Topological complexity is a central concept that bridges the abstract methodologies of algebraic topology with the practical challenges of robot motion planning. It provides a numerical invariant that ...

Machine learning is revolutionizing fundamental science by tackling long-standing mathematical challenges. A key example is ...

This is a preview. Log in through your library . Abstract The Lusternik-Schnirelmann category and topological complexity are important invariants of manifolds (and more generally, topological spaces).

A study led by Professor Ginestra Bianconi from Queen Mary University of London, in collaboration with international ...

The branch of mathematics known as topology has become a cornerstone of modern physics thanks to the remarkable -- and above all reliable -- properties it can impart to a material or system.

Higher-order topological dynamics combines higher-order interactions, topology and non-linear dynamics giving rise to new emergent phenomena. These phenomena encode information which can dramatically ...