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2018 MATRIX annals
- Available as
- Online
- Summary
-
MATRIX is Australias international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each...
MATRIX is Australias international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in 2018: - Non-Equilibrium Systems and Special Functions - Algebraic Geometry, Approximation and Optimisation - On the Frontiers of High Dimensional Computation - Month of Mathematical Biology - Dynamics, Foliations, and Geometry In Dimension 3 - Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type - Functional Data Analysis and Beyond - Geometric and Categorical Representation Theory The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Details
- Creator
- David R. Wood, editor-in-chief
- Format
- Books
- Language
- English
- Contributors
- Publication
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- Cham : Springer, 2020
- Series
- Physical Details
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- 1 online resource (430 pages)
- data file
- ISBNs
- 9783030382292, 9783030382308, 9783030382315, 9783030382322, 303038229X, 3030382303
- OCLC
- on1151188047
- 11 Accurate particle-based reaction algorithms for fixed timestep simulators
- References -- 3 Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients -- 1 Introduction -- 1.1 Variational eigenvalue problems -- 2 Bounding the spectral gap -- 3 Numerical results -- 4 Conclusion -- References -- 4 On the Power of Restricted Monte Carlo Algorithms -- 1 Introduction -- 2 Restricted Randomized Algorithms in a General Setting -- 3 The Power of Restricted Randomized Algorithms -- Reference -- 5 Exponential tractability of linear tensor product problems -- 1 Introduction and Preliminaries -- 2 Results -- References
- Intro -- Preface -- Contents -- I Refereed Articles -- Part 1 On the Frontiers of High Dimensional Computation -- 1 The radiative transport equation with heterogeneous cross-sections -- 1 Introduction -- 2 The main result -- 2.1 Some applications of Theorem 1 -- 2.1.1 Convergence of source iteration -- 2.1.2 Data-explicit estimates for the RTE -- 2.1.3 Spectral properties of the RTE -- References -- 2 A reduced-order-model Bayesian obstacle detection algorithm -- 1 Introduction -- 1.1 Variational egenvalue problems -- 2 Bounding the spectral gap -- 3 Numerical results -- 4 Conclusion
- 6 Worst-case error for unshifted lattice rules without randomisation -- 1 Introduction -- 2 Preliminaries -- 3 Existence result for worst-case error -- 4 Numerical experiments on the conjecture -- 5 Concluding remarks -- References -- 7 New preasymptotic estimates for approximation of periodic Sobolev functions -- 1 Introduction -- 2 Approximation in periodic spaces of Sobolev type -- 3 Preasymptotics for approximation in isotropic Sobolev spaces -- 4 Preasymptotics for approximation in mixed Sobolev spaces -- References -- 8 Data based construction of kernels for classification -- 1 Introduction
- 2 Background -- 3 Numerical algorithms for semi-supervised learning -- 4 Experimental results -- References -- 9 P1-nonconforming polyhedral finite elements in high dimensions -- 1 Introduction -- 1.1 The model problem -- 1.2 Notations and preliminary results -- 2 The parametric and nonparametric P1-simplicial and quadrilateral nonconforming finite elements -- 2.1 The parametric simplicial and rectangular NC elements in two and three dimensions -- 2.2 The nonparametric NC quadrilateral and hexahedral elements -- 2.2.1 The nonparametric DSSY-type nonconforming quadrilateral elements
- 2.2.2 The P1-NC quadrilateral element -- 3 The P1-nonconforming polyhedral finite element -- 3.1 Global P1-NC polyhedral finite element spaces -- 3.2 Basis and its dimension -- 3.3 Local and global Interpolation operators -- 3.4 The P1-NC polyhedral Galerkin methods -- References -- Part 2 Month of Mathematical Biology -- 10 The status of the QSSA approximation in stochastic simulations of reaction networks -- 1 Introduction -- 2 The QSSA assumption in well-mixed stochastic systems -- 2.1 Background -- 2.2 Analytical results for the errors of the stochastic QSSA -- 3 Conclusions -- References