A teoria das redes complexas tem se consolidado por seu forte caráter interdisciplinar, relativa simplicidade conceitual e ampla aplicabilidade na modelagem de sistemas reais. Embora tendo evoluído rapidamente, uma série de problemas ainda não foram estudados usando as redes complexas. Em especial, sistemas envolvendo acoplamento e interação entre diferentes redes complexas têm sido pouco investigados. Na presente monografia, apresentamos duas contribuições fundamentais no estudo desses sistemas. A primeira consiste num modelo que descreve a interação entre um padrão de massa evoluindo numa rede regular com uma rede complexa que se organiza para impedir a evolução desse padrão. Os vértices da rede complexa se ativam e se movem sobre a rede regular conforme são requisitados por seus vizinhos, que se ativam pela rede regular. Essa última ativação ocorre quando a concentração de massa ultrapassa um limiar na respectiva posição do vértice e consiste em liberar uma difusão oposta de massa neutralizadora contra a massa original. A dinâmica mostrou-se completamente relacionada à estrutura da rede de controle. A presença de concentradores no modelo de Barabási-Albert tem papel fundamental para acelerar o processo de geração de massa neutralizadora. Por outro lado, a distribuição uniforme de vizinhos da rede de Erdös-Rényi resultou numa melhora de desempenho na presença de várias regiões distintas contendo massa original. A segunda contribuição consiste num modelo de interação entre duas espécies (predador e presa) através de campos sensitivos, que dependem da distância Euclidiana entre dois indivíduos e do seu respectivo tipo. Padrões espaço-temporais emergem nesse sistema e estão diretamente relacionados à intensidade de atração entre os indivíduos da mesma espécie. Para entender a evolução do sistema e quantificar a transferência de informação entre os diferentes aglomerados, duas redes complexas são construídas onde os vértices representam os indivíduos. Na primeira rede, o peso das conexões é dado pela distância Euclidiana entre os indivíduos e na segunda, pelo tempo que eles permaneceram suficientemente próximos. A partir de um mecanismo de fusão entre as duas redes, obtemos uma terceira rede complexa onde os vértices correspondem a grupos espaciais definidos a partir de um processo de limiarização dos pesos da primeira rede. Algumas configurações de parâmetros privilegiam a sobrevivência de presas enquanto outras beneficiam a caça dos predadores. / Complex network theory has become very popular because of its interdisciplinarity, conceptual simplicity and wide applicability to model real systems. Although fast growing, there is a number of problems which have not been addressed by using complex networks. For example, few efforts have been directed to systems involving coupling and interaction between different complex networks. In the following monography, we present two fundamental contributions in the study of such systems. The first consists in a model which describes the interaction dynamics between a mass pattern evolving in a regular network with a complex network, which are expected to control the pattern evolution. As soon as a complex network node is activated by the regular network, it requests help from its topological neighbours and activates them. The activation is triggered when the mass concentration overcomes a threshold in the node position and consists in liberating an opposite diffusion intended to eliminate the original pattern. The dynamics is completely related to the structure of the control network. The existence of hubs in the Barabási-Albert model plays a fundamental role to accelerate the opposite mass generation. Conversely, the uniform distribution of neighbours in the Erdös-Rényi network provided an increase in the efficiency when several focuses of the original pattern were distributed in the regular network. The second contribution consists in a model based on interactions between two species (predator and prey) provided by sensitive fields which depends of the Euclidean distance between two agents and on their respective types. Spatio-temporal patterns emerge in the system which are directly related to the attraction intensity between same species agents. To understand the dynamics evolution and quantify the information transfer through different clusters, we built two complex networks where the nodes represent the agents. In the first network, the edge weight is given by the Euclidean distance between two agents and, in the second network, by the amount of time two agents become close one another. By following a merging process, another network is obtained whose nodes correspond to spatial groups defined by a weight thresholding process in the first network. Some configurations favor the preys survival, while predators efficiency are improved by other ones.

A existência de opiniões distintas em uma sociedade na qual indivíduos interagem constantemente atraiu o interesse de cientistas sociais e físicos estatísticos. Em 1997, Robert Axelrod propôs um modelo vetorial para o estudo da formação de domínios culturais diferentes em uma rede de agentes interagentes. Nesse modelo, os agentes são representados por um vetor de F componentes em que cada componente assume um dentre Q estados inteiros. O modelo apresenta uma transição de um estado monocultural (ordenado) para um estado multicultural (desordenado) que tem sido estudada na literatura através de parâmetros de ordem tais como o tamanho relativo do maior domínio cultural (S) e a fração de domínios culturais diferentes (g). Desde então, propriedades como robustez à introdução de ruídos, à variação de topologia e à introdução de campos local, global e externo foram investigadas. Nosso trabalho está organizado em três partes principais. Na primeira, apresentamos a proposta de novas medidas baseadas no conceito de atividade por agente para o estudo do modelo de Axelrod na rede quadrada. Mostramos que a variância da atividade do sistema (A) pode ser usada para indicar os pontos de transição e que sua distribuição de frequência pode indicar a ordem da transição. Na segunda, estimamos o diagrama de fases no plano (F,Q) e comparamos resultados obtidos em redes com condição de contorno aberta e fechada. Para isso, utilizamos as susceptibilidades dos parâmetros de ordem S e A para determinar os valores críticos Qc(F) para alguns valores de F. Na terceira, analisamos a formação de domínios culturais com a introdução de agentes persistentes para modelar efeitos de mídia interna. Nossos resultados revelam uma dependência de Qc com a probabilidade de ocupação p de agentes persistentes que nos permite obter o diagrama de fases no plano (p,Q). Interpretamos a linha crítica como resultado da competição de duas forças opostas (denominadas efeito de barreira e efeito de ligação) causadas por agentes não-persistentes que aderem aos persistentes. / The existence of different opinions in a society where individuals constantly interact has attracted the interest of social scientists and statistical physicists. In 1997, Robert Axelrod proposed a vectorial model to study the formation of cultural domains in a network of interacting agents. In this model, the agents are represented by a F components vector in which one from Q integer states is assigned to each component. The model presents a transition from a monocultural state (ordered) to a multicultural one (disordered) that has been studied by using order parameters such as the relative size of the biggest cultural domain (S) and the fraction of different domains (g). Since then, some properties as the robustness to the introduction of noise, to the variation of topology and to the introduction of local, global and external fields were studied. Our work is organized in three main parts. In the first part we present the proposal of new measurements based on the concept of activity per agent to study the Axelrod\'s model in a square lattice. We show the variance of system\'s activity (A) can be used to indicate the transition points and that the system\'s activity frequency distribution can be used to indicate the order of the transition. In the second part we estimate the phase diagram in the (F,Q) plane and compare the results obtained from simulations performed in lattices with open and closed boundary conditions. For this purpose, we use the susceptibility of order parameters S and A to determine the critical values Qc(F) for some values of F. In the third part we analyze the formation of cultural domains by introducing persistent agents to model effects of internal media. Our results reveal a dependence of Qc on the occupation probability p of persistent agents that allows us to obtain the phase diagram in the (p,Q) plane. We interpret the critical locus as a result of two opposite forces (called barrier effect and bonding effect) caused by non-persistent agents which adhere the persistent ones.

In the 1990s, physicists started looking beyond their disciplinary boundaries by using their methods to study various problems usually thrown up by financial economics. This dissertation deals with this extension of physics outside its disciplinary borders. It seeks to determine what sort of discipline econophysics is in relation to physics and to economics, how its emergence was made possible, and what sort of knowledge it produces. Using a variety of evidence including bibliometric analysis Chapter 1 explores the field’s disciplinary identity as a branch of physics even though its intellectual heart is better seen as the re-emergence of a 1960s research programme initiated in economics. Chapter 2 is historical: it identifies the key role played by the Santa Fe Institute and its pioneering complexity research in the shaping of methodological horizons of econophysics. These are in turn investigated in Chapter 3, which argues that there are in fact three methodological strands: statistical econophysics, bottom-up agent-based econophysics, and top-down agent-based econophysics. Viewed from a Lakatosian perspective they all share a conceptual hard-core but articulate the protective belt in distinctly different ways. The last and final chapter is devoted to the way econophysicists produce and justify their knowledge. It shows that econophysics operates by proposing empirically adequate analogies between physical and other systems in exactly the ways emphasised by Pierre Duhem. The contrast between such use of analogy in econophysics and modeling practices implemented by financial economics explains why econophysics remains so controversial to economists.

Children's sex-typed preferences for colours and toys are well-established, and often function as markers of sex-typicality in research on the development of sex-typed behaviour. However, children's sex-typed colour and toy preferences have not been tested cross-culturally, or in remote unindustrialised cultural settings. The present thesis tested children's preferences for sex-typed toys in four cultural settings: Shipibo villages in the Lake Imiria region of the Peruvian Amazon; kastom villages in the mountains of Tanna Island in Vanuatu in the South Pacific; children attending school in Lenakel town on Tanna Island; and in a large industrialised city in Australia. It also tested children's colour preferences in three of these cultures. It was hypothesised that colour and toy preferences would show some similarities across cultures, and further, that similarities in toy preferences across cultures would be explained by the different types of play afforded by the toys. Results suggested that colour preferences, specifically, a sex difference in preference for pink, are specific to industrialised cultures. Results further suggested that some sex differences in toy preferences replicate in different cultures, and that the relationship between toy preferences and children's preferences for play affordances is a potentially important area for further research. The present thesis also provided two demonstrations of how new statistical methods, adapted from complex and dynamic systems theory, could be applied to the cross-cultural dataset. A machine learning method suggested that sex, more than culture, affects children's sex-typed toy preferences. A multistate dynamic method further suggested that sex, more than culture, affects the dynamics of children's toy choices.

As preocupações, desejos e necessidades dos consumidores à jusante tendem a guiar, cada vez mais, as iniciativas dos produtores à montante e esta é uma realidade também na agricultura, com a seleção de alimentos mais saudáveis, saborosos e com valor agregado por parte dos compradores, gerando um ambiente propício para produtos com estas características. O azeite extra virgem de oliva, cujas características se enquadram nos novos hábitos alimentares, vem assumindo uma posição de destaque entre os consumidores do mundo todo e não é diferente no Brasil. A despeito da pouca tradição na produção olivícola, o Brasil e em especial o Rio Grande do Sul, ao longo da última década tem iniciado uma produção concreta deste alimento, o qual vem chegando lentamente às gôndolas dos supermercados locais e nacionais gozando de uma reputação excelente. Diante, portanto, da possível emergência deste sistema de produção agrícola, da demanda potencial deste produto e da possibilidade de satisfazê-la por meio da produção local em contraposição às importações, entendeu-se que um estudo deste fenômeno recente e por conseguinte pouco analisado pode lançar as bases teóricas para a sua compreensão. Assim, teorias ligadas à governança foram utilizadas para a identificação da organização e coordenação do sistema. Para a análise dos elementos básicos do sistema, o referencial teórico utilizado foi o de sistemas complexos e para a compreensão da relação dos elementos básicos na formação de um sistema complexo, aplicou-se o ferramental da economia institucional evolucionária. Em função deste referencial teórico e da problemática a ser trabalhada, optou-se por um método reconhecidamente institucional com uma abordagem qualitativa, ou seja, um estudo de caso em modo exploratório, realizando entrevistas com participantes considerados chave no sistema e submetendo posteriormente os dados colhidos no campo aos dados secundários e ao referencial teórico. Os resultados encontrados apontam para um gradual florescimento da organização do sistema, com a coordenação não mercadológica do setor, entende-se governança, a cargo dos governos estadual e federal, mas não foram encontrados, até o momento, indícios de uma governança por parte da base, isto é, dos produtores. No que tange ao relacionamento dos elementos para a emergência do sistema, verificou-se que esta se dá por meio das trocas de informações constantes e transações que ocorrem entre os agentes e a economia local, influenciando uns aos outros em uma dinâmica base-topo e no sentido inverso, topo-base, quando o sistema reage às influências e inicia a estimular as estruturas de governança e infra-estrutura institucional. Nesta perspectiva, entende-se que os elementos do sistema que está efetivamente emergindo foram caracterizados, bem como sua relação com a economia local e que é imprescindível, para os participantes, que este sistema complexo seja entendido e tratado como tal, com intervenções adequadas, de modo que possa, desta forma, propiciar ganhos a todos os envolvidos. / Consumers concerns, desires and necessities in downstream tend to increasingly guide initiatives of producers in the upstream and this is a reality also in agriculture, with the selection of healthier, tastier, and with higher market value food, which generates a welcoming environment for products with such characteristics. Extra virgin olive oil, whose characteristics fit in the new dietary habits, has been assuming a highlighted position among consumers from the whole world, which is not different in Brazil. Despite having little tradition in olive cultivation, Brazil, especially the state of Rio Grande do Sul, has started since the last decade a solid production of this product, which has slowly reached national and international supermarkets’ shelves while receiving an excellent reputation. Therefore, with the possible emergence of this agricultural production system, and by the high demand of the product as well as the possibility of fulfilling this demand through local production instead of imports, we assume that a study about this recent, and consequently little studied, phenomenon can provide theoretical basis for its comprehension. Hence, governance theories were used to identify the system’s organization and coordination. In order to analyze basic elements of the system, the theoretical background used was that of complex systems; for the comprehension of the basic elements’ relation in the formation of a complex system, the apparatus of institutional-evolutionary economics was applied. Having in mind this theoretical background and the problem studied, we opted for a method acknowledgedly institutional with a qualitative approach i.e. an exploratory case study conducting interviews with participants considered as fundamental in the system, submitting afterwards the data collected in field to the secondary data and the theoretical background. The results obtained point to a gradual blooming of the system’s organization, with coordination not subjected to the market action of the sector, by which is understood governance, of Federal and State responsibility. However, until the moment evidences were not found of a governance of the base i.e. the producers. In reference to the relationship of the elements for the system’s emergence, it was verified that this occurs by means of constant information exchange and transactions that occur between the agents and the local economy. The agents and the local economy influence each other reciprocally in a bottom-up dynamics and in the reverse, topdown, when the system reacts to influences and begins to stimulate governance structures and institutional infrastructure. In this perspective, it is understood that the system’s elements that are effectively emerging were characterized, as well as their relation with local economy. It is crucial for the participants that this complex system can be understood and treated as so, with adequate interventions in a way that it can propitiate gains to all parts involved.

<div>A tropical cyclone (TC) vortex is an immense, coherent, organized-convective system. Beneath this large-scale organization, is a litany of azimuthally asymmetric convective motions that exist on a spectrum of scales. These asymmetries are especially dominant during periods when the vortex undergoes critical transitions in its intensity and structure. However, the precise nature of influence of the organization of asymmetries on TC intensity change remains an enigma. The inherent difficulty in predicting their behavior is because asymmetries may arise due to different external or intrinsic sources and occur at different spatial and temporal scales while several complex mechanisms act near-simultaneously to dictate their evolution in time. As a result, multiple pathways are possible for a TC vortex that is influenced by these asymmetries. Our preliminary investigations using numerical models made it apparent that there wasn't a single, unifying way to address this problem. In this thesis, I outline multiple novel techniques of diagnosing and predicting which of the many pathways are likely for a TC vortex that is influenced by azimuthal asymmetries. </div><div> </div><div> First, using three-dimensional numerical simulations of a pair of sheared and non-sheared vortices, I demonstrate the diagnostic potential of the juxtaposition in the azimuthal phasing of: </div><div>(i) the asymmetrically distributed vertical eddy flux of moist-entropy across the top of the boundary layer, and the radial eddy flux of moist-entropy within the boundary layer; and (ii) eddy relative vorticity, eddy moist-entropy, and vertical velocity throughout the depth of the vortex. </div><div> </div><div> Second, I introduce an energetics-based diagnostic framework that computes the energy transactions occurring at asymmetries across various length-scales in the wavenumber domain. By applying it to select cases, this thesis uncovers the relative importance of all the energy pathways that support or disrupt the growth of asymmetries within the vortex. Contrary to the traditional explanations of convective aggregation/disaggregation and axi/asymmetrization through barotropic mean-eddy transactions, my thesis reveals that the growth or disruption of asymmetries are predominantly due to (i) the baroclinic conversion from available potential to kinetic energy at individual scales of asymmetries and (ii) the transactions of kinetic energy across asymmetries of different length scales. </div><div> </div><div>Finally, this thesis introduces two further diagnostic frameworks targeted at tackling the problem of real-time forecasting of TC rapid intensity changes. The first is an empirical framework which examines symmetric and asymmetric convection and other state variables within the vortex, and in the environment across a suite of TCs and identifies a set of `important' variables that are significantly different during time periods that precede a rapid intensification as opposed to a rapid weakening. My framework then ranks the variables identified based on how significantly they influence a rapid intensity change in a TC and the amplification factor of any associated variability. We recommend that future observational, and consequent TC modeling and data assimilation efforts prioritize the highest ranked variables identified here. </div><div><br></div><div>The second is a stochastic model wherein a scale-specific stochastic term is added to the equations describing the energy transactions within the TC vortex. By simulating a stochastic forcing that may arise from any scale, I compute the probability of the vortex transitioning into a rapidly intensifying or a rapidly weakening configuration across an ensemble of scenarios. </div><div><br></div><div>In summary, this thesis introduces and applies a variety of diagnostic techniques that help determine the impact of azimuthal asymmetries on TC intensity evolution.</div>

<div>This work proposes a framework for modeling an organization as a network of autonomous design agents who collectively work on the design of a complex system. The research objective is to identify a design process policy which best suits the current organization evaluated on the basis of the value that it provides to the organization. Consequently, the research question is, "How does an organization comprised of autonomous design teams select a design process policy which provides the highest value?" The proposed framework models design teams as agents who adapt their behavior using information on design variables available from other teams and the incentives in form of rewards from a system-level designer.</div><div><br></div><div><div>While extant literature on complex systems design has proposed several models of design processes, there is still a need for models that are versatile enough to represent different types of purposes and scopes of hierarchical levels. Further, models still do not account for the social, cultural, and political aspects of design. Due to the invariably long development times of a complex system, the environment's dynamics such as changing requirements would require all design teams to update their models and decisions during the process. They have to do this while accounting for the decisions of the other teams. The system-level designer, on the other hand, has to ensure that the design teams' decisions are in the best interest of the organization, which is to maximize value. The work proposed in this research addresses these issues by taking a bottom-up approach to modeling this complex, dynamic and uncertain design environment, where organizational-level outcomes are modeled as a result of decisions of individual teams who respond to local incentives.</div></div><div><br></div><div><div>The system-level designer and the subsystem design teams, are modeled to interact with other agents with whom they share design variables. The subsystem teams first solve their local design problems, and then exchange the results of these problems with other teams. The proposed modeling is versatile to represent human behaviors such as their adding of margins to design variables during the process of information exchange. In each interaction, the receiving teams make decisions to update their local variable values with the one newly available or to continue to use their own value. They make these decisions on the basis of which decision leads to the highest utility measured by a predened value function. Thus, each team acts in its self-interest and maximizes its local value. In case they do not arrive at a common design, the system-level designer attempts to assign rewards which incentivize the teams to update designs such that they are compatible with the other teams. In such cases, the teams would be willing to forgo a portion of their utility obtained from the design outcome if they are compensated for this loss by the system-level designer. Therefore, the task of a system-level designer is to solve a compatibility problem which trades off between different subsystems outcomes and arrives as the final design while maximizing the organization's value.</div></div><div><br></div><div><div>The framework is developed and then described through a series of increasingly complex design cases using a synthetic optimization problem. Following this, an aircraft design problem serves as a demonstration of application of this framework. The results obtained from both the synthetic and the demonstration problem then inform the discussion of various characteristics of a complex systems design process.</div></div>

Individuals with poor quality diets face an increased risk of developing a range of chronic diseases. Aspects of the local food environment, including food availability, have been linked to less healthy diets and increased body weight in adults. However, there is limited theory development to guide the synthesis of empirical studies or the design and evaluation of intervention strategies. Therefore, this dissertation sought to 1) develop a theory of change for unpacking the association between local food availability, diet quality and weight status through identifying hypothesized pathways of influence; and 2) test identified mechanisms using nationally representative data for adults across the United Kingdom and England. Firstly, a systematic review and realist synthesis were used to generate a novel theory of change for food availability, diet and obesity. This involved integration of tacit knowledge from an expert panel with evidence from a range of published food availability interventions. The resulting theory suggested that the influence of food availability on diet and weight status involves a complex set of pathways. Including the importance of understanding the link between the adoption of, and exposure to, different types of food outlets and the alignment of these factors with the preferences and needs of people of varying socioeconomic position (SEP). Thus, use of different away-from-home food outlets (i.e. fast food, restaurant and café) were examined in adults from the National Diet and Nutrition Survey showing that only use of fast food outlets (but not restaurants or cafés) was associated with poor diet quality and obesity, after accounting for SEP. Next, given the potential importance of exposure to the density of food outlets in their use, the same types of away-from-home food outlets were examined in a cross-sectional spatial study of adults from the first wave of the UK Household Longitudinal Study (UKHLS). This analysis showed that again, regardless of individual SEP, the density of fast food outlets around the home was positively associated with away-from-home food spending and obesity, while the density of restaurants was negatively associated with obesity and no link to the density of cafés. Lastly, preliminary longitudinal analysis using adults from five waves of the UKHLS explored the utility of residential relocation as a means of examining the effect of a change in exposure to away-from-home food outlet density on diet and obesity. Results suggest that relocation can lead to substantial change in food outlet exposures; however, relocation is also accompanied by changes in a variety of demographic and socioeconomic circumstances. Collectively, this work demonstrates that theory development and empirical testing can provide a solid conceptual foundation to improve our understanding of how food availability influences unhealthy diet and obesity, for different groups of people and across a range of circumstances. The application of this systematic approach could lead to a more nuanced view of mechanisms of action and thereby more effectively address complex public health problems.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Um nÃmero significativo de redes reais possui caracterÃsticas locais ou nÃo-locais bem definidas. NÃs estudamos como estas caracterÃsticas podem influenciar processos de navegaÃÃo e processos percolativos que venham a ocorrer nas mesmas. Primeiramente, estudamos o problema de navegaÃÃo em redes regulares com ligaÃÃes de longo alcance e sujeitas a um vÃnculo de custo. Neste caso, a rede à construÃda a partir de uma rede regular de dimensÃo d a ser melhorada por meio da adiÃÃo de ligaÃÃes de longo alcance (atalhos) com uma probabilidade $P_{ij} sim r_{ji}^{-alpha}$ , onde $r_{ij}$ à a distÃncia de Manhattan entre os sÃtios $i$ e $j$. Mostramos que a condiÃÃo de navegaÃÃo Ãtima, $alpha = d+1$, permanece Ãtima, independente da estratÃgia de navegaÃÃo utilizada, seja ela baseada em um conhecimento local ou global da estrutura da rede. Em seguida, apresentamos um processo de crescimento de agregados que fornece uma clara conexÃo entre a MecÃnica EstatÃstica no equilÃbrio e o processo percolativo nÃo-local conhecido como PercolaÃÃo Explosiva. Mostramos que dois ingredientes sÃo suficientes para obter uma transiÃÃo abrupta na fraÃÃo do sistema ocupada pelo maior agregado: (i) os tamanhos de todos os agregados devem ser mantidos aproximadamente iguais durante o processo percolativo e (ii) a inclusÃo de ligaÃÃes de fusÃo (i.e., ligaÃÃes que conectam agregados diferentes) deve dominar o processo em detrimento de ligaÃÃes redundantes (i.e., ligaÃÃes que conectam sÃtios em um mesmo agregado). Por Ãltimo, introduzimos um modelo que generaliza a regra do produto para PercolaÃÃo Explosiva que revela os efeitos da nÃo-localidade no comportamento crÃtico do processo de percolaÃÃo. Mais precisamente, pares de ligaÃÃes nÃo ocupadas sÃo escolhidos de acordo com uma probabilidade que decai em lei de potÃncia com sua distÃncia de Manhattan, e apenas a ligaÃÃo que conecta agregados para os quais o produto de seus tamanho à o menor, à ocupada. Nossos resultados para redes regulares finitas em diversas dimensÃes sugerem que, na criticalidade, o expoente da lei de potÃncia tem uma influÃncia significativa nos expoentes de escala, onde observa-se uma transiÃÃo nos expoentes da percolaÃÃo tradicional para os expoentes da percolaÃÃo explosiva (nÃo-local) em determinados casos. / A significant number of real networks have well-defined local and nonlocal features. We investigate the influence of these features in the navigation through small-world networks and in explosive percolation. First, we investigate the navigation problem in lattices with long-range connections and subject to a cost constraint. Our network is built from a regular d-dimensional lattice to be improved by adding long-range connections (shortcuts) with probability $P_{ij} sim r_{ij}^{-alpha}, where $r_{ij}$ is the Manhattan distance between nodes $i$ and $j$, and a is $alpha$ variable exponent. We find optimal transport in the system for $alpha = d+1$. Remarkably, this condition remains optimal, regardless of the strategy used for navigation being based on local or global knowledge of the network structure. Second, we present a cluster growth process that provides a clear connection between equilibrium statistical mechanics and the nonlocal explosive percolation process. We show that the following two ingredients are sufficient for obtaining an abrupt transition in the fraction of the system occupied by the largest cluster: (i) the size of all growing clusters should be kept approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds connecting nodes in different clusters) should dominate with respect to the redundant bonds (i.e., bonds connecting nodes in the same cluster). Finally, we introduce a generalization of the product rule for explosive percolation that reveals the effect of nonlocality on the critical behavior of the percolation process. Precisely, pairs of unoccupied bonds are chosen according to a probability that decays as a power law of their Manhattan distance, and only that bond connecting clusters whose product of their sizes is the smallest becomes occupied. Our results for d-dimensional lattices at criticality shows that the power law exponent of the product rule has a significant influence on the finite-size scaling exponents for the spanning cluster, the conducting backbone, and the cutting bonds of the system. For all these types of clusters, we observe a clear transition from ordinary to (nonlocal) explosive percolation.

A criação de Unidades de Conservação é uma estratégia mundialmente utilizada para garantir a conservação dos recursos naturais e a sustentabilidade ambiental, econômica e social, tendo como principal instrumento de planejamento e gestão o plano de manejo. Antes e depois a promulgação do Sistema Nacional de Unidades de Conservação vários planos de manejo foram elaborados a partir dos métodos consagrados que não consideram a variável tempo para a definição de ações de conservação e recuperação dos recursos naturais, a curto, médio e longo prazo. Visando contribuir para o aperfeiçoamento metodológico dos planos de manejo, a presente pesquisa apresenta uma compilação sobre as unidades de conservação e respectivos planos de manejo, tendo como estudo de caso, para a análise do método consagrado, o Plano de Manejo da APA Várzea do rio Tietê. Além disso, a pesquisa apresenta uma descrição das principais ferramentas de modelagem econômica - ecológica com intuito de conhecer conceitos e métodos alternativos e complementares para elaboração dos planos de manejo. Das fermentadas estudadas, o InVest se apresenta como sendo o mais operacional, produzindo modelos para a quantificação biofísica, o mapeamento e a valoração monetária dos benefícios providos por ecossistemas terrestres e marinhos, enquanto que o MIMES se apresenta como sendo o mais indicado para qualquer escala de modelos dinâmicos e integrados que, além de identificar, avalia e valora os serviços ecossistêmicos. Ambos os modelos consideram a variável tempo e estabelecem cenários a partir deles. Ao final, observou-se que, os métodos consagrados para elaboração dos planos de manejo das Unidades de Conservação não consideram a variável tempo na medida em que não definem os cenários e tendências para superação ou não do limiar de resiliência dos ecossistemas protegidos pelas unidades de conservação, o método tradicional analisa a situação atual, sem construir cenários para conservação e recuperação desses recursos naturais, a curto, médio e longo prazo. Desse modo, a questão que se coloca não é a definição de quanto vale os serviços ecossistêmicos para a sociedade e, sim, qual é o real limiar de resiliência do ecossistema. / The creation of Conservation Units is a globally used strategy to guarantee the conservation of natural resources and environmental, economic and social sustainability, having as main planning and management tool the management plan. Before and after the promulgation of the National System of Conservation Units, several management plans were elaborated based on established methods that do not consider the time variable for the definition of actions for conservation and recovery of natural resources in the short, medium and long term. Aiming to contribute to the methodological improvement of the management plans, the present research presents a compilation on the conservation units and respective management plans, having as case study, for the analysis of the established method, the APA Management Plan Várzea do Rio Tietê. In addition, the research presents a description of the main economic - ecological modeling tools in order to know alternative and complementary concepts and methods to elaborate management plans. From the studied ferments, InVest presents itself as the most operational, producing models for biophysical quantification, mapping and monetary valuation of the benefits provided by terrestrial and marine ecosystems, while MIMES presents itself as being the most suitable for any scale Of dynamic and integrated models that, in addition to identifying, evaluating and valuing ecosystem services. Both models consider the time variable and establish scenarios from them. At the end, it was observed that the methods established for the elaboration of the management plans of the Conservation Units do not consider the time variable insofar as they do not define the scenarios and trends for overcoming or not the resilience threshold of the ecosystems protected by the conservation units. Conservation, the traditional method analyzes the current situation without constructing scenarios for conservation and recovery of these natural resources in the short, medium and long term. Thus, the question is not the definition of how much ecosystem services are worth for society, but rather what is the real resilience threshold of the ecosystem.