Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions

DOI10.1007/BF03167571zbMath0814.58021OpenAlexW2024465860MaRDI QIDQ689913

Yoshimasa Nakamura

Publication date: 20 December 1993

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167571

zbMATH Keywords

Lax representationGaussian distributionsgradient systemscompletely integrable Hamiltonian systemsmultinomial distributions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (15)

An information-geometric approach to a theory of pragmatic structuring ⋮ Gradient systems in view of information geometry ⋮ SYMPLECTIC STRUCTURES ON STATISTICAL MANIFOLDS ⋮ On explicit solvable gradient systems of Moser-Karmarkar type ⋮ Yokes and symplectic structures ⋮ Lax-type equation unifying gradient systems in quantum and classical statistical models ⋮ Statistics, yokes and symplectic geometry ⋮ Geometric properties of beta distributions ⋮ Complete integrability of gradient systems on a manifold admitting a potential in odd dimension ⋮ Geodesic flows of \(\alpha \)-connections for statistical transformation models on a compact Lie group ⋮ Algorithms associated with arithmetic, geometric and harmonic means and integrable systems ⋮ Information geometry and Hamiltonian systems on Lie groups ⋮ Koszul information geometry, Liouville-Mineur integrable systems and Moser isospectral deformation method for Hermitian positive-definite matrices ⋮ Neurodynamics and nonlinear integrable systems of Lax type ⋮ Gradient systems associated with probability distributions

Cites Work

• Non-triviality of an element in the stable homotopy groups of spheres
• Differential-geometrical methods in statistics
• A completely integrable Hamiltonian system associated with line fitting in complex vector spaces
• The Nonlinear Geometry of Linear Programming. II Legendre Transform Coordinates and Central Trajectories
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