Behaviour of loops in a canonical coordinate system

1990 ◽  
Vol 55 (5) ◽  
pp. 498-502 ◽  
Author(s):  
J�zsef Kozma
Keyword(s):  
Coordinate System ◽  
Canonical Coordinate System ◽  
Canonical Coordinate

The Local Product Structure of Expansive Automorphisms of Solenoids and Their Associated C*-Algebras

1996 ◽  
Vol 48 (4) ◽  
pp. 692-709 ◽  
Author(s):  
Berndt Brenken
Keyword(s):  
Abelian Group ◽  
Dynamical Systems ◽  
Coordinate System ◽  
Finite Type ◽  
Crossed Product ◽  
C Algebras ◽  
Local Product ◽  
Subshifts Of Finite Type ◽  
Canonical Coordinate System ◽  
Canonical Coordinate

AbstractAn explicit description of a hyperbolic canonical coordinate system for an expansive automorphism of a compact connected abelian group is given. These dynamical systems are factors of subshifts of finite type. Some properties of the associated crossed product C*-algebra are discussed. In these examples, the C* -algebras of Ruelle are crossed product algebras.

scholarly journals Fast deep neural correspondence for tracking and identifying neurons in C. elegans using semi-synthetic training

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Xinwei Yu ◽  
Matthew S Creamer ◽  
Francesco Randi ◽  
Anuj Kumar Sharma ◽  
Scott W Linderman ◽  
...  
Keyword(s):  
Network Architecture ◽  
Synthetic Data ◽  
Color Information ◽  
Position Information ◽  
C Elegans ◽  
Automated Method ◽  
Real Time Applications ◽  
Group 2 ◽  
Canonical Coordinate System ◽  
Canonical Coordinate

We present an automated method to track and identify neurons in C. elegans, called 'fast Deep Neural Correspondence' or fDNC, based on the transformer network architecture. The model is trained once on empirically derived semi-synthetic data and then predicts neural correspondence across held-out real animals. The same pre-trained model both tracks neurons across time and identifies corresponding neurons across individuals. Performance is evaluated against hand-annotated datasets, including NeuroPAL [1]. Using only position information, the method achieves 79.1% accuracy at tracking neurons within an individual and 64.1% accuracy at identifying neurons across individuals. Accuracy at identifying neurons across individuals is even higher (78.2%) when the model is applied to a dataset published by another group [2]. Accuracy reaches 74.7% on our dataset when using color information from NeuroPAL. Unlike previous methods, fDNC does not require straightening or transforming the animal into a canonical coordinate system. The method is fast and predicts correspondence in 10ms making it suitable for future real-time applications.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

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