Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Special homomorphisms between Probabilistic Gene Regulatory Networks   In this paper we study finite dynamical systems with $n$ functions acting on
the same set $X$, and probabilities assigned to these functions, that it is
called Probabilistic Regulatory Gene Networks (PRN. his concept is the same or
a natural generalization of the concept Probabilistic Boolean Networks (PBN),
introduced by I. Shmulevich, E. Dougherty, and W. Zhang, particularly the model
PBN has been using to describe genetic networks and has therapeutic
applications. In PRNs the most important question is to describe the steady
states of the systems, so in this paper we pay attention to the idea of
transforming a network to another without lost all the properties, in
particular the probability distribution. Following this objective we develop
the concepts of homomorphism and $\epsilon$-homomorphism of probabilistic
regulatory networks, since these concepts bring the properties from one
networks to another. Projections are special homomorphisms, and they always
induce invariant subnetworks that contain all cycles and steady states in the
network.

9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph