Graph theory is now becoming a standard tool in system-level neuroscience. However,
endowing observed brain anatomy and dynamics with a complex network structure does not …

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 …

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 …

Epidemic outbreaks represent a significant concern for the current state of global health,
particularly in Brazil, the epicentre of several vector-borne disease outbreaks and where …

Euler characteristic (χ)⁠, a topological invariant, helps to understand the topology of a
network or complex. We demonstrate that the multi-scale topological information of …

We investigate the higher-order connectivity of scale-free networks using algebraic topology.
We model scale-free networks as preferential attachment graphs, and we study the …

This exploratory study delves into persistent homology, an integral component of TDA that
initially aimed at differentiating between signal and noise. We explore two methodologies for …

Chapter Highlights We discuss the modern mathematical tools for studying the topology of
pore space. In Sect. 3.1. Minkowski functionals are introduced through the paradigm of Mark …

Protein structure analysis and classification, which is fundamental for predicting protein
function, still poses formidable challenges in the fields of molecular biology, mathematics …

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 …