Complexity, Criticality, and Computation (C3) and beyond…

Complex systems is a new approach to science, engineering, health, management, and any other field that studies how relationships between parts give rise to the collective emergent behaviours of the entire system, and how the system interacts with its environment. The methods are not necessarily new (at least for physicists) but the way to approach problems is totally novel. The holistic approach and the focus of inquiry is totally different and transcends different disciplines’ methods. The focus is mainly the analysis of the underlying ”connectome” for detection of causal hotspots, attribution of patterns to causal factors, and design (where management is part of the design).

What makes a system ‘complex’? A system can be thought of as complex if its dynamics cannot be easily predicted, or explained, as a linear summation of the individual dynamics of its components. In other words, the many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part alone (‘the whole is more than the sum of the parts’). There is a growing awareness that complexity is strongly related to criticality: the behaviour of dynamical spatiotemporal systems at an order/disorder phase transition where scale invariance prevails. This is an important point, where criticality actually means optimality and resilience. Many theorems have been proven this result for many complex systems. At the moment, many bio-inspired technologies are designed by mimicking the optimal patterns in nature.

Complex systems can also be viewed as distributed information-processing systems, particularly in the domains of computational neuroscience, health, bioinformatics, systems biology and artificial life. That is why information theory based models are the majority of models used to analyze and design complex systems together with network and decision sciences. Consciousness emerging from neuronal activity and interactions, cell behaviour resultant from gene regulatory networks and swarming behaviour are all examples of global system behaviour emerging as a result of the local interactions of the individuals (neurons, genes, animals). Can these interactions be seen as a generic computational process? This question is a relevant questions linking computation to complexity and criticality with the aim of a general theory and methods.

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