Related papers: Pseudoparticle Multipole Method: A Simple Method t…

We present the outline of a research project aimed at designing and constructing a hybrid computing system that can be easily scaled up to petaflops speeds. As a first step, we envision building a prototype which will consist of three main…

We propose Monte Carlo Permutation Search (MCPS), a general-purpose Monte Carlo Tree Search (MCTS) algorithm that improves upon the GRAVE algorithm. MCPS is relevant when deep reinforcement learning is not an option or when the computing…

We present a new parallel PM N-body code named PMFAST that is freely available to the public. PMFAST is based on a two-level mesh gravity solver where the gravitational forces are separated into long and short range components. The…

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…

The multipole-expansion (MPE) model is an implicit solvation model used to efficiently incorporate solvent effects in quantum chemistry. Even within the recent direct approach, the multipole basis used in MPE to express the dielectric…

We describe a technique to analytically compute the multipole moments of a charge distribution confined to a planar triangle, which may be useful in solving the Laplace equation using the fast multipole boundary element method (FMBEM) and…

In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…

In this paper, we present a new method for estimating the $L_2$-gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using semidefinite programming. It has previously been shown that,…

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…

In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key…

An improved implementation of an N-body code for simulating collisionless cosmological dynamics is presented. TPM (Tree-Particle-Mesh) combines the PM method on large scales with a tree code to handle particle-particle interactions at small…

Gradient coding is a distributed computing technique aiming to provide robustness against slow or non-responsive computing nodes, known as stragglers, while balancing the computational load for responsive computing nodes. Among existing…

The auto-regressive decoding of Large Language Models (LLMs) results in significant overheads in their hardware performance. While recent research has investigated various speculative decoding techniques for multi-token generation, these…

Gradient boosted decision trees are some of the most popular algorithms in applied machine learning. They are a flexible and powerful tool that can robustly fit to any tabular dataset in a scalable and computationally efficient way. One of…

Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…

Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this…

This paper introduces the Partition Tree Weighting technique, an efficient meta-algorithm for piecewise stationary sources. The technique works by performing Bayesian model averaging over a large class of possible partitions of the data…

Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the…

The CLIP model has established itself as a cornerstone of large-scale retrieval systems. However, its performance often degrades under distributional shifts such as multilingual, long-form, or multimodal queries. To avoid the prohibitive…