Cellular sheaves are a discrete model for the theory of sheaves on cell complexes. They carry a canonical cochain complex computing their cohomology. This thesis develops the theory of the Hodge Laplacians of this complex, as well as avenues for their application to concrete engineering and data analysis problems. The sheaf Laplacians so developed are a vast generalization of the graph Laplacians studied in spectral graph theory. As such, they admit generalizations of many results from spectral graph theory and the spectral theory of discrete Hodge Laplacians. A theory of approximation of cellular sheaves is developed, and algorithms for producing spectrally good approximations are given, as well as a generalization of the notion of expande...
Abstract. We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms o...
Abstract. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order gener...
We compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficie...
This dissertation proposes cellular sheaf theory as a method for decomposing data analysis problems....
This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science...
This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science...
Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing pers...
This dissertation proposes cellular sheaf theory as a method for decomposing data analysis problems....
This dissertation proposes cellular sheaf theory as a method for decomposing data analysis problems....
This note advertises the theory of cellular sheaves and cosheaves, which are de-vices for conducting...
This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science...
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, rando...
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, rando...
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, rando...
Continuation of algebraic structures in families of dynamical systems is described using category th...
Abstract. We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms o...
Abstract. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order gener...
We compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficie...
This dissertation proposes cellular sheaf theory as a method for decomposing data analysis problems....
This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science...
This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science...
Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing pers...
This dissertation proposes cellular sheaf theory as a method for decomposing data analysis problems....
This dissertation proposes cellular sheaf theory as a method for decomposing data analysis problems....
This note advertises the theory of cellular sheaves and cosheaves, which are de-vices for conducting...
This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science...
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, rando...
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, rando...
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, rando...
Continuation of algebraic structures in families of dynamical systems is described using category th...
Abstract. We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms o...
Abstract. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order gener...
We compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficie...