# 2017 MATRIX Annals

The 2017 MATRIX Annals, the second book in the MATRIX Book Series, documents scientific activities at MATRIX in 2017. Pre-publication versions of the articles in the book are posted below.

### Preface

## Guest Editors

### Computational Inverse Problems

Tiangang Cui, Hans De Sterck

### Hypergeometric Motives and Calabi–Yau Differential Equations

Masha Vlasenko

### Integrability in Low-Dimensional Quantum Systems

Chaiho Rim and Paul Pearce

### Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book

Paul Bryan

### Mathematics of Risk

Alexander Novikov and Kostya Borovkov

### Tutte Centenary Retreat

Graham Farr, Marston Conder, Dillon Mayhew, Gordon Royle

### Geometric R-Matrices: from Geometry to Probability

Paul Zinn-Justin

## Refereed Articles

### Computational Inverse Problems

Johnathan M. Bardsley, Tiangang Cui.

A Metropolis-Hastings-within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems.

Colin Fox, Richard A. Norton, Malcolm E. K. Morrison, Timothy C. A. Molteno.

Sequential Bayesian Inference for Dynamical Systems Using the Finite Volume Method.

Heikki Haario, Janne Hakkarainen, Ramona Maraia, Sebastian Springer.

Correlation integral likelihood for stochastic differential equations.

Bastian Harrach, Janosch Rieger.

A set optimization technique for domain reconstruction from single-measurement electrical impedance tomography data.

Ivan Guo, Grégoire Loeper, Shiyi Wang.

Local Volatility Calibration by Optimal Transport.

Otto Lamminpää, Marko Laine, Simo Tukiainen, Johanna Tamminen.

Likelihood informed dimension reduction for remote sensing of atmospheric constituent profiles.

Shev MacNamara, William McLean, Kevin Burrage.

Wider contours and adaptive contours.

Adam Spannaus, Vasileios Maroulas, David J. Keffer, Kody J. H. Law.

Bayesian Point Set Registration.

Nan Ye, Farbod Roosta-Khorasani, Tiangang Cui.

Optimization Methods for Inverse Problems.

### Integrability in Low-Dimensional Quantum Systems

Zoltan Bajnok, Chao Wu.

Diagonal form factors from non-diagonal ones.

Sang Kwan Choi, Chaiho Rim, Hwajin Um.

Narayana number, Chebyshev polynomial and Motzkin path on RNA abstract shapes.

Gyorgy Z. Feher, Alexandr Garbali, Jan de Gier, Kareljan Schoutens.

A curious mapping between supersymmetric quantum chains.

Atsuo Kuniba.

Remarks on A_{n}^{(1)} face weights.

### Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book

Camillo De Lellis, Guido De Philippis, Jonas Hirsch, Annalisa Massaccesi.

Boundary regularity of mass-minimizing integral currents and a question of Almgren.

Jiakun Liu, Grégoire Loeper.

Optimal transport with discrete mean field interaction.

James McCoy, Glen Wheeler, Yuhan Wu.

A sixth order curvature flow of plane curves with boundary conditions.

Maria Michaela Porzio.

Quasilinear parabolic and elliptic equations with singular potentials.

Medet Nursultanov, Julie Rowlett, David Sher.

How to hear the corners of a drum.

### Mathematics of Risk

Shota Gugushvili, Frank van der Meulen, Moritz Schauer, Peter Spreij.

Nonparametric Bayesian volatility estimation.

Konstantin Borovkov, Zbigniew Palmowski.

The exact asymptotics for hitting probability of a remote orthant by a multivariate Lévy process: the Cramér case.

Budhi A. Surya.

Parisian excursion below a fixed level from the last record maximum of Lévy insurance risk process.

### Tutte Centenary Retreat

Marston Conder.

Simple group actions on arc-transitive graphs with prescribed transitive local action.

Nemanja Poznanović, Cheryl E. Praeger.

Biquasiprimitive oriented graphs of valency four.

Graham Far, James Oxley.

The contributions of W.T. Tutte to matroid theory.

### Geometric R-Matrices: from Geometry to Probability

Gleb Koshevoy.

Cluster decorated geometric crystals, generalized geometric RSK-correspondences, and Donaldson-Thomas transformations.

## Other Contributed Articles

### Computational Inverse Problems

Johnathan M. Bardsley.

A Matrix Theoretic Derivation of the Kalman Filter.

Yuqin Ke, Tianhai Tian.

Approximate Bayesian Computational methods for the inference of unknown parameters.

### Hypergeometric Motives and Calabi−Yau Differential Equations

Frits Beukers.

Fields of definition of finite hypergeometric functions.

David Broadhurst, David P. Roberts.

L-series and Feynman integrals.

Eric Delaygue.

Arithmetic properties of hypergeometric mirror maps and Dworks congruences.

Sharon Frechette, Holly Swisher, Fang-Ting Tu.

Appell-Lauricella hypergeometric functions over finite fields, and a new cubic transformation formula.

Dermot McCarthy, Robert Osburn, Armin Straub.

Sequences, modular forms and cellular integrals.

Ling Long, Ravi Ramakrishna.

Some supercongruences for truncated hypergeometric series.

David P. Roberts.

The explicit formula and a motivic splitting.

David P. Roberts, Fernando Rodriguez Villegas.

Hypergeometric supercongruences.

Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher.

Alternate mirror families and hypergeometric motives.

Abdellah Sebbar.

Schwarzian equations and equivariant functions.

Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, Fang-Ting Tu.

Hypergeometric functions over finite fields.

Ling Long, Fang-Ting Tu, Noriko Yui, Wadim Zudilin.

Supercongruences occurred to rigid hypergeometric type Calabi-Yau threefolds.

Fernando Rodriguez Villegas.

*p*-adic hypergeometrics.

Masha Vlasenko.

On *p*-adic unit-root formulas.

John Voight.

Triangular modular curves.

Mark Watkins.

Jacobi sums and Hecke Grossencharacters.

Yifan Yang.

Special values of hypergeometric functions and periods of CM elliptic curves.

Duco van Straten.

CY-operators and L-functions.

### Combinatorics, Statistical Mechanics, and Conformal Field Theory

Bernard Nienhuis, Kayed al Qasimi

The loop-weight changing operator in the completely packed loop model.

### Mathematics of Risk

Juri Hinz, Peter Taylor.

A note on optimal double spending attacks.

Qizhu Liang, Jie Xiong.

Stochastic Maximum Principle on a Continuous-time Behavioral Portfolio Model.

Yanhong Li, Zbigniew Palmowski, Chunming Zhao, Chunsheng Zhang.

Number of claims and ruin time for a refracted risk process.

Dan Wu, Lin Yee Hin, Nino Kordzakhia, Alexander Novikov.

Numerical approximations to distributions of weighted Kolmogorov-Smirnov statistics via integral equations.

Marie Kratz.

Introduction to Extreme Value Theory. Applications to Risk Analysis & Management.

Mikhail Zhitlukhin.

Monotone Sharpe ratios and related measures of investment performance.

Alexey Muravlev, Mikhail Zhitlukhin.

A Bayesian sequential test for the drift of a fractional Brownian motion.

### Geometric R-Matrices: from Geometry to Probability

Yaping Yang, Gufang Zhao.

How to sheafify an elliptic quantum group.