Constructing minimal periods of quadratic irrationalities in Zagier's reduction theory
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2017.09.002
Abstract: Dirichlet's version of Gauss's reduction theory for indefinite binary quadratic forms includes a map from Gauss-reduced forms to strings of natural numbers. It attaches to a form the minimal period of the continued fraction of… read more here.
Keywords: reduction; reduced forms; theory; zagier reduction ... See more keywords
Jacobian-free algorithm to calculate the phase sensitivity function in the phase reduction theory and its applications to Kármán's vortex street.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review. E"
DOI: 10.1103/physreve.99.062203
Abstract: Phase reduction theory has been applied to many systems with limit cycles; however, it has limited applications in incompressible fluid systems. This is because the calculation of the phase sensitivity function, one of the fundamental… read more here.
Keywords: phase sensitivity; phase; reduction theory; phase reduction ... See more keywords
An Algorithmic Reduction Theory for Binary Codes: LLL and More
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2022.3143620
Abstract: In this article, we propose an adaptation of the algorithmic reduction theory of lattices to binary codes. This includes the celebrated LLL algorithm (Lenstra, Lenstra, Lovasz, 1982), as well as adaptations of associated algorithms such… read more here.
Keywords: binary codes; theory; theory binary; reduction theory ... See more keywords