Toward a spectral theory of cellular sheaves
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Publication:2304007
DOI10.1007/s41468-019-00038-7zbMath1439.05137arXiv1808.01513OpenAlexW3105346780MaRDI QIDQ2304007
Robert W. Ghrist, Jakob K. Hansen
Publication date: 6 March 2020
Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.01513
Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Sheaf cohomology in algebraic topology (55N30)
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Cites Work
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- On Kirchhoff's theorems with coefficients in a line bundle
- Angular synchronization by eigenvectors and semidefinite programming
- Graph spectra in computer science
- Spectra of graphs
- Spanning forests and the vector bundle Laplacian
- Representation theoretic patterns in three-dimensional cryo-electron microscopy. II: The class averaging problem
- User-friendly tail bounds for sums of random matrices
- Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry
- Posets, regular CW complexes and Bruhat order
- Homological connectivity of random 2-complexes
- Discretization of vector bundles and rough Laplacian
- Manifolds, tensor analysis, and applications.
- Hilbert complexes
- Computing Betti numbers via combinatorial Laplacians
- Computational homology
- The Schur complement and its applications
- Persistent local systems
- The geometry of synchronization problems and learning group actions
- Persistent homology and microlocal sheaf theory
- Isoperimetric inequalities in simplicial complexes
- Spectra of combinatorial Laplace operators on simplicial complexes
- On factor width and symmetric \(H\)-matrices
- Diffusion maps
- Harmonic functions and boundary value problems on a chain complex
- Ranking and Sparsifying a Connection Graph
- Vector diffusion maps and the connection Laplacian
- Euler Calculus with Applications to Signals and Sensing
- Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
- Spectral Sparsification of Graphs
- Linear-time encodable and decodable error-correcting codes
- Expander graphs and their applications
- Reaching a Consensus
- Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
- Sparse Sums of Positive Semidefinite Matrices
- Kron Reduction of Graphs With Applications to Electrical Networks
- Assignments to sheaves of pseudometric spaces
- Random Walks on Simplicial Complexes and the Normalized Hodge 1-Laplacian
- Spectral sparsification of simplicial complexes for clustering and label propagation
- Coordination of groups of mobile autonomous agents using nearest neighbor rules
- Positive Alexander Duality for Pursuit and Evasion
- Mixing in High-Dimensional Expanders
- Limits in dagger categories
- A Cheeger Inequality for the Graph Connection Laplacian
- Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture: with an Appendix by Warren Dicks
- Local Systems and Constructible Sheaves
