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Related Concept Videos

Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Semi-Markov graph dynamics.

Marco Raberto1, Fabio Rapallo, Enrico Scalas

  • 1Dipartimento di Ingegneria Biofisica ed Elettronica, Università degli Studi di Genova, Genova, Italy.

Plos One
|September 3, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel model for graph dynamics by combining a Markov chain with a semi-Markov process. This approach allows for random transitions in network structures, offering insights into complex systems.

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Area of Science:

  • Mathematics
  • Network Science
  • Probability Theory

Background:

  • Understanding dynamic network structures is crucial in various scientific fields.
  • Existing models may not fully capture the stochastic nature of graph evolution.

Purpose of the Study:

  • To propose a new mathematical model for graph dynamics.
  • To integrate Markov chains and semi-Markov processes for modeling network evolution.

Main Methods:

  • A Markov chain is defined on the space of possible graphs.
  • A semi-Markov counting process of renewal type is employed.
  • The Markov chain is subordinated to the semi-Markov process, with transitions occurring at random epochs.

Main Results:

  • The developed model allows for random transitions in graph structures.
  • The model is demonstrated to be rich, with potential connections to algebraic geometry.
  • A simplified focus is placed on undirected graphs, with extensions to directed and weighted graphs illustrated via an interbank market model.

Conclusions:

  • The subordinated Markov chain model provides a flexible framework for analyzing graph dynamics.
  • The model's applicability extends to various network types, including directed and weighted graphs.
  • Further research may explore deeper connections with algebraic geometry and more complex network structures.