Results 21 to 30 of about 6,627,879 (323)
Knots, links, and long-range magic
Journal of High Energy Physics, 2021 We study the extent to which knot and link states (that is, states in 3d Chern-Simons theory prepared by path integration on knot and link complements) can or cannot be described by stabilizer states. States which are not classical mixtures of stabilizer
Jackson R. Fliss
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Geometric learning of knot topology [PDF]
Soft Matter, 2023 Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves.
J. Sleiman +3 more
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Knot theory for proteins: Gauss codes, quandles and bondles [PDF]
Journal of Mathematical Chemistry, 2019 Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications.
C. Adams +3 more
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Quantum Reports, 2022 We recently proposed that topological quantum computing might be based on SL(2,C) representations of the fundamental group π1(S3\K) for the complement of a link K in the three-sphere.
Michel Planat +3 more
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NP–hard problems naturally arising in knot theory [PDF]
Transactions of the American Mathematical Society. Series B, 2018 We prove that certain problems naturally arising in knot theory are NP–hard or NP–complete. These are the problems of obtaining one diagram from another one of a link in a bounded number of Reidemeister moves, determining whether a link has an unlinking ...
Dale Koenig, A. Tsvietkova
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Computation of Gordian distances and H2-Gordian distances of knots [PDF]
Yugoslav Journal of Operations Research, 2015 One of the most complicated problems in Knot theory is to compute unknotting number. Hass, Lagarias and Pippenger proved that the unknotting problem is NP hard.
Zeković Ana
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Knots and Knot-Hyperpaths in Hypergraphs
Mathematics, 2022 This paper deals with some theoretical aspects of hypergraphs related to hyperpaths and hypertrees. In ordinary graph theory, the intersecting or adjacent edges contain exactly one vertex; however, in the case of hypergraph theory, the adjacent or ...
Saifur Rahman +3 more
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Developing the tube theory for polymer knots
Physical Review Research, 2020 Entanglements make polymers fundamentally different from other molecules and thus are a major theme in polymer physics research. Interchain entanglements have been extensively investigated in past decades, while intrachain entanglements, often appearing ...
Liang Dai
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Generalized Circuit Topology of Folded Linear Chains
iScience, 2020 Summary: A wide range of physical systems can be formally mapped to a linear chain of sorted objects. Upon introduction of intrachain interactions, such a chain can “fold” to elaborate topological structures, analogous to folded linear polymer systems ...
Anatoly Golovnev, Alireza Mashaghi
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Knot topology of exceptional point and non-Hermitian no-go theorem
Physical Review Research, 2022 Exceptional points (EPs) are peculiar band singularities and play a vital role in a rich array of unusual optical phenomena and non-Hermitian band theory.
Haiping Hu, Shikang Sun, Shu Chen
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