Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of Fundamental Networks   In the framework of coupled cell systems, a coupled cell network describes
graphically the dynamical dependencies between individual dynamical systems,
the cells. The fundamental network of a network reveals the hidden symmetries
of that network. Subspaces defined by equalities of coordinates which are
flow-invariant for any coupled cell system consistent with a network structure
are called the network synchrony subspaces. Moreover, for every synchrony
subspaces, each network admissible system restricted to that subspace is a
dynamical systems consistent with a smaller network. The original network is
then said to be a lift of the smaller network. We characterize networks such
that: its fundamental network is a lift of the network; the network is a
subnetwork of its fundamental network, and the network is a fundamental
network. The size of cycles in a network and the distance of a cell to a cycle
are two important properties concerning the description of the network
architecture. In this paper, we relate these two architectural properties in a
network and its fundamental network.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat