The ability to effectively control brain dynamics holds great promise for the enhancement of
cognitive function in humans and the betterment of their quality of life. Yet, successfully …

Traditional approaches to understanding the brain's resilience to neuropathology have
identified neurophysiological variables, often described as brain or cognitive “reserve,” …

The biologist JBS Haldane, when asked what we can learn about the Creator by examining
the world, is said to have replied “an inordinate fondness for beetles”[705]. Today's …

Circuit building blocks of gene regulatory networks (GRN) have been identified through the
fibration symmetries of the underlying biological graph. Here, we analyse analytically six of …

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 …

A major ambition of systems science is to uncover the building blocks of any biological
network to decipher how cellular function emerges from their interactions. Here, we …

In this paper, we use the language of operads to study open dynamical systems. More
specifically, we study the algebraic nature of assembling complex dynamical systems from …

We consider the general model for dynamical systems defined on a simplicial complex. We
describe the conjugacy classes of these systems and show how symmetries in a given …

Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from
the perspectives of symmetries, offering a framework for introducing problem-specific …

Dynamical systems with a network structure can display remarkable phenomena such as
synchronisation and anomalous synchrony breaking. A methodology for classifying patterns …