Related papers: HyperPrecision: A Mathematica package for High-Pre…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number of F_p points on algebraic varieties and…
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the…
Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm…
Fractional physics-informed neural networks (fPINNs) have been successfully introduced in [Pang, Lu and Karniadakis, SIAM J. Sci. Comput. 41 (2019) A2603-A2626], which observe relative errors of $10^{-3} \, \sim \, 10^{-4}$ for the…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
This paper presents a convergence analysis for the Hessian Discretisation Method (HDM) applied to fourth-order semilinear elliptic equations involving a trilinear nonlinearity and general source, based on two complementary approaches. The…
We present an explicit formula for the resolvent of the discrete Laplacian on the square lattice, and compute its asymptotic expansions around thresholds in low dimensions. As a by-product we obtain a closed formula for the fundamental…
I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and…
A new highly accurate algorithm for the solution of the Falkner-Skan equation of boundary layer theory is presented. The algorithm, based on a Maclaurin series representation, finds its coefficients from recurrence. In addition,…
Recent advances in deep representation learning on Riemannian manifolds extend classical deep learning operations to better capture the geometry of the manifold. One possible extension is the Fr\'echet mean, the generalization of the…
We introduce a class of algorithms for constructing Fourier representations of Gaussian processes in $1$ dimension that are valid over ranges of hyperparameter values. The scaling and frequencies of the Fourier basis functions are evaluated…
In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…