L’objet de cette thèse est la convergence structure-fonction dans les systèmes complexes et ses applications aux systèmes vivants et aux systèmes technico-économiques. Après avoir défini la modularité et identifié les difficultés associées à sa définition, cette thèse formalise le concept de convergence structure-fonction dans les systèmes évolutifs et fonctionnels et montre son intérêt pour l’évolutivité et la robustesse de ces systèmes. Ensuite, elle applique ce concept à des problématiques réelles de systèmes évolutifs et fonctionnels en biologie et en économie afin d’illustrer son utilité. Ainsi, dans le cadre de la génomique, cette thèse montre que la longueur des opérons bactériens, qui sont à la fois des modules structurels et fonctionnels, est limitée du fait de contraintes dues à l’interaction des mécanismes de transcription et de réplication. Ensuite, elle fait l’hypothèse que la modularité structurelle des points chauds de recombinaison correspond au moins partiellement à la modularité fonctionnelle des gènes. Ceci permet de développer une nouvelle méthode d’analyse des études d’association génétique basée sur un découpage en régions géniques du génome dans le but de faciliter la compréhension du mécanisme fonctionnel de leur action sur le caractère étudié en analysant directement l’association de gènes ou de groupe de gènes avec ce caractère. Sur le plan structurel, les résultats sont d’une qualité comparable à ceux des méthodes classiques. En revanche, le découpage en régions devra encore être affiné afin d’obtenir une analyse fonctionnelle pleinement utile. Enfin, dans le cadre de la libéralisation du marché européen de l’électricité, la correspondance effective entre structure et fonction de chaque acteur issu de la restructuration fait supposer que le principe de convergence structure-fonction y est bien appliqué. Cependant, des difficultés subsistent avant de parvenir à mettre en place des relations structurelles permettant d’atteindre l’optimum souhaité. Celui-ci inclut des échanges d’énergie à l’origine des contraintes couplantes entre les acteurs. A partir de la théorie de la décomposition par les prix, nous proposons un cadre permettant de définir des tarifs propres à les faciliter, en particulier celles liant producteurs et transporteurs. En conclusion, cette thèse montre (a) la limite à la convergence structure-fonction que constitue la limite de la longueur des opérons bactériens, (b) la faisabilité de l’utilisation d’un découpage basé sur les limites de gènes afin d’analyser des études d’association génétique à grande échelle et (c) l’importance d’améliorer « la grande boucle » des relations entre producteurs et transporteurs d’électricité afin d’assurer l’optimisation conjointe des investissements en capacité de production et de transport. Elle synthétise l’ensemble de ces résultats dans le cadre conceptuel de la convergence structure-fonction qui postule que la modularité structurelle des systèmes évolutifs et fonctionnels tend à se superposer à leur modularité fonctionnelle afin de leur apporter robustesse et évolutivité. / The aim of this thesis is to investigate the structure-function convergence in complex systems by way of applications to living systems and technical-economical systems. Once having both defined modularity and identified the difficulties coupled to its core definition, this thesis formalizes the structure-function convergence in evolutive and functional systems and illustrates the interest of this concept with regard to the evolvability and robustness of these systems. Furthermore, this concept is applied to open questions in real biological and economic systems. In the field of genomics, this thesis establishes that the length of bacterial operons, which are structural and functional modules at the same time, is limited by the interactions of transcription and replication mechanisms. Then, this thesis make the hypothesis that the modular structure defined by recombination hotspots at least partially corresponds to the functional modularity defined by genes. This enables to develop a new method to analyse genetic association studies. It is based on a partition of the genome into bins with boundaries based on gene boundaries. This method renders easier the understanding of the functional mechanism of their action on the studied character. Indeed, it analyses directly the association of individual or group of genes with this character. On the structural level, results are of a quality comparable to those obtained obtained through standard methods. However, the gene based partition will need to be refined in order to obtain a fully useful functional analysis. Finally, when considering the opening-up of the European electricity market, the correspondence between structure and function of actors issued from the reorganization suggests that the structure-function convergence principle is correctly applied. However, the present structural relationships between actors prevent the system from reaching the desired optimality. This optimality includes energy exchanges which impose coupling constraints on the system. Thanks to the price decomposition theory, we propose a framework to define tariffs useful to improve such relationships, particularly those linking production and transmission operators. As a conclusion, this thesis shows (a) the limit of structure-function convergence implied by the length limit of bacterial operons, (b) the feasibility of a gene based bin analysis of genome-wide genetic association studies, (c) the importance of improving the relationships between production and transmission operators in order to assume a joint optimization of investments in production and transmission capacities. This thesis sums up these results in the conceptual framework of structure-function convergence, which postulates that the modular structure of evolutive and functional systems tend to superimpose their functional modularity in order to give them robustness and evolvability.

Les systèmes multi-agents sont caractérisés par le travail coopératif d'un ensemble d'agents autonomes, fonctionnant de manière décentralisée en vue de la réalisation d'un objectif global. Au sein de ces systèmes se produisent des phénomènes dits d'émergence, ou d'auto-organisation, par lesquels des structures ou des organisations particulières peuvent apparaître au niveau collectif qui n'étaient pas décrites de manière explicite au niveau individuel. Ainsi des fourmis qui s'organisent en files d'individus sans qu'aucune n'ait de représentation correspondant à la notion de "file". De par leurs interactions au niveau local, les agents produisent et maintiennent dynamiquement des structures au niveau global qui contraignent en retour l'activité de chacun des individus. Ces phénomènes sont fondamentaux dans l'étude des systèmes biologiques complexes mais sont pourtant très difficiles à formaliser car liés généralement à une interprétation en partie subjective d'un observateur extérieur au système. Le sujet proposé vise à aborder le problème du passage d'un niveau d'abstraction à un autre, ainsi que l'interaction, au sein d'un système, entre agents de différents niveaux, en combinant plusieurs approches complémentaires: une première approche concerne l'étude de formalismes adaptés à la représentation de phénomènes émergents. Cela passe notamment par la prise en compte de relations entre entités de différents niveaux d'abstraction, et par la prise en compte de comportements qui s'expriment différemment en fonction du niveau d'abstraction auquel l'entité est considérée. une deuxième approche qui s'appuiera sur la précédente concerne la détection automatique de phénomènes émergents. Pour ce faire, il sera nécessaire de développer des mécanismes permettant aux entités qui participent au système de détecter l'apparition de structures particulières (spatiales et/ou temporelles, statiques ou dynamiques) et de caractériser le passage d'un niveau d'abstraction donné au niveau supérieur. du fait de la très grande difficulté d'aborder le problème précédent dans toute sa généralité, nous prévoyons de développer une approche semi-interactive dans laquelle un observateur humain pourra avoir un rôle pour orienter le système vers la détection de structures particulières et leur caractérisation d'une manière particulière. Outre l'aide apportée au système, il s'agit d'orienter ce dernier vers la prise en compte d'abstractions a priori utiles et intéressantes. Cela passe notamment par la conception de modalités de visualisation et d'interaction adaptées à ce problème. ces différentes problématiques seront étudiées dans le cadre de plusieurs problèmes de simulation multi-agent pour la biologie. / Multi-agent systems are characterized by the cooperative work of a set of autonomous agents, operating in a decentralized manner with a view to achieving a goal. Within these systems produce phenomena known as emergence, or self-organization, in which structures or organizations may appear on a collective level that were not explicitly described at the individual level. Thus ants that are organized into files of individuals without having representation corresponding to the "file". Through their interactions at the local level, the agents produce and maintain structural dynamics at the global level which in turn constrain the activities of each individual. These phenomena are fundamental in the study of complex biological systems but are very difficult to formalize because usually related to a subjective interpretation of an observer outside the system. The subject is intended to address the problem of transition from one level of abstraction to another, and the interaction, within a system between officers of different levels, combining several complementary approaches: a first approach concerns study formalisms adapted to the representation of emergent phenomena. This includes taking account of relationships between entities of different levels of abstraction, and by taking behaviors that are expressed differently depending on the level of abstraction to which the entity is considered. a second approach which builds on the previous concerns the automatic detection of emergent phenomena. To do this, it will be necessary to develop mechanisms that allow entities that participate in the system to detect the emergence of structures (spatial and / or temporal, static or dynamic) and characterize the passage of a given level of abstraction to the next level. because of the great difficulty of dealing with the previous problem in all its generality, we plan to develop a semi-interactive approach in which a human observer may have a role to guide the system to detect structures and their characterization of a particular way. In addition to assisting the system, it is the guide to take into account a priori abstractions useful and interesting. This includes the design of procedures for display and interaction adapted to this problem. these issues will be explored in several issues of multi-agent simulation in biology.

The Totally Asymmetric Simple Exclusion Process (TASEP) is often considered one of the fundamental models of non-equilibrium statistical mechanics, due to its well understood steady state and the fact that it can exhibit condensation, phase separation and phase transitions in one spatial dimension. As a minimal model of traffic flow it has enjoyed many applications, including the transcription of proteins by ribosomal motors moving along an mRNA track, the transport of cargo between cells and more human-scale traffic flow problems such as the dynamics of bus routes. It consists of a one-dimensional lattice of sites filled with a number of particles constrained to move in a particular direction, which move to adjacent sites probabilistically and interact by mutual exclusion. The study of non-Markovian interacting particle systems is in its infancy, due in part to a lack of a framework for addressing them analytically. In this thesis we extend the TASEP to allow the rate of transition between sites to depend on how long the particle in question has been stationary by using non-Poissonian waiting time distributions. We discover that if the waiting time distribution has infinite variance, a dynamic condensation effect occurs whereby every particle on the system comes to rest in a single traffic jam. As the lattice size increases, so do the characteristic condensate lifetimes and the probability that a condensate will interact with the preceding one by forming out of its remnants. This implies that the thermodynamic limit depends on the dynamics of such spatially complete condensates. As the characteristic condensate lifetimes increase, the standard continuous time Monte Carlo simulation method results in an increasingly large fraction of failed moves. This is computationally costly and led to a limit on the sizes of lattice we could simulate. We integrate out the failed moves to create a rejection-free algorithm which allows us to see the interacting condensates more clearly. We find that if condensates do not fully dissolve, the condensate lifetime ages and saturates to a particular value. An unforeseen consequence of this new technique, is that it also allowed us to gain a mathematical understanding of the ageing of condensates, and its dependence on system size. Using this we can see that the fraction of time spent in the spatially complete condensate tends to one in the thermodynamic limit. A random walker in a random force field has to escape potential wells of random depth, which gives rise to a power law waiting time distribution. We use the non-Markovian TASEP to investigate this model with a number of interacting particles. We find that if the potential well is re-sampled after every failed move, then this system is equivalent to the non-Markovian TASEP. If the potential well is only re-sampled after a successful move, then we restore particle-hole symmetry, allow condensates to completely dissolve, and the thermodynamic limit spends a finite fraction of time in the spatially complete state. We then generalised the non-Markovian TASEP to allow for particles to move in both directions. We find that the full condensation effect remains robust except for the case of perfect symmetry.

Doctor of Philosophy(PhD) / The aim of this thesis is to support the evaluation of sustainable development strategies for industrial networks in the context of industrial ecology (IE). Industrial networks are a group of units which carry out, or contribute to, industrial activity, and are connected by material and energy flows, but also capital and information exchanges. The components of an industrial network encompass resource extraction, processing and refining, forming and assembly, use, disposal, as well as recycling and reprocessing. The motivation behind this research is the realisation that much of the current environmental system analysis focus within IE lacks a structured approach to considering: • system environment • dynamic nature of the system and its environment • economic and social impacts • the effect of uncertainty on analysis outcomes. It is argued in this thesis that current environmental analysis approaches used in IE can be improved in their capacity to capture the complexity of industrial systems, with the objective of promoting sustainable development. While IE emphasises the benefit of a systems approach to identifying environmental strategies in industry, analysis tools have to date not engaged extensively with important aspects such as the influence of system environment and dynamics on the viability of an environmental strategy, or with the economic or social impacts of industrial system development, which are equally important for sustainable development. Nor is the assessment of the effect of uncertainty on analysis outcomes an integral part of environmental analysis tools in IE. This is particularly significant when, in fact, the degree of uncertainty in assumptions and data used increases with the scope, and therefore the abstraction, of the system under consideration. IE will have to engage with the network and contextual complexities to a greater degree if it is to evolve from a concept to the application of its principles in practice. The main contribution of this thesis is therefore the development of a structured approach to analysing industrial networks for the purpose of identifying strategies to encourage sustainable development, while accounting for the complexity of the underlying system as well as the problem context. This analysis is intended to allow the identification of preferred network development pathways and to test the effectiveness of sustainable development strategies. A top-down, prescriptive approach is adopted for this purpose. This approach is chosen as the industrial network analysis is intended to identify how a network should develop, rather than focusing on how it could develop. Industrial networks are systems which are complex in both their structure and behaviour. This thesis also delivers a characterisation of these networks, which serves two purposes – quantifying key elements of structure and behaviour; and using this information to build a foundation for subsequent industrial network analysis. The value of such an approach can be seen in the following example. With a detailed understanding of individual network characteristics, both separately and collectively, it is possible to determine the source of issues, the means available to address them, any barriers that might exist, and the consequences of implementing any strategic interventions. The analysis approach proposed in this thesis is based on multi-criteria decisions analysis (MCDA), which, as a process, combines initial problem structuring and subsequent quantitative analysis stages. The tools employed within MCDA have been employed variously around considerations of sustainable development. Their value in this thesis is their integration within a rigorous analytical framework. Rigorous problem structuring is attractive as it helps elucidate the complexities of the system and its environment and is, by definition, designed to deal with multiple environmental social and economic criteria that would have to be considered to promote sustainable development. For the quantitative analysis, the industrial network analysis draws from existing analysis tools in IE, but predominately from other systems research disciplines, such as process systems engineering (PSE) and supply chain management (SCM). These fields, due to their maturity and practical focus, have invested a lot of research into system design and strategic planning, capturing system dynamics and uncertainty to ensure, within selected system constraints, that a proposed system or changes to a system are viable, and that the system is capable of achieving the stated objectives. Both PSE and SCM rely heavily on optimisation for system design and planning, and achieve good results with it as an analytical tool. The similarity between industrial networks and process systems / supply chains, suggests that an optimisation platform, specifically multi-objective dynamic optimisation, could be employed fruitfully for the analysis of industrial networks. This is the approach taken in this thesis. It is consistent with the “top down” approach advocated previously, which is deemed preferable for the identification and implementation analysis of strategic interventions. This enables the determination of a structure (design) that is “best” able to operate under future conditions (planning) with respect to the chosen sustainable development objectives. However, an analysis is only ever as good as its underlying data and assumptions. The complexity and scope of the industrial network and the challenge of articulating sustainable development target(s) give rise to significant uncertainties. For this reason a framework is developed within this thesis that integrates uncertainty analysis into the overall approach, to obtain insight into the robustness of the analysis results. Quantifying all the uncertainties in an industrial network model can be a daunting task for a modeller, and a decision-maker can be confused by modelling results. Means are therefore suggested to reduce the set of uncertainties that have to be engaged with, by identifying those which impact critically on model outcomes. However, even if uncertainty cannot be reduced, and the implementation of any strategy retains a degree of risk, the uncertainty analysis has the benefit that it forces an analyst to engage in more detail with the network in question, and to be more critical of the underlying assumptions. The analysis approach is applied to two case studies in this thesis: one deals with waste avoidance in an existing wood-products network in a large urban metropolis; the other with the potential for renewable energy generation in a developing economy. Together, these case studies provide a rich tableau within which to demonstrate the full features of the industrial network analysis. These case studies highlight how the context within which the relevant industrial network functions influences greatly the evolution of the network over time; how uncertainty is managed; and what strategies are preferred in each case in order to enhance the contribution of each network to sustainable development. This thesis makes an intellectual contribution in the following areas: • the characterisation of industrial networks to highlight sources of environmental issues, role the characteristics (could) play in the identification of (preferred) sustainable development strategies, and the need to explicitly consider these in a systems analysis. • the synthesis, adaptation and application of existing tools to fulfil the need for analysis tools in IE that can handle both contextual and system complexity, and address the above mentioned issues of lacking consideration of o system environment o dynamic nature of the system and its environment o economic and social impacts o the effect of uncertainty on analysis outcomes. • the development and demonstration of an industrial network analysis approach that o is flexible enough to model any industrial network at the inter-firm level, regardless of form and configuration of materials and products circulated, and depending on the existing network and the proposed strategies. o is able to encompass a wide range of environmental strategies, either individually or in combination depending on what best suits the situation, rather than focusing on any strategy in particular. o ensures long term viability of strategies, rather than short term solutions delivering incremental improvement. • the development of a comprehensive approach to capturing and assessing the effect of uncertainty on solution robustness for industrial network analysis, including the screening to determine the most important parameters, considering valuation and technical uncertainties, including future uncertainty. The industrial network analysis approach presented in this thesis looks more to how a network should develop (according to a set of sustainable development objectives), rather than how it may in actual fact develop. Consequently, the influence of agent interests and behaviour is not considered explicitly. This may be construed as a limitation of the industrial analysis approach. However, it is argued that the “top down” modelling approach favoured here is useful at a policy-making level. Here, for example, government instrumentalities, trade organisations and industry groupings, non-government organisations and community-based organisations are likely to be interested more in the performance of the network as a whole, rather than (necessarily) following the behaviour of individual agents within the network. Future work could well entertain the prospect of a mixed approach, in which the top-down approach of this thesis is complemented by a “bottom-up”, agent-based analysis. In this manner, it would be possible to give an indication of how attainable the identified industrial network development pathways are. Furthermore, the use of government incentives can be explored to assess if network development could approach the preferred development pathway which is identified using the methodology and results articulated in this thesis.

Doctor of Philosophy(PhD) / The aim of this thesis is to support the evaluation of sustainable development strategies for industrial networks in the context of industrial ecology (IE). Industrial networks are a group of units which carry out, or contribute to, industrial activity, and are connected by material and energy flows, but also capital and information exchanges. The components of an industrial network encompass resource extraction, processing and refining, forming and assembly, use, disposal, as well as recycling and reprocessing. The motivation behind this research is the realisation that much of the current environmental system analysis focus within IE lacks a structured approach to considering: • system environment • dynamic nature of the system and its environment • economic and social impacts • the effect of uncertainty on analysis outcomes. It is argued in this thesis that current environmental analysis approaches used in IE can be improved in their capacity to capture the complexity of industrial systems, with the objective of promoting sustainable development. While IE emphasises the benefit of a systems approach to identifying environmental strategies in industry, analysis tools have to date not engaged extensively with important aspects such as the influence of system environment and dynamics on the viability of an environmental strategy, or with the economic or social impacts of industrial system development, which are equally important for sustainable development. Nor is the assessment of the effect of uncertainty on analysis outcomes an integral part of environmental analysis tools in IE. This is particularly significant when, in fact, the degree of uncertainty in assumptions and data used increases with the scope, and therefore the abstraction, of the system under consideration. IE will have to engage with the network and contextual complexities to a greater degree if it is to evolve from a concept to the application of its principles in practice. The main contribution of this thesis is therefore the development of a structured approach to analysing industrial networks for the purpose of identifying strategies to encourage sustainable development, while accounting for the complexity of the underlying system as well as the problem context. This analysis is intended to allow the identification of preferred network development pathways and to test the effectiveness of sustainable development strategies. A top-down, prescriptive approach is adopted for this purpose. This approach is chosen as the industrial network analysis is intended to identify how a network should develop, rather than focusing on how it could develop. Industrial networks are systems which are complex in both their structure and behaviour. This thesis also delivers a characterisation of these networks, which serves two purposes – quantifying key elements of structure and behaviour; and using this information to build a foundation for subsequent industrial network analysis. The value of such an approach can be seen in the following example. With a detailed understanding of individual network characteristics, both separately and collectively, it is possible to determine the source of issues, the means available to address them, any barriers that might exist, and the consequences of implementing any strategic interventions. The analysis approach proposed in this thesis is based on multi-criteria decisions analysis (MCDA), which, as a process, combines initial problem structuring and subsequent quantitative analysis stages. The tools employed within MCDA have been employed variously around considerations of sustainable development. Their value in this thesis is their integration within a rigorous analytical framework. Rigorous problem structuring is attractive as it helps elucidate the complexities of the system and its environment and is, by definition, designed to deal with multiple environmental social and economic criteria that would have to be considered to promote sustainable development. For the quantitative analysis, the industrial network analysis draws from existing analysis tools in IE, but predominately from other systems research disciplines, such as process systems engineering (PSE) and supply chain management (SCM). These fields, due to their maturity and practical focus, have invested a lot of research into system design and strategic planning, capturing system dynamics and uncertainty to ensure, within selected system constraints, that a proposed system or changes to a system are viable, and that the system is capable of achieving the stated objectives. Both PSE and SCM rely heavily on optimisation for system design and planning, and achieve good results with it as an analytical tool. The similarity between industrial networks and process systems / supply chains, suggests that an optimisation platform, specifically multi-objective dynamic optimisation, could be employed fruitfully for the analysis of industrial networks. This is the approach taken in this thesis. It is consistent with the “top down” approach advocated previously, which is deemed preferable for the identification and implementation analysis of strategic interventions. This enables the determination of a structure (design) that is “best” able to operate under future conditions (planning) with respect to the chosen sustainable development objectives. However, an analysis is only ever as good as its underlying data and assumptions. The complexity and scope of the industrial network and the challenge of articulating sustainable development target(s) give rise to significant uncertainties. For this reason a framework is developed within this thesis that integrates uncertainty analysis into the overall approach, to obtain insight into the robustness of the analysis results. Quantifying all the uncertainties in an industrial network model can be a daunting task for a modeller, and a decision-maker can be confused by modelling results. Means are therefore suggested to reduce the set of uncertainties that have to be engaged with, by identifying those which impact critically on model outcomes. However, even if uncertainty cannot be reduced, and the implementation of any strategy retains a degree of risk, the uncertainty analysis has the benefit that it forces an analyst to engage in more detail with the network in question, and to be more critical of the underlying assumptions. The analysis approach is applied to two case studies in this thesis: one deals with waste avoidance in an existing wood-products network in a large urban metropolis; the other with the potential for renewable energy generation in a developing economy. Together, these case studies provide a rich tableau within which to demonstrate the full features of the industrial network analysis. These case studies highlight how the context within which the relevant industrial network functions influences greatly the evolution of the network over time; how uncertainty is managed; and what strategies are preferred in each case in order to enhance the contribution of each network to sustainable development. This thesis makes an intellectual contribution in the following areas: • the characterisation of industrial networks to highlight sources of environmental issues, role the characteristics (could) play in the identification of (preferred) sustainable development strategies, and the need to explicitly consider these in a systems analysis. • the synthesis, adaptation and application of existing tools to fulfil the need for analysis tools in IE that can handle both contextual and system complexity, and address the above mentioned issues of lacking consideration of o system environment o dynamic nature of the system and its environment o economic and social impacts o the effect of uncertainty on analysis outcomes. • the development and demonstration of an industrial network analysis approach that o is flexible enough to model any industrial network at the inter-firm level, regardless of form and configuration of materials and products circulated, and depending on the existing network and the proposed strategies. o is able to encompass a wide range of environmental strategies, either individually or in combination depending on what best suits the situation, rather than focusing on any strategy in particular. o ensures long term viability of strategies, rather than short term solutions delivering incremental improvement. • the development of a comprehensive approach to capturing and assessing the effect of uncertainty on solution robustness for industrial network analysis, including the screening to determine the most important parameters, considering valuation and technical uncertainties, including future uncertainty. The industrial network analysis approach presented in this thesis looks more to how a network should develop (according to a set of sustainable development objectives), rather than how it may in actual fact develop. Consequently, the influence of agent interests and behaviour is not considered explicitly. This may be construed as a limitation of the industrial analysis approach. However, it is argued that the “top down” modelling approach favoured here is useful at a policy-making level. Here, for example, government instrumentalities, trade organisations and industry groupings, non-government organisations and community-based organisations are likely to be interested more in the performance of the network as a whole, rather than (necessarily) following the behaviour of individual agents within the network. Future work could well entertain the prospect of a mixed approach, in which the top-down approach of this thesis is complemented by a “bottom-up”, agent-based analysis. In this manner, it would be possible to give an indication of how attainable the identified industrial network development pathways are. Furthermore, the use of government incentives can be explored to assess if network development could approach the preferred development pathway which is identified using the methodology and results articulated in this thesis.

The creation and use of models is critical not only to the scientific process, but also to life in general. Selected features of a system are abstracted into a model that can then be used to gain knowledge of the workings of the observed system and even anticipate its future behaviour. A key feature of the modelling process is the identification of commonality. This allows previous experience of one model to be used in a new or unfamiliar situation. This recognition of commonality between models allows standards to be formed, especially in areas such as measurement. How everyday physical objects are measured is built on an ingrained acceptance of their underlying commonality. Complex systems, often with their layers of interwoven interactions, are harder to model and, therefore, to measure and predict. Indeed, the inability to compute and model a complex system, except at a localised and temporal level, can be seen as one of its defining attributes. The establishing of commonality between complex systems provides the opportunity to find common metrics. This work looks at two dimensional cellular automata, which are widely used as a simple modelling tool for a variety of systems. This has led to a very diverse range of systems using a common modelling environment based on a lattice of cells. This provides a possible common link between systems using cellular automata that could be exploited to find a common metric that provided information on a diverse range of systems. An enhancement of a categorisation of cellular automata model types used for biological studies is proposed and expanded to include other disciplines. The thesis outlines a new metric, the C-Value, created by the author. This metric, based on the connectedness of the active elements on the cellular automata grid, is then tested with three models built to represent three of the four categories of cellular automata model types. The results show that the new C-Value provides a good indicator of the gathering of active cells on a grid into a single, compact cluster and of indicating, when correlated with the mean density of active cells on the lattice, that their distribution is random. This provides a range to define the disordered and ordered state of a grid. The use of the C-Value in a localised context shows potential for identifying patterns of clusters on the grid.

This dissertation covers the two major parts of my Ph.D. research: i) developing a theoretical framework of complex networks and applying simulation and numerical methods to study the robustness of the network system, and ii) applying statistical physics concepts and methods to quantitatively analyze complex systems and applying the theoretical framework to study real-world systems. In part I, we focus on developing theories of interdependent networks as well as building computer simulation models, which includes three parts: 1) We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the networks significantly changes the critical density of failures, which can trigger the total disruption of the two-network system. Specifically, we find that the assortativity within a single network decreases the robustness of the entire system. 2) We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-p fraction of nodes. We find that as the coupling strength q between the two networks reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths q1 and q2 , which separate the behaviors of the giant component as a function of p into three different regions, and for q2 < q < q1 , we observe a hybrid order phase transition phenomenon. 3) We study the robustness of n interdependent networks with partially support-dependent relationship both analytically and numerically. We study a starlike network of n Erdos-Renyi (ER), SF networks and a looplike network of n ER networks, and we find for starlike networks, their phase transition regions change with n, but for looplike networks the phase regions change with average degree k . In part II, we apply concepts and methods developed in statistical physics to study economic systems. We analyze stock market indices and foreign exchange daily returns for 60 countries over the period of 1999-2012. We build a multi-layer network model based on different correlation measures, and introduce a dynamic network model to simulate and analyze the initializing and spreading of financial crisis. Using different computational approaches and econometric tests, we find atypical behavior of the cross correlations and community formations in the financial networks that we study during the financial crisis of 2008. For example, the overall correlation of stock market increases during crisis while the correlation between stock market and foreign exchange market decreases. The dramatic increase in correlations between a specific nation and other nations may indicate that this nation could trigger a global financial crisis. Specifically, core countries that have higher correlations with other countries and larger Gross Domestic Product (GDP) values spread financial crisis quite effectively, yet some countries with small GDPs like Greece and Cyprus are also effective in propagating systemic risk and spreading global financial crisis.

This dissertation concerns modeling two aspects of dynamics of complex networks: (1) response dynamics and (2) growth and formation. A particularly challenging class of networks are ones in which both nodes and links are evolving over time – the most prominent example is a financial network. In the first part of the dissertation we present a model for the response dynamics in networks near a metastable point. We start with a Landau-Ginzburg approach and show that the most general lowest order Lagrangians for dynamical weighted networks can be used to derive conditions for stability under external shocks. Using a closely related model, which is easier to solve numerically, we propose a powerful and intuitive set of equations for response dynamics of financial networks. We find the stability conditions of the model and find two phases: “calm” phase , in which changes are sub-exponential and where the system moves to a new, close-by equilibrium; “frantic” phase, where changes are exponential, with negative blows resulting in crashes and positive ones leading to formation of "bubbles". We empirically verify these claims by analyzing data from Eurozone crisis of 2009-2012 and stock markets. We show that the model correctly identifies the time-line of the Eurozone crisis, and in the stock market data it correctly reproduces the auto-correlations and phases observed in the data. The second half of the dissertation addresses the following question: Do networks that form due to local interactions (local in real space, or in an abstract parameter space) have characteristics different from networks formed of random or non-local interactions? Using interacting fields obeying Fokker-Planck equations we show that many network characteristics such as degree distribution, degree-degree correlation and clustering can either be derived analytically or there are analytical bounds on their behaviour. In particular, we derive recursive equations for all powers of the ensemble average of the adjacency matrix. We analyze a few real world networks and show that some networks that seem to form from local interactions indeed have characteristics almost identical to simulations based on our model, in contrast with many other networks.

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The drive toward robust systems design, especially with respect to system affordablility throughout the system life-cycle, has led to the development of several advanced design methods. While these methods have been extremely successful in satisfying the needs for which they have been developed, they inherently leave a critical area unaddressed. None of them fully considers the effect of requirements on the selection of solution systems. The goal of all of current modern design methodologies is to bring knowledge forward in the design process to the regions where more design freedom is available and design changes cost less. Therefore, it seems reasonable to consider the point in the design process where the greatest restrictions are placed on the final design, the point in which the system level requirements are set. Historically the requirements have been treated as something handed down from above. However, neither the customer nor the solution provider completely understood all of the options that are available in the broader requirements space. If a method were developed that provided the ability to understand the full scope of the requirements space, it would allow for a better comparison of potential solution systems with respect to both the current and potential future requirements. The key to a requirements conscious method is to treat requirements differently from the traditional approach. The method proposed herein is known as Requirements Controlled Design (RCD). By treating the requirements as a set of variables that control the behavior of the system, instead of variables that only define the response of the system, it is possible to determine a-priori what portions of the requirements space that any given system is capable of satisfying. Additionally, it should be possible to identify which systems can satisfy a given set of requirements and the locations where a small change in one or more requirements poses a significant risk to a design program. This thesis puts forth the theory and methodology to enable RCD, and details and validates a specific method called the Modified Strength Pareto Evolutionary Algorithm (MSPEA).