Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The effect of network topology on the stability of discrete state models
  of genetic control   Boolean networks have been proposed as potentially useful models for genetic
control. An important aspect of these networks is the stability of their
dynamics in response to small perturbations. Previous approaches to stability
have assumed uncorrelated random network structure. Real gene networks
typically have nontrivial topology significantly different from the random
network paradigm. In order to address such situations, we present a general
method for determining the stability of large Boolean networks of any specified
network topology and predicting their steady-state behavior in response to
small perturbations. Additionally, we generalize to the case where individual
genes have a distribution of `expression biases,' and we consider
non-synchronous update, as well as extension of our method to non-Boolean
models in which there are more than two possible gene states. We find that
stability is governed by the maximum eigenvalue of a modified adjacency matrix,
and we test this result by comparison with numerical simulations. We also
discuss the possible application of our work to experimentally inferred gene
networks.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con