografi bedöms som en bra metod för att observera kalvningsfronter, men har ett flertal problem som relaterar till det lokala vädret.Längre tidsperioder behövs för att bedöma om förhållanden stämmer på lång sikt. Data är svår att förvärva och tidskrävande att behandla. SOC stämmer bra in på kalvningsfronter vilket öppnar upp nya diskussioner inom forskningsvärlden.

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Mahmoodi, Korosh. "Emergence of Cooperation and Homeodynamics as a Result of Self Organized Temporal Criticality: From Biology to Physics." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1248467/.

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This dissertation is an attempt at establishing a bridge between biology and physics leading naturally from the field of phase transitions in physics to the cooperative nature of living systems. We show that this aim can be realized by supplementing the current field of evolutionary game theory with a new form of self-organized temporal criticality. In the case of ordinary criticality, the units of a system choosing either cooperation or defection under the influence of the choices done by their nearest neighbors, undergo a significant change of behavior when the intensity of social influence has a critical value. At criticality, the behavior of the individual units is correlated with that of all other units, in addition to the behavior of the nearest neighbors. The spontaneous transition to criticality of this work is realized as follows: the units change their behavior (defection or cooperation) under the social influence of their nearest neighbors and update the intensity of their social influence spontaneously by the feedback they get from the payoffs of the game (environment). If units, which are selfish, get higher benefit with respect to their previous play, they increase their interest to interact with other units and vice versa. Doing this, the behavior of single units and the whole system spontaneously evolve towards criticality, thereby realizing a global behavior favoring cooperation. In the case when the interacting units are oscillators with their own periodicity, homeodynamics concerns, the individual payoff is the synchronization with the nearest neighbors (i.e., lowering the energy of the system), the spontaneous transition to criticality generates fluctuations characterized by the joint action of periodicity and crucial events of the same kind as those revealed by the current analysis of the dynamics of the brain. This result is expected to explain the efficiency of enzyme catalyzers, on the basis of a new non-equilibrium statistical physics. We argue that the results obtained apply to sociological and psychological systems as well as to elementary biological systems.

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Costa, Ariadne de Andrade. "Quasi-criticalidade auto-organizada em avalanches neuronais." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/59/59135/tde-17112011-204509/.

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Experimentos têm revelado que redes de neurônios, tanto in vitro como in vivo, mantêm atividade descrita por avalanches e se organizam em um estado crítico no qual essas avalanches são distribuídas de acordo com leis de potência. Mostramos no presente trabalho que um modelo de rede de elementos excitáveis com sinapses dinâ- micas é capaz de exibir criticalidade auto-organizada para ampla região do espaço de parâmetros. Nossos resultados estão de acordo com outros estudos que indicam que a depressão sináptica de curto prazo constitui mecanismo suciente para produzir criticalidade em avalanches neuronais. No entanto, segundo diversos pesquisadores, embora o ajuste de parâmetros seja grosso para que haja criticalidade no modelo, é mais preciso dizer que o sistema não apresenta criticalidade auto-organizada genu ína, mas sim quasi-criticalidade auto-organizada, como os demais modelos não conservativos presentes na literatura. Experiments have shown that neuronal networks, both in vitro and in vivo, maintain activity described by avalanches and they are organized into a critical state in which these avalanches are distributed according to power laws. We have demonstrated that a model based on a network of excitable elements with dynamical synapses is able to exhibit self-organized criticality for a wide range of the parameter\'s space. Our results are consistent with other studies that suggest short-term synaptic depression is enough to produce criticality in neuronal avalanches. However, according to several researchers, in spite of the tuning to be gross to ensure that there is criticality in the model, it is more accurate do not say that the system presents genuine self-organized criticality, but self-organized quasi-criticality as the other non-conservative models in the literature.

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9

Wu, Jingwei. "Open Source Software Evolution and Its Dynamics." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/1095.

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This thesis undertakes an empirical study of software evolution by analyzing open source software (OSS) systems. The main purpose is to aid in understanding OSS evolution. The work centers on collecting large quantities of structural data cost-effectively and analyzing such data to understand software evolution dynamics (the mechanisms and causes of change or growth). We propose a multipurpose systematic approach to extracting program facts (e. g. , function calls). This approach is supported by a suite of C and C++ program extractors, which cover different steps in the program build process and handle both source and binary code. We present several heuristics to link facts extracted from individual files into a combined system model of reasonable accuracy. We extract historical sequences of system models to aid software evolution analysis. We propose that software evolution can be viewed as Punctuated Equilibrium (i. e. , long periods of small changes interrupted occasionally by large avalanche changes). We develop two approaches to study such dynamical behavior. One approach uses the evolution spectrograph to visualize file level changes to the implemented system structure. The other approach relies on automated software clustering techniques to recover system design changes. We discuss lessons learned from using these approaches. We present a new perspective on software evolution dynamics. From this perspective, an evolving software system responds to external events (e. g. , new functional requirements) according to Self-Organized Criticality (SOC). The SOC dynamics is characterized by the following: (1) the probability distribution of change sizes is a power law; and (2) the time series of change exhibits long range correlations with power law behavior. We present empirical evidence that SOC occurs in open source software systems.

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10

Russo, Elena Tea. "Fluctuation properties in random walks on networks and simple integrate and fire models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9565/.

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In questa tesi si è studiato l’insorgere di eventi critici in un semplice modello neurale del tipo Integrate and Fire, basato su processi dinamici stocastici markoviani definiti su una rete. Il segnale neurale elettrico è stato modellato da un flusso di particelle. Si è concentrata l’attenzione sulla fase transiente del sistema, cercando di identificare fenomeni simili alla sincronizzazione neurale, la quale può essere considerata un evento critico. Sono state studiate reti particolarmente semplici, trovando che il modello proposto ha la capacità di produrre effetti "a cascata" nell’attività neurale, dovuti a Self Organized Criticality (auto organizzazione del sistema in stati instabili); questi effetti non vengono invece osservati in Random Walks sulle stesse reti. Si è visto che un piccolo stimolo random è capace di generare nell’attività della rete delle fluttuazioni notevoli, in particolar modo se il sistema si trova in una fase al limite dell’equilibrio. I picchi di attività così rilevati sono stati interpretati come valanghe di segnale neurale, fenomeno riconducibile alla sincronizzazione.

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Shimo, Helder Ken. "Auto-organização da população em sistemas imunológicos artificiais aplicada ao docking de proteínas." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/95/95131/tde-30082012-161501/.

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Vários problemas do mundo real podem ser analisados como problemas de otimização. Na bioinformática, em especial, como exemplos podem ser citados o alinhamento múltiplo de sequências, a filogenia, a predição de estruturas de proteínas e RNA, entre outros. As Meta-heurísticas Populacionais (MhP) são técnicas baseadas em interações de conjuntos de soluções candidatas, como elementos de uma população, utilizadas na otimização de funções. Seu uso é especialmente interessante na otimização de problemas onde há conhecimento parcial ou nenhum do espaço de busca. O objetivo deste trabalho é investigar o uso de auto-organização da população de um sistema imunológico artificial (AIS) a fim de aplicá-lo no problema de docking, que pode ser visto como um problema de otimização multimodal complexo. O AIS é um tipo de MhP inspirado na microevolução do sistema imunológico adaptativo de organismos complexos. Neste, as soluções candidatas representam células do sistema imunológico que busca se adaptar para a eliminação de um patógeno. O desenvolvimento do algoritmo foi baseado no opt-aiNet, que utiliza dos princípios das teorias de seleção clonal e maturação de afinidade para realizar a otimização de funções. Adicionalmente, o opt-aiNet, inspirado na teoria de redes imunológicas, realiza uma etapa de supressão, que busca eliminar soluções semelhantes, aumentando assim a diversidade populacional. Esta etapa é computacionalmente custosa, dado que é feito o cálculo da distância entre todos os possíveis pares de células (soluções) afim de eliminar aquelas próximas de acordo com um dado critério. A proposta deste trabalho é o desenvolvimento de um algoritmo de supressão auto-organizável, inspirado no fenômeno da criticalidade auto-organizada, buscando diminuir a influência da seleção de parâmetros e a complexidade da etapa de supressão. O algoritmo proposto foi testado em um conjunto de funções contínuas conhecidas e comumente utilizadas pela comunidade de computação evolutiva. Os resultados obtidos foram comparados com aqueles de uma implementação do opt-aiNet. Em adição, foi proposta a utilização de operadores de mutação com distribuição q-gaussiana nos AISs desenvolvidos. O algoritmo foi também aplicado no problema de docking rígido baseado em complementaridade de superfícies e minimização de colisões, especificamente no docking de proteínas. Os resultados foram comparados com aqueles de um algoritmo genético, resultando em um melhor desempenho obtido pelo algoritmo proposto. Many real world problems can be described as optimization problems. In bioinformatics in special, there is multiple sequence alignment, filogeny and RNA and Protein structure prediction, among others. Population based metaheuristics are techniques based in the interaction of a set of candidate solutions as elements of a population. Its use is specially interesting in optimization problems where there is little or no knowledge of the search space. The objective of this work is to study the use of self-organization of population in an artificial imune system for use in the docking problem, considered a complex multimodal optimization problem. The artificial imunme system is a type of population based methaheuristics inspired in the microevolution of the adaptive immune system of complex organisms. Candidate solutions represent cells of the immune system adapting its antibodies to eliminate a pathogen. The development of the algorithm was based in the opt-aiNet, based in the principles of clonal selection and affinity maturation for function optimization. Additionally, the opt-aiNet, inspired in theories of immune network, makes a suppression stage to eliminate similiar solutions and control diversity. This stage is computationally expensive as it calculates the distance between every possible pair of cells (solutions) eliminating those closer than a threshold. This work proposes a self-organized suppression algorithm inspired in the self-organized criticality, looking to minimize the influence of parameter selection and complexity of the suppression stage in opt-aiNet. The proposed algorithm was tested in a set of well-known functions in the evolutionary computation community. The results were compared to those of an implementation of the opt-aiNet. In addition, we proposed a mutation operator with q-Gaussian distribution for the artificial immune systems. The algorithm was then applied in the rigid protein docking problem based in surface complementarity and colision avoidance. The results were compared with a genetic algorithm and achieved a better performance.

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Castillo, Guevara Ramon D. "Coordination of Local and Global Features: Fractal Patterns in a Categorization Task." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321372828.

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Pinheiro, Neto João 1989. "A study on the structure and dynamics of complex networks." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276962.

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Orientadores: José Antônio Brum, Marcus Aloizio Martinez de Aguiar Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin Made available in DSpace on 2018-08-26T08:49:23Z (GMT). No. of bitstreams: 1 PinheiroNeto_Joao_M.pdf: 16027257 bytes, checksum: ff0a08fdba027bd6f2bc28198e34d482 (MD5) Previous issue date: 2014 Resumo: Nesta dissertação de mestrado estudamos a dinâmica e estrutura de redes complexas. Começamos com uma revisão da literatura de redes complexas, apresentando as métricas de rede e modelos de conectividade mais comuns. Estudamos então em detalhe a dinâmica do modelo das Random Threshold Networks (RTN). Desenvolvemos uma nova aproximação de campo médio para a dinâmica de RTNs, consideravelmente mais simples que aproximações anteriores. Esta nova aproximação é útil de um ponto de vista prático, pois permite a geração de RTNs onde a atividade média da rede é controlável. Fazemos então uma revisão da literatura de redes adaptativas, apresentando alguns modelos de redes adaptativas com características interessantes. Por fim, desenvolvemos dois modelos de redes adaptativas inspirados pela evolução da estrutura neuronal no cérebro. O primeiro modelo utiliza regras simples e uma evolução baseada na remoção de links para controlar a atividade sobre a rede. A inspiração é a remoção de neurônios e conexões neuronais após a infância. Este modelo também consegue controlar a atividade de grupos individuais dentro de uma mesma rede. Exploramos uma variante deste modelo em um espaço bidimensional, onde conseguimos gerar redes modulares e small-world. O segundo modelo utiliza inputs externos para controlar a evolução da topologia da rede. A inspiração neste caso é o desenvolvimento das conexões neuronais durante a infância, que é influenciado por interações com o ambiente. O modelo gera avalanches finitas de atividade, e é capaz de gerar topologias especificas e modulares utilizando regras simples Abstract: In this Masters Dissertation we study the structure and dynamics of complex networks. We start with a revision of the literature of complex networks, presenting the most common network metrics and models of network connectivity. We then study in detail the dynamics of the Random Threshold Network (RTN) model. We develop a new mean-field approximation for the RTN dynamics that is considerably more simple than previous results. This new approximation is useful from a practical standpoint, since it allows the generation of RTNs where the average activity of the network is controlled. We then review the literature of Adaptive Networks, explaining some of the adaptive models with interesting characteristics. At last, we develop two models of adaptive networks inspired by the evolution of neuronal structure in the brain. The first model uses simple rules and a link-removing evolution to control the activity on the network. The inspiration is the removal of neurons and neuronal connections after infancy. This model can also control the activity of individual groups within the same network. We explore a variant of this model in a bi-dimensional space, where we are able to generate modular and small-world networks. The second model uses external inputs to control the topological evolution of the network. The inspiration in this case is the development of neuronal connections during the infancy, which is influenced by interactions with the environment. The model generates finite avalanches of activity, and is capable of generating specific and modular topologies using simple rules Mestrado Física Mestre em Física

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Araújo, Sabrina Borges Lino. "Dinâmica adaptativa em populações de predadores e presas." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278384.

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Orientador: Marcus Aloizio Martinez de Aguiar Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin Made available in DSpace on 2018-08-17T01:49:08Z (GMT). No. of bitstreams: 1 Araujo_SabrinaBorgesLino_D.pdf: 18627531 bytes, checksum: aed18ab505ee489e8cde08b6d2850bba (MD5) Previous issue date: 2010 Resumo: Neste trabalho estudamos a dinâmica espaço-temporal de cadeias alimentares compostas por duas e três espécies. Utilizamos uma modelagem baseada nos indivíduos, que consiste em tratar cada membro da população de forma explícita. Um dos ingredientes do modelo é a possibilidade de restringir a área de forrageio dos predadores à uma região circular, de raio R, em torno da sua residência. O tamanho desta região é tratado como uma característica adaptativa, sujeita à pequenas variações aleatórias ao longo das gerações. Observamos que existe um raio de predação ótimo R', para o qual os predadores evoluem. Desenvolvemos cálculos analíticos utilizando aproximações de Campo Médio com correlações de pares e verificamos que a estratégia de predação é um mecanismo crucial para a ocorrência do raio ótimo. Observamos também que a distribuição da abundância de indivíduos por região espacial pode exibir um comportamento invariante de escala, indicando que o sistema é criticamente auto-organizado, e que a ocorrência de surtos populacionais locais é uma característica intrínseca do sistema Abstract: In this work we study the spatial dynamics of two and three species food chains. We use an individual based model, which treats each member of the population explicitly. One of the model ingredients is the possibility to control the size of the predators foraging area, defined as a circular neighborhood, of radius R, around their home position. This home range size is treated as an adaptive, subject to small random variations along generations. We find that the predators evolve to a optimum predation radius R'. We develop analytical approximations using mean field and pair correlation techniques that indicate that the predation strategy is crucial for existence of this optimum radius. We also find that the population abundance distributions display a scale invariant power law tail, indicating self-organized criticality and that the occurrence of local outbreaks is an intrinsic characteristic of the system Doutorado Ciências Exatas e da Terra Doutora em Ciências

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Carvalho, Josué Xavier de. "Criticalidade auto-organizada no modelo olami-feder-christensen." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-13122013-123300/.

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Neste trabalho estudamos o modelo Olami-Feder-Christensen (OFC). Fortes correlações espaciais e temporais dificultam a obtenção de resultados analíticos para este modelo. Assim, nossas investigações foram realizadas através de simulações computacionais. A fim de identificar o regime estacionário de forma eficiente e econômica desenvolvemos algumas estatrégias. Também percebemos que a escolha adequada da configuração inicial pode antecipar ou retardar o início do regime estacionário. Por fim, a criticalidade do modelo foi estudada através de uma abordagem totalmente nova. Em vez de tentarmos identificar o comportamento crítico do sistema por meio da distribuição de avalanches, definimos uma grandeza , que em um processo ramificado simples seria a taxa de ramificação do sistema. Analisando o comportamento dessa variável em um espaço de fases verificamos que o modelo OFC e sua versão aleatória (que de antemão sabemos que só apresenta criticalidade no regime conservativo) tem um comportamento bastante similar. Obtivemos, ao contrário do que se acreditava, fortes evidências de que o modelo OFC apenas exibe criticalidade no regime conservativo. We have investigated the Olami-Feder-Christensen model. The model presents strong temporal and spatial correlations what makes it very difficult to perform analytical calculations. So our treatment was numerical. We developed strategies to identify the regime with high level of accuracy. We noticed that depending on the initial configurations, the statistical stationary state can be reached faster. Finally we have investigated the criticality of the model through new strategy. Instead of looking for powers laws, we defined a quantity , very similar to the branching ratio in a simple branching process. We were able to show the behavior of the Olami-Feder-Christensen and the random version of this model are similar. We got strong numerical evidences that, in opposition to previous results, the Olami-Fedel-Christensen model is critical only in the conservative regime.

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Gorny, Matthias. "Un modèle d'Ising Curie-Weiss de criticalité auto-organisée." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112074/document.

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Dans leur célèbre article de 1987, les physiciens Per Bak, Chao Tang et Kurt Wiesenfeld ont montré que certains systèmes complexes, composés d'un nombre important d'éléments en interaction dynamique, évoluent vers un état critique, sans intervention extérieure. Ce phénomène, appelé criticalité auto-organisée, peut être observé empiriquement ou simulé par ordinateur pour de nombreux modèles. Cependant leur analyse mathématique est très ardue. Même des modèles dont la définition est apparemment simple, comme les modèles décrivant la dynamique d'un tas de sable, ne sont pas bien compris mathématiquement. Le but de cette thèse est la construction d'un modèle de criticalité auto-organisée, qui est aussi simple que possible, et qui est accessible à une étude mathématique rigoureuse. Pour cela, nous modifions le modèle d'Ising Curie-Weiss généralisé en introduisant un contrôle automatique du paramètre de température. Pour une classe de distributions symétriques satisfaisant une certaine condition d'intégrabilité, nous montrons que la somme Sn des variables aléatoires du modèle a le comportement typique du modèle d'Ising Curie-Weiss généralisé critique: les fluctuations sont d'ordre n^(3/4) et la loi limite est C exp(- lambda*x^4) dx, où C et lambda sont des constantes strictement positives. Notre étude nous a menés à généraliser ce modèle dans plusieurs directions : cas de la dimension supérieure, fonctions d'interactions plus générales, extension à des auto-interactions menant à des fluctuations d'ordre n^(5/6). Nous étudions aussi des modèles dynamiques dont la distribution invariante est la loi de notre modèle d'Ising Curie-Weiss de criticalité auto-organisée In their famous 1987 article, Per Bak, Chao Tang and Kurt Wiesenfeld showed that certain complex systems, composed of a large number of dynamically interacting elements, are naturally attracted by critical points, without any external intervention. This phenomenon, called self-organized criticality, can be observed empirically or simulated on a computer in various models. However the mathematical analysis of these models turns out to be extremely difficult. Even models whose definition seems simple, such as the models describing the dynamics of a sandpile, are not well understood mathematically. The goal of this thesis is to design a model exhibiting self-organized criticality, which is as simple as possible, and which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse temperature. For a class of symmetric distributions whose density satisfies some integrability conditions, we prove that the sum Sn of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model: the fluctuations are of order n^(3/4) and the limiting law is C exp(- lambda*x^4) dx where C and lambda are suitable positive constants. Our study led us to generalize this model in several directions: the multidimensional case, more general interacting functions, extension to self-interactions leading to fluctuations with order n^(5/6). We also study dynamic models whose invariant distribution is the law of our Curie-Weiss model of self-organized criticality

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Navin, Natália. "Percolação em sistemas financeiros simulados." Master's thesis, Instituto Superior de Economia e Gestão, 2012. http://hdl.handle.net/10400.5/10427.

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Mestrado em Matemática Financeira Sendo conhecido que as curvas de preços em mercados financeiros apresentam variâncias não finitas e não seguem um movimento Browniano, este facto dificulta a aplicação das ferramentas existentes de matemática financeira. O objectivo deste trabalho é estudar as medidas económicas que melhoram a previsibilidade em modelos descritos por equações diferenciais estocásticas relativamente ao movimento Browniano. Deste modo, pretende-se analisar outras medidas retiradas dos mesmos mecanismos de interacção entre agentes económicos cuja dinâmica apresenta variações com variâncias finitas e, consequentemente, a aplicação de equações diferenciais estocásticas com movimento Browniano seja válida. Sendo a economia feita por trocas entre os agentes económicos, pretende-se olhar para a mesma como sendo um cluster das ligações, em que cada nó representa um agente económico e cada ligação entre dois nós representa as trocas entre estes. Pretende-se assim, analisar se estas medidas podem substituir as medidas de preço na modelação de mercados financeiros. A formação dos clusters será analisada à luz da teoria das redes complexas e o estudo das medidas dos mesmos é feito através da teoria da percolação e criticalidade autoorganizada, conceitos estes que serão explicados neste trabalho. Por fim, pretende-se verificar se as medidas dos clusters seguem um movimento Browniano, de modo que seja possível avaliar o mercado em função das medidas dos clusters em vez das medidas financeiras. It is known that price curves in financial markets have no finite variances and do not follow a Brownian motion and, therefore, this makes it difficult to apply existing tools of financial mathematics. The aim of this work is to study economic measures that improve predictability in models based on stochastic differential equations driven by Brownian motion. Here we intend to study other measures taken from the same mechanisms of interaction between economic agents, whose dynamic shows variations with finite variances and, therefore, the application of stochastic differential equations driven by Brownian motion is valid. As the economy is based on trade between economic operators, we want to look at the economy as a cluster of links, where each node represents an economic agent and each link between two nodes represents the exchanges made by them. The aim is to examine whether such measures may replace the measures of price modeling in financial markets. The formation of clusters is explained by the theory of complex networks. The study of measures of clusters is based on percolation theory and self-organized criticality, assuming that the economy has a behavior of self-organized criticality, concepts that will be explained in this dissertation. Finally, we want to verify whether the measures of the clusters follow a Brownian motion to be able to assess the marke according to the clusters of measures rather than financial measures.

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Borda, Jorge Victor Quiñones. "Log periodic analysis of critical crashes in the portuguese stock market." Master's thesis, Instituto Superior de Economia e Gestão, 2015. http://hdl.handle.net/10400.5/11082.

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Mestrado em Ciências Empresariais O estudo de fenómenos críticos que se originaram nas ciências naturais e encontraram muitos campos de aplicação foi estendido nos últimos anos aos campos da economia de finanças, fornecendo aos investigadores novas abordagens para problemas conhecidos, nomeadamente aos que estão relacionados com a gestão de risco, a previsão, o estudo de bolhas financeiras e crashes, e muitos outros tipos de problemas que envolvem sistemas com criticalidade auto-organizada. A teoria de singularidades de tempo oscilatório auto-similares é apresentada, uma metodologia prática é exposta, juntamente com alguns resultados de análises semelhantes de diferentes mercados em todo o mundo, como uma maneira de obter de alguns exemplos da forma como a função "linear" log-periódica de potências funciona. Apresento alguns contextos onde o tempo de crise é apresentado aos mercados internacionais - como uma maneira de demonstração de antecedentes -, assim como apresento também três aplicações práticas do mercado de acções português (1997, 2008 e 2015). A sensibilidade dos resultados e do significado das oscilações log-periódicas são avaliadas. Concluo com algumas recomendações e futuras propostas de investigação. The study of critical phenomena that originated in the natural sciences and found many fields of applications has been extended in the last years to the financial economics? field, giving researchers new approaches to known problems, namely those related to risk management, forecasting, the study of bubbles and crashes, and many kind of problems involving complex systems with self-organized criticality. The theory of self-similar oscillatory time singularities is presented. A practical methodology is exposed along with some results from similar analysis from different markets around the world, as a way to get some examples of the way the ´Linear´ Log-Periodic Power Law formula works. Some context presenting the international markets at the time of crisis is given as a way of having some background, and three practical applications for the Portuguese stock market are made (1997, 2008 and 2015). The sensitivity of the results and the significance from the log-periodic oscillations is assessed. It concludes with some recommendations and future proposed research.

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Öberg, Oskar. "Critical Branching Regulation of the E-I Net Spiking Neural Network Model." Thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-76770.

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Spiking neural networks (SNN) are dynamic models of biological neurons, that communicates with event-based signals called spikes. SNN that reproduce observed properties of biological senses like vision are developed to better understand how such systems function, and to learn how more efficient sensor systems can be engineered. A branching parameter describes the average probability for spikes to propagate between two different neuron populations. The adaptation of branching parameters towards critical values is known to be important for maximizing the sensitivity and dynamic range of SNN. In this thesis, a recently proposed SNN model for visual feature learning and pattern recognition known as the E-I Net model is studied and extended with a critical branching mechanism. The resulting modified E-I Net model is studied with numerical experiments and two different types of sensory queues. The experiments show that the modified E-I Net model demonstrates critical branching and power-law scaling behavior, as expected from SNN near criticality, but the power-laws are broken and the stimuli reconstruction error is higher compared to the error of the original E-I Net model. Thus, on the basis of these experiments, it is not clear how to properly extend the E-I Net model properly with a critical branching mechanism. The E-I Net model has a particular structure where the inhibitory neurons (I) are tuned to decorrelate the excitatory neurons (E) so that the visual features learned matches the angular and frequency distributions of feature detectors in visual cortex V1 and different stimuli are represented by sparse subsets of the neurons. The broken power-laws correspond to different scaling behavior at low and high spike rates, which may be related to the efficacy of inhibition in the model.

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Angus, Simon Douglas Economics Australian School of Business UNSW. "Economic networks: communication, cooperation & complexity." Awarded by:University of New South Wales. Economics, 2007. http://handle.unsw.edu.au/1959.4/27005.

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This thesis is concerned with the analysis of economic network formation. There are three novel sections to this thesis (Chapters 5, 6 and 8). In the first, the non-cooperative communication network formation model of Bala and Goyal (2000) (BG) is re-assessed under conditions of no inertia. It is found that the Strict Nash circle (or wheel) structure is still the equilibrium outcome for n = 3 under no inertia. However, a counter-example for n = 4 shows that with no inertia infinite cycles are possible, and hence the system does not converge. In fact, cycles are found to quickly dominate outcomes for n > 4 and further numerical simulations of conditions approximating no inertia (probability of updating > 0.8 to 1) indicate that cycles account for a dramatic slowing of convergence times. These results, together with the experimental evidence of Falk and Kosfeld (2003) (FK) motivate the second contribution of this thesis. A novel artificial agent model is constructed that allows for a vast strategy space (including the Best Response) and permits agents to learn from each other as was indicated by the FK results. After calibration, this model replicates many of the FK experimental results and finds that an externality exploiting ratio of benefits and costs (rather than the difference) combined with a simple altruism score is a good proxy for the human objective function. Furthermore, the inequity aversion results of FK are found to arise as an emergent property of the system. The third novel section of this thesis turns to the nature of network formation in a trust-based context. A modified Iterated Prisoners' Dilemma (IPD) model is developed which enables agents to play an additional and costly network forming action. Initially, canonical analytical results are obtained despite this modification under uniform (non-local) interactions. However, as agent network decisions are 'turned on' persistent cooperation is observed. Furthermore, in contrast to the vast majority of non-local, or static network models in the literature, it is found that a-periodic, complex dynamics result for the system in the long-run. Subsequent analysis of this regime indicates that the network dynamics have fingerprints of self-organized criticality (SOC). Whilst evidence for SOC is found in many physical systems, such dynamics have been seldom, if ever, reported in the strategic interaction literature.

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Castro, Paulo Alexandre de. "Algoritmos de otimização e criticalidade auto-organizada." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-27092007-100001/.

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As teorias científicas surgiram da necessidade do homem entender o funcionamento das coisas. Novos métodos e técnicas são então criados com o objetivo não só de melhor compreender, mas também de desenvolver essas próprias teorias. Nesta dissertação, vamos estudar várias dessas técnicas (aqui chamadas de algoritmos) com o objetivo de obter estados fundamentais em sistemas de spin e de revelar suas possíveis propriedades de auto-organização crítica. No segundo capítulo desta dissertação, apresentamos os algoritmos de otimização: simulated annealing, algoritmo genético, otimização extrema (EO) e evolutivo de Bak-Sneppen (BS). No terceiro capítulo apresentamos o conceito de criticalidade auto-organizada (SOC), usando como exemplo o modelo da pilha de areia. Para uma melhor compreensão da importância da criticalidade auto-organizada, apresentamos vários outros exemplos de onde o fenômeno é observado. No quarto capítulo apresentamos o modelo de relógio quiral de p-estados que será nosso sistema de testes. No caso unidimensional, determinamos a matriz de transferência e utilizamos o teorema de Perron-Frobenius para provar a inexistência de transição de fase a temperaturas finitas a temperaturas finitas. Esboçamos os diagramas de fases dos estados fundamentais que obtivemos de maneira analítica e numérica para os casos de p = 2, 3, 4, 5 e 6, no caso numérico fazendo uso do algoritmo de Bak-Sneppen com sorteio (BSS). Apresentamos ainda um breve estudo do número de mínimos locais para o modelo de relógio quiral de p-estados, para os casos de p = 3 e 4. Por último, no quinto capítulo, propomos uma dinâmica Bak-Sneppen com ruído (BSR) como uma nova técnica de otimização para tratar sistemas discretos. O ruído é introduzido diretamente no espaço de configuração de spins. Conseqüentemente, o fitness (adaptabilidade) passa a assumir valores contínuos, num pequeno intervalo em torno do seu valor original (discreto). Os resultados dessa dinâmica indicam a presença de criticalidade auto-organizada, evidenciada pelo decaimento em leis de potências das correlações espacial e temporal. Também estudamos o método EO e obtivemos uma confirmação numérica de que sua dinâmica exibe um comportamento não crítico com alcance espacial infinito e decaimento exponencial das avalanches. Finalmente, para o modelo de relógio quiral, comparamos a eficiência das três dinâmicas (EO, BSS e BSR) no que tange às suas habilidades de encontrar o estado fundamental do sistema. In order to understand how things work, man has formulated scientific theories. New methods and techniques have been created not only to increase our understanding on the subject but also to develop and even expand those theories. In this thesis, we study several techniques (here called algorithms) designed with the objective to get the ground states of some spin systems and eventually to reveal possible properties of critical self-organization. In the second chapter, we introduce four fundamental optimization algorithms: simulated annealing, genetics algorithms, extremal optimization (EO) and Bak-Sneppen (BS). In the third chapter we present the concept of self-organized criticality (SOC), using as an example the sandpile model. To understand the importance of the self-organized criticality, we show many other situations where the phenomenon can be observed. In the fourth chapter, we introduce the p-states chiral clock model. This will be our test or toy system. For the one-dimensional case, we first determined the corresponding transfer-matrix and then proved the nonexistence of phase transitions by using the Perron-Frobenius theorem. We calculate the ground state phase diagrams both analytically and numerically in the cases of p = 2, 3, 4, 5 and 6. We also present a brief study of the number of local minima for the cases p = 3 and 4 of the chiral clock model. Finally, in the fifth chapter, we propose a Bak-Sneppen dynamics with noise (BSN) as a new technique of optimization to treat discrete systems. The noise is directly introduced into the spin configuration space. Consequently, the fitness now take values in a continuum but small interval around its original value (discrete). The results of this dynamics indicate the presence of self-organized criticality, which becomes evident with the power law scaling of the spacial and temporal correlations. We also study the EO algorithm and found a numerical con_rmation that it does not show a critical behavior since it has an in_nite space range and an exponential decay of the avalanches. At the end, we compare the e_ciency of the three dynamics (EO, BSD and BSN) for the chiral clock model, concerning their abilities to _nd the system\'s ground state.

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Forien, Nicolas. "Autour de la criticité auto-organisée." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM012.

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De nombreux modèles physiques présentent un phénomène appelé transition de phase : il existe un point critique ou une courbe critique dans l'espace des paramètres qui sépare deux régimes distincts caractérisés par des propriétés macroscopiques très différentes. Le comportement de ces systèmes au point critique est particulièrement intéressant et fait apparaître des lois d'échelle qui sont souvent communes à tout un ensemble de systèmes très différents. Les physiciens Per Bak, Chao Tang et Kurt Wiesenfeld ont remarqué que ces comportements "critiques" sont étonnamment communs dans la nature, alors qu'ils ne devraient survenir que lorsque les paramètres se trouvent être précisément ajustés au point critique. Pour expliquer cela, ils ont montré que certains systèmes ont tendance à être naturellement attirés vers des points ou des régimes critiques. Ces systèmes présentent un phénomène appelé "criticité auto-organisée". Cette thèse porte sur la construction de plusieurs modèles simples présentant ce phénomène. Pour cela, nous partons d'un modèle présentant une transition de phase et nous le modifions pour forcer un comportement "auto-critique". Nous étudions notamment une variante d'un modèle construit par Matthias Gorny à partir du modèle d'Ising Curie-Weiss généralisé, en passant d'un modèle de type champ moyen à une interaction limitée à une certaine portée. Nous construisons également quelques modèles de criticité auto-organisée à partir de la percolation Bernoulli dans des boîtes finies, ainsi qu'à partir du modèle d'Ising en dimension 2 Many models in physics present a phenomenon called phase transition: there is a critical point or a critical curve in the parameter space separating two distinct regions characterized by very different macroscopic properties. In such systems, the behaviour at the critical point is of particular interest and presents some scaling laws which appear to be universal across a wide range of different systems. The physicists Per Bak, Chao Tang and Kurt Wiesenfeld pointed out that these "critical" features are very common in nature, although they should only appear when the parameters happen to be finely tuned to the critical point. To explain this, they showed that some systems tend to be naturally attracted by critical points or critical regimes. This phenomenon is called "self-organized criticality". The goal of this thesis is to construct several simple models which present this phenomenon. To achieve this, we consider a model with a phase transition and we modify it in order to obtain a "self-critical" behaviour. We study a modification of a model constructed by Matthias Gorny from the generalized Ising Curie-Weiss model, in which the mean-field Hamiltonian is replaced by a long-range interaction. Several other models of self-organized criticality are constructed from Bernoulli percolation in finite boxes, and from the planar Ising model

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Bevilacqua, Decio. "Crescimento urbano : relações críticas entre sistemas de serviços urbanos e consumidores e seus reflexos no crescimento da cidade." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/132136.

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Em distintos momentos da história, pesquisadores investigaram e propuseram, com relativo sucesso, modelos locacionais que explicassem a origem e os processos dos crescimentos das cidades, mas, de modo frequente, esbarrando na complexidade desses sistemas. Recentemente, apoiados nas teorias sobre Sistemas Complexos, Nova Geografia Econômica e Modelos Configuracionais Urbanos, alguns conceitos proporcionam uma fundamentação mais consistente para a verificação das variáveis e suas interações espaciais, as quais identifiquem esses processos. Dentre os sistemas complexos, são representativos os conceitos sobre a resiliência e a criticalidade auto-organizada enquanto os conceitos do modelo centro-periferia, propostos pela nova geografia econômica, contribuem para compreensão das formações de aglomerações econômicas e populacionais. Tais abordagens conduzem ao desenvolvimento da hipótese de que a localização relativa dos serviços urbanos e dos moradores, no espaço intraurbano, estaria condicionada a duas forças que se contrapõem, “centrípeta e centrífuga”, que são geradoras de “tensões” as quais conduzem o sistema a atingir níveis críticos por determinados períodos até que novas condições movam o sistema, de maneira surpreendente, a um novo limiar. O processo de crescimento do sistema urbano seria, assim, sujeito às variações de densidades populacionais e das localizações dos diferentes serviços urbanos e suas externalidades econômicas existentes na cidade. A averiguação e os comportamentos destas forças foram testados em uma situação real, na cidade de Santa Maria – RS. Os dados populacionais e dos serviços urbanos foram espacializados recorrendo a um Sistema de Informação Geográfica – SIG e suas interações avaliadas com o uso de medidas configuracionais urbanas. Espera-se, com isso, contribuir para a consolidação do conhecimento da dinâmica urbana e das condições dos diversos estados do sistema urbano. At different times, researchers have investigated and proposed, with relative success, locational models that explain the origin and the processes of urban growth, but, often, failing to account for the complexity of these systems. Recently, the theories of Complex Systems, New Economic Geography and Urban Configurational Models, have provided concepts with a more consistent rationale for checking variables and the spatial interactions that identify these processes. The Complex Systems framework has provided the concepts of resiliency and self-organized criticality, whereas New Economic Geography has furnished the center-periphery model, which aids in understanding economic and population agglomerations. These approaches support the hypothesis that the relative location of urban services and residents in the intraurban space is subject to centripetal and centrifugal forces, which generate tensions that lead the system toward critical levels for determined periods until new conditions move the system, unexpectedly, to a new threshold. The growth process of the urban system is thus subject to variations in population density and in localization of the different urban services and their economic externalities that exist in the city. The behaviors of these forces were tested in a real situation, in the city of Santa Maria, RS. Population and urban services data were spatialized using a Geographic Information System – GIS and their interactions were evaluated with the use of urban configurational measures to contribute to our knowledge of urban dynamics and the conditions of the various states of the urban system.

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Sclocchi, Antonio. "A new critical phase in jammed models : jamming is even cooler than before." Thesis, université Paris-Saclay, 2020. https://tel.archives-ouvertes.fr/tel-03179833.

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Au cours des vingt dernières années, un courant de recherche important a caractérisé la transition de brouillage, un point critique à température zéro des systèmes ayant des interactions répulsives à courte portée. Plusieurs de ses propriétés sont indépendantes de la dimension spatiale, avec des prédictions de champ moyen étant valables même pour les systèmes bidimensionnels. Dans cette thèse, nous montrons l’existence de ce comportement critique du point de brouillage ("jamming") dans toute une phase brouillée ("jammed"). Ce comportement est observé en étudiant le potentiel de répulsion linéaire dans les sphères molles et le modèle de champ moyen correspondant, c’est-à-dire le perceptron. Nous montrons que le point non différentiable du potentiel d’interaction produit un réseau de contact de sphères tangentes à chaque densité surcomprimée, même loin de la transition de jamming.Les réseaux de contact caractérisant les minima du système sont isostatiques, critiquement auto-organisés et marginalement stables. Dans la première partie, nous utilisons la théorie du champ moyen pour le cas du perceptron et nous la validons par des simulations numériques. Ensuite, nous utilisons des simulations numériques pour étudier le cas des sphères molles en deux et trois dimensions. Dans les deux cas, nous caractérisons la phase marginalement stable et nous montrons que les exposants critiques correspondent à ceux connus pour la transition de jamming. De plus, nous définissons un protocole de compression et nous étudions numériquement les propriétés statistiques des avalanches dans la phase critique du perceptron. Nos résultats sont en accord parfait avec la théorie sous-jacente. Ce travail montre l’existence d’une phase critique dans les dimensions finies dont la classe d’universalité correspond au jamming des sphères. Cela ouvre de nouvelles perspectives pour l’étude des verres marginalement stables et des paysages énergétiques qui leur sont associés Over the last two decades, an intensive stream of research has characterized the jamming transition, a zero-temperature critical point of systems with short-range repulsive interactions. Many of its properties are independent of spatial dimensionality, with mean-field scalings being valid even for two-dimensional systems. In this thesis, we show the existence of this critical behaviour not only at the jamming point, but also in an entire jammed phase. This is observed by studying the linear repulsive interaction potential for soft spheres and in its correspondent mean-field model, i.e. the perceptron. We show that the non-differentiable point in the interaction potential produces a contact network of tangent spheres at every overcompressed density, even far away from the jamming transition. The contact networks characterizing the minima of the system are isostatic, critically self-organized and marginally stable. First, we solve the mean-field theory for the perceptron case and we validate it through numerical simulations. Furthermore, we use numerical simulations to study the soft spheres case in two and three dimensions. In both cases, we characterize the marginally stable phase and we show that the critical exponents correspond to those known for the jamming transition. Moreover, we define a compression protocol and we study numerically the avalanche statistics in the critical phase of the perceptron. Our findings are strongly consistent with the underlying theory. This work shows the existence of a critical phase in finite dimensions whose universality class corresponds to the jamming of spheres. This opens new perspectives to study marginally stable glasses and their related energy landscapes

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Castro, Paulo Alexandre de. "Rede complexa e criticalidade auto-organizada: modelos e aplicações." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-14012008-165356/.

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Modelos e teorias científicas surgem da necessidade do homem entender melhor o funcionamento do mundo em que vive. Constantemente, novos modelos e técnicas são criados com esse objetivo. Uma dessas teorias recentemente desenvolvida é a da Criticalidade Auto-Organizada. No Capítulo 2 desta tese, apresentamos uma breve introdução a Criticalidade Auto-Organizada. Tendo a criticalidade auto-organizada como pano de fundo, no Capítulo 3, estudamos a dinâmica Bak-Sneppen (e diversas variantes) e a comparamos com alguns algoritmos de otimização. Apresentamos no Capítulo 4, uma revisão histórica e conceitual das redes complexas. Revisamos alguns importantes modelos tais como: Erdös-Rényi, Watts-Strogatz, de configuração e Barabási-Albert. No Capítulo 5, estudamos o modelo Barabási-Albert não-linear. Para este modelo, obtivemos uma expressão analítica para a distribuição de conectividades P(k), válida para amplo espectro do espaço de parâmetros. Propusemos também uma forma analítica para o coeficiente de agrupamento, que foi corroborada por nossas simulações numéricas. Verificamos que a rede Barabási-Albert não-linear pode ser assortativa ou desassortativa e que, somente no caso da rede Barabási-Albert linear, ela é não assortativa. No Capítulo 6, utilizando dados coletados do CD-ROM da revista Placar, construímos uma rede bastante peculiar -- a rede do futebol brasileiro. Primeiramente analisamos a rede bipartida formada por jogadores e clubes. Verificamos que a probabilidade de que um jogador tenha participado de M partidas decai exponencialmente com M, ao passo que a probabilidade de que um jogador tenha marcado G gols segue uma lei de potência. A partir da rede bipartida, construímos a rede unipartida de jogadores, que batizamos de rede de jogadores do futebol brasileiro. Nessa rede, determinamos várias grandezas: o comprimento médio do menor caminho e os coeficientes de agrupamento e de assortatividade. A rede de jogadores de futebol brasileiro nos permitiu analisar a evolução temporal dessas grandezas, uma oportunidade rara em se tratando de redes reais. Models and scientific theories arise from the necessity of the human being to better understand how the world works. Driven by this purpose new models and techniques have been created. For instance, one of these theories recently developed is the Self-Organized Criticality, which is shortly introduced in the Chapter 2 of this thesis. In the framework of the Self-Organized Criticality theory, we investigate the standard Bak-Sneppen dynamics as well some variants of it and compare them with optimization algorithms (Chapter 3). We present a historical and conceptual review of complex networks in the Chapter 4. Some important models like: Erdös-Rényi, Watts-Strogatz, configuration model and Barabási-Albert are revised. In the Chapter 5, we analyze the nonlinear Barabási-Albert model. For this model, we got an analytical expression for the connectivity distribution P(k), which is valid for a wide range of the space parameters. We also proposed an exact analytical expression for the clustering coefficient which corroborates very well with our numerical simulations. The nonlinear Barabási-Albert network can be assortative or disassortative and only in the particular case of the linear Barabási-Albert model, the network is no assortative. In the Chapter 6, we used collected data from a CD-ROM released by the magazine Placar and constructed a very peculiar network -- the Brazilian soccer network. First, we analyzed the bipartite network formed by players and clubs. We find out that the probability of a footballer has played M matches decays exponentially with M, whereas the probability of a footballer to score G gols follows a power-law. From the bipartite network, we built the unipartite Brazilian soccer players network. For this network, we determined several important quantities: the average shortest path length, the clustering coefficient and the assortative coefficient. We were also able to analise the time evolution of these quantities -- which represents a very rare opportunity in the study of real networks.

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Lee, Chung-Wein, and 李忠文. "The study of self-organized criticality." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/93751228521645246122.

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碩士 國立中央大學 物理學系 85 Self-organized criticality(SOC) was introduced by Per Bak in 1988. When thesystem reaches the critical state by SOC process, any minor perturbation might cause catastrophe. Bak proposed sandpile model to illustrate theidea of SOC. He used height difference to be a basic quantity. In this paper,we used height to be a basic quantity and compared to the results of experiments. The data demonstrates that randomness is a prime factor toform the power law.

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Levina, Anna. "A Mathematical Approach to Self-Organized Criticality in Neural Networks." Doctoral thesis, 2008. http://hdl.handle.net/11858/00-1735-0000-0006-B3B3-B.

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Lin, Wei-Jou, and 林維柔. "Lee-Yang Zeros in Self-Organized Criticality of a Sandpile." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/85089500062232799842.

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碩士 國立中正大學 物理所 94 A self-organized criticality system (SOC) exhibits scale invariance and power-law behavior which are the features of critical phenomena. In this thesis, a SOC system is studied by the methods of the traditional critical phenomena. Following the steps of B.Cessac and J.L.Meunier, we use Lee-Yang theorem to form the generating function for the probability distributions of BTW sandpile model proposed by Bak, Tang and Wiesenfeld. Here, we also use the concepts of finite-size effects and scaling law to investigate the critical exponents and universality. We find that some zeros defined by Lee-Yang theorem will pinch on the real axis of a complex plane as the system size approaches infinity. It establishes a new link between the classical theory of critical phenomena and SOC systems.

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Levina, Anna [Verfasser]. "A mathematical approach to self-organized criticality in neural networks / vorgelegt von Anna Levina." 2008. http://d-nb.info/993515274/34.

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Blok, Hendrik Jan. "Life without bounds: does the game of life exhibit self-organized criticality in the thermodynamic limit?" Thesis, 1995. http://hdl.handle.net/2429/4037.

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Recently, a class of phenomena known as self-organized criticality (SOC) has been discovered. SOC is characterized by two properties: firstly, the system exhibits power law behavior typical of a critical state, with no characteristic time or length scales; and secondly, this state is approached naturally, without tuning any external parameters. Early studies explained SOC in terms of conserved quantities [1,2]. Then Bak et al. [3] suggested that the Game of Life, GL, a cellular automaton lacking any conserved quantities, also exhibited SOC. This sparked a debate as to whether GL truly is SOC; conflicting data suggested it was subcritical [4,5,6]. In this paper I explore both sides of the argument in an attempt to resolve the issue. By finding an explicit form for the scaling function the opposing arguments are reconciled and, with some slight reservations, GL is judged to be subcritical. The differences between the analysis herein and other studies is highlighted. I also introduce the reader to some other interesting features of GL, and cellular automata in general, in order to elicit the proper respect for these simple yet complex models. In doing so I hope to impress upon the reader the insufficiencies of the available analytical tools. New methods are required to account for the long-range correlations which develop in GL and other deterministic automata.

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Perachia, Florencia. "Estudio de la dinámica temporal de un modelo de urnas : probabilidades de primer pasaje y criticalidad auto-organizada." Bachelor's thesis, 2020. http://hdl.handle.net/11086/15293.

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Tesis (Lic. en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2020. En este trabajo estudiamos una combinación de los clásicos modelos de urnas de Ehrenfest y del votante. En nuestro modelo, a cada paso temporal se efectúa el modelo de Ehrenfest con probabilidad α, o el del votante con probabilidad (1 − α). Este modelo puede ser visto como una caminata aleatoria unidimensional en una red finita. Analizamos los estados de equilibrio del sistema y determinamos una transición de fase para α = 1/N . Asimismo, definiendo el tamaño de avalancha como la cantidad de pasos necesarios para volver al estado de equilibrio por primera vez, estudiamos la distribuciones de tamaños de avalanchas y de retornos, para determinar si el comportamiento del sistema presenta, además, criticalidad auto- organizada. Desde el punto de vista de la sociofı́sica, este modelo representa un modelo de opinión, donde el cambio de opinión puede darse por interacción, (modelo del votante), o sin interacción, (modelo de Ehrenfest). Para valores de α relativamente chicos (∼ 1/N ), el sistema evoluciona a una sociedad polarizada. In this work we present a combination of two classical urn models: Ehrenfest and voter . At every time step of our model either an Ehrenfest step is performed with probability \alpha or a voter step is performed with probability (1 − α). This model can be seen as an unidimensional random walk in a finite lattice. We analyzed the equilibrium states of the system and found a phase transition at α = 1/N. Furthermore, by defining the size of an avalanche as the amount of steps needed for the system to return to the equilibrium state for the first time, we studied the distribution of avalanches sizes and returns, in order to determine also if the system has Self-Organized Criticality. From the point of view of social physics this model represents an opinion model, where an agent can change its opinion by interacting with other agents (voter model) or without any interaction at all (Ehrenfest model). For relatively small α values (∼ 1 / N), the system evolves into a polarized society. Fil: Perachia, Florencia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.

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Xu, Huangjian. "Computer simulations of critical phenomena in systems with long range interaction: A study of ising dipoles and self-organized criticality in earthquakes." Thesis, 1992. http://hdl.handle.net/2429/3143.

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This thesis discusses scaling and critical behavior of two different models. One model describes Ising dipoles, originates in condensed matter physics and depicts equilibrium critical phenomena. The other model, taken from the earth sciences, describes faulting instabilities and the resulting earthqnakes, and involves self-organized criticality — a nonequilibrium phenomenon. Both models are characterized by long range interactions, with a resulting sensitivity to boundary conditions. The ordering properties of Ising dipoles on lattices are studied in a mean field theory and by Monte Carlo simulations. The mean field theory is manifestly shape independent in zero external field. In the case of dipoles on a diluted lattice the mean field theory predicts a critical concentration above which the low temperature phase is ferroelectric (or anti-ferroelectric depending on the lattice structure). Extensive Monte Carlo simulation results are in agreement with those of mean field theory. We propose a finite size scaling form that includes logarithmic corrections for systems at the critical dimensionality. In the case of dipoles on a body centered tetragonal lattice we found that the finite scaling form significantly improved the data collapse over the scaling form with mean field exponents. With lattice parameters appropriate to the Ising ferromagnetic compound LiHoF4,we obtain a ferromagnetic transition temperature Tc= 1.51K in excellent agreement with experiment. This indicates that the material LiHoF4 is dominated by the dipole-dipole interaction; since in the simulations we only include dipole-dipole interactions. For dipoles on the simple cubic lattice, the ordered state is made up of anti-ferromagnetic rows. The critical exponents obtained by finite size scaling are ß~1/7,y ~ 8/7 and a ~4/7. These results are in good agreement with those of high temperature series expansions. A model of self—organized ruptures in an elastic medium is developed; and applied to earthquakes. In the model the local ruptures are represented by double couples to be consistent with elastic theory. The explicit form of this double couple source is derived. The system is driven by slowly increasing the shear stress. The model evolves towards a self-organized critical state in which the earthquake distribution follows the Gutenberg Richter law with an exponent in agreement with observational data. By modeling the local static fatigue for the rocks, we also obtained Omori’s law for the rate of aftershocks. The effects of annealing are investigated.

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Molnárová, Orsolya. "Studium nestabilní plastické deformace metodou akustické emise." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-336591.

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The influence of the strain rate and heat treatment on the occurrence of plastic instabilities in extruded AlSi1MgMn (6082) and cold rolled AlMg4.5Mn0.4 (5182) alloys was studied. The samples were uniaxially loaded at various strain rates and at room temperature (RT). The results are discussed using concurrent acoustic emission (AE) monitoring during mechanical testing and the AE parameters are correlated to the microstructure and to the stress-time curves. All samples exhibited the Portevin-Le Châtelier (PLC) effect of different types, dependently on the heat treatment and the applied strain rate. The occurrence of the PLC effect is manifested by burst AE signals with high amplitudes. Statistical analysis of the AE signals has shown the power-law probability distribution.

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Vallières-Nollet, Michel-André. "Un modèle à criticalité auto-régulée de la magnétosphère terrestre." Thèse, 2009. http://hdl.handle.net/1866/8038.

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Milanowski, Piotr. "Critical Transitions in Epileptic Systems." Doctoral thesis, 2018. https://depotuw.ceon.pl/handle/item/2771.

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Complex systems exhibiting rapid regime shifts have been observed in manydifferent fields like economics, medicine, ecology and geology. Some demonstrateearly warning signals, or predictors, of incoming transition. Epilepticbrain is often used as an example of such system, however very little proofof this claim is given. This thesis presents results of systematic research onthis topic. By an analysis of mathematical model of seizures, investigationof EEG recording of epileptic rats, and a study of over 300 EEG recordingsof seizures from human subjects we aim at answering the question whetherepilepsy seizures exhibit early warning signals, thus showing that epileptictransition can be described using critical transition theory. Because of thelarge number of examined signals a novel, automatic method of analysis is devised.Three predictors commonly discovered in other fields, are investigated:variance, lag-1 autoregressive coefficient (AR(1)), and skewness. In the caseof theoretical model and signals from rats, there is a strong indication ofexistence of early warning signals. About 23% of rat signals display expectedbehavior in all three predictors at the same time, while 65% showed agreementwith the the theory with respect to AR(1) coefficient and variance increasingsimultaneously. In human subjects only 8% of subjects showed statisticallysignificant increase in variance and AR(1) coefficients and no patient exhibitedchanges in all three preditors consistently. The discrepancies betweentheoretical and animal models, and human data indicate that complexitymay be a fundamental issue in transferring theoretical concepts to complexsystems such as human brain. Złożone systemy przejawiające gwałtowne zmiany stanu są obserwowane wwielu dziedzinach, takich jak ekonomia, medycyna, ekologia czy geologia.Jednocześnie mogą być obserwowane predyktory, czyli sygnały zapowiadającetakie przejścia. Mózg epileptyczny często przedstawiany jest jako systemzawierający takie oznaki, zazwyczaj jednak nie podaje się wystarczającychdowodów na potwierdzenie tej tezy. Przedmiotem badan przedstawionych wtej pracy jest gruntowne zbadanie tego zagadnienia. Systematyczna analizamatematycznego modelu napadów epileptycznych, badanie sygnałów EEGpochodzących od szczurów z epilepsją oraz nagrań ponad 300 sygnałów EEGpochodzenia ludzkiego ma na celu zweryfikowanie tezy, ze napady epileptycznepoprzedzone są sygnałami zapowiadającymi. To z kolei oznaczałoby,iż przejścia stanu widoczne w epilepsji da się opisać, stosując metodologięprzejść krytycznych. Z powodu dużej liczby badanych sygnałów opracowanonowy, automatyczny algorytm analizy. Przebadano trzy najczęściej opisywanepredyktory przejść: wariancje, współczynnik autokorelacji pierwszegorzędu (AR(1)) oraz skośność. W przypadku sygnału szczurów oraz modelumatematycznego wykazano duże prawdopodobieństwo istnienia sygnałówzapowiadających. Około 23% sygnałów szczurów przejawiało oczekiwanezachowanie w trzech predyktorach, jednak aż 65% sygnałów pokazywałozgodność z teoria, jeśli brano pod uwagę jednocześnie wariancje i współczynnikautokorelacji. W przypadku ludzi tylko 8% pacjentów wykazywałostatystycznie istotne zmiany w wariancji lub współczynniku autokorelacjii żaden nie pokazywał spójnych zmian w skośności. Niezgodność modelumatematycznego i wyników badan nad zwierzętami z rezultatami analizy ludzkichsygnałów pokazuje, jak wiele może zmienić wzrost złożoności badanegosystemu.

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Champagne-Ruel, Alexandre. "De la théorie des jeux à l’exobiologie : l’émergence de la coopération comme phénomène critique." Thesis, 2020. http://hdl.handle.net/1866/25125.

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L’émergence de la complexité, et de la vie en particulier, demeure l’une des énigmes les plus complexes pour la science moderne. Des travaux récents ont souligné la pertinence d’un apport de la physique statistique et de la théorie des phénomènes critiques — et en particulier de la théorie des phénomènes à criticalité auto-régulée — relativement à ces champs d’intérêt, tout autant que du rôle des phénomènes de coopération biochimique dans les premiers instants du vivant. La description des mécanismes par lesquels la vie a pu apparaître est par ailleurs d’un intérêt pratique pour l’astrophysique, puisque notre compréhension de ceux-ci module la manière dont l’analyse de biosignatures s’eﬀectue dans le cadre de la recherche de la vie ailleurs dans l’Univers. L’analyse proposée ici porte sur un modèle en théorie des jeux permettant d’étudier les phénomènes de coopération implémenté dans un contexte spatial servant à émuler la dynamique d’un système ayant pu voir apparaître la vie. Une analyse de l’espace des paramètres du modèle révèle que celui-ci aﬃche des phénomènes de transition de phase et d’auto-organisation de structures spatiales, ces éléments se révélant des adjuvants à l’émergence de la coopération entre joueurs a priori égoïstes, dans un contexte qui à prime abord n’est pas d’emblée favorable à l’apparition de comportements coopératifs. Les résultats obtenus ici semblent supporter que la coopération biochimique puisse apparaître via un phénomène de transition de phase et que le modèle sous-jacent de dilemme du prisonnier itéré sur réseau présenté ici agit comme un système à criticalité autorégulée. The emergence of complexity, and of life more speciﬁcally, is still one of the most intractable conundrums for modern science. Recent work emphasized the relevance of statistical physics and critical phenomena theory’s contribution to those questions — especially of self-organized criticality theory — just as much as the role of biochemical cooperation in life’s ﬁrst moments. Moreover, the description of the mechanisms by which life could have appeared is of particular interest for astrophysics, because our comprehension of those mechanisms inﬂuences how biosignatures are analyzed in the context of the search for life elsewhere in the Universe. The analysis presented here concerns a model in game theory that allows to study cooperation phenomena — implemented in spatial context as to emulate the dynamics of a system in which life could have appeared. An analysis of the model’s parameter space reveals that it displays phase transition and self-organization of spatial structures phenomenon, those elements being adjuvants to the emergence of cooperation between a priori egoist players, in a context that is initially not favorable to the emergence of cooperative behavior. The results obtained here thus seem to support the idea that both biochemical cooperation can emerge through phase transition phenomena, and that the underlying lattice iterated prisoner’s dilemma model used here behaves like a self-organized critical system.

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Morales, Laura F. "A new avalanche model for solar flares." Thèse, 2008. http://hdl.handle.net/1866/6406.

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