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Related Concept Videos

Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
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A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
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Related Experiment Video

Updated: Jun 12, 2026

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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Published on: February 15, 2017

Long-range disassortative correlations in generic random trees.

Piotr Bialas1, Andrzej K Oleś

  • 1Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krakow, Poland. pbialas@th.if.uj.edu.pl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2010
PubMed
Summary
This summary is machine-generated.

Correlations in random tree networks remain disassortative across all distances, diminishing slowly. This study explores these network properties, particularly in scale-free trees.

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Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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Area of Science:

  • Network science
  • Statistical physics
  • Graph theory

Background:

  • Understanding the structure and properties of random networks is crucial in various scientific fields.
  • Correlation functions quantify relationships between network components at different distances.

Purpose of the Study:

  • To explicitly calculate distance-dependent correlation functions in a maximal entropy ensemble of random trees.
  • To analyze the behavior of these correlations at different scales and in specific network types.

Main Methods:

  • Calculation of correlation functions within a maximal entropy ensemble.
  • Analysis of distance-dependent properties in random tree structures.
  • Examination of scale-free trees with diverging second moments of degree distribution.

Main Results:

  • Correlations in random trees are consistently disassortative across all distances.
  • These correlations decay as a second inverse power of the distance.
  • Scale-free trees exhibit unique phenomena due to their diverging degree distribution moments.

Conclusions:

  • The disassortative nature of correlations is a fundamental property of random trees studied.
  • The slow decay rate of correlations has implications for information propagation and network robustness.
  • Scale-free networks present distinct correlation behaviors requiring further investigation.