Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Architecture of Idiotypic Networks: Percolation and Scaling
  Behaviour   We investigate a model where idiotypes (characterizing B-lymphocytes and
antibodies of an immune system) and anti-idiotypes are represented by
complementary bitstrings of a given length d allowing for a number of
mismatches (matching rules). In this model, the vertices of the hypercube in
dimension d represent the potential repertoire of idiotypes. A random set of
(with probability p) occupied vertices corresponds to the expressed repertoire
of idiotypes at a given moment. Vertices of this set linked by the above
matching rules build random clusters. We give a structural and statistical
characterisation of these clusters - or in other words - of the architecture of
the idiotypic network. Increasing the probability p one finds at a critical p a
percolation transition where for the first time a large connected graph occures
with probability one. Increasing p further, there is a second transition above
which the repertoire is complete in the sense that any newly introduced
idiotype finds a complementary anti-idiotype. We introduce structural
characteristics such as the mass distributions and the fragmentation rate for
random clusters, and determine the scaling behaviour of the cluster size
distribution near the percolation transition, including finite size
corrections. We find that slightly above the percolation transition the large
connected cluster (the central part of the idiotypic network) consists
typically of one highly connected part and a number of weakly connected
constituents and coexists with a number of small, isolated clusters. This is in
accordance with the picture of a central and a peripheral part of the idiotypic
network and gives some support to idealized architectures of the central part
used in recent dynamical mean field models.

27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ