Melvin Leok
Melvin Leok
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Lie group collision variational integrator - bouncing cube/dice simulation - Example 5
This simulation demonstrates the sensitive dependence on initial conditions of rigid body collisional dynamics, two cubes are initialized with slightly different orientations and allowed to collide with a plane, and the trajectories eventually diverge after a few collisions.
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Видео

PIMS Marsden Memorial Lecture by Melvin Leok at UNBC in March 2023
Просмотров 507Год назад
The Connections Between Discrete Geometric Mechanics, Information Geometry, Accelerated Optimization and Machine Learning Melvin Leok, University of California, San Diego Abstract: Geometric mechanics describes Lagrangian and Hamiltonian mechanics geometrically, and information geometry formulates statistical estimation, inference, and machine learning in terms of geometry. A divergence functio...
EM algorithm applied to Gaussian mixtures
Просмотров 5352 года назад
EM algorithm applied to Gaussian mixtures
Minimizing divergence between a model manifold and a data manifold
Просмотров 3532 года назад
Minimizing divergence between a model manifold and a data manifold
Boltzmann machine with hidden units
Просмотров 2192 года назад
Boltzmann machine with hidden units
Gaussian mixture model as a system with hidden variables
Просмотров 2412 года назад
Gaussian mixture model as a system with hidden variables
Statistical models with hidden variables
Просмотров 2672 года назад
Statistical models with hidden variables
Asymptotic Theory of Hypothesis Testing
Просмотров 6012 года назад
Asymptotic Theory of Hypothesis Testing
Higher-order Asymptotic Theory of Estimation
Просмотров 1842 года назад
Higher-order Asymptotic Theory of Estimation
First-order Asymptotic Theory of Estimation
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First-order Asymptotic Theory of Estimation
Estimation in a Curved Exponential Family
Просмотров 4372 года назад
Estimation in a Curved Exponential Family
Estimation in the Exponential Family
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Estimation in the Exponential Family
Estimation in the context of statistical inference
Просмотров 2632 года назад
Estimation in the context of statistical inference
Canonical divergence in dually flat manifolds
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Canonical divergence in dually flat manifolds
Dually Flat Manifolds
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Dually Flat Manifolds
Metric and Cubic Tensor Derived from Divergence or Convex Functions
Просмотров 2262 года назад
Metric and Cubic Tensor Derived from Divergence or Convex Functions
Dual affine connections
Просмотров 2962 года назад
Dual affine connections
Levi-Civita (Riemannian) connection
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Levi-Civita (Riemannian) connection
Holonomy (Round-the-world transport)
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Holonomy (Round-the-world transport)
Flat manifolds
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Flat manifolds
Parallel transport of a vector
Просмотров 8662 года назад
Parallel transport of a vector
Geodesics
Просмотров 2422 года назад
Geodesics
Covariant derivatives using affine connections
Просмотров 3312 года назад
Covariant derivatives using affine connections
Tensors
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Tensors
Affine connections
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Affine connections
Riemannian metric
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Riemannian metric
Manifolds and Tangent Spaces
Просмотров 1,6 тыс.2 года назад
Manifolds and Tangent Spaces
Tangent vectors under changes of coordinates
Просмотров 3212 года назад
Tangent vectors under changes of coordinates
Repeated observations and maximum likelihood estimators
Просмотров 1802 года назад
Repeated observations and maximum likelihood estimators
Mutual information
Просмотров 1532 года назад
Mutual information