Immunology as a Metaphor for Computational ... - Napier University

J:¡Chapter 6. A Self-Organising SDM — SOSDM 151j L1 i f V c jA c i £ ¥ a j∑ (6.1)£ ¤ a¥1 j 0 otherwise:The affinity of each of the N antibodies for the input antigens is calculated. Followingthis, the antibody that is closest in distance to the antigen a, denoted by A 6 canbe determined:A6 max £ A £ c 1 ¤ a¥H¤§¦¨¦©¦¨¦©¤ A £ c N ¤ a¥§¥ (6.2)This value A6 is then used to determine the strength of the antigen-antibody encouter,i.e. the affinity of the antibody for the antigen. From an SDM perspective, thisvalue determines how much signal from the input data is distributed to each centre.The affinity of any antibody for an antigen is proportional to the ratio of the distance ofthe antibody from the antigen compared to the distance of the ’winning’ antibody fromthe antigen, i.e. A £ c i ¤ a¥ to A6 . A further parameter known as the affinity-thresholdt is introduced, such that (0 t 1¥ . Antigens are only considered to bind to thoseantibodies in which S is greater than this threshold. This is shown in equation 6.3.Again, from an SDM perspective, this means that only centres where Sc¤ a ¡their counters updated due to the incoming signal.At haveS a¥ AV i f S £ c¤ a¥ t(6.3)c¤0 £ otherwiseBinding between an antigen and antibody implies updating the counters at thatantibody. The counter C £ c i j ¥ for each bit j at each antibody c i is updated according toequation 6.4, where γ is equal to 1 if V £ c i j ¥ 1 and to -1 if V £ c i j ¥ 0.C c i j ¥ C £ c i j ¥ γS £ c¤ a¥ (6.4)Each time an antibody binds with an antigen, it increments an internal variableR which relects the total amount of binding exhibited by the antibody, as shown inequation 6.5:c : R £ c¥ R £ c¥ S £ c¤ a¥ (6.5)