Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Mathematics (67)
- 42C15 (8)
- Characteristic methods (6)
- Radial basis functions (5)
- Collagen (4)
-
- Combinatorics (4)
- Competitive coloring (4)
- Equiangular tight frame (4)
- Error estimates (4)
- Fibroblasts (4)
- Particular solution (4)
- Cell motion (3)
- Commensurability (3)
- Convergence analysis (3)
- Eulerian–Lagrangian methods (3)
- Finite time blow-up (3)
- Hadamard matrix (3)
- Machine learning (3)
- Mathematics, Statistics (3)
- Method of particular solutions (3)
- Relaxed coloring (3)
- Spectral methods (3)
- Topology (3)
- 3-manifolds (2)
- APPROXIMATION (2)
- Additive coloring (2)
- Alignment (2)
- Analysis of PDEs (2)
- Anomaly detection (2)
- Biological control (2)
Articles 1 - 30 of 276
Full-Text Articles in Physical Sciences and Mathematics
Complete Solution Of The Lady In The Lake Scenario, Alexander Von Moll, Meir Pachter
Complete Solution Of The Lady In The Lake Scenario, Alexander Von Moll, Meir Pachter
Faculty Publications
In the Lady in the Lake scenario, a mobile agent, L, is pitted against an agent, M, who is constrained to move along the perimeter of a circle. L is assumed to begin inside the circle and wishes to escape to the perimeter with some finite angular separation from M at the perimeter. This scenario has, in the past, been formulated as a zero-sum differential game wherein L seeks to maximize terminal separation and M seeks to minimize it. Its solution is well-known. However, there is a large portion of the state space for which the canonical solution does not …
Legendre Pairs Of Lengths ℓ ≡ 0 (Mod 5), Ilias S. Kotsireas, Christopher Koutschan, Dursun Bulutoglu, David M. Arquette, Jonathan S. Turner, Kenneth J. Ryan
Legendre Pairs Of Lengths ℓ ≡ 0 (Mod 5), Ilias S. Kotsireas, Christopher Koutschan, Dursun Bulutoglu, David M. Arquette, Jonathan S. Turner, Kenneth J. Ryan
Faculty Publications
By assuming a type of balance for length ℓ = 87 and nontrivial subgroups of multiplier groups of Legendre pairs (LPs) for length ℓ = 85 , we find LPs of these lengths. We then study the power spectral density (PSD) values of m compressions of LPs of length 5 m . We also formulate a conjecture for LPs of lengths ℓ ≡ 0 (mod 5) and demonstrate how it can be used to decrease the search space and storage requirements for finding such LPs. The newly found LPs decrease the number of integers in the range ≤ 200 for …
Anomaly Detection In The Molecular Structure Of Gallium Arsenide Using Convolutional Neural Networks, Timothy Roche *, Aihua W. Wood, Philip Cho *, Chancellor Johnstone
Anomaly Detection In The Molecular Structure Of Gallium Arsenide Using Convolutional Neural Networks, Timothy Roche *, Aihua W. Wood, Philip Cho *, Chancellor Johnstone
Faculty Publications
This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope in training and testing. The methodology developed allows for the creation of a defect detection model, without any labeled images of defects being required for training. The model performed well on all tests under the established assumptions, allowing for reliable anomaly detection. To the best of our knowledge, such methods are not currently available in the open …
Numerical Simulation Of The Korteweg–De Vries Equation With Machine Learning, Kristina O. F. Williams *, Benjamin F. Akers
Numerical Simulation Of The Korteweg–De Vries Equation With Machine Learning, Kristina O. F. Williams *, Benjamin F. Akers
Faculty Publications
A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg–de Vries equation. It is observed to be more accurate than finite difference or spectral methods on coarse …
A Bit-Parallel Tabu Search Algorithm For Finding Es2 -Optimal And Minimax-Optimal Supersaturated Designs, Luis B. Morales, Dursun A. Bulotuglu
A Bit-Parallel Tabu Search Algorithm For Finding Es2 -Optimal And Minimax-Optimal Supersaturated Designs, Luis B. Morales, Dursun A. Bulotuglu
Faculty Publications
We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, smax=4t+i, where i ∈ {0,2}, t ∈ Z≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most (N+4t+i)/4 points. Using this equivalence, we formulate the search for two-symbol E(s2)-optimal and minimax-optimal SSDs with smax ∈ {2,4,6} as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found E(s2)-optimal and minimax-optimal SSDs achieving the sharpest known E(s2) lower bound with …
A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign
A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign
Faculty Publications
This research paper focuses on quaternion neural networks (QNNs) - a type of neural network wherein the weights, biases, and input values are all represented as quaternion numbers. Previous studies have shown that QNNs outperform real-valued neural networks in basic tasks and have potential in high-dimensional problem spaces. However, research on QNNs has been fragmented, with contributions from different mathematical and engineering domains leading to unintentional overlap in QNN literature. This work aims to unify existing research by evaluating four distinct QNN backpropagation algorithms, including the novel GHR-calculus backpropagation algorithm, and providing concise, scalable implementations of each algorithm using a …
Solving Inverse Conductivity Problems In Doubly Connected Domains By The Homogenization Functions Of Two Parameters, Jun Lu, Lianpeng Shi, Chein-Shan Liu, C.S. Chen
Solving Inverse Conductivity Problems In Doubly Connected Domains By The Homogenization Functions Of Two Parameters, Jun Lu, Lianpeng Shi, Chein-Shan Liu, C.S. Chen
Faculty Publications
In the paper, we make the first attempt to derive a family of two-parameter homogenization functions in the doubly connected domain, which is then applied as the bases of trial solutions for the inverse conductivity problems. The expansion coefficients are obtained by imposing an extra boundary condition on the inner boundary, which results in a linear system for the interpolation of the solution in a weighted Sobolev space. Then, we retrieve the spatial- or temperature-dependent conductivity function by solving a linear system, which is obtained from the collocation method applied to the nonlinear elliptic equation after inserting the solution. Although …
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
Faculty Publications
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann-Enskog equation. Based on a McKean-Vlasov equation with jumps, the associated stochastic process was recently constructed by modified Picard iterations with the mean-field interactions, and more generally, by a system of interacting particles. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measure-valued solutions to the Boltzmann-Enskog equation. As a …
Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc
Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc
Faculty Publications
We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals.
A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang
A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang
Faculty Publications
Immunotherapy is an innovative treatment that enlists the patient's immune system to battle tumors. The optimal dose for treating patients with an immunotherapeutic agent may differ according to their biomarker status. In this article, we propose a biomarker-based phase I/II dose-finding design for identifying subgroup-specific optimal dose for immunotherapy (BSOI) that jointly models the immune response, toxicity, and efficacy outcomes. We propose parsimonious yet flexible models to borrow information across different types of outcomes and subgroups. We quantify the desirability of the dose using a utility function and adopt a two-stage dose-finding algorithm to find the optimal dose for each …
A New Matroid Lift Construction And An Application To Group-Labeled Graphs, Zach Walsh
A New Matroid Lift Construction And An Application To Group-Labeled Graphs, Zach Walsh
Faculty Publications
A well-known result of Brylawski constructs an elementary lift of a matroid M from a linear class of circuits of M. We generalize this result by constructing a rank-k lift of M from a rank-k matroid on the set of circuits of M. We conjecture that every lift of M arises via this construction. We then apply this result to group-labeled graphs, generalizing a construction of Zaslavsky. Given a graph G with edges labeled by a group, Zaslavsky's lift matroid K is an elementary lift of the graphic matroid M(G) that respects the group-labeling; specifically, the cycles of G that …
Node Generation For Rbf-Fd Methods By Qr Factorization, Tony Liu, Rodrigo B. Platte
Node Generation For Rbf-Fd Methods By Qr Factorization, Tony Liu, Rodrigo B. Platte
Faculty Publications
Polyharmonic spline (PHS) radial basis functions (RBFs) have been used in conjunction with polynomials to create RBF finite-difference (RBF-FD) methods. In 2D, these methods are usually implemented with Cartesian nodes, hexagonal nodes, or most commonly, quasi-uniformly distributed nodes generated through fast algorithms. We explore novel strategies for computing the placement of sampling points for RBF-FD methods in both 1D and 2D while investigating the benefits of using these points. The optimality of sampling points is determined by a novel piecewise-defined Lebesgue constant. Points are then sampled by modifying a simple, robust, column-pivoting QR algorithm previously implemented to find sets of …
Maximal Spacelike Surfaces In A Certain Homogeneous Lorentzian 3-Manifold, Sungwook Lee
Maximal Spacelike Surfaces In A Certain Homogeneous Lorentzian 3-Manifold, Sungwook Lee
Faculty Publications
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula for maximal spacelike surfaces in the homogeneous Lorentzian 3-manifolds is obtained. The normal Gauß map of maximal spacelike surfaces and its harmonicity are discussed.
Estimating Turbulence Distribution Over A Heterogeneous Path Using Time‐Lapse Imagery From Dual Cameras, Benjamin Wilson, Santasri Bose-Pillai, Jack E. Mccrae, Kevin J. Keefer, Steven T. Fiorino
Estimating Turbulence Distribution Over A Heterogeneous Path Using Time‐Lapse Imagery From Dual Cameras, Benjamin Wilson, Santasri Bose-Pillai, Jack E. Mccrae, Kevin J. Keefer, Steven T. Fiorino
Faculty Publications
Knowledge of turbulence distribution along an experimental path can help in effective turbulence compensation and mitigation. Although scintillometers are traditionally used to measure the strength of turbulence, they provide a path-integrated measurement and have limited operational ranges. A technique to profile turbulence using time-lapse imagery of a distant target from spatially separated cameras is presented here. The method uses the turbulence induced differential motion between pairs of point features on a target, sensed at a single camera and between cameras to extract turbulence distribution along the path. The method is successfully demonstrated on a 511 m almost horizontal path going …
2-Adic Valuations Of Quadratic Sequences, Will Boultinghouse, Jane H. Long, Olena Kozhushkina, Justin Trulen
2-Adic Valuations Of Quadratic Sequences, Will Boultinghouse, Jane H. Long, Olena Kozhushkina, Justin Trulen
Faculty Publications
We determine properties of the 2-adic valuation sequences for general quadratic polynomials with integer coefficients directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at terminating nodes. We completely describe the periodic sequences in the bounded case. Throughout, we frame results in terms of trees and sequences.
Defect Detection In Atomic Resolution Transmission Electron Microscopy Images Using Machine Learning, Philip Cho, Aihua W. Wood, Krishnamurthy Mahalingam, Kurt Eyink
Defect Detection In Atomic Resolution Transmission Electron Microscopy Images Using Machine Learning, Philip Cho, Aihua W. Wood, Krishnamurthy Mahalingam, Kurt Eyink
Faculty Publications
Point defects play a fundamental role in the discovery of new materials due to their strong influence on material properties and behavior. At present, imaging techniques based on transmission electron microscopy (TEM) are widely employed for characterizing point defects in materials. However, current methods for defect detection predominantly involve visual inspection of TEM images, which is laborious and poses difficulties in materials where defect related contrast is weak or ambiguous. Recent efforts to develop machine learning methods for the detection of point defects in TEM images have focused on supervised methods that require labeled training data that is generated via …
Meta-Heuristic Optimization Methods For Quaternion-Valued Neural Networks, Jeremiah Bill, Lance E. Champagne, Bruce Cox, Trevor J. Bihl
Meta-Heuristic Optimization Methods For Quaternion-Valued Neural Networks, Jeremiah Bill, Lance E. Champagne, Bruce Cox, Trevor J. Bihl
Faculty Publications
In recent years, real-valued neural networks have demonstrated promising, and often striking, results across a broad range of domains. This has driven a surge of applications utilizing high-dimensional datasets. While many techniques exist to alleviate issues of high-dimensionality, they all induce a cost in terms of network size or computational runtime. This work examines the use of quaternions, a form of hypercomplex numbers, in neural networks. The constructed networks demonstrate the ability of quaternions to encode high-dimensional data in an efficient neural network structure, showing that hypercomplex neural networks reduce the number of total trainable parameters compared to their real-valued …
Commuting Perturbations Of Operator Equations, Xue Xu, Jiu Ding
Commuting Perturbations Of Operator Equations, Xue Xu, Jiu Ding
Faculty Publications
Let X be a Banach space and let T: X →X be a bounded linear operator with closed range. We study a class of commuting perturbations of the corresponding operator equation, using the concept of the spectral radius of a bounded linear operator. Our results extend the classic perturbation theorem for invertible operators and its generalization for arbitrary operators under the commutability assumption.
A Radial Basis Function Finite Difference Scheme For The Benjamin–Ono Equation, Benjamin F. Akers, Tony Liu, Jonah A. Reeger
A Radial Basis Function Finite Difference Scheme For The Benjamin–Ono Equation, Benjamin F. Akers, Tony Liu, Jonah A. Reeger
Faculty Publications
A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on ℝ, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.
Acceleration Of Boltzmann Collision Integral Calculation Using Machine Learning, Ian Holloway, Aihua W. Wood, Alexander Alekseenko
Acceleration Of Boltzmann Collision Integral Calculation Using Machine Learning, Ian Holloway, Aihua W. Wood, Alexander Alekseenko
Faculty Publications
The Boltzmann equation is essential to the accurate modeling of rarefied gases. Unfortunately, traditional numerical solvers for this equation are too computationally expensive for many practical applications. With modern interest in hypersonic flight and plasma flows, to which the Boltzmann equation is relevant, there would be immediate value in an efficient simulation method. The collision integral component of the equation is the main contributor of the large complexity. A plethora of new mathematical and numerical approaches have been proposed in an effort to reduce the computational cost of solving the Boltzmann collision integral, yet it still remains prohibitively expensive for …
A Fictitious Points One-Step Mps-Mfs Technique, Xiaomin Zhu, Fangfang Dou, Andreas Karageorghis, C. S. Chen
A Fictitious Points One-Step Mps-Mfs Technique, Xiaomin Zhu, Fangfang Dou, Andreas Karageorghis, C. S. Chen
Faculty Publications
© 2020 The method of fundamental solutions (MFS) is a simple and efficient numerical technique for solving certain homogenous partial differential equations (PDEs) which can be extended to solving inhomogeneous equations through the method of particular solutions (MPS). In this paper, radial basis functions (RBFs) are considered as the basis functions for the construction of a particular solution of the inhomogeneous equation. A hybrid method coupling these two methods using both fundamental solutions and RBFs as basis functions has been effective for solving a large class of PDEs. In this paper, we propose an improved fictitious points method in which …
Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, Cem Y. Yıldırım
Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, Cem Y. Yıldırım
Faculty Publications
We show that for any positive integer n, there is some fixed A such that d(x) = d(x +n) = A infinitely often where d(x) denotes the number of divisors of x. In fact, we establish the stronger result that both x and x +n have the same fixed exponent pattern for infinitely many x. Here the exponent pattern of an integer x > 1is the multiset of nonzero exponents which appear in the prime factorization of x.
Shake Slice And Shake Concordant Links, Anthony Bosman
Shake Slice And Shake Concordant Links, Anthony Bosman
Faculty Publications
© 2020 World Scientific Publishing Company. We can construct a 4-manifold by attaching 2-handles to a 4-ball with framing r along the components of a link in the boundary of the 4-ball. We define a link as r-shake slice if there exists embedded spheres that represent the generators of the second homology of the 4-manifold. This naturally extends r-shake slice, a generalization of slice that has previously only been studied for knots, to links of more than one component. We also define a relative notion of shaker-concordance for links and versions with stricter conditions on the embedded spheres that we …
Legendrian Dga Representations And The Colored Kauffman Polynomial, Justin Murray, Dan Rutherford
Legendrian Dga Representations And The Colored Kauffman Polynomial, Justin Murray, Dan Rutherford
Faculty Publications
For any Legendrian knot K in standard contact R-3 we relate counts of ungraded (1-graded) representations of the Legendrian contact homology DG-algebra (A(K), partial derivative) with the n-colored Kauffman polynomial. To do this, we introduce an ungraded n-colored ru-ling polynomial, R-n,K(1)(q), as a linear combination of reduced ruling polynomials of positive permutation braids and show that (i) R-n,K(1)(q) arises as a specialization F-n,F-K(a, q)vertical bar(a-1) = 0 of the n-colored Kauffman polynomial and (ii) when q is a power of two R-n,K(1)(q) agrees with the total ungraded representation number, Rep(1) (K, F-q(n)), which is a normalized count of n-dimensional representations …
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Matthew C. Fickus, Courtney A. Schmitt
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Matthew C. Fickus, Courtney A. Schmitt
Faculty Publications
An equiangular tight frame (ETF) is a sequence of unit-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs which equate to difference sets in finite abelian groups. Recently, it was shown that some harmonic ETFs are comprised of regular simplices. In this paper, we continue the investigation into these special harmonic ETFs. We begin …
Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon
Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon
Faculty Publications
We investigate how Legendre G-array pairs are related to several different perfect binary G-array families. In particular we study the relations between Legendre G-array pairs, Sidelnikov-Lempel-Cohn-Eastman ℤq−1-arrays, Yamada-Pott G-array pairs, Ding-Helleseth-Martinsen ℤ2×ℤmp-arrays, Yamada ℤ(q−1)/2-arrays, Szekeres ℤmp-array pairs, Paley ℤmp-array pairs, and Baumert ℤm1p1×ℤm2p2-array pairs. Our work also solves one of the two open problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we provide several computer search based existence and non-existence results regarding Legendre ℤn-array pairs. …
Cell Velocity Is Asymptotically Independent Of Force: A Differential Equation Model With Random Switching., J. C. Dallon, Emily J. Evans, Christopher P. Grant, William V. Smith
Cell Velocity Is Asymptotically Independent Of Force: A Differential Equation Model With Random Switching., J. C. Dallon, Emily J. Evans, Christopher P. Grant, William V. Smith
Faculty Publications
Numerical simulations suggest that average velocity of a biological cell depends largely on attachment dynamics and less on the forces exerted by the cell. We determine the relationship between two models of cell motion, one based on finite spring constants modeling attachment properties (a randomly switched differential equation) and a limiting case (a centroid model-a generalized random walk) where spring constants are infinite. We prove the main result of this paper, the Expected Velocity Relationship theorem. This result shows that the expected value of the difference between cell locations in the differential equation model at the initial time and at …
Polyphase Equiangular Tight Frames And Abelian Generalized Quadrangles, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson, Cody E. Watson
Polyphase Equiangular Tight Frames And Abelian Generalized Quadrangles, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson, Cody E. Watson
Faculty Publications
An equiangular tight frame (ETF) is a type of optimal packing of lines in a finite-dimensional Hilbert space. ETFs arise in various applications, such as waveform design for wireless communication, compressed sensing, quantum information theory and algebraic coding theory. In a recent paper, signature matrices of ETFs were constructed from abelian distance regular covers of complete graphs. We extend this work, constructing ETF synthesis operators from abelian generalized quadrangles, and vice versa. This produces a new infinite family of complex ETFs as well as a new proof of the existence of certain generalized quadrangles. This work involves designing matrices whose …
A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad
A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad
Faculty Publications
The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for biological control of non-native species. The strategy works by manipulating the sex ratio of a population through the introduction of supermales that guarantee male offspring. In the current manuscript, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting …
Hadamard Equiangular Tight Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson
Hadamard Equiangular Tight Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson
Faculty Publications
An equiangular tight frame (ETF) is a type of optimal packing of lines in Euclidean space. They are often represented as the columns of a short, fat matrix. In certain applications we want this matrix to be flat, that is, have the property that all of its entries have modulus one. In particular, real flat ETFs are equivalent to self-complementary binary codes that achieve the Grey-Rankin bound. Some flat ETFs are (complex) Hadamard ETFs, meaning they arise by extracting rows from a (complex) Hadamard matrix. These include harmonic ETFs, which are obtained by extracting the rows of a character table …