Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed point theorems for Boolean networks expressed in terms of
  forbidden subnetworks   We are interested in fixed points in Boolean networks, {\em i.e.} functions
$f$ from $\{0,1\}^n$ to itself. We define the subnetworks of $f$ as the
restrictions of $f$ to the subcubes of $\{0,1\}^n$, and we characterizes a
class $\mathcal{F}$ of Boolean networks satisfying the following property:
Every subnetwork of $f$ has a unique fixed point if and only if $f$ has no
subnetwork in $\mathcal{F}$. This characterization generalizes the fixed point
theorem of Shih and Dong, which asserts that if for every $x$ in $\{0,1\}^n$
there is no directed cycle in the directed graph whose the adjacency matrix is
the discrete Jacobian matrix of $f$ evaluated at point $x$, then $f$ has a
unique fixed point. Then, denoting by $\mathcal{C}^+$ (resp. $\mathcal{C}^-$)
the networks whose the interaction graph is a positive (resp. negative) cycle,
we show that the non-expansive networks of $\mathcal{F}$ are exactly the
networks of $\mathcal{C}^+\cup \mathcal{C}^-$; and for the class of
non-expansive networks we get a "dichotomization" of the previous forbidden
subnetwork theorem: Every subnetwork of $f$ has at most (resp. at least) one
fixed point if and only if $f$ has no subnetworks in $\mathcal{C}^+$ (resp.
$\mathcal{C}^-$) subnetwork. Finally, we prove that if $f$ is a conjunctive
network then every subnetwork of $f$ has at most one fixed point if and only if
$f$ has no subnetwork in $\mathcal{C}^+$.

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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg