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Related Concept Videos

Scaling01:26

Scaling

413
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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Colloids and Suspensions01:17

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Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera paint. These suspensions are heterogeneous mixtures composed of relatively large particles visible to the naked eye or seen with a magnifying glass. They are cloudy, and the suspended particles settle out after mixing. The suspended particles in a suspension settle out after some time of mixing. The separation of particles from a suspension is...
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Protein Networks02:26

Protein Networks

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An organism can have thousands of different proteins, and these proteins must cooperate to ensure the health of an organism. Proteins bind to other proteins and form complexes to carry out their functions. Many proteins interact with multiple other proteins creating a complex network of protein interactions.
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Cells Coordinate Growth and Proliferation02:36

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Cell size is a significant factor impacting cellular design, function, and fitness. There exists some internal coordination by which cells double their masses before division, thus, achieving homeostasis. Coordination between cell growth and proliferation depends on the checkpoints in between cell cycle phases. Loss of coordination or failure in the checkpoint mechanism can drive the cell to uncontrolled growth and loss of cellular function. Like dividing cells that coordinate cellular growth,...
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Updated: Nov 27, 2025

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Scaling in Colloidal and Biological Networks.

Michael Nosonovsky1, Prosun Roy1

  • 1Department of Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 North Cramer St., Milwaukee, WI 53211, USA.

Entropy (Basel, Switzerland)
|December 8, 2020
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Summary

This study applies scaling and dimensional analysis to complex networks, revealing fractal and scale-free properties. Network information content is quantified using Shannon entropy, offering insights into physical and biological systems.

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allometrybiomimeticscolloidal crystalsdroplet clustersnetwork topology

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Area of Science:

  • Complex Systems Science
  • Network Theory
  • Information Theory

Background:

  • Many physical systems can be modeled as networks with properties like fractality, scale-free behavior, and small-world characteristics.
  • Understanding the information content and scaling laws in these networks is crucial for diverse scientific and technological applications.

Purpose of the Study:

  • To apply scaling and dimensional analysis to various complex networks.
  • To quantify the information content of networks using Shannon entropy.
  • To explore scaling relationships and topological properties in physical and biological systems.

Main Methods:

  • Application of scaling and dimensional analysis techniques.
  • Calculation of Shannon entropy to determine network information content.
  • Analysis of networks from granular, colloidal, vascular, and neural systems.

Main Results:

  • Networks in colloidal systems exhibit self-organization via percolation and self-organized criticality.
  • Allometric laws are observed in branching vascular, artificial neural, cortical neural, and immune networks.
  • Characteristic time constants in hierarchical neocortical networks appear independent of brain size across species.

Conclusions:

  • Scaling and dimensional analysis provide a unified framework for understanding complex networks.
  • Shannon entropy effectively quantifies information content in diverse network structures.
  • Network properties offer insights applicable to surface engineering and information technology.