Mathematics and the Internet: A Source of Enormous Confusion and Great Potential

Abstract

For many mathematicians and physicists, the Internet has become a popular real-world domain for the application and/or development of new theories related to the organization and behavior of large-scale, complex, and dynamic systems. In some cases, the Internet has served both as inspiration and justification for the popularization of new models and mathematics within the scientific enterprise. For example, scale-free network models of the preferential attachment type [8] have been claimed to describe the Internet's connectivity structure, resulting in surprisingly general and strong claims about the network's resilience to random failures of its components and its vulnerability to targeted attacks against its infrastructure [2]. These models have, as their trademark, power-law type node degree distributions that drastically distinguish them from the classical Erdos-Renyi type random graph models [13]. These "scale-free" network models have attracted significant attention within the scientific community and have been partly responsible for launching and fueling the new field of network science [42, 4].

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2009
Accession Number
ADA527773

Entities

People

  • David Alderson
  • John Doyle
  • Walter Willinger

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Cyber
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Central Nervous System
  • Computer Networks
  • Computers
  • Data Analysis
  • Data Sets
  • Electronic Mail
  • Engineering
  • Infrastructure
  • Internet
  • Mathematics
  • Network Architecture
  • Network Protocols
  • Network Science
  • Networks
  • Neurobehavioral Manifestations
  • Statistics

Readers

  • Distributed Systems and Data Platform Development
  • Educational Psychology
  • Neural Network Machine Learning.