130 citations · 345 across the 38 of their papers we have counts for
6 papers · 1 filter
Finiteness and exponential growth of full graph -spectra
Matthew J. Colbrook
We prove that the full spectrum of the graph -Laplacian is finite for every finite graph and every real . This resolves the problem of finiteness of the full graph spectrum…
A Novel Use of Pseudospectra in Mathematical Biology: Understanding HPA Axis Sensitivity
Catherine Drysdale, Matthew J. Colbrook
The Hypothalamic-Pituitary-Adrenal (HPA) axis is a major neuroendocrine system, and its dysregulation is implicated in various diseases. This system also presents interesting mathe…
Computing Spectral Size: Rigorous Algorithms and the Limits of Computation
Matthew J. Colbrook, Mark Embree, Jake Fillman
Many structures in mathematical physics and dynamics exhibit intricate fractal geometry. Such behavior appears prominently in quantum mechanics and materials science through spectr…
On the computation of geometric features of spectra of linear operators on Hilbert spaces
Matthew J. Colbrook
Computing spectra is a central problem in computational mathematics with an abundance of applications throughout the sciences. However, in many applications gaining an approximatio…
The foundations of spectral computations via the Solvability Complexity Index hierarchy
Matthew J. Colbrook, Anders C. Hansen
The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general boun…
Computing Spectral Measures and Spectral Types
Matthew John Colbrook
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, abso…