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Related Concept Videos

Law of Rational Indices01:29

Law of Rational Indices

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The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.To...
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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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The fineness modulus (FM) of aggregate is a numerical index that measures the coarseness or fineness of the particles. It is calculated by adding the cumulative percentages of aggregate retained on each of a specified series of sieves and dividing the sum by 100.
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Wilcoxon Rank-Sum Test

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The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a nonparametric test used to determine if there is a significant difference between the distributions of two independent samples. This test is designed specifically for two independent populations and has the following key requirements:
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Related Experiment Video

Updated: May 5, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
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Sharp bounds and normalization of Wiener-type indices.

Dechao Tian1, Kwok Pui Choi

  • 1Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore.

Plos One
|November 22, 2013
PubMed
Summary

This study introduces a normalized f-Wiener index to measure network similarity across varying node counts. This new index significantly improves hierarchical clustering compared to non-normalized methods.

Area of Science:

  • Network science
  • Graph theory
  • Data analysis

Background:

  • Complex networks are prevalent across scientific disciplines.
  • Topological quantification aids network analysis and comparison.
  • Existing Wiener-type indices are sensitive to network size.

Purpose of the Study:

  • To address the need for normalized network similarity measures.
  • To introduce a generalized f-Wiener index.
  • To improve network clustering and classification.

Main Methods:

  • Generalization of Wiener-type indices to an f-Wiener index.
  • Identification of extremal values of the f-Wiener index.
  • Development and application of a normalized f-Wiener index.

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Main Results:

  • The proposed f-Wiener index encompasses various known Wiener-type indices.
  • Normalization effectively corrects for the number of nodes in a network.
  • Normalized f-Wiener indices enhance hierarchical clustering performance.

Conclusions:

  • The normalized f-Wiener index provides a robust measure for comparing networks of different sizes.
  • This normalization is crucial for accurate network similarity assessment.
  • The method offers improved hierarchical clustering outcomes in network analysis.