Results 1 to 10 of about 235,705 (108)
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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Quantum geometric bound and ideal condition for Euler band topology [PDF]
Physical review B, 2023 Understanding the relationship between quantum geometry and topological invariants is a central problem in the study of topological states. In this work, we establish the relationship between the quantum metric and the Euler curvature in two-dimensional ...
Soonhyun Kwon, Bohm-Jung Yang
semanticscholar +1 more source
Geometric Knowledge Distillation: Topology Compression for Graph Neural Networks [PDF]
Neural Information Processing Systems, 2022 We study a new paradigm of knowledge transfer that aims at encoding graph topological information into graph neural networks (GNNs) by distilling knowledge from a teacher GNN model trained on a complete graph to a student GNN model operating on a smaller
Chenxiao Yang, Qitian Wu, Junchi Yan
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Scientific Reports, 2022 Cellular biological networks represent the molecular interactions that shape function of living cells. Uncovering the organization of a biological network requires efficient and accurate algorithms to determine the components, termed communities ...
J. Sia +4 more
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Optics Express, 2021 We investigate the topology optimization of geometric phase metasurfaces for wide-angle and high-efficiency deflection, where adjoint-based multi-object optimization approach is adopted to improve the absolute efficiency while maintaining the ...
Mingfeng Xu +8 more
semanticscholar +1 more source
Engineering optimization (Print), 2021 In this article, robust topology optimization under geometric uncertainty is proposed. The design domain is discretized by an extended finite element method. A bi-directional evolutionary structural optimization carries out the optimization process.
S. A. Latifi Rostami +3 more
semanticscholar +1 more source
Meccanica (Milano. Print), 2021 Structural Topology optimization is attracting increasing attention as a complement to additive manufacturing techniques. The optimization algorithms usually employ continuum-based Finite Element analyses, but some important materials and processes are ...
C. O’Shaughnessy +2 more
semanticscholar +1 more source
Geometric approach to fragile topology beyond symmetry indicators
Physical review B, 2020 We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands.
Adrien Bouhon +2 more
semanticscholar +1 more source
The loop expansion of the Kontsevich integral, the null move and S-equivalence [PDF]
, 2003 This is a substantially revised version. The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev degree of graphs) is characterized by a universal property; namely it is a universal Vassiliev invariant of knots ...
Garoufalidis, Stavros, Rozansky, Lev
core +5 more sources
Manipulating the Topology of Nanoscale Skyrmion Bubbles by Spatially Geometric Confinement. [PDF]
ACS Nano, 2019 The discovery of magnetic skyrmion bubbles in centrosymmetric magnets has been receiving increasing interest from the research community, due to the fascinating physics of topological spin textures and its possible applications to spintronics.
Z. Hou +12 more
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