Table of Contents

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   Book Overview
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   Chapter 1 Lie Group Quaternion Attitude-Reconstruction of Quadrotor UAV
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   Chapter 2 A Variational Principle of Minimum for Navier-Stokes Equation Based on the Symplectic Formalism
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   Chapter 3 A Variational Symplectic Scheme Based on Simpson’s Quadrature
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   Chapter 4 Generalized Galilean Geometries
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   Chapter 5 Continuum Mechanics of Defective Media: An Approach Using Fiber Bundles
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   Chapter 6 Singular Cotangent Models in Fluids with Dissipation
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   Chapter 7 Multisymplectic Unscented Kalman Filter for Geometrically Exact Beams
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   Chapter 8 Towards Full ‘Galilei General Relativity’: Bargmann-Minkowski and Bargmann-Galilei Spacetimes
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    Chapter 9 Existence of Global Minimizer for Elastic Variational Obstacle Avoidance Problems on Riemannian Manifolds
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    Chapter 10 Virtual Affine Nonholonomic Constraints
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    Chapter 11 Nonholonomic Systems with Inequality Constraints
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    Chapter 12 Nonholonomic Brackets: Eden Revisited
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    Chapter 13 The Momentum Mapping of the Affine Real Symplectic Group
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    Chapter 14 Polysymplectic Souriau Lie Group Thermodynamics and the Geometric Structure of Its Coadjoint Orbits
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    Chapter 15 Polysymplectic Souriau Lie Group Thermodynamics and Entropy Geometric Structure as Casimir Invariant Function
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    Chapter 16 Riemannian Geometry of Gibbs Cones Associated to Nilpotent Orbits of Simple Lie Groups
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    Chapter 17 Symplectic Foliation Transverse Structure and Libermann Foliation of Heat Theory and Information Geometry
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    Chapter 18 Poisson Geometry of the Statistical Frobenius Manifold
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    Chapter 19 Canonical Hamiltonian Systems in Symplectic Statistical Manifolds
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    Chapter 20 A Dually Flat Geometry for Spacetime in 5d
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    Chapter 21 Structure-preserving Discretization of the Cahn-Hilliard Equations Recast as a Port-Hamiltonian System
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    Chapter 22 Infinite Dimensional Lagrange–Dirac Mechanics with Boundary Conditions
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    Chapter 23 Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups
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    Chapter 24 Hamiltonian Variational Formulation for Non-simple Thermodynamic Systems
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    Chapter 25 Madelung Transform and Variational Asymptotics in Born-Oppenheimer Molecular Dynamics
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    Chapter 26 Conservation Laws as Part of Lagrangian Reduction. Application to Image Evolution
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    Chapter 27 Casimir-Dissipation Stabilized Stochastic Rotating Shallow Water Equations on the Sphere
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    Chapter 28 High-Order Structure-Preserving Algorithms for Plasma Hybrid Models
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    Chapter 29 Hydrodynamics of the Probability Current in Schrödinger Theory
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    Chapter 30 Variational Geometric Description for Fluids with Permeable Boundaries
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    Chapter 31 Lagrangian Trajectories and Closure Models in Mixed Quantum-Classical Dynamics
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    Chapter 32 A Discrete Version for Vortex Loops in 2D Fluids
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    Chapter 33 Expressiveness and Structure Preservation in Learning Port-Hamiltonian Systems
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    Chapter 34 Signature Estimation and Signal Recovery Using Median of Means
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    Chapter 35 Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networks
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    Chapter 36 Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks
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    Chapter 37 Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising Chains
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    Chapter 38 Can Čencov Meet Petz
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    Chapter 39 Souriau’s Geometric Principles for Quantum Mechanics
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    Chapter 40 Unitarity Excess in Schwartzschild Metric
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    Chapter 41 Modelling and Structure-Preserving Discretization of the Schrödinger as a Port-Hamiltonian System, and Simulation of a Controlled Quantum Box
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    Chapter 42 Some Remarks on the Notion of Transition
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    Chapter 43 Geometric Quantum States and Lagrangian Polar Duality: Quantum Mechanics Without Wavefunctions
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    Chapter 44 Complete Integrability of Gradient Systems on a Manifold Admitting a Potential in Odd Dimension
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    Chapter 45 Geometry-Preserving Lie Group Integrators for Differential Equations on the Manifold of Symmetric Positive Definite Matrices
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    Chapter 46 The Phase Space Description of the Geodesics on the Statistical Model on a Finite Set
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    Chapter 47 Geodesic Flows of  $$\alpha $$ α -connections for Statistical Transformation Models on a Compact Lie Group
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    Chapter 48 Differential Operators Heterogenous in Orientation and Scale in the  $$V_1$$ V 1 Cortex
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    Chapter 49 Gabor Frames and Contact Structures: Signal Encoding and Decoding in the Primary Visual Cortex
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    Chapter 50 A Sub-Riemannian Model of the Functional Architecture of M1 for Arm Movement Direction
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    Chapter 51 Geometry of Saccades and Saccadic Cycles
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    Chapter 52 MacKay-Type Visual Illusions via Neural Fields
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    Chapter 53 Pseudo-dihedral Angles in Proteins Providing a New Description of the Ramachandran Map
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    Chapter 54 A Study on the Covalent Geometry of Proteins and Its Impact on Distance Geometry
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    Chapter 55 Exploration of Conformations for an Intrinsically Disordered Protein
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    Chapter 56 Temporal Alignment of Human Motion Data: A Geometric Point of View
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    Chapter 57 A Linear Program for Points of Interest Relocation in Adaptive Maps
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    Chapter 58 Diffeomorphic ICP Registration for Single and Multiple Point Sets
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    Chapter 59 Chan-Vese Attention U-Net: An Attention Mechanism for Robust Segmentation
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    Chapter 60 Using a Riemannian Elastic Metric for Statistical Analysis of Tumor Cell Shape Heterogeneity
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    Chapter 61 Perturbation of Fiedler Vector: Interest for Graph Measures and Shape Analysis
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    Chapter 62 Generative OrnsteinUhlenbeck Markets via Geometric Deep Learning
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    Chapter 63 $${{\,\textrm{SL}\,}}(2,\mathbb {Z})$$ SL ( 2 , Z ) -Equivariant Machine Learning with Modular Forms Theory and Applications
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    Chapter 64 K-Splines on SPD Manifolds
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    Chapter 65 Geometric Deep Learning: A Temperature Based Analysis of Graph Neural Networks