"Complexity Science: Percolation, Networks and Information Theory"

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Complexity science is rapidly evolving and finds wide application in fields as diverse as physics, biology, linguistics, and sociology. The present proposal deals with three areas: percolation, networks, and mutual information. Percolation is the sudden emergence of long-range connectivity as a control parameter is varied. Percolation phenomena on individual networks with simple links have been studied in detail but in reality most networks do not exist in isolation, may have more than one type of link, or exhibit different forms of propagation referred to as generalized contagion. For example infrastructure and technological networks are often coupled or 'interdependent'. Social dynamics can reflect the history of exposure. Recently, several generalizations of percolation have been proposed to deal with these situations. They exhibit unexpected behaviour, inconsistent with that of ordinary percolation. It is not clear, for example, how coupling can change the nature of breakdown near the transition. The details and interrelationships between these models as well as an overarching theory are still unclear, but their applicability to real world problems is increasingly evident. We will contribute to understanding these models and identify scenarios to which they or similar models apply and what the consequences might be.