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
Online Handwriting Recognition Method with a Non-Inertial Reference Frame Based on the Measurement of Linear Accelerations and Differential Geometry: An Alternative to Quaternions [PDF]
MicromachinesThis work describes a mathematical model for handwriting devices without a specific reference surface (SRS). The research was carried out on two hypotheses: the first considers possible circular segments that could be made during execution for the ...
Griselda Stephany Abarca Jiménez +5 more
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Affine differential geometry of osculating hypersurfaces
Lietuvos Matematikos Rinkinys, 2012 Osculating surfaces of second order have been studied in classical affine differential geometry [1]. In this article we generalize this notion to osculating hypersurfaces of higher order of hypersurfaces in Euclidean n-space.
Kazimieras Navickis
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Revisiting Volterra defects: geometrical relation between edge dislocations and wedge disclinations [PDF]
Royal Society Open ScienceThis study presents a comprehensive mathematical model for Volterra defects and explores their relations using differential geometry on Riemann–Cartan manifolds.
Shunsuke Kobayashi +2 more
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Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency [PDF]
IEEE Open Access Journal of Power and Energy, 2022 This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the definition of IF ...
Federico Milano +4 more
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Centro-affine differential geometry and the log-Minkowski problem [PDF]
Journal of the European Mathematical Society (Print), 2021 We interpret the log-Brunn-Minkowski conjecture of B\"or\"oczky-Lutwak-Yang-Zhang as a spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert-Brunn-Minkowski operator coincides with the centro-affine Laplacian ...
E. Milman
semanticscholar +1 more source
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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∗-K-Operator Frame for Hom∗A(X)
European Journal of Mathematical Analysis, 2021 In this work, we introduce the concept of ∗-K-operator frames in Hilbert pro-C∗-modules, which is a generalization of K-operator frame. We present the analysis operator, the synthesis operator and the frame operator.
Mohamed Rossafi +2 more
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Nutrigonometry III: curvature, area and differences between performance landscapes
Royal Society Open Science, 2022 Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the ...
Juliano Morimoto +2 more
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