Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-order interactions improve optimal collective dynamics on
  networks   Collective behavior plays a key role in the function of a wide range of
physical, biological, and neurological systems where empirical evidence has
recently uncovered the prevalence of higher-order interactions, i.e.,
structures that represent interactions between more than just two individual
units, in complex network structures. Here, we study the optimization of
collective behavior in networks with higher-order interactions encoded in
clique complexes. Our approach involves adapting the Synchrony Alignment
Function framework to a new composite Laplacian matrix that encodes multi-order
interactions including, e.g., both dyadic and triadic couplings. We show that
as higher-order coupling interactions are equitably strengthened, so that
overall coupling is conserved, the optimal collective behavior improves. We
find that this phenomenon stems from the broadening of a composite Laplacian's
eigenvalue spectrum, which improves the optimal collective behavior and widens
the range of possible behaviors. Moreover, we find in constrained optimization
scenarios that a nontrivial, ideal balance between the relative strengths of
pair-wise and higher-order interactions leads to the strongest collective
behavior supported by a network. This work provides insight into how systems
balance interactions of different types to optimize or broaden their dynamical
range of behavior, especially for self-regulating systems like the brain.

24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th