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Related Concept Videos

Symmetry01:26

Symmetry

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The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
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Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Second Uniqueness Theorem01:16

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Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
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Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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A universal symmetry detection algorithm.

Peter M Maurer1

  • 1Department of Computer Science, Baylor University, Waco, TX 76798-7356 USA.

Springerplus
|August 25, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a novel algorithm for detecting any permutation-based symmetry, offering a faster and simpler approach than existing methods. It efficiently identifies symmetries, including parameterized types, without relying on external libraries.

Keywords:
Generalized symmetrySymmetric Boolean functionsSymmetry detection

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Area of Science:

  • Computer Science
  • Mathematics
  • Data Analysis

Background:

  • Symmetry detection is crucial in various scientific fields.
  • Existing algorithms often struggle with diverse symmetry types.
  • Parameterizable symmetries (total, partial, rotational, dihedral) require specialized library-based approaches.

Purpose of the Study:

  • To present a universal algorithm for detecting permutation-based symmetries.
  • To enable detection of symmetries without relying on external libraries.
  • To offer a simpler, faster, and more versatile symmetry detection method.

Main Methods:

  • Development of a novel algorithm for general symmetry detection.
  • Implementation of library-free detection for parameterizable symmetries.
  • Adaptation of the algorithm for matrix-based symmetries, including conjugate symmetry.

Main Results:

  • The algorithm successfully detects any permutation-based symmetry, including previously undetectable types.
  • Parameterized symmetries (total, partial, rotational, dihedral) are detected without libraries.
  • The new method is often faster and simpler than existing techniques.
  • The algorithm demonstrates compatibility with various matrix-based symmetries.

Conclusions:

  • The proposed algorithm offers a significant advancement in symmetry detection capabilities.
  • Its simplicity and efficiency facilitate integration into existing software.
  • The algorithm broadens the scope of detectable symmetries, enhancing data analysis across disciplines.