O processo de auto-organização da estrutura proteica a partir da cadeia de aminoácidos é conhecido como enovelamento. Apesar de conhecermos a estrutura tridimencional de muitas proteínas, para a maioria delas, não possuímos uma compreensão suficiente para descrever em detalhes como a estrutura se organiza a partir da sequência de aminoácidos. É bem conhecido que a formação de núcleos de estruturas locais, conhecida como estrutura secundária, apresenta papel fundamental no enovelamento final da proteína. Desta forma, o desenvolvimento de métodos que permitam não somente predizer a estrutura secundária adotada por um dado resíduo, mas também, a maneira como esse processo deve ocorrer ao longo do tempo é muito relevante em várias áreas da biologia estrutural. Neste trabalho, desenvolvemos dois métodos de predição de estruturas secundárias utilizando modelos com o potencial de fornecer informações mais detalhadas sobre o processo de predição. Um desses modelos foi construído utilizando autômatos celulares, um tipo de modelo dinâmico onde é possível obtermos informações espaciais e temporais. O outro modelo foi desenvolvido utilizando redes neurais residuais profundas. Com este modelo é possível extrair informações espaciais e probabilísticas de suas múltiplas camadas internas de convolução, o que parece refletir, em algum sentido, os estados de formação da estrutura secundária durante o enovelamento. A acurácia da predição obtida por esse modelo foi de ~78% para os resíduos que apresentaram consenso na estrutura atribuída pelos métodos DSSP, STRIDE, KAKSI e PROSS. Tal acurácia, apesar de inferior à obtida pelo PSIPRED, o qual utiliza matrizes PSSM como entrada, é superior à obtida por outros métodos que realizam a predição de estruturas secundárias diretamente a partir da sequência de aminoácidos. / The process of self-organization of the protein structure is known as folding. Although we know the structure of many proteins, for a majority of them, we do not have enough understanding to describe in details how the structure is organized from its amino acid sequence. In this work, we developed two methods for secondary structure prediction using models that have the potential to provide detailed information about the prediction process. One of these models was constructed using cellular automata, a type of dynamic model where it is possible to obtain spatial and temporal information. The other model was developed using deep residual neural networks. With this model it is possible to extract spatial and probabilistic information from its multiple internal layers of convolution. The accuracy of the prediction obtained by this model was ~ 78% for residues that showed consensus in the structure assigned by the DSSP, STRIDE, KAKSI and PROSS methods. Such value is higher than that obtained by other methods which perform the prediction of secondary structures from the amino acid sequence only.

Estuda-se o espalhamento de doenças contagiosas utilizando modelos suscetível-infectado-recuperado (SIR) representados por equações diferenciais ordinárias (EDOs) e por autômatos celulares probabilistas (ACPs) conectados por redes aleatórias. Cada indivíduo (célula) do reticulado do ACP sofre a influência de outros, sendo que a probabilidade de ocorrer interação com os mais próximos é maior. Efetuam-se simulações para investigar como a propagação da doença é afetada pela topologia de acoplamento da população. Comparam-se os resultados numéricos obtidos com o modelo baseado em ACPs aleatoriamente conectados com os resultados obtidos com o modelo descrito por EDOs. Conclui-se que considerar a estrutura topológica da população pode dificultar a caracterização da doença, a partir da observação da evolução temporal do número de infectados. Conclui-se também que isolar alguns infectados causa o mesmo efeito do que isolar muitos suscetíveis. Além disso, analisa-se uma estratégia de vacinação com base em teoria dos jogos. Nesse jogo, o governo tenta minimizar os gastos para controlar a epidemia. Como resultado, o governo realiza campanhas quase-periódicas de vacinação. / The spreading of contagious diseases is studied by using susceptible-infected-recovered (SIR) models represented by ordinary differential equations (ODE) and by probabilistic cellular automata (PCA) connected by random networks. Each individual (cell) of the PCA lattice experiences the influence of others, where the probability of occurring interaction with the nearest ones is higher. Simulations for investigating how the disease propagation is affected by the coupling topology of the population are performed. The numerical results obtained with the model based on randomly connected PCA are compared to the results obtained with the model described by ODE. It is concluded that considering the topological structure of the population can pose difficulties for characterizing the disease, from the observation of the time evolution of the number of infected individuals. It is also concluded that isolating a few infected subjects can cause the same effect than isolating many susceptible individuals. Furthermore, a vaccination strategy based on game theory is analyzed. In this game, the government tries to minimize the expenses for controlling the epidemic. As consequence, the government implements quasi-periodic vaccination campaigns.

Unidades de conservação possuem o objetivo de preservar a natureza, evitando o desmatamento e promovendo a sustentabilidade do meio ambiente. Contudo, para que estas atendam aos propósitos para os quais foram criadas, sem acarretar prejuízos sociais ou conflitos com as populações locais, estudos aplicados interdisciplinares são essenciais, agregando conhecimento útil à gestão e ao planejamento das unidades de conservação. Sob a ótica da ciência da complexidade, o objetivo principal deste trabalho foi desenvolver modelos que auxiliassem na compreensão das mudanças no uso e cobertura da terra, realizassem simulações de cenários futuros, e permitissem observar os efeitos da implantação de políticas de preservação sobre a paisagem. Construímos modelos dinâmicos baseados em cadeias de Markov e autômatos celulares, aliados a técnicas de geoprocessamento. Os modelos foram aplicados a um estudo de caso, o Parque estadual do Itinguçu, ao longo de uma série temporal de materiais aerofotográficos de quase 50 anos (1962-2010). Os resultados dos modelos mostraram que a implantação da unidade de conservação foi essencial para barrar o desmatamento, mas que as práticas tradicionais de agricultura itinerante não estavam diretamente relacionadas à conversão da área de floresta, indicando que a incompatibilidade entre preservação e presença humana, muitas vezes usada como justificativa para a implantação de unidades de proteção integral, deve ser reavaliada sob outra perspectiva. Os resultados também apontaram para um desempenho satisfatório do modelo de Markov em projetar tendências, apesar de possuir certa aleatoriedade na alocação dos elementos no espaço. O incremento do autômato celular diminuiu tal aleatoriedade, mas não foi tão eficiente em reproduzir as tendências observadas nas matrizes de transição quanto o modelo de Markov. Concluímos que a metodologia aplicada no presente trabalho foi útil para compreendermos as mudanças na paisagem da área de estudo, e que a escolha do modelo (Markov ou Markov com autômato celular) deve ser feita com base em uma análise criteriosa caso a caso, em conformidade com as prioridades do estudo a ser realizado. Espera-se que esta pesquisa possa fomentar a discussão sobre o uso desta metodologia como uma ferramenta para planejamento e análise de políticas de conservação da natureza e gestão do território / Conservation units have the purpose to preserve the nature, avoiding the deforestation and promoting the environment sustainability. However, for these to be effective in that purpose, without causing social injuries or conflicts with the local population, interdisciplinary applied studies are essential and must be made by different areas of science, adding useful knowledge to the management of protected areas. Under the vision of the Complexity Science, the main goal of this research was to develop models that help in understanding the land use and cover changes, perform simulations of future scenarios, and allow observing the effects of the implementation of conservation policies on the landscape. We built Markov and cellular automata models, allied to the geoprocessing techniques. The models were applied to a case study, the Parque Estadual do Itinguçu, over a time series of aero photographic materials of almost 50 years (1962-2010). The results of the models showed that the implementation of the conservation unit was essential to stop the deforestation, but the traditional practices of shifting cultivation were not directly related to the conversion of forest area, indicating that the incompatibility between conservation and human presence, often used as justification for the implementation of some strict protection units, should be reviewed from a different perspective. The results also pointed to a satisfactory performance of the Markov model to project trends, despite having certain randomness in the allocation of elements in space. Add cellular automata to model decreased this randomness, but was not so effective in reproducing the observed trends in transition matrices than the Markov model. We concluded that the methodology applied in this study was useful for understanding the changes in the landscape of the study area, and that the choice of model (Markov or Markov with cellular automata) should be based on a careful analysis in accordance with the priorities of the study to be applied. We hope that this research can encourage the discussion of this methodology as a tool for analysis of conservation policies of nature and land management

Els paradigmes cel·lulars, com les xarxes neuronals cel·lulars (CNN, en anglès) i els autòmats cel·lulars (CA, en anglès), són una eina excel·lent de càlcul, al ser equivalents a una màquina universal de Turing. La introducció de la màquina universal CNN (CNN-UM, en anglès) ha permès desenvolupar hardware, el nucli computacional del qual funciona segons la filosofia cel·lular; aquest hardware ha trobat aplicació en diversos camps al llarg de la darrera dècada. Malgrat això, encara hi ha moltes preguntes a obertes sobre com definir els algoritmes d'una CNN-UM i com estudiar la dinàmica dels autòmats cel·lulars. En aquesta tesis es tracten els dos problemes: primer, es demostra que es possible acotar l'espai dels algoritmes per a la CNN-UM i explorar-lo gràcies a les tècniques genètiques; i segon, s'expliquen els fonaments de l'estudi dels CA per mitjà de la dinàmica no lineal (segons la definició de Chua) i s'il·lustra com aquesta tècnica ha permès trobar resultats innovadors. / Los paradigmas celulares, como las redes neuronales celulares (CNN, eninglés) y los autómatas celulares (CA, en inglés), son una excelenteherramienta de cálculo, al ser equivalentes a una maquina universal deTuring. La introducción de la maquina universal CNN (CNN-UM, eninglés) ha permitido desarrollar hardware cuyo núcleo computacionalfunciona según la filosofía celular; dicho hardware ha encontradoaplicación en varios campos a lo largo de la ultima década. Sinembargo, hay aun muchas preguntas abiertas sobre como definir losalgoritmos de una CNN-UM y como estudiar la dinámica de los autómatascelular. En esta tesis se tratan ambos problemas: primero se demuestraque es posible acotar el espacio de los algoritmos para la CNN-UM yexplorarlo gracias a técnicas genéticas; segundo, se explican losfundamentos del estudio de los CA por medio de la dinámica no lineal(según la definición de Chua) y se ilustra como esta técnica hapermitido encontrar resultados novedosos. / Cellular paradigms, like Cellular Neural Networks (CNNs) and Cellular Automata (CA) are an excellent tool to perform computation, since they are equivalent to a Universal Turing machine. The introduction of the Cellular Neural Network - Universal Machine (CNN-UM) allowed us to develop hardware whose computational core works according to the principles of cellular paradigms; such a hardware has found application in a number of fields throughout the last decade. Nevertheless, there are still many open questions about how to define algorithms for a CNN-UM, and how to study the dynamics of Cellular Automata. In this dissertation both problems are tackled: first, we prove that it is possible to bound the space of all algorithms of CNN-UM and explore it through genetic techniques; second, we explain the fundamentals of the nonlinear perspective of CA (according to Chua's definition), and we illustrate how this technique has allowed us to find novel results.

Economic changes such as rising açaí prices and the availability of off-farm employment are transforming the landscape of the Amazonian várzea, subject to decision-making at the farming household level. Land use change results from complex human-environment interactions which can be addressed by an agent-based model. An agent-based model is a simulation model composed of autonomous interacting entities known as agents, built from the bottom-up. Coupled with cellular automata, which forms the agents’ environment, agent-based models are becoming an important tool of land use science, complementing traditional methods of induction and deduction. The decision-making methods employed by agent-based models in recent years have included optimization, imitation, heuristics, classifier systems and genetic algorithms, among others, but multiple methods have rarely been comparatively analyzed. A modular agent-based model is designed to allow the researcher to substitute alternative decision-making methods. For a smallholder farming community in Marajó Island near Ponta de Pedras, Pará, Brazil, 21 households are simulated over a 40-year period. In three major scenarios of increasing complexity, these households first face an environment where goods sell at a constant price throughout the simulated period and there are no outside employment opportunities. This is followed by a scenario of variable prices based on empirical data. The third scenario combines variable prices with limited employment opportunities, creating multi-sited households as members emigrate. In each scenario, populations of optimizing agents and heuristic agents are analyzed in parallel. While optimizing agents allocate land cells to maximize revenue using linear programming, fast and frugal heuristic agents use decision trees to quickly pare down feasible solutions and probabilistically select between alternatives weighted by expected revenue. Using distributed computing, the model is run through several parameter sweeps and results are recorded to a cenral database. Land use trajectories and sensitivity analyses highlight the relative biases of each decision-making method and illustrate cases where alternative methods lead to significantly divergent outcomes. A hybrid approach is recommended, employing alternative decision-making methods in parallel to illustrate inefficiencies exogenous and endogenous to the decision-maker, or allowing agents to select among multiple methods to mitigate bias and best represent their real-world analogues.

Economic changes such as rising açaí prices and the availability of off-farm employment are transforming the landscape of the Amazonian várzea, subject to decision-making at the farming household level. Land use change results from complex human-environment interactions which can be addressed by an agent-based model. An agent-based model is a simulation model composed of autonomous interacting entities known as agents, built from the bottom-up. Coupled with cellular automata, which forms the agents’ environment, agent-based models are becoming an important tool of land use science, complementing traditional methods of induction and deduction. The decision-making methods employed by agent-based models in recent years have included optimization, imitation, heuristics, classifier systems and genetic algorithms, among others, but multiple methods have rarely been comparatively analyzed. A modular agent-based model is designed to allow the researcher to substitute alternative decision-making methods. For a smallholder farming community in Marajó Island near Ponta de Pedras, Pará, Brazil, 21 households are simulated over a 40-year period. In three major scenarios of increasing complexity, these households first face an environment where goods sell at a constant price throughout the simulated period and there are no outside employment opportunities. This is followed by a scenario of variable prices based on empirical data. The third scenario combines variable prices with limited employment opportunities, creating multi-sited households as members emigrate. In each scenario, populations of optimizing agents and heuristic agents are analyzed in parallel. While optimizing agents allocate land cells to maximize revenue using linear programming, fast and frugal heuristic agents use decision trees to quickly pare down feasible solutions and probabilistically select between alternatives weighted by expected revenue. Using distributed computing, the model is run through several parameter sweeps and results are recorded to a cenral database. Land use trajectories and sensitivity analyses highlight the relative biases of each decision-making method and illustrate cases where alternative methods lead to significantly divergent outcomes. A hybrid approach is recommended, employing alternative decision-making methods in parallel to illustrate inefficiencies exogenous and endogenous to the decision-maker, or allowing agents to select among multiple methods to mitigate bias and best represent their real-world analogues.

The impact of spatial characteristics on the dynamics of urban development is a topic of great interest in urban studies. The interaction between the residents and the spatial characteristics is of particular interest in the context of urban models where some of the most famous urban models have been based on the process of individual settlements in some specific parts of cities.This research investigates the dynamism of urban development modeled by Cellular Automata and Multi-Agent System. The urban development, in this study embraces urban renewal and residential mobility. It corresponds to the residential mobility of households, attracted by residential and centrality comfort; these comforts are crystallized in some areas and residences of Strasbourg. The diversity and quality of these comforts become criteria for residential choice in a way that the households seek for proximity to these comforts.The Cellular Automata in this study, models the spatial characteristics of urban spatial units and they are identified by some inherent attributes that are equal to the comfort in residences and urban areas. The Multi- Agent System represent a system in which the population of the city interact between them and between them and the city; the agents delegate the socio-professional classes of households. During the spatiotemporal change, the aspiration of households forms the socio-spatio-temporal development of the city.

Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / In this thesis we consider the modelling of a particular layout optimisation problem, namely, the LEGO construction problem. The LEGO construction problem, in short, concerns the optimal layout of a set of LEGO bricks to represent a given object. Our goal is to develop a software package which LEGO enthusiasts can use to construct LEGO sculptures for any real-world object. We therefore not only consider the layout optimisation problem, but also the generation of the input data required by the LEGO construction problem. We show that by using 3D geometric models to represent the real-world object, our implemented voxelisation technique delivers accurate input data for the LEGO construction problem. The LEGO construction problem has previously been solved with optimisation techniques based on simulated annealing, evolutionary algorithms, and a beam search approach. These techniques all indicate that it is possible to generate LEGO building instructions for real-world objects, albeit not necessarily in reasonable time. We show that the LEGO construction problem can be modelled easily with cellular automata, provided that cells are considered as clusters which can merge or split during each time step of the evolution of the cellular automaton. We show that the use of cellular automata gives comparable layout results in general, and improves the results in many respects. The cellular automata method requires substantially less memory and generally uses fewer LEGO bricks to construct the LEGO sculpture when using comparable execution times.

Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.

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