Geometric Science of Information

Table of Contents

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   Book Overview
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   Chapter 1 Three Methods to Put a Riemannian Metric on Shape Space
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   Chapter 2 Riemannian Locally Linear Embedding with Application to Kendall Shape Spaces
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   Chapter 3 A Product Shape Manifold Approach for Optimizing Piecewise-Smooth Shapes
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   Chapter 4 On Canonical Parameterizations of 2D-Shapes
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   Chapter 5 Shape Spaces of Nonlinear Flags
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   Chapter 6 A Neurogeometric Stereo Model for Individuation of 3D Perceptual Units
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   Chapter 7 Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks
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   Chapter 8 Continuous Kendall Shape Variational Autoencoders
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    Chapter 9 Can Generalised Divergences Help for Invariant Neural Networks?
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    Chapter 10 Group Equivariant Sparse Coding
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    Chapter 11 On a Cornerstone of Bare-Simulation Distance/Divergence Optimization
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    Chapter 12 Extensive Entropy Functionals and Non-ergodic Random Walks
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    Chapter 13 Empirical Likelihood with Censored Data
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    Chapter 14 Aggregated Tests Based on Supremal Divergence Estimators for Non-regular Statistical Models
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    Chapter 15 Quasi-arithmetic Centers, Quasi-arithmetic Mixtures, and the Jensen-Shannon $$\nabla $$-Divergences
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    Chapter 16 Geometry of Parametric Binary Choice Models
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    Chapter 17 A q-Analogue of the Family of Poincaré Distributions on the Upper Half Plane
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    Chapter 18 On the f-Divergences Between Hyperboloid and Poincaré Distributions
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    Chapter 19 $$\lambda $$-Deformed Evidence Lower Bound ($$\lambda $$-ELBO) Using Rényi and Tsallis Divergence
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    Chapter 20 On the Tangent Bundles of Statistical Manifolds
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    Chapter 21 Geometric Properties of Beta Distributions
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    Chapter 22 KV Cohomology Group of Some KV Structures on $$\mathbb {R}^2$$
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    Chapter 23 Alpha-parallel Priors on a One-Sided Truncated Exponential Family
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    Chapter 24 Conformal Submersion with Horizontal Distribution and Geodesics
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    Chapter 25 Higher Information from Families of Measures
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    Chapter 26 A Categorical Approach to Statistical Mechanics
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    Chapter 27 Categorical Information Geometry
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    Chapter 28 Categorical Magnitude and Entropy
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    Chapter 29 A Historical Perspective on Schützenberger-Pinsker Inequalities
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    Chapter 30 On Fisher Information Matrix, Array Manifold Geometry and Time Delay Estimation
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    Chapter 31 Revisiting Lattice Tiling Decomposition and Dithered Quantisation
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    Chapter 32 Geometric Reduction for Identity Testing of Reversible Markov Chains
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    Chapter 33 On the Entropy of Rectifiable and Stratified Measures
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    Chapter 34 Exploring Uniform Finite Sample Stickiness
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    Chapter 35 Types of Stickiness in BHV Phylogenetic Tree Spaces and Their Degree
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    Chapter 36 Towards Quotient Barycentric Subspaces
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    Chapter 37 Rethinking the Riemannian Logarithm on Flag Manifolds as an Orthogonal Alignment Problem
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    Chapter 38 Characterization of Invariant Inner Products
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    Chapter 39 Variational Gaussian Approximation of the Kushner Optimal Filter
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    Chapter 40 Learning with Symmetric Positive Definite Matrices via Generalized Bures-Wasserstein Geometry
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    Chapter 41 Fisher-Rao Riemannian Geometry of Equivalent Gaussian Measures on Hilbert Space
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    Chapter 42 The Gaussian Kernel on the Circle and Spaces that Admit Isometric Embeddings of the Circle
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    Chapter 43 Determinantal Expressions of Certain Integrals on Symmetric Spaces
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    Chapter 44 Projective Wishart Distributions
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    Chapter 45 Convex Hulls of Curves: Volumes and Signatures
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    Chapter 46 Avoiding the General Position Condition When Computing the Topology of a Real Algebraic Plane Curve Defined Implicitly
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    Chapter 47 Dynamical Geometry and a Persistence K-Theory in Noisy Point Clouds
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    Chapter 48 An Approximate Projection onto the Tangent Cone to the Variety of Third-Order Tensors of Bounded Tensor-Train Rank
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    Chapter 49 Toric Fiber Products in Geometric Modeling
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    Chapter 50 Twirled Products and Group-Covariant Symbols
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    Chapter 51 Coherent States and Entropy
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    Chapter 52 A Non-formal Formula for the Rankin-Cohen Deformation Quantization
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    Chapter 53 Equivalence of Invariant Star-Products: The “Retract” Method
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    Chapter 54 DL4TO : A Deep Learning Library for Sample-Efficient Topology Optimization
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    Chapter 55 Learning Hamiltonian Systems with Mono-Implicit Runge-Kutta Methods
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    Chapter 56 A Geometric View on the Role of Nonlinear Feature Maps in Few-Shot Learning
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    Chapter 57 Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves
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    Chapter 58 Gauge Transformations in Stochastic Geometric Mechanics
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    Chapter 59 Couplings of Brownian Motions on $$SU(2,\mathbb {C})$$
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    Chapter 60 A Finite Volume Scheme for Fractional Conservation Laws Driven by Lévy Noise
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    Chapter 61 The Total Variation-Wasserstein Problem: A New Derivation of the Euler-Lagrange Equations