Properties of the bersini experiment on self-assertion

ABSTRACT

The approach of H. Bersini to shape-spaces and in particular his definition of affinity are analysed. It is shown that the definition of the affinity function in Bersini style implies a special form of an affinity region, namely a rhombus. However, variants of the function can be defined with rectangular or square but rotated affinity regions. In all cases, the affinity function has the form of a pyramid over the affinity region. The definition of the affinity function can be modified in such a way that it describes a lopsided pyramid. Experimental results with a reimplementation of Bersini's simulation procedure show that the form of the affinity region has a strong influence on the form of the recognition/tolerance separation of the shape-space.

REFERENCES

• 1: Bersini, H. Self-assertion versus self-recognition: A tribute to Francisco Varela. Proceedings of ICARIS 2002. Canterbury, 2002.
• 2: Calenbuhr, V., Varela, F., and Bersini, H. Immune idiotypic network. Int. Journal of Bifurcation and Chaos 6 (9), 1996, 1691--1702.
• 3: Detours, V., Bersini, H., Stewart, J., and F. Varela. Development of an idiotypic network in shape space. J. of Theoretical Biology, 170, 1994.
• 4: Hart, E. Not all balls are round: An investigation of alternative recognition-region shapes. Proceedings of ICARIS 2005. Springer, 2005, 29--42.
• 5: Hart, E. and Ross, P. Studies on the implications of shape-space models for idiotypic networks. Proceedings of ICARIS 2004. Springer, 2004, 413--426.
• 6: Perelson, A. and Oster, G.F. Theoretical studies of clonal selection:Minimal antibody repertoire size and reliability of self-nonself discrimination in the immune system. J. of Theoretical Biology, 158, 1979, 645--670.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.4 Model Validation and Analysis

General Terms:
Algorithms, Experimentation

Keywords:
affinity function, affinity region, shape-space