Foundations of Complex Systems

Effective collective response in multi-agent systems critically depends on suitable information transfers among agents, and thus on the topology of their interaction network. Here, we present an archetypal model of distributed decision-making—the leader-follower linear consensus—and discuss how the network topology affects the collective capacity of the system to follow a dynamic driving signal (the “leader”).

Recent developments in understanding the structure and dynamics of networks have transformed research in many fields, however, the Geosciences have not benefited much from this new conceptual framework. We focus our study on River deltas, which exhibit complex channel networks, whose connectivity constrains, if not drives, their morphology and evolution. Thus, understanding and quantifying properties of these complex patterns is an essential step to solve the inverse problem of inferring process from form and predict their response in a heavily anthropogenic impacted environment.

We study a spreading pattern of epidemics over a complex network. In susceptible-infected (SI) model, it has been well known that the initial growth of infected nodes follows the exponential form as a function of time t with a time scale described by degree statistics, and that so does the final growth with an infection rate as a time scale. We put focus on the dynamics in the intermediate range except for both the early- and late- time regime and examine on the complex networks governed by degree distribution P_d(k)^{-γ}.

The coupling and coordination of competing elements in a system have been studied. Notions such as the Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution in game theoretic models (Cobb and Sen, 2014). Also, it has been established that natural dynamics are leading to a particular system equilibrium or coordination, according to the players’ interactions.

Infectious diseases are of the most fatal threats in human history[1]. Many studies have been made to investigate the way these diseases become epidemic and how it is possible to prevent them from spreading to the whole society. Of the most interesting properties of the phenomenon is the outbreak of the disease which resembles a phase transition. There are some examples of coinections that two or more pathogens cooperate in infecting individuals; i.e. if one is infected by one disease, the chance to become infected by the second one will be much more.

The multiplex network paradigm has proven quite useful in the study of many real-world complex systems, by allowing to retain full information about the several kind of relationships among the elements of a system. However, to date there is not any established way of comparing the structural complexity of two multiplex networks. In this work, we use techniques inspired by algorithmic information theory to define a new metric for evaluating the information complexity of a multiplex network.

Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the stochastic rules, the ability to predict system configurations is generally characterized by large uncertainty. Selecting a fraction of the nodes and observing their state may help to reduce the uncertainty about the unobserved nodes.

Recently higher order networks describing the interactions between two or more nodes are attracting large attention [1] because they describe systems as different as functional brain networks or collaboration networks beyond the framework of pairwise interactions. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. glued along their faces. Simplicial complexes are structures that can be generalized by cell complexes formed by gluing “motifs” having a polytope structure.

Most epidemic spreading models assume memoryless agents and independent processes. Nevertheless, many real-life cases are manifestly time-sensitive and show strong correlations. We develop a microscopic description of the infection mechanism that is equipped with memory of past exposures and incorporates the combined effect of multiple infectious sources.

Complex Network theory applied to many real-world systems has proven to be a powerful tool to analyze and solve problems in complex systems. The Static Network approach is a developed field with lots of existing theories and models. However, real-world complex systems are not static, they evolve over time, change in size, create new connections etc. Approximating them as static is not always appropriate and sometimes it is possible to lose the crucial information by neglecting the time steps of interaction in the network.