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A fast full-wave simulation technique is presented for the analysis of large irregular planar arrays of identical 3-D metallic antennas. The solution method relies on the Macro Basis Functions (MBF) approach and an interpolatory technique…

We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…

Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves…

We recently introduced the Fast Newton Transform (FNT), an hierarchical algorithm for performing multivariate Newton interpolation in arbitrary downward closed polynomial spaces of spatial dimension $m$. Here, we analyze the FNT in the…

Large language models (LLMs) require substantial compute, and thus energy, at inference time. While quantizing weights and activations is effective at improving efficiency, naive quantization of LLMs can significantly degrade performance…

Smoothed particle hydrodynamics (SPH) is positioned as having ideal conservation properties. When properly implemented, conservation of total mass, energy, and both linear and angular momentum is guaranteed exactly, up to machine precision.…

In boundary element methods (BEM) in $\mathbb{R}^3$, matrix elements and right hand sides are typically computed via analytical or numerical quadrature of the layer potential multiplied by some function over line, triangle and tetrahedral…

Evaluation of pair potentials is critical in a number of areas of physics. The classicalN-body problem has its root in evaluating the Laplace potential, and has spawned tree-algorithms, the fast multipole method (FMM), as well as kernel…

I describe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a "gridlet") of effective masses. The effective masses on a gridlet…

We present a parallel FFT algorithm for SIMD systems following the `Transpose Algorithm' approach. The method is based on the assignment of the data field onto a 1-dimensional ring of systolic cells. The systolic array can be universally…

We study nonparametric estimation of a probability mass function (PMF) on a large discrete support, where the PMF is multi-modal and heavy-tailed. The core idea is to treat the empirical PMF as a signal on a line graph and apply a…

Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…

The article considers linear functions of many (n) variables - multilinear polynomials (MP). The three-steps evaluation is presented that uses the minimal possible number of floating point operations for non-sparse MP at each step. The…

Recently, Large language models (LLMs) with in-context learning have demonstrated remarkable potential in handling neural machine translation. However, existing evidence shows that LLMs are prompt-sensitive and it is sub-optimal to apply…

Fast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the…

We propose a novel algorithmic framework of Variable Metric Over-Relaxed Hybrid Proximal Extra-gradient (VMOR-HPE) method with a global convergence guarantee for the maximal monotone operator inclusion problem. Its iteration complexities…

We derive and discuss a technique for manipulating power series which is complementary to standard procedures. We begin with the translation operator, but we express the operator as an infinite product instead of expanding it as a series…

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function…

In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even…