Your browser doesn't support javascript.
loading
Mostrar: 20 | 50 | 100
Resultados 1 - 1 de 1
Filtrar
Más filtros










Base de datos
Asunto principal
Intervalo de año de publicación
1.
Chaos ; 32(2): 023128, 2022 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-35232052

RESUMEN

Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, k-dimensional "simplices") and how they are influenced through higher-order interactions. A prime example lies in neuroscience where groups of neurons (not individual ones) may provide building blocks for neurocomputation. Here, we study consensus dynamics on edges in simplicial complexes using a type of Laplacian matrix called a Hodge Laplacian, which we generalize to allow higher- and lower-order interactions to have different strengths. Using techniques from algebraic topology, we study how collective dynamics converge to a low-dimensional subspace that corresponds to the homology space of the simplicial complex. We use the Hodge decomposition to show that higher- and lower-order interactions can be optimally balanced to maximally accelerate convergence and that this optimum coincides with a balancing of dynamics on the curl and gradient subspaces. We additionally explore the effects of network topology, finding that consensus over edges is accelerated when two-simplices are well dispersed, as opposed to clustered together.


Asunto(s)
Neuronas , Consenso
SELECCIÓN DE REFERENCIAS
DETALLE DE LA BÚSQUEDA
...