Stochastic Search with Locally Clustered Targets: Learning from T Cells

  • Rüdiger Reischuk
  • Johannes Textor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6825)

Abstract

Searching a space with locally clustered targets (think picking apples from trees) leads to an optimization problem: When should the searcher leave the current region, and invest the time to travel to another one? We consider here a model of such a search process: infection screening by T cells in the immune system. Taking an AIS perspective, we ask whether this model could provide insight for similar problems in computing, for example Las Vegas algorithms with expensive restarts or agent-based intrusion detection systems. The model is simple, but presents a rich phenomenology; we analytically derive the optimal behavior of a single searcher, revealing the existence of two characteristic regimes in the search parameter space. Moreover, we determine the impact of perturbations and imprecise knowledge of the search space parameters, as well as the speedup gained by searching in parallel. The results provide potential new directions for developing tools to tune stochastic search algorithms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Stephens, D.W., Krebs, J.R.: Foraging Theory. Princeton University Press, Princeton (1987)Google Scholar
  2. 2.
    Hofmeyr, S., Forrest, S.: Architecture for an artificial immune system. Evolutionary Computation 7(1), 1289–1296 (2000)Google Scholar
  3. 3.
    Hilker, M., Luther, K.: Artificial cell communication in distributed systems. In: AINA 2008, pp. 1034–1041. IEEE Computer Society Press, Washington, DC, USA (2008)Google Scholar
  4. 4.
    Hoos, H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann (2005)MATHGoogle Scholar
  5. 5.
    Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of las vegas algorithms. Inf. Process. Lett. 47, 173–180 (1993)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Janeway, C., Travers, P., Walport, M., Shlomchick, M.: Immunobiology. Garland Science (2005)Google Scholar
  7. 7.
    Blattman, J.N., Antia, R., Sourdive, D.J., Wang, X., Kaech, S.M., Murali-Krishna, K., Altman, J.D., Ahmed, R.: Estimating the precursor frequency of naive antigen-specific CD8 T cells. Journal of Experimental Medicine 195(5), 657–664 (2002)CrossRefGoogle Scholar
  8. 8.
    Westermann, J., Pabst, R.: Distribution of lymphocyte subsets and natural killer cells in the human body. Clin. Investig. 70, 539–544 (1992)CrossRefGoogle Scholar
  9. 9.
    von Andrian, U.H.: Intravital microscopy of the peripheral lymph node mirocirculation in mice. Microcirculation 3, 287–300 (1996)CrossRefGoogle Scholar
  10. 10.
    Wei, S.H., Parker, I., Miller, M.J., Cahalan, M.D.: A stochastic view of lymphocyte motility and trafficking within the lymph node. Immunological Reviews 195, 136–159 (2003)CrossRefGoogle Scholar
  11. 11.
    Glasser, M.L., Zucker, I.J.: Extended watson integrals for the cubic lattices. PNAS 74, 1800–1801 (1977)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Weiss, G.H.: Asymptotic form for random walk survival probabilities on three-dimensional lattices with traps. PNAS 77(8), 4391–4392 (1980)CrossRefMATHGoogle Scholar
  13. 13.
    Soderberg, K.A., Payne, G.W., Sato, A., Medzhitov, R., Segal, S.S.: Innate control of adaptive immunity via remodeling of lymph node feed arteriole. PNAS 102(45), 16315–16320 (2005)CrossRefGoogle Scholar
  14. 14.
    Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert W function. Advances in Computational Mathematics 5, 329–359 (1996)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Mempel, T.R., Henrickson, S.E., von Andrian, U.H.: T-cell priming by dendritic cells in lymph nodes occurs in three distinct phases. Nature 427, 154–159 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rüdiger Reischuk
    • 1
  • Johannes Textor
    • 1
  1. 1.Institut für Theoretische InformatikUniversität zu LübeckLübeckGermany

Personalised recommendations