Optimisation in ‘Self-modelling’ Complex Adaptive Systems

When a dynamical system with multiple point attractors is released from an arbitrary initial condition it will relax into a configuration that locally resolves the constraints or opposing forces between interdependent state variables. However, when there are many conflicting interdependencies between variables, finding a configuration that globally optimises these constraints by this method is unlikely, or may take many attempts. Here we show that a simple distributed mechanism can incrementally alter a dynamical system such that it finds lower energy configurations, more reliably and more quickly. Specifically, when Hebbian learning is applied to the connections of a simple dynamical system undergoing repeated relaxation, the system will develop an associative memory that amplifies a subset of its own attractor states. This modifies the dynamics of the system such that its ability to find configurations that minimise total system energy, and globally resolve conflicts between interdependent variables, is enhanced. Moreover, we show that the system is not merely ‘recalling’ low energy states that have been previously visited but ‘predicting’ their location by generalising over local attractor states that have already been visited. This ‘self-modelling’ framework, i.e. a system that augments its behaviour with an associative memory of its own attractors, helps us better-understand the conditions under which a simple locally-mediated mechanism of self-organisation can promote significantly enhanced global resolution of conflicts between the components of a complex adaptive system. We illustrate this process in random and modular network constraint problems equivalent to graph colouring and distributed task allocation problems

If you can't be with the one you love, love the one you're with: How individual habituation of agent interactions improves global utility

Simple distributed strategies that modify the behaviour of selfish individuals in a manner that enhances cooperation or global efficiency have proved difficult to identify. We consider a network of selfish agents who each optimise their individual utilities by coordinating (or anti-coordinating) with their neighbours, to maximise the pay-offs from randomly weighted pair-wise games. In general, agents will opt for the behaviour that is the best compromise (for them) of the many conflicting constraints created by their neighbours, but the attractors of the system as a whole will not maximise total utility. We then consider agents that act as 'creatures of habit' by increasing their preference to coordinate (anti-coordinate) with whichever neighbours they are coordinated (anti-coordinated) with at the present moment. These preferences change slowly while the system is repeatedly perturbed such that it settles to many different local attractors. We find that under these conditions, with each perturbation there is a progressively higher chance of the system settling to a configuration with high total utility. Eventually, only one attractor remains, and that attractor is very likely to maximise (or almost maximise) global utility. This counterintutitve result can be understood using theory from computational neuroscience; we show that this simple form of habituation is equivalent to Hebbian learning, and the improved optimisation of global utility that is observed results from wellknown generalisation capabilities of associative memory acting at the network scale. This causes the system of selfish agents, each acting individually but habitually, to collectively identify configurations that maximise total utility

Global adaptation in networks of selfish components: emergent associative memory at the system scale

In some circumstances complex adaptive systems composed of numerous self-interested agents can self-organise into structures that enhance global adaptation, efficiency or function. However, the general conditions for such an outcome are poorly understood and present a fundamental open question for domains as varied as ecology, sociology, economics, organismic biology and technological infrastructure design. In contrast, sufficient conditions for artificial neural networks to form structures that perform collective computational processes such as associative memory/recall, classification, generalisation and optimisation, are well-understood. Such global functions within a single agent or organism are not wholly surprising since the mechanisms (e.g. Hebbian learning) that create these neural organisations may be selected for this purpose, but agents in a multi-agent system have no obvious reason to adhere to such a structuring protocol or produce such global behaviours when acting from individual self-interest. However, Hebbian learning is actually a very simple and fully-distributed habituation or positive feedback principle. Here we show that when self-interested agents can modify how they are affected by other agents (e.g. when they can influence which other agents they interact with) then, in adapting these inter-agent relationships to maximise their own utility, they will necessarily alter them in a manner homologous with Hebbian learning. Multi-agent systems with adaptable relationships will thereby exhibit the same system-level behaviours as neural networks under Hebbian learning. For example, improved global efficiency in multi-agent systems can be explained by the inherent ability of associative memory to generalise by idealising stored patterns and/or creating new combinations of sub-patterns. Thus distributed multi-agent systems can spontaneously exhibit adaptive global behaviours in the same sense, and by the same mechanism, as the organisational principles familiar in connectionist models of organismic learning

Cluster damage robustness analysis and space independent community detection in complex networks

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis investigates the evolution of two very different complex systems using network theory. This multi-disciplinary technique is widely used to model and analyse vastly diverse systems of multiple interacting components, and therefore, it is applied in this thesis to study the complexity of the systems. This complexity is rooted in the components’ interactions such that the whole system is more than the sum of all the individual parts. The first novelty in this research is the proposal of a new type of structural perturbation, cluster damage, for measuring another dimension of network robustness. The second novelty is the first application of a community detection method, which uncovers space-independent communities in spatial networks, to airport and linguistic networks. A critical property of complex systems – robustness – is explored within a partial model of the Internet, by demonstrating a novel perturbation strategy based on the iterative removal of clusters. The main contribution of this theoretical case study is the methodology for cluster damage, which has not been investigated by literature on the robustness of complex networks. The model, part of the Internet at the Autonomous System level, only serves as a domain where the novel methodology is demonstrated, and it is chosen because the Internet is known to be robust due to its distributed (non-centralised) nature, even though it is often subjected to large perturbations and failures. The first applied case study is in the field of air transportation. Specifically, it explores the topology and passenger flows of the United States Airport Network (USAN) over two decades. The network model consists of a time-series of six network snapshots for the years 1990, 2000 and 2010, which capture bi-monthly passenger flows among US airports. Since the network is embedded in space, the volume of these flows is naturally affected by spatial proximity, and therefore, a model (recently proposed in the literature) accounting for this phenomenon is used to identify the communities of airports that have particularly high flows among them, given their spatial separation. The second applied case study – in the field of language acquisition – investigates the word co-occurrence network of children, as they develop their linguistic abilities at an early age. Similarly to the previous case study, the network model consists of six children and three discrete developmental stages. These networks are not embedded in physical space, but they are mapped to an artificial semantic space that defines the semantic distance between pairs of words. This novel approach allows for an additional dimension of network information that results in a more complete dataset. Then, community detection identifies groups of words that have particularly high co-occurrence frequency, given their semantic distance. This research highlights the fact that some general techniques from network theory, such as network modelling and analysis, can be successfully applied for the study of diverse systems, while others, such as community detection, need to be tailored for the specific system. However, methods originally developed for one domain may be applied somewhere completely new, as illustrated by the application of spatial community detection to a non-spatial network. This underlines the importance of inter-disciplinary research

Biologically inspired methods for organizing distributed services on sensor networks

Tales HeimfarthPaderborn, Univ., Diss., 200