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Related Concept Videos

Random Variables01:09

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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.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
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Related Experiment Video

Updated: Jul 4, 2026

Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits
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Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits

Published on: April 15, 2015

Cascades on correlated and modular random networks.

James P Gleeson1

  • 1Department of Mathematics and Statistics, University of Limerick, Ireland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

A new analytical method determines mean avalanche size in dynamical models on random networks. This approach unifies percolation and epidemic models, offering insights into cascade dynamics and network structures.

Area of Science:

  • Network science
  • Statistical physics
  • Dynamical systems

Background:

  • Avalanche phenomena are common in complex systems.
  • Understanding cascade sizes is crucial for various models.
  • Existing methods often lack generality.

Purpose of the Study:

  • Introduce a unified analytical framework for mean avalanche size.
  • Demonstrate the method's applicability to diverse network models.
  • Extend the analysis to complex network structures.

Main Methods:

  • Developed a novel analytical approach for cascade size determination.
  • Applied the method to random networks with various dynamical models.
  • Investigated extensions for modular networks and degree-degree correlations.

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Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits
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Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits

Published on: April 15, 2015

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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Main Results:

  • Unified treatment of percolation transitions and epidemic sizes.
  • Analytical solutions for cascade dynamics and innovation spread.
  • Validated theoretical predictions with numerical simulations.

Conclusions:

  • The introduced analytical method provides a general framework for studying avalanches.
  • The approach enhances understanding of cascade dynamics in complex networks.
  • This work offers a powerful tool for analyzing network-based phenomena.