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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
Maksim Kitsak +2 more
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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, Koschorke Ulrich
exaly +3 more sources
THE COMMON EVOLUTION OF GEOMETRY AND ARCHITECTURE FROM A GEODETIC POINT OF VIEW [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2017 Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are ...
T. Bellone, F. Fiermonte, L. Mussio
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Evolution of cortical geometry and its link to function, behaviour and ecology
Nature Communications, 2023 Studies in comparative neuroanatomy and of the fossil record demonstrate the influence of socio-ecological niches on the morphology of the cerebral cortex, but have led to oftentimes conflicting theories about its evolution.
Ernst Schwartz +8 more
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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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3D STRUCTURE ANALYSIS: ARCHITECTURE AS AN EXPRESSION OF THE TIES BETWEEN GEOMETRY AND PHILOSOPHY [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2019 In recent decades many Geomatics-based methods have been created to reconstruct and visualize objects, and these include digital photogrammetry, Lidar, remote sensing and hybrid techniques. The methods used to process such data are the result of research
T. Bellone, L. Mussio, C. Porporato
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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 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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ANALYSIS OF FRACTURE GEOMETRY IN FLUID DRAINAGE AFTER HYDRAULIC FRACTURING. CASE OF WINK MS-09 IN MAKELEKESE FIELD, D.R. CONGO [PDF]
Romanian Journal of Petroleum & Gas TechnologyIn this paper, we analyze stimulation by hydraulic fracturing with the aim of establishing a relationship between fracture geometry and hydrocarbon drainage.
Rachidi Opuluku +5 more
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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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