Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- 42C15 (3)
- Equiangular tight frame (2)
- 05E30 (1)
- Classification (1)
- Computer applications (1)
-
- Difference sets (1)
- Differential equations (1)
- Eigenvalues (1)
- Equiangular tight frames (1)
- Frames (Mathematics) (1)
- Fuel efficiency (1)
- Graph theory (1)
- Group divisible design (1)
- Hadamard matrix (1)
- Learning (1)
- Machine (1)
- Military aircraft operations (1)
- Nonlinear waves (1)
- Numerical analysis (1)
- Polynomials (1)
- Runge Kutta Method (1)
- Schrodinger Equation (1)
- Steiner system (1)
- Strongly regular graph (1)
- Text (1)
- Publication
- Publication Type
Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Equiangular Tight Frames That Contain Regular Simplices, Matthew C. Fickus, John Jasper, Emily J. King, Dustin G. Mixon
Equiangular Tight Frames That Contain Regular Simplices, Matthew C. Fickus, John Jasper, Emily J. King, Dustin G. Mixon
Faculty Publications
An equiangular tight frame (ETF) is a type of optimal packing of lines in Euclidean space. A regular simplex is a special type of ETF in which the number of vectors is one more than the dimension of the space they span. In this paper, we consider ETFs that contain a regular simplex, that is, have the property that a subset of its vectors forms a regular simplex. As we explain, such ETFs are characterized as those that achieve equality in a certain well-known bound from the theory of compressed sensing. We then consider the so-called binder of such an …
Equiangular Tight Frames From Group Divisible Designs, Matthew C. Fickus, John Jasper
Equiangular Tight Frames From Group Divisible Designs, Matthew C. Fickus, John Jasper
Faculty Publications
An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an open problem in many cases. In this paper, we observe that many of the known constructions of ETFs are of one of two types. We further provide a new method for combining a given ETF of one of these two types with an appropriate group divisible design (GDD) in order to produce a larger ETF of the same type. By applying this method to known …
Text Classification Of Installation Support Contract Topic Models For Category Management, William C. Sevier
Text Classification Of Installation Support Contract Topic Models For Category Management, William C. Sevier
Theses and Dissertations
Air Force Installation Contracting Agency manages nearly 18 percent of total Air Force spend, equating to approximately 57 billion dollars. To improve strategic sourcing, the organization is beginning to categorize installation-support spend and assign accountable portfolio managers to respective spend categories. A critical task in this new strategic environment includes the appropriate categorization of Air Force contracts into newly created, manageable spend categories. It has been recognized that current composite categories have the opportunity to be further distinguished into sub-categories leveraging text analytics on the contract descriptions. Furthermore, upon establishing newly constructed categories, future contracts must be classified into these …
Shortest Path Across Stochastic Network With Correlated Random Arcs, Stephanie M. Boone
Shortest Path Across Stochastic Network With Correlated Random Arcs, Stephanie M. Boone
Theses and Dissertations
This paper introduces a new approach to identify the shortest path across a stochastic network with correlated random arcs utilizing nonparametric samples of arc lengths. This approach is applied to find optimal aircraft routes that minimize expected fuel consumption for a given airspeed utilizing predicted wind output from NWP ensemble models. Results from this new methodology are then compared to the current fuel minimization route planning method that utilizes deterministic NWP wind data for arc lengths. Comparisons are also made to other previously proposed alternative fuel minimization methodologies that utilize mean and median wind data calculated from NWP ensemble wind …
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng
Theses and Dissertations
Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows …
Equiangular Tight Frames With Centroidal Symmetry, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson, Cody E. Watson
Equiangular Tight Frames With Centroidal Symmetry, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson, Cody E. Watson
Faculty Publications
An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated by the connection between real ETFs and graph theory, we introduce the notion of ETFs that are symmetric about their centroid. We then discuss how well-known constructions, such as harmonic ETFs and Steiner ETFs, can have centroidal symmetry. Finally, we establish a new equivalence between centroid-symmetric real ETFs and certain types of strongly regular graphs (SRGs). Together, these results give …
Tremain Equiangular Tight Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson
Tremain Equiangular Tight Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson
Faculty Publications
Equiangular tight frames provide optimal packings of lines through the origin. We combine Steiner triple systems with Hadamard matrices to produce a new infinite family of equiangular tight frames. This in turn leads to new constructions of strongly regular graphs and distance-regular antipodal covers of the complete graph.