Maximum caliber networks
A recipe goes viral on social media. It reaches so many people that the prices of the ingredients used in it increase. The higher prices drive farmers to focus on these products, straining the nutrients in the ground and the local water cycle. Water use then surpasses a tipping point, triggering a drought that strains food supply. Places both near and far that secure their stocks from the strained region must then demand more from other locations, and so the effects keep spreading.
None of these steps is particularly surprising on its own. What is surprising is how quickly and how far the consequences travel. The main reason for this is that most environmental, social and economic systems - especially modern ones - are well described as networks: their components influence each other through connections that are not constrained by physical distances. Because these interactions produce change over time, such systems must be studied dynamically, and random properties of this evolution call for a probabilistic treatment.
In his thesis, Noam Abadi develops a statistical framwork for integrating the three components – networks, dynamics and randomness. It applies the method of maximum caliber – the dynamic extension of maximum entropy – to networks, allowing the construction of probabilistic models for out-of-equilibrium network processes. Abadi applies the framework to models of social and population dynamics, and empirical data on European energy systems. Together, these applications illustrate how statistical descriptions of dynamic networks can be used to analyse the emergence, amplification, and propagation of non-local effects in complex systems.