Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semigroup Models for Biochemical Reaction Networks   The CRS (chemical reaction system) formalism by Hordijk and Steel is a
versatile method to model self-sustaining biochemical reaction networks. Its
distinguishing feature is the explicit assignment of catalytic function to
chemicals that are part of the network. In this work, we show the introduction
of subsequent and simultaneous catalytic functions gives rise to an algebraic
structure of a semigroup with additional compatible data of idempotent addition
and a partial order. The aim of this paper is to demonstrate that such
semigroup models are a natural setup to treat the emergence of autocatalytic
biochemical reaction networks. We establish the basic algebraic properties of
the algebraic models and show that it is natural to define the function of any
subnetwork on the whole reaction network in a mathematically correct way. This
leads to a natural discrete dynamics on the network, which results from
iteratively considering the self-action on a subnetwork by its own function.
Finally, we demonstrate that the identification of the maximal self-sustaining
subnetwork of any reaction network is very straightforward in our setup. This
leads to an algebraic characterization of the lattice of self-sustaining
subsets for any CRS. Moreover, we show that algebraic models for reaction
networks with a self-sustaining subnetwork cannot be nilpotent, thus
establishing a link to the combinatorial theory of finite semigroups.

37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph