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Using Parametric Mathematical Modeling to Develop a Geometric and Topological Intuition for Molecular Knots

Applied Mathematics, 2020
Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have been applied to synthetic molecular design. Mathematics
Tahmineh Azizi, Jacob Pichelmeyer
openaire   +2 more sources

An outlined tour of geometry and topology as perceived through physics and mathematics emphasizing geometrization, elliptization, uniformization, and projectivization for Thruston's 8-geometries covering Riemann over Teichmuller spaces

, 2022
<p>Equivalence, duality, and invariance are the pin-points of unification in modern theoretical physics that got the twist of topologies when going beyond the notions of differential and conformal domains to geometries to the symplectic norm of topologies with the pillars being the algebraic geometry taking the counting of specified states ...
openaire   +1 more source

Geometry and quantum brachistochrone analysis of multiple entangled spin-1/2 particles under all-range Ising interaction. [PDF]

Sci Rep
Amghar B, Yachi M, Amghar M, Almousa M, El-Latif AAA, Slaoui A.   +5 more
europepmc   +1 more source

Topological data analysis and topological deep learning beyond persistent homology: a review. [PDF]

Artif Intell Rev
Su Z, Liu X, Hamdan LB, Maroulas V, Wu J, Carlsson G, Wei GW, Wei GW.   +7 more
europepmc   +1 more source

Maximum persistent Betti numbers of Čech complexes. [PDF]

J Appl Comput Topol
Edelsbrunner H, Kahle M, Kanazawa S.
europepmc   +1 more source

An integrated method for lightweight design and additive manufacturing of UAV arms. [PDF]

PLoS One
Wang R, Yang W, Pang G, Liu Z, Rao X, Yu Y.   +5 more
europepmc   +1 more source

Integral Betti signatures of brain, climate and financial networks compared to hyperbolic, Euclidean and spherical models. [PDF]

Sci Rep
Caputi L, Pidnebesna A, Hlinka J.
europepmc   +1 more source

A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences. [PDF]

J Chem Inf Model
Wee J, Jiang J.
europepmc   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
Ren Y, Wei GW.
europepmc   +1 more source

Topological metrics as evolutionary and dynamical descriptors of conformational landscapes within protein families. [PDF]

PLoS Comput Biol
Ramesh N, Ozkan SB, Panagiotou E.
europepmc   +1 more source