Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

J. Appl. Cryst.の発刊に際して

https://hal.archives-ouvertes.fr/hal-01513346/document

Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement

The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

/pdf/the-quickhull-algorithm-for-convex-hulls-ug134bwaff.pdf

The quickhull algorithm for convex hulls

Patient-Specific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow

We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. A possible application is the rapid computer model reconstruction of an existing part or prototype from a three dimensional (3D) points scan of its surface. Color, texture or some scalar material property of the physical part, define natural scalar fields over the surface of the CAD model. Our reconstruction algorithm does not impose any convexity or differentiability restrictions on the surface of the original physical part or the scalar field function, except that it assumes that there is a sufficient sampling of the input point data to unambiguously reconstruct the CAD model. Compared to earlier methods our algorithm has the advantages of simplicity, efficiency and uniformity (both CAD model and scalar field reconstruction). The simplicity and efficiency of our approach is based on several novel uses of appropriate sub-structures (alpha shapes) of a three-dimensional Delaunay Triangulation, its dual the three-dimensional Voronoi diagram, and dual uses of trivariate Bernstein-Bezier forms. The boundary of the CAD model is modeled using implicit cubic Bernstein-Bezier patches, while the scalar field is reconstructed with functional cubic Bernstein-Bezier patches. CR

/pdf/automatic-reconstruction-of-surfaces-and-scalar-fields-from-3dzrjo47ss.pdf

Automatic reconstruction of surfaces and scalar fields from 3D scans

For 2D or 3D meshes that represent the domain of continuous function to the reals, the contours|or isosurfaces|of a speci ed value are an important way to visualize the function To nd such contours, a seed set can be used for the starting points from which the traversal of the contours can begin This paper gives the rst methods to obtain seed sets that are provably small in size They are based on a variant of the contour tree (or topographic change tree) We give a new, simple algorithm to compute such a tree in regular and irregular meshes that requires O(n logn) time in 2D for meshes with n elements, and in O(n) time in higher dimensions The additional storage overhead is proportial to the maximum size of any contour (linear in the worst case, but typically less) Given the contour tree, a minimum size seed set can be computed in roughly quadratic time Since in practice this can be excessive, we develop a simple approximation algorithm giving a seed set of size at most twice the size of the minimum It requires O(n log n) time and linear storage once the contour tree is known We also give experimental results, showing the size of the seed sets for several data sets

/pdf/contour-trees-and-small-seed-sets-for-isosurface-traversal-2qhsv421z9.pdf

Contour trees and small seed sets for isosurface traversal

We introduce the contour spectrllm, a user interface component that improves qualitative user interaction and provides real-time exad quantification in the visualization of isoconlours. The contour spectrum is a signature consisting of a variety of scalar data and conlour attributes, computed over the range of scalar values wE!R. We explore the use of surface area, volume, and gradient integral of the contour that are shown to be univariate B-spline functions of the scalar value w for multi-dimensional unstructured triangulal' grids. These quantitative propcrties arc calculated in real-time and presented to the user as a collection of signature graphs (plots of functions of w) to assist in selecting relevant isovalues Wo for informative visualization. For timevarying data, these quantitativc properties can also be computed over time, and displaycd using a 2D interface, giving the user an overview of the time-varying function, and allowing interaction in both isovalue and timestep. The effectiveness of the current system and potential extensions are discussed.

http://www.pascucci.org/pdf-presentations/contour-spectrum-slides97.pdf

The contour spectrum

Direct volume rendering is a key technology for visualizing large 3D data sets from scientific or medical applications. Transfer functions are particularly important to the quality of direct volume-rendered images. A transfer function assigns optical properties, such as color and opacity, to original values of the data set being visualized. Unfortunately, finding good transfer functions proves difficult. It is one of the major problems in volume visualization. The article examines four of the currently most promising approaches to transfer function design. The four approaches are: trial and error, with minimum computer aid; data-centric, with no underlying assumed model; data-centric, using an underlying data model; and image-centric, using organized sampling.

Chandrajit L. Bajaj

Papers

Patient-Specific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow

Automatic reconstruction of surfaces and scalar fields from 3D scans

Contour trees and small seed sets for isosurface traversal

The contour spectrum

The transfer function bake-off