The brain is an extraordinarily complex system that facilitates the optimal integration of
information from different regions to execute its functions. With the recent advances in …

Functional brain networks are often constructed by quantifying correlations between time
series of activity of brain regions. Their topological structure includes nodes, edges …

The grain boundary character distribution strongly affects the properties of polycrystalline
materials. Grain boundaries of similar characters form networks, whose topological …

In recent years, persistent homology (PH) and topological data analysis (TDA) have gained
increasing attention in the fields of shape recognition, image analysis, data analysis …

In this review work, we outline a conceptual path that, starting from the numerical
investigation of the transition between weak chaos and strong chaos in Hamiltonian systems …

We study continuum percolation with disks, a variant of continuum percolation in two-
dimensional Euclidean space, by applying tools from topological data analysis. We interpret …

Living systems are subject to the arrow of time; from birth, they undergo complex
transformations (self-organization) in a constant battle for survival, but inevitably ageing and …

In econophysics, the achievements of information filtering methods over the past 20 years,
such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered …

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three
spatial dimensions. Our model Hamiltonian is defined on the basis of a continuum version of …

The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined
with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary …