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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Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics [PDF]
Entropy, 2020 In this paper, we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau’s symplectic model of statistical ...
Frédéric Barbaresco +1 more
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Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation [PDF]
Entropy, 2020 In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
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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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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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Homogeneous spaces of unsolvable Lie groups that do not admit equiaffine connections of nonzero curvature [PDF]
Известия Саратовского университета. Новая 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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Cohomology of Lie groups [PDF]
Illinois Journal of Mathematics, 1962 G. Hochschild, G. D. Mostow
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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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