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Title: Information, causality, and observability approaches to understand complex systems
Author: Bianco-Martinez, Ezequiel Julian
ISNI:       0000 0004 5914 4957
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 2015
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The objective of this thesis is to propose fundamental concepts, analytical and numerical tools, and approaches to characterize, understand, and better observe complex systems. The scientific contribution of this thesis can be separated in tree topics. In the first one, we show how to theoretically estimate the Mutual Information Rate (MIR), the amount of mutual information transmitted per unit of time between two time-series. We then show how a quantity derived from it can be successfully used to infer the network structure of a complex system. The proposed inference methodology shows to be robust in the presence of additive noise, different time-series lengths, and heterogeneous node dynamics and coupling strengths. It also shows to be superior in performance for networks formed by nodes possessing different time-scales, as compared to inference methods based on mutual information (MI). In the second topic, a deep analysis of causality from the space-time properties of the observed probabilistic space is performed. We show the existence of special regions in the state space which indicate variable ranges responsible for most of the information exchanged between two variables. We define a new causality measure named CaMI that explores a property we have understood: in order to detect if there is a flow of information from X to Y, one only needs to check the positiveness of the MI between trajectories in X and Y, however assuming that the observational resolution in Y is larger than in X. Moreover, we show how the assessment of causality can be done when we consider partitions with arbitrary, but equal rectangular cells in the probabilist space, what naturally facilitates the calculation of CaMI. In the third topic, we develop a symbolic coefficient of observability that allows us to understand what is the reduced set of accessible variables to observe a complex system, such that it can be fully reconstructed from the set of observed variables, regardless of its dimension. Using this symbolic coefficient, we explain how it is possible to compare different complex systems from the point of view of observability and how to construct systems of any dimensionality that can be fully observed by only one variable.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: System analysis ; Chaotic behavior in systems ; Information theory ; Time-series analysis ; Network inference