Bulletin of Mathematical Biology

, Volume 57, Issue 1, pp 109–136 | Cite as

Memory capacity in large idiotypic networks

  • Jacques H. Boutet de Monvel
  • Olivier C. Martin
Article
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Abstract

Many models of immune networks have been proposed since the original work of Jerne [1974,Ann. Immun. (Inst. Pasteur) 125C, 373–389]. Recently, a limited class of models (Weisbuchet al., 1990,J. theor. Biol. 146, 483–499) have been shown to maintain immunological memory by idiotypic network interactions. We examine generalizations of these models when the networks are both large and highly connected to study their memory capacity, i.e. their ability to account for immunization to a large number of random antigens. Our calculations show that in these minimal models, random connectivities with continuously distributed affinities reduce the memory capacity to essentially nil.

Keywords

Memory Capacity Random Matrix Theory Cayley Tree Immune Network Affinity Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Society for Mathematical Biology 1994

Authors and Affiliations

  • Jacques H. Boutet de Monvel
    • 1
  • Olivier C. Martin
    • 1
  1. 1.Division de Physique Théorique, Unité de Recherche des Universités Paris XI et Paris VI associée au CNRSInstitut de Physique NucléaireOrsay CedexFrance

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