Related papers: A Hierarchical O(N) Force Calculation Algorithm

We report on a lattice based algorithm, completely vectorized for molecular dynamics simulations. Its algorithmic complexity is of the order $O(N)$, where $N$ is the number of particles. The algorithm works very effectively when the…

We give a full description of the code NBODY2 for direct integration of the gravitational N-body problem. The method of solution is based on the neighbour scheme of Ahmad & Cohen (1973) which speeds up the force calculation already for…

We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a…

We present a new algorithm for efficiently computing the $N$-point correlation functions (NPCFs) of a 3D density field for arbitrary $N$. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By…

This paper develops a new technique for proving amortized, randomized cell-probe lower bounds on dynamic data structure problems. We introduce a new randomized nondeterministic four-party communication model that enables "accelerated",…

Nucleon-nucleon (NN) forces from chiral perturbation theory at next-to-leading (NLO) and next-to-next-to-leading order (NNLO) are applied to systems with two, three and four nucleons. At NNLO, we consider two versions of the chiral…

Computing a Single-Linkage Dendrogram (SLD) is a key step in the classic single-linkage hierarchical clustering algorithm. Given an input edge-weighted tree $T$, the SLD of $T$ is a binary dendrogram that summarizes the $n-1$ clusterings…

A fast algorithm to study one-dimensional self-gravitating systems, and, more generally, systems that are Lagrangian integrable between collisions, is presented. The algorithm is event-driven, and uses a heap-ordered set of predicted future…

We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…

An extensive number of numerical computations of energy 1/$N$ series using a recursive Taylor series method are presented in this paper. The series are computed to a high order of approximation and their behaviour on increasing the order of…

We report an N-Body approach to computing the Fock exchange matrix with and without permutational symmetry. The method achieves an O(N lg N) computational complexity through an embedded metric-query, allowing hierarchical application of…

We employ neural networks to improve and speed up optical force calculations for dielectric particles. The network is first trained on a limited set of data obtained through accurate light scattering calculations, based on the Transition…

We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity,…

Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…

We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…

I describe here the performance of a parallel treecode with individual particle timesteps. The code is based on the Barnes-Hut algorithm and runs cosmological N-body simulations on parallel machines with a distributed memory architecture…

We study the importance of few-nucleon forces in chiral effective field theory for describing many-nucleon systems. A combinatorial argument suggests that three-nucleon forces -- which are conventionally regarded as next-to-next-to-leading…

We derive the long-range contributions to the tree-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion. We give both momentum and coordinate space representations.

We report a development of a new fast surface-based method for numerical calculations of solvation energy of biomolecules with a large number of charged groups. The procedure scales linearly with the system size both in time and memory…

The lattice $A_n^*$ is an important lattice because of its covering properties in low dimensions. Clarkson \cite{Clarkson1999:Anstar} described an algorithm to compute the nearest lattice point in $A_n^*$ that requires $O(n\log{n})$…