图书简介
This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021.The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.
Probability and Statistics on Riemannian Manifolds.- From Bayesian inference to MCMC and convex optimisation in Hadamard manifolds.- Finite Sample Smeariness on Spheres.- Gaussian distributions on Riemannian symmetric spaces in the large N limit.- Smeariness Begets Finite Sample Smeariness.- Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces.- Quinten Tupker, Salem Said and Cyrus MostajeranSub-Riemannian Geometry and Neuromathematics.- Submanifolds of fixed degree in graded manifolds for perceptual completion.- An auditory cortex model for sound processing.- Conformal model of hypercolumns in V1 cortex and the Moebius group. Application to the visual stability problem.- Extremal controls for Duits car.- Multi-Shape Registration with Constrained Deformations.- Shapes Spaces.- Geodesics of the Quotient-Affine Metrics on Full-Rank Correlation Matrices.- Parallel Transport on Kendall Shape Spaces.- Diffusion Means and Heat Kernel on Manifolds.- A reduced parallel transport equation on Lie Groups with a left-invariant metric.- Currents and K-functions for Fiber Point Processes.- Geometry of Quantum States.- Q-Information Geometry of Systems.- Group actions and Monotone Metric Tensors: The qubit case.- Quantum Jensen-Shannon divergences between infinite-dimensional positive definite operators.- Towards a geometrization of quantum complexity and chaos.- Hunt’s colorimetric effect from a quantum measurement viewpoint.- Geometric and Structure Preserving Discretizations.- The Herglotz principle and vakonomic dynamics.- Structure-preserving discretization of a coupled heat-wave system, as interconnected port-Hamiltonian systems.- Examples of symbolic and numerical computation in Poisson geometry.-New directions for contact integrators.- Information Geometry in Physics.- Space-time thermo-mechanics for a material continuum.- Entropic dynamics yields reciprocal relations.- Lie Group Machine Learning.- Gibbs states on symplectic manifolds with symmetries.- Gaussian Distributions on the Space of Symmetric Positive Definite Matrices from Souriau’s Gibbs State for Siegel Domains by Coadjoint Orbit and Moment Map.- On Gaussian Group Convex Models.- Exponential-wrapped probability densities on SL(2,C).- Information Geometry and Hamiltonian Systems on Lie Groups.- Geometric and Symplectic Methods for Hydrodynamical Models.- Multisymplectic variational integrators for fluid models with constraints.- Metriplectic Integrators for Dissipative Fluids.- From quantum hydrodynamics to Koopman wavefunctions I.- From quantum hydrodynamics to Koopman wavefunctions II.- Harmonic Analysis on Lie Groups.- The Fisher information of curved exponential families and the elegant Kagan inequality.- Continuous Wavelet transforms for vector-valued functions.- Entropy under disintegrations.- Koszul Information Geometry, Liouville-Mineur Integrable Systems and Moser Isospectral Deformation Method for Hermitian Positive-Definite Matrices.- Flapping Wing Coupled Dynamics in Lie Group Setting.- Statistical Manifold and Hessian Information Geometry.- Canonical foliations of statistical manifolds with hyperbolic compact leaves.- Open problems in global analysis. Structured foliations and the information Geometry.- Curvature inequalities and Simons’ type formulas in statistical geometry.- Harmonicity of Conformally-Projectively Equivalent Statistical Manifolds and Conformal Statistical Submersions.- Algorithms for approximating means of semi-infinite quasi-Toeplitz matrices.- Geometric Mechanics.- Archetypal Model of Entropy by Poisson Cohomology as Invariant Casimir Function in Coadjoint Representation and Geometric Fourier Heat Equation.- Bridge Simulation and Metric Estimation on Lie Groups.- Constructing the Hamiltonian from the behaviour of a dynamical system by pro
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