Related papers: An adaptive fast Gauss transform in two dimensions
The discretization of velocity space plays a crucial role in the accuracy and efficiency of multiscale Boltzmann solvers. Conventional velocity space discretization methods suffer from uneven node distribution and mismatch issues, limiting…
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…
Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal…
By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general…
We present a novel compression framework for 3D Gaussian splatting (3DGS) data that leverages transform coding tools originally developed for point clouds. Contrary to existing 3DGS compression methods, our approach can produce compressed…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation…
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…
Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
Within the emerging field of quantum thermodynamics the issues of heat transfer and heat rectification are basic ingredients for the understanding and design of heat engines or refrigerators at nanoscales. Here, a consistent and versatile…
Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…
We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore,…
We explicitly reorganise the partition function of an arbitrary CFT in four spacetime dimensions into a heat kernel form for the dual string spectrum on AdS(5). On very general grounds, the heat kernel answer can be expressed in terms of a…
We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
We present a general framework for reconstructing effective Hamiltonians from known gravitational energy density profiles in curved spacetime. Starting from local thermal equilibrium and Liouville dynamics, we establish an inverse procedure…