Parallelized Natural Extension Reference Frame: Parallelized Conversion from Internal to Cartesian Coordinates

ABSTRACTThe conversion of polymer parameterization from internal coordinates (bond lengths, angles, and torsions) to Cartesian coordinates is a fundamental task in molecular modeling, often performed using the Natural Extension Reference Frame (NeRF) algorithm. NeRF can be parallelized to process multiple polymers simultaneously, but is not parallelizable along the length of a single polymer. A mathematically equivalent algorithm, pNeRF, has been derived that is parallelizable along a polymer’s length. Empirical analysis demonstrates an order-of-magnitude speed up using modern GPUs and CPUs. In machine learning-based workflows, in which partial derivatives are backpropagated through NeRF equations and neural network primitives, switching to pNeRF can reduce the fractional computational cost of coordinate conversion from over two-thirds to around 10%. An optimized TensorFlow-based implementation of pNeRF is available on GitHub.

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Cartesian coordinates

10.1093/oso/9780198786399.003.0001 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Reference Frame ◽

Euclidean Geometry ◽

Absolute Space ◽

Mathematical Framework ◽

Cartesian Coordinates ◽

Newtonian Physics ◽

Common Space ◽

The Absolute ◽

Physical Objects

This chapter introduces Euclidean geometry, which provides the mathematical framework in which the laws of Newtonian physics are formulated. It first discusses how the concepts of ‘space’ and ‘relative, apparent, and common’ place are represented by a mathematical ensemble of points—the ‘absolute’ space ε‎3. A Cartesian frame of absolute space is materialized in ‘relative, apparent, and common’ space by a reference frame. Specifically, this reference frame is a solid trihedral—that is, an ensemble of physical objects whose relative distances are invariable in time and for which an orientation of the axes has been chosen. This chapter postulates that if the labeling of the points of ε‎3 is changed, the distance between two points remains unchanged. It then goes on to explain further the various associated formulas associated with Cartesian coordinates.

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Practical Realization of a Reference System for Earth Dynamics by Satellite Methods

International Astronomical Union Colloquium ◽

10.1017/s0252921100051150 ◽

1975 ◽

Vol 26 ◽

pp. 341-380 ◽

Cited By ~ 5

Author(s):

R. J. Anderle ◽

M. C. Tanenbaum

Keyword(s):

Reference Frame ◽

Polar Motion ◽

Pole Position ◽

Control Points ◽

Significant Information ◽

Crustal Motion ◽

Average Reference ◽

Future Data ◽

Existing Data

AbstractObservations of artificial earth satellites provide a means of establishing an.origin, orientation, scale and control points for a coordinate system. Neither existing data nor future data are likely to provide significant information on the .001 angle between the axis of angular momentum and axis of rotation. Existing data have provided data to about .01 accuracy on the pole position and to possibly a meter on the origin of the system and for control points. The longitude origin is essentially arbitrary. While these accuracies permit acquisition of useful data on tides and polar motion through dynamio analyses, they are inadequate for determination of crustal motion or significant improvement in polar motion. The limitations arise from gravity, drag and radiation forces on the satellites as well as from instrument errors. Improvements in laser equipment and the launch of the dense LAGEOS satellite in an orbit high enough to suppress significant gravity and drag errors will permit determination of crustal motion and more accurate, higher frequency, polar motion. However, the reference frame for the results is likely to be an average reference frame defined by the observing stations, resulting in significant corrections to be determined for effects of changes in station configuration and data losses.

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High-resolution electron microscopy of Cu2O surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143584 ◽

1986 ◽

Vol 44 ◽

pp. 396-397

Author(s):

V. Castano ◽

W. Krakow

Keyword(s):

High Resolution ◽

Natural Extension ◽

High Resolution Electron Microscopy ◽

Point Of View ◽

Initial Oxidation ◽

System A ◽

Resolution Electron ◽

Surface Reconstructions ◽

Atomic Surface ◽

Au Thin Films

In non-UHV microscope environments atomic surface structure has been observed for flat-on for various orientations of Au thin films and edge-on for columns of atoms in small particles. The problem of oxidation of surfaces has only recently been reported from the point of view of high resolution microscopy revealing surface reconstructions for the Ag2O system. A natural extension of these initial oxidation studies is to explore other materials areas which are technologically more significant such as that of Cu2O, which will now be described.

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Universal ESEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100149763 ◽

1993 ◽

Vol 51 ◽

pp. 786-787

Author(s):

G.D. Danilatos

Keyword(s):

Electron Microscope ◽

Scanning Electron Microscope ◽

High Vacuum ◽

Natural Extension ◽

Necessary Condition ◽

Environmental Scanning ◽

Detection Systems ◽

Small Gain ◽

Detection Medium ◽

Scanning Electron

The environmental scanning electron microscope (ESEM) has evolved as the natural extension of the scanning electron microscope (SEM), both historically and technologically. ESEM allows the introduction of a gaseous environment in the specimen chamber, whereas SEM operates in vacuum. One of the detection systems in ESEM, namely, the gaseous detection device (GDD) is based on the presence of gas as a detection medium. This might be interpreted as a necessary condition for the ESEM to remain operational and, hence, one might have to change instruments for operation at low or high vacuum. Initially, we may maintain the presence of a conventional secondary electron (E-T) detector in a "stand-by" position to switch on when the vacuum becomes satisfactory for its operation. However, the "rough" or "low vacuum" range of pressure may still be considered as inaccessible by both the GDD and the E-T detector, because the former has presumably very small gain and the latter still breaks down.

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