70 citations · 316 across the 56 of their papers we have counts for
19 papers · 1 filter
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…
Precision-Graded Cohomology and Arithmetic Persistence for Network Sheaves
Robert Ghrist, Cassie Ding
Persistent homology tracks topological features across geometric scales, encoding birth and death of cycles as barcodes. We develop a complementary theory where the filtration para…
Obstructions to Reality: Torsors & Visual Paradox
Robert Ghrist, Zoe Cooperband
Visual paradoxes like the Penrose staircase present a fundamental tension: locally coherent geometric relationships that cannot be realized globally. Inspired by Penrose's observat…
Unified Origami Kinematics via Cosheaf Homology
Zoe Cooperband, Robert Ghrist
We establish a novel local-global framework for analyzing rigid origami mechanics through cosheaf homology, proving the equivalence of truss and hinge constraint systems via an ind…
A Cosheaf Theory of Reciprocal Figures: Planar and Higher Genus Graphic Statics
Zoe Cooperband, Robert Ghrist, Jakob Hansen
This paper introduces cellular sheaf theory to graphical methods and reciprocal constructions in structural engineering. The elementary mechanics and statics of trusses are derived…