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Physical Sciences and Mathematics Commons™
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
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 …
Induced Correlation And Its Effects In The Performance Of Fused Classification Systems, Mary K. Collins
Induced Correlation And Its Effects In The Performance Of Fused Classification Systems, Mary K. Collins
Theses and Dissertations
Classification systems are abundant in modern-day life. The United States Air Force uses classification systems across many applications such as radar, satellite, and infrared sensing just to name a few. Combining classification systems allows an opportunity to get more accurate results. Using the known information from already built and tested systems that can be mathematically combined can give insight into the performance of the fused system without having to build a combined system. Leveraging this can save time, resources, and money. This work examines the correlation effects of fusing two classifier systems, each with only two labels, using the Boolean …
Regular Simplices Within Doubly Transitive Equiangular Tight Frames, Evan C. Lake
Regular Simplices Within Doubly Transitive Equiangular Tight Frames, Evan C. Lake
Theses and Dissertations
An equiangular tight frame (ETF) yields an optimal way to pack a given number of lines into a given space of lesser dimension. Every ETF has minimal coherence, and this makes it potentially useful for compressed sensing. But, its usefulness also depends on its spark: the size of the smallest linearly dependent subsequence of the ETF. When formed into a sensing matrix, a larger spark means a lower chance that information is lost when sensing a sparse vector. Spark is difficult to compute in general, but if an ETF contains a regular simplex, then every such simplex is a linearly …