1 Introduction Two basic types of simulations exist for modeling systems of many particles: grid-based (point particles indirectly interacting with one another through the potential calculated from equivalent particle densities on a mesh) and particle-based (point particles directly interacting with a one another through potentials at their positions calculated from the other particles in the system). Grid-based solvers traditionally model continuum problems, such as fluid and gas systems, and mixed particle-continuum systems. Particle-based solvers find more use modeling discrete systems such as stars within galaxies or other rarefied gases. Many different physical systems, including electromagnetic interactions, gravitational interactions, and fluid vortex interactions, all are governed by Poisson's Equation: r 2 OE = \Gamma4ßGae; (1) for the gravitational case. To evolve N particles in time, the exact solution to the problem requires calculating the force contribution to each pa...

The tree-structured vector quantization (TSVQ) is an efficient method for the vector quantization (VQ). In this paper, we propose a new tree structure model, hierarchical tree structure (HTS), to reduce encoding time. Briefly, the HTSVQ decreases the dimension of the vector on the upper levels

by the Degree of Merger (DoM), a measure for the complexity of tree structures. In the present study, we hypothesize that the DoM is also critical in mathematical calculations, and clarify whether the DoM in the hierarchical tree structures modulates activations in these regions. We tested an arithmetic task

environments. This paper discusses a systematic technique to develop dynamic virtual environments and to manage virtual objects in their virtual environment. The technique is called hierarchical, tree-structured approach. To implement the technique, object-oriented programming language was used such as Java

bounding box trees. At runtime, the algorithm traverses the tree and tests for overlaps between oriented bounding boxes based on a new separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures

We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM’s). Learning is treated as a max-imum likelihood

In this paper, we propose a new method for index-ing large amounts of point and spatial data in high-dimensional space. An analysis shows that index structures such as the R*-tree are not adequate for indexing high-dimensional data sets. The major problem of R-tree-based index structures

The proliferation of topic hierarchies for text documents has resulted in a need for tools that automatically classify new documents within such hierarchies. Existing classification schemes which ignore the hierarchical structure and treat the topics as separate classes are often inadequate in text

A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems

This paper describes a novel method for the visualization of hierarchically structured information. The Tree-Map visualization technique makes 100 % use of the available display space, mapping the full hierarchy onto a rectangular region in a space-filling manner. This efficient use of space allows