scholarly journals Improved Linear Programming Bounds for Antipodal Spherical Codes

2002 ◽  
Vol 28 (1) ◽  
pp. 107-114 ◽  
Author(s):  
Anstreicher
Keyword(s):  
Linear Programming ◽  
Spherical Codes

scholarly journals k-Point semidefinite programming bounds for equiangular lines

2021 ◽  
Author(s):  
David de Laat ◽  
Fabrício Caluza Machado ◽  
Fernando Mário de Oliveira Filho ◽  
Frank Vallentin
Keyword(s):  
Linear Programming ◽  
Euclidean Space ◽  
Semidefinite Programming ◽  
Spherical Codes ◽  
Equiangular Lines

AbstractWe propose a hierarchy of k-point bounds extending the Delsarte–Goethals–Seidel linear programming 2-point bound and the Bachoc–Vallentin semidefinite programming 3-point bound for spherical codes. An optimized implementation of this hierarchy allows us to compute 4, 5, and 6-point bounds for the maximum number of equiangular lines in Euclidean space with a fixed common angle.

scholarly journals On Linear Programming Bounds for Spherical Codes and Designs

2004 ◽  
Vol 31 (3) ◽  
pp. 385-394
Author(s):  
Alex Samorodnitsky
Keyword(s):  
Linear Programming ◽  
Spherical Codes

scholarly journals High-dimensional sphere packing and the modular bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
David de Laat ◽  
Amirhossein Tajdini
Keyword(s):  
Linear Programming ◽  
Numerical Study ◽  
Sphere Packing ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Conformal Field Theories ◽  
Spherical Codes ◽  
Conformal Field ◽  
Detailed Picture ◽  
Rule Out

Abstract We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra U(1)c× U(1)c, or equivalently the linear programming bound for sphere packing in 2c dimensions. We give a more detailed picture of the behavior for finite c than was previously available, and we extrapolate as c → ∞. Our extrapolation indicates an exponential improvement for sphere packing density bounds in high dimen- sions. Furthermore, we study when these bounds can be tight. Besides the known cases c = 1/2, 4, and 12 and the conjectured case c = 1, our calculations numerically rule out sharp bounds for all other c < 90, by combining the modular bootstrap with linear programming bounds for spherical codes.

Elementary Linear Programming (2nd edition)

1997 ◽  
Vol 48 (7) ◽  
pp. 757-758
Author(s):  
B Kolman ◽  
R E Beck ◽  
M J Panik
Keyword(s):  
Linear Programming

Robust state estimation in power systems using sparse linear programming

1985 ◽  
Vol 132 (3) ◽  
pp. 123 ◽  
Author(s):  
B.C. Clewer ◽  
M.R. Irving ◽  
M.J.H. Sterling
Keyword(s):  
Linear Programming ◽  
Power Systems ◽  
State Estimation

Optimal approaches to manage power system decarbonation

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1447-1452
Author(s):  
Vincent Mazauric ◽  
Ariane Millot ◽  
Claude Le Pape-Gardeux ◽  
Nadia Maïzi
Keyword(s):  
Free Energy ◽  
Linear Programming ◽  
Phase Transitions ◽  
Power System ◽  
Energy System ◽  
Energy Sources ◽  
Low Carbon ◽  
Faraday’S Law ◽  
Optimal Description ◽  
Low Carbon Technologies

To overcome the negative environemental impact of the actual power system, an optimal description of quasi-static electromagnetics relying on a reversible interpretation of the Faraday’s law is given. Due to the overabundance of carbon-free energy sources, this description makes it possible to consider an evolution towards an energy system favoring low-carbon technologies. The management for changing is then explored through a simplified linear-programming problem and an analogy with phase transitions in physics is drawn.

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