Gradient systems associated with probability distributions

DOI10.1007/BF03167211zbMath0811.58036MaRDI QIDQ1325129

Yoshimasa Nakamura

Publication date: 18 April 1995

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

zbMATH Keywords

gradient systemsLax pair representationmanifolds of probability 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)

SYMPLECTIC STRUCTURES ON STATISTICAL MANIFOLDS ⋮ On explicit solvable gradient systems of Moser-Karmarkar type ⋮ Yokes and symplectic structures ⋮ Statistics, yokes and symplectic geometry ⋮ Weyl geometric approach to the gradient-flow equations in information geometry ⋮ Geodesic flows of \(\alpha \)-connections for statistical transformation models on a compact Lie group ⋮ Diffusion equations from master equations—A discrete geometric approach ⋮ Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps ⋮ Contact Hamiltonian Systems for Probability Distribution Functions and Expectation Variables: A Study Based on a Class of Master Equations ⋮ Holonomic gradient descent and its application to the Fisher-Bingham integral ⋮ An eikonal equation approach to thermodynamics and the gradient flows in information geometry ⋮ Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics ⋮ 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

Cites Work

• Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions
• A new polynomial-time algorithm for linear programming
• A geometric method in nonlinear programming
• Differential-geometrical methods in statistics
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• The Nonlinear Geometry of Linear Programming. III Projective Legendre Transform Coordinates and Hilbert Geometry
• The Nonlinear Geometry of Linear Programming. II Legendre Transform Coordinates and Central Trajectories
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Gradient systems associated with probability distributions