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Research on the Necessity of Lie Group Strapdown Inertial Integrated Navigation Error Model Based on Euler Angle [PDF]
Sensors, 2022 In response to the lack of specific demonstration and analysis of the research on the necessity of the Lie group strapdown inertial integrated navigation error model based on the Euler angle, two common integrated navigation systems, strapdown inertial ...
Leiyuan Qian +3 more
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Multi-Stage Meta-Learning for Few-Shot with Lie Group Network Constraint [PDF]
Entropy, 2020 Deep learning has achieved many successes in different fields but can sometimes encounter an overfitting problem when there are insufficient amounts of labeled samples.
Fang Dong, Li Liu, Fanzhang Li
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Lie Group Methods in Blind Signal Processing [PDF]
Sensors, 2020 This paper deals with the use of Lie group methods to solve optimization problems in blind signal processing (BSP), including Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). The paper presents the theoretical fundamentals of
Dariusz Mika, Jerzy Jozwik
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The Affine Group of a Lie Group [PDF]
Proceedings of the American Mathematical Society, 1963 1. If G is a Lie group, then the group Aut(G) of all continuous automorphisms of G has a natural Lie group structure. This gives the semidirect product A(G) = G-Aut(G) the structure of a Lie group. When G is a vector group R", A(G) is the ordinary affine group A(re). Following L. Auslander [l ] we will refer to A(G) as the affine group of G, and regard
Joseph A. Wolf
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Lie group integrators for mechanical systems [PDF]
International Journal of Computational Mathematics, 2021 Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two important classes
E. Celledoni +4 more
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Homogeneous spaces of unsolvable Lie groups that do not admit equiaffine connections of nonzero curvature [PDF]
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, 2023 An important subclass among homogeneous spaces is formed by isotropically-faithful homogeneous spaces, in particular, this subclass contains all homogeneous spaces admitting invariant affine connection.
Mozhey, Natalya Pavlovna
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Advances in the Theory of Compact Groups and Pro-Lie Groups in the Last Quarter Century
Axioms, 2021 This article surveys the development of the theory of compact groups and pro-Lie groups, contextualizing the major achievements over 125 years and focusing on some progress in the last quarter century.
Karl H. Hofmann, Sidney A. Morris
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TorusE: Knowledge Graph Embedding on a Lie Group [PDF]
AAAI Conference on Artificial Intelligence, 2017 Knowledge graphs are useful for many artificial intelligence (AI) tasks. However, knowledge graphs often have missing facts. To populate the graphs, knowledge graph embedding models have been developed.
Takuma Ebisu, R. Ichise
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Screw and Lie group theory in multibody dynamics [PDF]
Multibody system dynamics, 2017 Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS), and at the same they give rise to computationally efficient recursive algorithms.
A. Müller
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Screw and Lie group theory in multibody kinematics [PDF]
Multibody system dynamics, 2017 After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user-friendly yet computationally efficient formulations for the analysis of complex MBS.
A. Müller
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