70 citations · 78 across the 6 of their papers we have counts for
8 papers
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…
Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding
Thomas Gebhart, Jakob Hansen, Paul Schrater
Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting represent…
Sheaf Neural Networks
Jakob Hansen, Thomas Gebhart
We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are…
Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions
Hans Riess, Jakob Hansen, Robert Ghrist
Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers a…
Expansion in Matrix-Weighted Graphs
Jakob Hansen
A matrix-weighted graph is an undirected graph with a positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacen…
Opinion Dynamics on Discourse Sheaves
Jakob Hansen, Robert Ghrist
We introduce a novel class of Laplacians and diffusion dynamics on discourse sheaves as a model for network dynamics, with application to opinion dynamics on social networks. These…