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DG-GL: Differential geometry-based geometric learning of molecular datasets. [PDF]
Int J Numer Method Biomed Eng, 2019 Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding ...
Nguyen DD, Wei GW.
europepmc +3 more sources
DIFFERENTIAL GEOMETRY FROM DIFFERENTIAL EQUATIONS [PDF]
The Ninth Marcel Grossmann Meeting, 2001 37 pages, revised version with ...
Carlos Kozameh +2 more
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DIFFERENTIAL GEOMETRY OF THE q-PLANE [PDF]
International Journal of Modern Physics A, 2000 Hopf algebra structure on the differential algebra of the extended q-plane is defined. An algebra of forms which is obtained from the generators of the extended q-plane is introduced and its Hopf algebra structure is given.
Çelik, Salih, Çelik, Sultan
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Multiview Differential Geometry of Curves
International Journal of Computer Vision, 2016 The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry.
R. Fabbri, B. Kimia
semanticscholar +3 more sources
A quantum complexity lower bound from differential geometry [PDF]
Nature Physics, 2021 Quantum operations can be considered as points in a high-dimensional space in which distance reflects the similarity of two operations. Applying differential-geometric methods in this picture gives insights into the complexity of quantum systems ...
Adam R. Brown
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An Introduction to Infinite-Dimensional Differential Geometry [PDF]
, 2021 Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak ...
Alexander Schmeding
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Differential geometry of weightings
Advances in Mathematics, 2023 We describe the notion of a \emph{weighting} along a submanifold $N\subset M$, and explore its differential-geometric implications. This includes a detailed discussion of weighted normal bundles, weighted deformation spaces, and weighted blow-ups. We give a description of weightings in terms of subbundles of higher tangent bundles, which leads us to ...
Loizides, Yiannis, Meinrenken, Eckhard
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Geometry-Informed Neural Operator for Large-Scale 3D PDEs [PDF]
Neural Information Processing Systems, 2023 We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries.
Zong-Yi Li +10 more
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On the geometry of differential privacy [PDF]
Proceedings of the forty-second ACM symposium on Theory of computing, 2010 We consider the noise complexity of differentially private mechanisms in the setting where the user asks $d$ linear queries $f\colon\Rn\to\Re$ non-adaptively. Here, the database is represented by a vector in $\Rn$ and proximity between databases is measured in the $\ell_1$-metric.
Moritz Hardt, Kunal Talwar
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