2018 MATRIX Annals

The 2018 MATRIX Annals, the third book in the MATRIX Book Series, documents scientific activities at MATRIX in 2018. Pre-publication versions of the articles in the book are posted below.


Guest Editors

Algebraic Geometry, Approximation and Optimisation

Enrico Carlini, Jochen Garcke, James Saunderson

On the Frontiers of High Dimensional Computation

Frances Kuo

Month of Mathematical Biology

Mark Flegg, James Osborne

Dynamics, Foliations, and Geometry In Dimension 3

Jonathan Bowden, Andy Hammerlindl

Recent Trends on Nonlinear PDEs of Elliptic And Parabolic Type

Daniel Hauer

Geometric and Categorical Representation Theory

Peter McNamara

Refereed Articles

On the Frontiers of High Dimensional Computation

J.C.H. Blake, I. Graham, F. Scheben, A. Spence
The radiative transport equation with heterogeneous cross-sections
pages 5-15, doi: 10.1007/978-3-030-38230-8_1

Mahadevan Ganesh, Stuart Hawkins
A reduced-order-model Bayesian obstacle detection algorithm
pages 17-27, doi: 10.1007/978-3-030-38230-8_2

Alexander Gilbert, Ivan Graham, Robert Scheichl, Ian Sloan
Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients
pages 29-43, doi: 10.1007/978-3-030-38230-8_3

Stefan Heinrich
On the power of restricted Monte Carlo algorithms
pages 45-59, doi: 10.1007/978-3-030-38230-8_4

Fred Hickernell, Peter Kritzer, Henryk Wozniakowski
Exponential tractability of linear tensor product problems
pages 61-78, doi: 10.1007/978-3-030-38230-8_5

Yoshihito Kazashi, Ian Sloan
Worst-case error for unshifted lattice rules without randomization
pages 79-96, doi: 10.1007/978-3-030-38230-8_6

Thomas Kuhn
New preasymptotic estimates for approximation of Sobolev functions
pages 97-112, doi: 10.1007/978-3-030-38230-8_7

Hrushikesh Mhaskar, Sergei Pereverzyev, Vasyl Semenov, Evgeniya Semenova
Data based construciton of kernels for classification
pages 113-119, doi: 10.1007/978-3-030-38230-8_8

Dongwoo Sheen
P1-nonconforming polyhedral finite elements in high dimensions
pages 121-133, doi: 10.1007/978-3-030-38230-8_9

Month of Mathematical Biology

Stuart T. Johnston, Christopher N. Angstmann, Satya N.V. Arjunan, Casper H.L. Beentjes, Adrien Coulier, Samuel A. Isaacson, Ash A. Khan, Karen Lipkow, Steven S. Andrews
Accurate particle-based reaction algorithms for fixed timestep simulators
pages 149-164, doi: 10.1007/978-3-030-38230-8_11

Ana Victoria Ponce Bobadilla, Bartosz Jan Bartmanski, Ramon Grima, Hans G. Othmer
The status of the QSSA approximation in stochastic simulations of reaction networks
pages 137-147, doi: 10.1007/978-3-030-38230-8_10

Recent Trends on Nonlinear PDEs Of Elliptic And Parabolic Type

Elisa Affili, Serena Dipierro, Enrico Valdinoci
Decay estimates in time for classical and anomalous diffusion
pages 167-183, doi: 10.1007/978-3-030-38230-8_12

Ben Andrews
Multi-point maximum principles and eigenvalue estimates
pages 185-213, doi: 10.1007/978-3-030-38230-8_13

Jérôme Coville
A note on Liouville type results for a fractional obstacle problem
pages 215-228, doi: 10.1007/978-3-030-38230-8_14

Serena Dipierro, Pietro Miraglio, Enrico Valdinoci
Symmetry results for the solutions of a partial differential equation arising in water waves
pages 229-248, doi: 10.1007/978-3-030-38230-8_15

Francois Hamel, Nikolai Nadirashvili, Yannick Sire
Geometric properties of superlevel sets of semilinear elliptic equations in convex domains
pages 249-263, doi: 10.1007/978-3-030-38230-8_16

Michinori Ishiwata, Bernhard Ruf, Federica Sani, Elide Terraneo
A potential well argument for a semilinear parabolic equation with exponential nonlinearity
pages 265-273, doi: 10.1007/978-3-030-38230-8_17

Dario Mazzoleni, Benedetta Pellacci, Gianmaria Verzini
Quantitative analysis of a singularly perturbed shape optimization problem in a polygon
pages 275-283, doi: 10.1007/978-3-030-38230-8_18

James McCoy, Glen Wheeler
A rigidity theorem for ideal surfaces with flat boundary
pages 285-291, doi: 10.1007/978-3-030-38230-8_19

Robin Neumayer
On minimizers and critical points for anisotropic isoperimetric problems
pages 293-302, doi: 10.1007/978-3-030-38230-8_20

Philippe Souplet
Liouville-type theorems for nonlinear elliptic and parabolic problems
pages 303-325, doi: 10.1007/978-3-030-38230-8_21

Other Contributed Articles

Algebraic Geometry, Approximation and Optimisation

Nadezda Sukhorukova, Julien Ugon, David Yost
Schur functions for approximation problems
pages 331-337, doi: 10.1007/978-3-030-38230-8_22

Dynamics, Foliations, and Geometry In Dimension 3

Thomas Barthelmé, Sergio R. Fenley, Steven Frankel, Rafael Potrie
Research announcement: Partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds
pages 341-357, doi: 10.1007/978-3-030-38230-8_23

Jonathan Bowden, Christian Bonatti, Rafael Potrie
Some remarks on projective Anosov flows in hyperbolic 3-manifolds
pages 359-369, doi: 10.1007/978-3-030-38230-8_24

Andy Hammerlindl
Notes on global product structure
pages 371-379, doi: 10.1007/978-3-030-38230-8_25

Geometric and Categorical Representation Theory

Geoff Vooys
The Greenberg functor is site cocontinuous
pages 383-427, doi: 10.1007/978-3-030-38230-8_26