Related papers: TreePM Method for Two-Dimensional Cosmological Sim…
We present an implementation of the hierarchical tree algorithm on the individual timestep algorithm (the Hermite scheme) for collisional $N$-body simulations, running on GRAPE-9 system, a special-purpose hardware accelerator for…
Tree codes that approximate groups of distant particles with multipole expansions are the standard way to accelerate the computation of self-gravity on particles. While momentum-conserving fast multipole methods exist, parallelisation is…
We introduce our new binary tree code for neighbour search and gravitational force calculations in an N-particle system. The tree is built in a "top-down" fashion by "recursive coordinate bisection" where on each tree level we split the…
Two-part models and Tweedie generalized linear models (GLMs) have been used to model loss costs for short-term insurance contract. For most portfolios of insurance claims, there is typically a large proportion of zero claims that leads to…
In this article, we propose a new approach for simulating trees, including their branches, sub-branches, and leaves. This approach combines the theory of biological development, mathematical models, and computer graphics, producing…
Cosmological N-Body simulations have become an essential tool for studying formation of large scale structure. These simulations are computationally challenging even though the available computing power gets better every year. A number of…
Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…
The basic idea of the kd-tree algorithm is to recursively partition a point set P by hyperplanes, and to store the obtained partitioning in a binary tree. Due to its immense popularity, many applications in astronomy have been implemented.…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
The code we describe (FLY) is a newly written code (using the tree N-body method), for three-dimensional self-gravitating collisionless systems evolution. FLY is a fully parallel code based on the tree Barnes-Hut algorithm and periodical…
We describe the implementation and performance of the ${\rm P^3T}$ (Particle-Particle Particle-Tree) scheme for simulating dense stellar systems. In ${\rm P^3T}$, the force experienced by a particle is split into short-range and long-range…
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming…
I describe a nested-grid particle-mesh (NGPM) code designed to study gravitational instability in three-dimensions. The code is based upon a standard PM code. Within the parent grid I am able to define smaller sub-grids allowing us to…
We developed a new direct-tree hybrid N-body algorithm for fully self-consistent N-body simulations of star clusters in their parent galaxies. In such simulations, star clusters need high accuracy, while galaxies need a fast scheme because…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are…
We describe a parallel version of our tree-code for the simulation of self-gravitating systems in Astrophysics. It is based on a dynamic and adaptive method for the domain decomposition, which exploits the hierarchical data arrangement used…
N-body simulations are essential tools in physical cosmology to understand the large-scale structure (LSS) formation of the Universe. Large-scale simulations with high resolution are important for exploring the substructure of universe and…
Direct $N$-body simulations of star clusters are accurate but expensive, largely due to the numerous $\mathcal{O} (N^2)$ pairwise force calculations. To solve the post-million-body problem, it will be necessary to use approximate force…