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Link prediction with hyperbolic geometry [PDF]
Physical Review Research, 2020 Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The network model with hyperbolic latent spaces has a number of attractive properties suggesting it must be a powerful ...
Maksim Kitsak, Dmitri Krioukov
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Link maps and the geometry of their invariants
Manuscripta Mathematica, 1988 This paper investigates several invariants of link homotopy. A link map consists of two maps \(f_ 1: S^ p\to S^ m\), \(f_ 2: S^ q\to S^ m\) whose images are disjoint; a link homotopy is a one-parameter continuous family of such maps. \(LM^ m_{p,q}\) denotes the set of link homotopy classes.
Ulrich Koschorke
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Linking Geometry and Algebra in the School Mathematics Curriculum [PDF]
, 2010 This chapter focuses on the linking of geometry and algebra in the teaching and learning of mathematics - and how, through such linking, the mathematics curriculum might be strengthened. Through reviewing the case of the school mathematics curriculum in England, together with examples of how the power of geometry can bring contemporary mathematics to ...
Keith Jones
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Centerpoints: A Link between Optimization and Convex Geometry [PDF]
SIAM Journal on Optimization, 2016 We introduce a concept that generalizes several different notions of a "centerpoint" in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based on centerpoints are "best possible" in a certain sense.
Amitabh Basu, Timm Oertel
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Rational Linking and Contact Geometry [PDF]
, 2011 In the note we study Legendrian and transverse knots in rationally null-homologous knot types. In particular we generalize the standard definitions of self-linking number, Thurston-Bennequin invariant and rotation number. We then prove a version of Bennequin's inequality for these knots and classify precisely when the Bennequin bound is sharp for ...
Baker, Kenneth L., Etnyre, John B.
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Geometry of alternating links on surfaces
Transactions of the American Mathematical Society, 2020 We consider links that are alternating on surfaces embedded in a compact 3-manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the polyhedral decomposition of alternating links of Menasco.
Howie, Joshua A., Purcell, Jessica S.
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Geometry of biperiodic alternating links
Journal of the London Mathematical Society, 2018 A biperiodic alternating link has an alternating quotient link in the thickened torus. In this paper, we focus on semi-regular links, a class of biperiodic alternating links whose hyperbolic structure can be immediately determined from a corresponding Euclidean tiling. Consequently, we determine the exact volumes of semi-regular links.
Abhijit Champanerkar +2 more
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Influence of the silent chain link geometry on the link / chain guide contact
IOP Conference Series: Materials Science and Engineering, 2019 M T Lates, C C Gavrila
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Transitive Decompositions of Graphs and Their Links with Geometry and Origami [PDF]
The American Mathematical Monthly, 2010 A transitive decomposition of a graph is a partition of the edge or arc set giving a set of subgraphs which are preserved and permuted transitively by a group of automorphisms of the graph. In this paper we give some background to the study of transitive decompositions and highlight a connection with partial linear spaces.
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