Spectral decomposition of turbulent mixing and broadband shock-associated noise from a high-performance military aircraft

2017 ◽  
Vol 142 (4) ◽  
pp. 2513-2513 ◽  
Author(s):  
Aaron Vaughn ◽  
Tracianne B. Neilsen ◽  
Kent L. Gee ◽  
Alan T. Wall ◽  
Micah Downing ◽  
...  
Author(s):  
Tracianne B. Neilsen ◽  
Aaron B. Vaughn ◽  
Kent L. Gee ◽  
S Hales Swift ◽  
Alan T. Wall ◽  
...  

Author(s):  
Jack Poulson

Determinantal point processes (DPPs) were introduced by Macchi (Macchi 1975 Adv. Appl. Probab. 7 , 83–122) as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a recommender system (Kulesza & Taskar 2012 Found. Trends Mach. Learn. 5 , 123–286). The standard sampling scheme for finite DPPs is a spectral decomposition followed by an equivalent of a randomly diagonally pivoted Cholesky factorization of an orthogonal projection, which is only applicable to Hermitian kernels and has an expensive set-up cost. Researchers Launay et al. 2018 ( http://arxiv.org/abs/1802.08429 ); Chen & Zhang 2018 NeurIPS ( https://papers.nips.cc/paper/7805-fast-greedy-map-inference-for-determinantal-point-process-to-improve-recommendation-diversity.pdf ) have begun to connect DPP sampling to LDL H factorizations as a means of avoiding the initial spectral decomposition, but existing approaches have only outperformed the spectral decomposition approach in special circumstances, where the number of kept modes is a small percentage of the ground set size. This article proves that trivial modifications of LU and LDL H factorizations yield efficient direct sampling schemes for non-Hermitian and Hermitian DPP kernels, respectively. Furthermore, it is experimentally shown that even dynamically scheduled, shared-memory parallelizations of high-performance dense and sparse-direct factorizations can be trivially modified to yield DPP sampling schemes with essentially identical performance. The software developed as part of this research, Catamari ( hodgestar.com/catamari ) is released under the Mozilla Public License v.2.0. It contains header-only, C++14 plus OpenMP 4.0 implementations of dense and sparse-direct, Hermitian and non-Hermitian DPP samplers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.


Author(s):  
Brent O. Reichman ◽  
Kent L. Gee ◽  
Tracianne B. Neilsen ◽  
S Hales Swift ◽  
Alan T. Wall ◽  
...  

2014 ◽  
Vol 135 (4) ◽  
pp. 2382-2382
Author(s):  
Tracianne B. Neilsen ◽  
Kent L. Gee ◽  
Michael M. James

2017 ◽  
Vol 142 (4) ◽  
pp. 2514-2514 ◽  
Author(s):  
Kevin M. Leete ◽  
Alan T. Wall ◽  
Kent L. Gee ◽  
Tracianne B. Neilsen ◽  
Micah Downing ◽  
...  

AIAA Journal ◽  
2019 ◽  
Vol 57 (8) ◽  
pp. 3467-3479 ◽  
Author(s):  
Tracianne B. Neilsen ◽  
Aaron B. Vaughn ◽  
Kent L. Gee ◽  
S. Hales Swift ◽  
Alan T. Wall ◽  
...  

2021 ◽  
Vol 149 (4) ◽  
pp. 2403-2414
Author(s):  
Aaron B. Vaughn ◽  
Kevin M. Leete ◽  
Kent L. Gee ◽  
Bradley R. Adams ◽  
J. Micah Downing

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