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The immune system is a highly complex system with several functional components, which performs, among other things, the defense of our body (and of vertebrates in general) against foreign material (or antigens). To accomplish this task the immune system must be able to identify each molecular shape that confronts with him, in order to mount the adequate immune response. Therefore it must be able to distinguish the molecules of the body from antigens, or, in other words, it must be capable of classifying each molecule as self and non-self. This self--non-self classification problem is one of the major assignments that the immune system must solve. The models that we present an analyze in this work are inspired by the hypothesis of clonal selection theory presented by Sir John MacFarlane Burnet and idiotypic network introduced by Niels Jerne. These two hypothesis provide us the mathematical framework for describing the immune system as a dynamic system of interacting species. From a computational point of view, the importance of the immune system is due to the emergent properties that arise from the idiotypic network and clonal selection theories, namely the capacity of learning, memory, and pattern recognition. In this work one highlight and study the principal computational properties of the immune system, namely the pattern recognition, classification and memory. For that we present a mathematical model that describes same of the properties of the idiotypic network hypothesis and its applicability to a real problem---the museum problem---which let us illustrate and explore the computational power of the immune system. The model that we devise describes two fundamental aspects of the immune system: its dynamics and its methadynamics. The dynamics is described by a non-linear system of differential equations that models the variation of lymphocytes concentration. The methadynamics uses genetic operators, namely selection, crossover and mutation to build new species and remove those species that recognize the self. The model presented belongs to the class of models introduced by Farmer el al. The results that we've got from applying the model to the museum problem were very promising and confirm our expectations with respect to the emergent properties of the idiotypic network, namely learning. Actually, the system was able to adapt the initial immune repertoire, generated randomly, to classify almost all the elements of the search space. The more elaborated tests that we've done to cover other kinds of situations (e.g. more that one pattern in motion) lets us conclude that the learning capabilities of the system extends beyond the results that we have achieved and illustrated in this work. Thus we believe that this model is suitable for giving insights in problems similar to the one that was studied.

Francisco Martins