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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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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some instructors may use the normal distribution to help determine students’ grades. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is...
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Topological resilience in non-normal networked systems.

Malbor Asllani1, Timoteo Carletti1

  • 1Department of Mathematics and naXys, Namur Institute for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium.

Physical Review. E
|May 16, 2018
PubMed
Summary

Complex systems

Area of Science:

  • Network science
  • Complex systems dynamics
  • Mathematical modeling

Background:

  • Network topology significantly impacts system resilience and recovery from disturbances.
  • Understanding network features crucial for resilience is a key challenge in designing robust systems.
  • Resilience is vital in diverse systems, from ecosystems to engineered networks.

Purpose of the Study:

  • Introduce non-normal networks and their generating model.
  • Investigate how non-normal network features alter system dynamics and resilience.
  • Explore novel dynamical instabilities and applications in ecology and transportation networks.

Main Methods:

  • Definition and modeling of non-normal networks.
  • Analysis of global dynamics and system response amplification.

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  • Application to ecological models (Allee effect) and transportation networks (London Tube virus spread).

    • Main Results:

    • Non-normal networks can drastically amplify responses to disturbances, impacting resilience.
    • Transient dynamics in non-normal networks can lead to pattern formation, akin to Turing instability.
    • Demonstrated a mechanism to mute the Allee effect in ecological systems.
    • Modeled virus spread on a non-normal transport network (London Tube).

    Conclusions:

    • Non-normal networks represent a novel class of complex systems with unique dynamic properties.
    • These properties offer new insights into system resilience and pattern formation.
    • The findings have implications for designing robust systems and understanding phenomena in ecology and epidemiology.