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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
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On the relationship between topological and geometric defects [PDF]
Journal of Physics: Condensed Matter, 2017 The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding skyrmionic lattices.
S. Griffin, N. Spaldin
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Evolutionary Khovanov homology. [PDF]
AIMS MathKnot theory, a subfield in geometric topology, is the study of the embedding of closed circles into three-dimensional Euclidean space, motivated by the ubiquity of knots in daily life and human civilization.
Shen L, Liu J, Wei GW.
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A tropical geometric approach to exceptional points [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2023 Significance A unified tropical geometric framework is proposed to study different facets of non-Hermitian systems. We demonstrate the versatility of our framework by identifying and tuning to exceptional points in different experimental platforms ...
Ayan Banerjee +3 more
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ON TOPOLOGY OF CENTROSYMMETRIC MATRICES WITH APPLICATIONS
Advances in Mathematics: Scientific Journal, 2023 In this work, we investigate the algebraic and geometric properties of centrosymmetric matrices over the positive reals. We show that the set of centrosymmetric matrices, denoted as $\mathcal{C}_n$, forms a Lie algebra under the Hadamard product with the
S. Koyuncu, C. Ozel, M. Albaity
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A Distributed Combinatorial Topology Approach to Arrow's Impossibility Theorem
ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, 2022 Baryshnikov presented a remarkable algebraic topology proof of Arrow's impossibility theorem trying to understand the underlying reason behind the numerous proofs of this fundamental result of social choice theory.
S. Rajsbaum, A. Raventós-Pujol
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Topology of complexity one quotients [PDF]
Pacific Journal of Mathematics, 2018 We describe of the topology of the geometric quotients of 2n dimensional compact connected symplectic manifolds with n-1 dimensional torus actions. When the isotropy weights at each fixed point are in general position, the quotient is homeomorphic to a ...
Yael Karshon, S. Tolman
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Euler flows and singular geometric structures [PDF]
Philosophical Transactions of the Royal Society A, 2019 Tichler proved (Tischler D. 1970 Topology 9, 153–154. (doi:10.1016/0040-9383(70)90037-6)) that a manifold admitting a smooth non-vanishing and closed one-form fibres over a circle. More generally, a manifold admitting k-independent closed one-form fibres
R. Cardona +2 more
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Unifying lattice models, links and quantum geometric Langlands via branes in string theory [PDF]
Advances in Theoretical and Mathematical Physics, 2019 We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's ...
M. Ashwinkumar, M. Tan
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2007 IEEE International Conference on Bioinformatics and Biomedicine (BIBM 2007), 2007 GENMINER is a smart adaptation of closed itemsets based association rules extraction to genomic data. It takes advantage of the novel NORDI discretization method and of the JCLOSE algorithm to efficiently generate minimal non-redundant association rules.
Joel H. Saltz +5 more
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