Intro; Preface; Hypergeometric Motives and Calabi-Yau Differential Equations; Computational Inverse Problems; Integrability in Low-Dimensional Quantum Systems; Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger's Book; Combinatorics, Statistical Mechanics, and Conformal Field Theory; Mathematics of Risk; Tutte Centenary Retreat; Geometric R-Matrices: From Geometry to Probability; Contents; Part I Refereed Articles; A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems; 1 Introduction

2 The Randomize-Then-Optimize Proposal Density3 RTO-Metropolis-Hastings and Its Embedding Within Hiererichical Gibbs; 3.1 RTO-MH-Within-Hierarchical Gibbs; 4 Numerical Experiment; 5 Conclusions; References; Sequential Bayesian Inference for Dynamical Systems Using the Finite Volume Method; 1 Introduction; 1.1 A Stylized Problem; 2 Sequential Bayesian Inference for Dynamical Systems; 2.1 The Frobenius-Perron Operator is a PDE; 3 Finite Volume Solver; 4 Continuous-Time Frobenius-Perron Operator and Convergence of the FVM Approximation; 5 Computed Examples

5.1 FVF Tracking of a Pendulum from Measured Force6 Conclusions; References; Correlation Integral Likelihood for Stochastic Differential Equations; 1 Introduction; 2 Background; 2.1 Likelihood via Filtering; 2.2 Correlation Integral Likelihood; 3 Numerical Experiments; 3.1 Ornstein-Uhlenbeck with Modification for Dynamics; 3.2 Stochastic Chaos; 4 Conclusions; References; A Set Optimization Technique for Domain Reconstruction from Single-Measurement Electrical Impedance Tomography Data; 1 Introduction; 2 The Convex Source Support in Electrical Impedance Tomography

3 An Optimization Problem in Kc(Rd)4 Galerkin Approximations to Kc(R2); 5 Gradients of Functions on GA; 6 A First Numerical Simulation; References; Local Volatility Calibration by Optimal Transport; 1 Introduction; 2 Optimal Transport; 3 Formulation; 3.1 The Martingale Problem; 3.2 Augmented Lagrangian Approach; 4 Numerical Method; 5 Numerical Results; 6 Summary; References; Likelihood Informed Dimension Reduction for Remote Sensing of Atmospheric Constituent Profiles; 1 Introduction; 2 Methodology; 2.1 Bayesian Formulation of the Inverse Problem; 2.2 Prior Reduction

2.3 Likelihood-Informed Subspace3 Results; 4 Conclusions; References; Wider Contours and Adaptive Contours; 1 Introduction; 2 Three Fundamental Models; 2.1 Monomolecular, Bimolecular and Trimolecular Models; 3 Pseudospectra Are Important for Stochastic Processes; 4 A Mittag-Leffler Stochastic Simulation Algorithm; 5 Computing a Mittag-Leffler Matrix Function; 5.1 Computing Contour Integrals; 5.2 Estimating the Field of Values; 6 Conclusion; References; Bayesian Point Set Registration; 1 Introduction; 2 Problem Statement and Statistical Model; 2.1 Bayesian Formulation; 3 Hamiltonian Monte Carlo