Geometric Science of Information

Part I: Shape Space.- On geometric properties of the textile set and strict textile set.- Inexact elastic shape matching in the square root normal field framework.- Signatures in Shape Analysis: an Efficient Approach to Motion Identification.- Dilation operator approach for time/Doppler spectra characterization on SU(n).- Selective metamorphosis for growth modelling with applications to landmarks.- Part II: Geometric Mechanics.- Intrinsic Incremental Mechanics.- -Multi-symplectic Extension of Lie Group Thermodynamics for Covariant Field Theories.- Euler-Poincare equation for Lie groups with non null symplectic cohomology. Application to the Mechanics.- Geometric numerical methods for mechanics.- Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups.- Part 3: Geometry of Tensor-Valued Data.- R-Complex Finsler Information Geometry Applied to Manifolds of Systems.- Minkowski Sum of Ellipsoids and Means of Covariance Matrices.- Hyperquaternions: An Efficient Mathematical Formalism for Geometry.- Alpha-power sums on symmetric cones.- Packing Bounds for Outer Products with Applications to Compressive Sensing.- Part 4: Lie Group Machine Learning.- On a method to construct exponential families by representation theory.- Lie Group Machine Learning & Gibbs Density on Poincare Unit Disk from Souriau Lie Groups Thermodynamics and SU(1,1) Coadjoint Orbits.- Irreversible Langevin MCMC on Lie Groups.- Predicting Bending Moments with Machine Learning.- The exponential of nilpotent supergroups in the theory of Harish-Chandra representations.- Part 5: Geometric structures in thermodynamics and statistical physics.- Dirac structures in open thermodynamics.- From variational to single and double bracket formulations in nonequilibrium thermodynamics of simple systems.- A omological Approach to Belief Propagation and Bethe Approximations.- - About some systems-theoretic properties of Port Thermodynamic systems.- Expectation variables on a para-contact metric manifold exactly derived from master equations.- Part 6: Monotone embedding and affine immersion of probability models.- Doubly autoparallel structure and its applications.- Toeplitz Hermitian Positive Definite Matrix Machine Learning based on Fisher metric.- Deformed exponential and the behavior of the normalizing function.- Normalization problems for deformed exponential families.- New Geometry of parametric statistical Models.- Part 7: Divergence Geometry.- The Bregman chord divergence.- Testing the number and nature of components in a mixture distribution.- Robust etsimation by means of scaled Bregman power distances. Part I: Non-homogeneous data.- Robust estimation by means of scaled Bregman power distances. Part II: Extreme values.- Part 8: Computational Information Geometry.- Topological methods for unsupervised learning.- Geometry and fixed-rate quantization in Riemannian metric spaces induced by separable Bregman divergences.- The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models.- Parameter estimation with generalized empirical localization.- Properties of the cross entropy of ARMA processes.- Part 9: Statistical Manifold & Hessian Information Geometry.- Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian curvature.- Inequalities for statistical submanifolds in sasakian statistical manifolds.- Generalized Wintgen Inequality for Legendrian Submanifolds in Sasakian statistical manifolds.- Logarithmic divergence: geometry and interpretation of curvature.- Hessian Curvature and Optimal Transport.- Part 10: Non-parametric Information Geometry.- Divergence functions in Information Geometry.- Sobolev Statistical Manifolds and Exponential Models.- Minimization of the Kullback-Leibler divergence over a log-normal exponential arc.- Riemannian distance and diameter of the space of probability measures and the parametrix.- Part 11: Statistics on non-linear data.- A unified formulation for the Bures-Wassersteinand Log-Euclidean/Log-Hilbert-Schmidt distances between positive definite operators.- Exploration of Balanced Metrics on Symmetric Positive Definite Matrices.- Affine-invariant midrange statistics.- Is affine-invariance well defined on SPD matrices? A principled continuum of metrics.- Shape part transfer via semantic latent space factorization.- Part 12: Geometric and structure preserving discretizations.- Variational discretization framework for geophysical flows.- Finite element methods for geometric evolution equations.- Local truncation error of low-order fractional variational integrators.- A partitioned finite element method for the structure-preserving discretization of damped in finite-dimensional port-Hamiltonian systems with boundary control.- Geometry, Energy, and Entropy Compatible (GEEC) variational approaches to various numerical schemes for fluid dynamics.- Part 13: Optimization on Manifold.- Canonical Moments for Optimal Uncertainty Quantification on a Variety.- Computational investigations of an obstacle-type shape optimization problem in the space of smooth shapes.- Bezier curves and C^2 interpolation in Riemannian Symmetric Spaces.- A Formalization of The Natural Gradient Method for General Similarity Measures.- The Frenet-Serret framework for aligning geometric curves.- Part 14: Geometry of Quantum States.- When geometry meets psycho-physics and quantum mechanics: Modern perspectives on the space of perceived colors.- Quantum statistical manifolds: The finite-dimensional case.- Generalized Gibbs Ensembles in Discrete Quantum Gravity.- On the notion of composite system, classical and quantum.- Part 15: Probability on Riemannian Manifolds.- The Riemannian barycentre as a proxy for global optimization.- Hamiltonian Monte Carlo on Lie groups and constrained mechanics on homogeneous manifolds.- On the Fisher Rao information metric in the space of normal distributions.- Simulation of Conditioned Diffusions on the Flat Torus.- Towards parametric bi-invariant density estimation on SE(2).- Part 16: Wasserstein Information Geometry / Optimal Transport.- Affine Natural Proximal Learning.- Parametric Fokker-Planck equation.- Multi-marginal Schroedinger bridges.- Hopf-Cole transformation and Schrodinger problems.- - Curvature of the manifold of fixed-rank positive-semidefinite matrices endowed with the Bures-Wasserstein metric.- Part 17: Geometric Science of Information Libraries.- Second-order networks in PyTorch.- Symmetric Algorithmic Components for Shape Analysis with Dieomorphisms.