All beauty, richness and harmony in the emergent dynamics of a complex system largely
depend on the specific way in which its elementary components interact. The last twenty-five …

The complexity of many biological, social and technological systems stems from the richness
of the interactions among their units. Over the past decades, a variety of complex systems …

Complex networks have been successfully used to describe the spread of diseases in
populations of interacting individuals. Conversely, pairwise interactions are often not …

Various systems in physics, biology, social sciences and engineering have been
successfully modeled as networks of coupled dynamical systems, where the links describe …

Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

Higher-order interactions might play a significant role in the collective dynamics of the brain.
With this motivation, we here consider a simplicial complex of neurons, in particular …

Encoding brain regions and their connections as a network of nodes and edges captures
many of the possible paths along which information can be transmitted as humans process …

We provide a short introduction to the field of topological data analysis (TDA) and discuss its
possible relevance for the study of complex systems. TDA provides a set of tools to …

Many complex systems find a convenient representation in terms of networks: structures
made by pairwise interactions (links) of elements (nodes). For many biological and social …

Networks are a widely used and efficient paradigm to model real-world systems where basic
units interact pairwise. Many body interactions are often at play, and cannot be modelled by …