Foundations of Complex Systems

Many systems in nature can be described using discrete input–output maps. Essentially, these maps describe any system where an input space or parameter space maps into an output space. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another.

Many systems obey principles of least action, such as electricity taking paths of least resistance through a network and even drivers taking paths of shortest travel time. The dependence of such flows on the underlying network topology often results in a substantial waste of network resources and even sub-optimality caused by the topology itself. The Price of Anarchy (PoA) provides a measure of sub-optimality, being defined as the ratio of the cost of the worst case Nash equilibrium to that of the system’s global optimum.

Information is a key concept for understanding complex biological, economic and social systems. However, there is still no solid framework for analyzing non-intuitive high-order phenomena that take place in complex scenarios involving three or more agents. Recent efforts for addressing this issue by providing a multivariate extension of Shannon’s information theory often rely in one of two alternative notions: the total correlation (TC) [1] or the dual total correlation (DTC) [2].

Many complex systems, both natural, and man-made, can be represented as multiplex or interdependent networks. Multiple dependencies make a system more fragile: damage to one element can lead to avalanches of failures throughout the system. In this talk I will present recent developments about the structural properties of multiplex networks. The transition founded is asymmetric. It is hybrid in nature, having a discontinuity like a first-order transition, but exhibiting critical behavior, only above the transition, like a second-order transition.

Populations of identical Kuramoto oscillators are known to synchronize in a connected network. In a previous work [1], we introduced a frustration parameter in a population of identical oscillators that produces remote synchronization in units that are not connected but are related through some type of symmetry in the network topology. Here we present new results on the application of this principle to local perturbations of the frustration parameter that induce additional patterns of synchrony in the system.

We develop a Bayesian hierarchical model to identify communities of time series. Fitting the model provides an end-to-end community detection algorithm that does not extract information as a sequence of point estimates but propagates uncertainties from the raw data to the community labels. Our approach naturally supports multiscale community detection as well as the selection of an optimal scale using model comparison.

The heterogeneity of a spatially-embedded complex system quite often
carries important information about the function of the system as a
whole. This is the reason why the quantitative characterisation of
complex spatial patterns has received much attention in different
fields, from urbanism to neuroscience, from geography to economics,
from transportation to engineering. A particularly interesting problem
in this area is the quantification of spatial segregation, i.e., the
tendency of people to cluster around uniform patches of residential

We are interested in developing a computational architecture to support the dynamic creation of multilevel representations in the design and implementation of complex systems, including physical artefacts, social systems, and socio-technical systems. This is motivated by a longer term goal of understanding how to model autonomous evolving multilevel systems, e.g. to create self-programming computer systems, or to model and forecast the evolving dynamics of multilevel narratives in social media.

We are studying a society of agents that are exposed to information directly or indirectly via mass media and word of mouth. This is a social learning study, rather than a study on bounded confidence. Assuming that directly perceived information shows high accuracy, we show how the degree of exposure to the mass media projection and to the word of mouth interactions with neighbours in the social networks is decisive for the accuracy of the final opinion of agents.

Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected networks as inter-network interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point.