Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronization Invariance Under Network Structural Transformations   Synchronization processes are ubiquitous despite the many connectivity
patterns that complex systems can show. Usually, the emergence of synchrony is
a macroscopic observable, however, the microscopic details of the system, as
e.g. the underlying network of interactions, is many times partially or totally
unknown. We already know that different interaction structures can give rise to
a common functionality, understood as a common macroscopic observable. Building
upon this fact, here, we propose network transformations that keep the
collective behavior of a large system of Kuramoto oscillators functionally
invariant. We derive a method based on information theory principles, that
allows us to adjust the weights of the structural interactions to map random
homogeneous -in degree- networks into random heterogeneous networks and
vice-versa, keeping synchronization values invariant. The results of the
proposed transformations reveal an interesting principle; heterogeneous
networks can be mapped to homogeneous ones with local information, but the
reverse process needs to exploit higher-order information. The formalism
provides new analytical insight to tackle real complex scenarios when dealing
with uncertainty in the measurements of the underlying connectivity structure.

4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys