70 citations · 316 across the 56 of their papers we have counts for
4 papers · 1 filter
Clearing in Liability Networks via Sheaves on Directed Hypergraphs
Robert Ghrist
We associate to a decorated liability network a liability sheaf on a directed hypergraph whose hyperedges separate the distribution of payments from the collection of receipts. Cle…
Neural Networks as Local-to-Global Computations
Vicente Bosca, Robert Ghrist
We construct a cellular sheaf from any feedforward ReLU neural network by placing one vertex for each intermediate quantity in the forward pass and encoding each computational step…
Impossible by Degrees: Cohomology & Bistable Visual Paradox
Lewis Ghrist, Robert Ghrist
The Penrose triangle, staircase, and related ``impossible objects'' have long been understood as related to first cohomology : the obstruction to extending locally consistent…
Selective Adaptation of Beliefs and Communication on Cellular Sheaves
Vicente Bosca, Robert Ghrist
We extend opinion dynamics on discourse sheaves to incorporate "directional stubbornness": agents may hold fixed positions in specified directions of their opinion stalk while rema…