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Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...
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Maximum Power Transfer

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The Maximum Power Transfer Theorem01:20

The Maximum Power Transfer Theorem

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Updated: Jun 22, 2026

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke
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Published on: October 10, 2025

Maximizing influence propagation in networks with community structure.

Aram Galstyan1, Vahe Musoyan, Paul Cohen

  • 1Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA. galstyan@isi.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary

Selecting optimal nodes for network activation cascades is challenging in critical systems. Strategies must account for community structure to avoid suboptimal performance in influence propagation models.

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Last Updated: Jun 22, 2026

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke
05:30

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Published on: October 10, 2025

Area of Science:

  • Network Science
  • Algorithmic Decision Making
  • Computational Social Science

Background:

  • Traditional methods for selecting target nodes in network activation cascades assume diminishing returns, which limits their applicability.
  • Influence propagation models exhibiting critical behavior deviate from diminishing returns, necessitating new approaches for node selection.
  • Understanding network structure is crucial for effective influence maximization in complex systems.

Purpose of the Study:

  • To investigate node selection strategies for maximizing activation cascades in networks with critical behavior.
  • To analyze the impact of network community structure on influence propagation and targeting effectiveness.
  • To develop improved targeting strategies that account for network topology.

Main Methods:

  • Analysis of influence propagation models exhibiting critical phenomena.
  • Focus on networks with two loosely coupled communities to study 'double-critical' behavior.
  • Evaluation of simple hill-climbing selection mechanisms versus community-aware strategies.

Main Results:

  • In critical systems without diminishing returns, network structure significantly impacts activation cascades.
  • Double-critical behavior in two-community networks highlights limitations of homogenous network strategies.
  • Simple targeting strategies can be suboptimal, underperforming when community structure is ignored.

Conclusions:

  • Network community structure is a critical factor in designing effective node selection strategies for activation cascades.
  • Modified targeting approaches that incorporate community information can outperform generic methods.
  • Further research into complex network topologies and their influence dynamics is warranted.