Search Results - "Shonkwiler, Clayton"

Fusion Frame Homotopy and Tightening Fusion Frames by Gradient Descent by Needham, Tom, Shonkwiler, Clayton

“…Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on…”
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Symplectic geometry and connectivity of spaces of frames by Needham, Tom, Shonkwiler, Clayton

“…Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic…”
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THE SYMPLECTIC GEOMETRY OF CLOSED EQUILATERAL RANDOM WALKS IN 3-SPACE by Cantarella, Jason, Shonkwiler, Clayton

“…A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of…”
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Probability Theory of Random Polygons from the Quaternionic Viewpoint by Cantarella, Jason, Deguchi, Tetsuo, Shonkwiler, Clayton

“…We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Hausmann and Knutson, using the Hopf map on…”
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Robocasting of Ceramic Fischer-Koch S Scaffolds for Bone Tissue Engineering by Baumer, Vail, Gunn, Erin, Riegle, Valerie, Bailey, Claire, Shonkwiler, Clayton, Prawel, David

“…Triply Periodic Minimal Surfaces (TPMS) are promising structures for bone tissue engineering scaffolds due to their relatively high mechanical energy…”
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Higher-dimensional linking integrals by SHONKWILER, CLAYTON, VELA-VICK, DAVID SHEA

“…We derive an integral formula for the linking number of two submanifolds of the n, of the product S^n \times \mathbb{R}^m…”
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Admissibility and frame homotopy for quaternionic frames by Needham, Tom, Shonkwiler, Clayton

“…We consider the following questions: when do there exist quaternionic frames with given frame spectrum and given frame vector norms? When such frames exist, is…”
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Toric symplectic geometry and full spark frames by Needham, Tom, Shonkwiler, Clayton

“…The collection of d×N complex matrices with prescribed column norms and singular values forms an algebraic variety, which we refer to as a frame space…”
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New Stick Number Bounds from Random Sampling of Confined Polygons by Eddy, Thomas D., Shonkwiler, Clayton

“…The stick number of a knot is the minimum number of segments needed to build a polygonal version of the knot. Despite its elementary definition and relevance…”
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Distributions of distances and volumes of balls in homogeneous lens spaces by Balch, Brenden, Peterson, Chris, Shonkwiler, Clayton

“…Lens spaces are a family of manifolds that have been a source of many interesting phenomena in topology and differential geometry. Their concrete construction,…”
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The Complete Dirichlet-to-Neumann Map for Differential Forms by Sharafutdinov, Vladimir, Shonkwiler, Clayton

“…The Dirichlet-to-Neumann map for differential forms on a Riemannian manifold with boundary is a generalization of the classical Dirichlet-to-Neumann map which…”
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Random Triangles and Polygons in the Plane by Cantarella, Jason, Needham, Tom, Shonkwiler, Clayton, Stewart, Gavin

“…In 1997, Jean-Claude Hausmann and Allen Knutson introduced a natural and beautiful correspondence between planar n-gons and the Grassmann manifold of 2-planes…”
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Spherical geometry and the least symmetric triangle by Bowden, Laney, Haynes, Andrea, Shonkwiler, Clayton, Shukert, Aaron

“…We study the problem of determining the least symmetric triangle, which arises both from pure geometry and from the study of molecular chirality in chemistry…”
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New Superbridge Index Calculations from Non-Minimal Realizations by Shonkwiler, Clayton

“…Journal of Knot Theory and Its Ramifications 31 (2022), no. 10, 2250063 Previous work used polygonal realizations of knots to reduce the problem of computing…”
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All Prime Knots Through 10 Crossings Have Superbridge Index $\leq 5 by Shonkwiler, Clayton

“…Journal of Knot Theory and Its Ramifications 31 (2022), no. 4, 2250023 This paper gives new upper bounds on the stick numbers of the knots $9_{18}$, $10_{18}$,…”
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Geometric Approaches to Matrix Normalization and Graph Balancing by Needham, Tom, Shonkwiler, Clayton

“…Normal matrices, or matrices which commute with their adjoints, are of fundamental importance in pure and applied mathematics. In this paper, we study a…”
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New Computations of the Superbridge Index by Shonkwiler, Clayton

“…Journal of Knot Theory and Its Ramifications 29 (2020), no. 14, 2050096 The knots $8_1$, $8_2$, $8_3$, $8_5$, $8_6$, $8_7$, $8_8$, $8_{10}$, $8_{11}$,…”
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Fusion Frame Homotopy and Tightening Fusion Frames by Gradient Descent by Needham, Tom, Shonkwiler, Clayton

“…Journal of Fourier Analysis and Applications 29 (2023), no. 4, 51 Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool…”
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THE EXPECTED TOTAL CURVATURE OF RANDOM POLYGONS by Cantarella, Jason, Grosberg, Alexander Y., Kusner, Robert, Shonkwiler, Clayton

“…We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes…”
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Toric Symplectic Geometry and Full Spark Frames by Needham, Tom, Shonkwiler, Clayton

“…Applied and Computational Harmonic Analysis 61 (2022), 254-287 The collection of $d \times N$ complex matrices with prescribed column norms and prescribed…”
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