Experimental Survey of Discrete Minimizers of the p- Energy

Dmitriy Bilyk; Alexey Glazyrin; Ryan W. Matzke; Josiah Park; Oleksandr Vlasiuk

doi:10.1109/IEEECONF59524.2023.10476892

Experimental Survey of Discrete Minimizers of the p- Energy

Dmitriy Bilyk, Alexey Glazyrin, Ryan W. Matzke, Josiah Park, Oleksandr Vlasiuk

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We provide a detailed analysis of results from a large-scale computational exploration of real and complex (weighted) point configurations that minimize p-frame energies, uncovering phase transition behavior exhibited by the minimizers. We utilize numerical linear programming methodologies to offer complementary lower bounds that support our experimentally obtained upper bounds on minimal energy values. Furthermore, we present the development of an exceptionally symmetric weighted design consisting of 85 points, which outperforms the current best known lower bounds for a minimal-sized weighted design in the realm of five-dimensional complex projective space. In conclusion, based on our thorough observations and in-depth analysis, we conjecture that the support of this novel weighted design is universally optimal.

Original language	English (US)
Title of host publication	Conference Record of the 57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023
Editors	Michael B. Matthews
Publisher	IEEE Computer Society
Pages	522-529
Number of pages	8
ISBN (Electronic)	9798350325744
DOIs	https://doi.org/10.1109/IEEECONF59524.2023.10476892
State	Published - 2023
Event	57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023 - Pacific Grove, United States Duration: Oct 29 2023 → Nov 1 2023

Publication series

Name	Conference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)	1058-6393

Conference

Conference	57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023
Country/Territory	United States
City	Pacific Grove
Period	10/29/23 → 11/1/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

Equiangular tight frames
MIMO
complex projective codes
discrete geometry
line packings
manifold optimization

Publisher link

10.1109/IEEECONF59524.2023.10476892

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Bilyk, D., Glazyrin, A., Matzke, R. W., Park, J., & Vlasiuk, O. (2023). Experimental Survey of Discrete Minimizers of the p- Energy. In M. B. Matthews (Ed.), Conference Record of the 57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023 (pp. 522-529). (Conference Record - Asilomar Conference on Signals, Systems and Computers). IEEE Computer Society. https://doi.org/10.1109/IEEECONF59524.2023.10476892

Experimental Survey of Discrete Minimizers of the p- Energy. / Bilyk, Dmitriy; Glazyrin, Alexey; Matzke, Ryan W. et al.
Conference Record of the 57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023. ed. / Michael B. Matthews. IEEE Computer Society, 2023. p. 522-529 (Conference Record - Asilomar Conference on Signals, Systems and Computers).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Bilyk, D, Glazyrin, A, Matzke, RW, Park, J & Vlasiuk, O 2023, Experimental Survey of Discrete Minimizers of the p- Energy. in MB Matthews (ed.), Conference Record of the 57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023. Conference Record - Asilomar Conference on Signals, Systems and Computers, IEEE Computer Society, pp. 522-529, 57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023, Pacific Grove, United States, 10/29/23. https://doi.org/10.1109/IEEECONF59524.2023.10476892

Bilyk D, Glazyrin A, Matzke RW, Park J, Vlasiuk O. Experimental Survey of Discrete Minimizers of the p- Energy. In Matthews MB, editor, Conference Record of the 57th Asilomar Conference on Signals, Systems and Computers, ACSSC 2023. IEEE Computer Society. 2023. p. 522-529. (Conference Record - Asilomar Conference on Signals, Systems and Computers). doi: 10.1109/IEEECONF59524.2023.10476892

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AB - We provide a detailed analysis of results from a large-scale computational exploration of real and complex (weighted) point configurations that minimize p-frame energies, uncovering phase transition behavior exhibited by the minimizers. We utilize numerical linear programming methodologies to offer complementary lower bounds that support our experimentally obtained upper bounds on minimal energy values. Furthermore, we present the development of an exceptionally symmetric weighted design consisting of 85 points, which outperforms the current best known lower bounds for a minimal-sized weighted design in the realm of five-dimensional complex projective space. In conclusion, based on our thorough observations and in-depth analysis, we conjecture that the support of this novel weighted design is universally optimal.

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Experimental Survey of Discrete Minimizers of the p- Energy

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