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Related Concept Videos

Correlation01:09

Correlation

In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
Correlations02:20

Correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
2D NMR: Overview of Homonuclear Correlation Techniques01:16

2D NMR: Overview of Homonuclear Correlation Techniques

Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
COSY90 is the standard two-dimensional (2D) COSY experiment that...
Coefficient of Correlation01:12

Coefficient of Correlation

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...

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Networks with given two-point correlations: hidden correlations from degree correlations.

Agata Fronczak1, Piotr Fronczak

  • 1Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
Summary

This study reveals that uncorrelated networks at the hidden variable level also lack node degree correlations. We present methods to extract hidden variables and correlations, aiding network generation algorithms.

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Area of Science:

  • Network science
  • Statistical physics

Background:

  • Understanding network structure and correlations is crucial.
  • Hidden variables play a significant role in network properties.
  • Existing algorithms for network generation require further mathematical grounding.

Purpose of the Study:

  • To analyze uncorrelated and correlated networks with hidden variables.
  • To demonstrate the relationship between hidden variable correlations and node degree correlations.
  • To provide a mathematical framework for network generation algorithms.

Main Methods:

  • Depoissonization to extract hidden variable distributions from degree distributions.
  • Analysis of the interplay between hidden attributes and node degrees.
  • Derivations for extracting hidden correlations from degree correlations.

Main Results:

  • Networks uncorrelated at the hidden level exhibit no node degree correlations.
  • A method to extract hidden variable distributions is presented.
  • Mathematical background for generating correlated networks is established.

Conclusions:

  • The findings clarify the relationship between hidden variables and network correlations.
  • The study completes and mathematically supports existing network generation algorithms.
  • This work offers a deeper understanding of network formation and properties.