Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Community Integration Algorithms (CIAs) for Dynamical Systems on
  Networks   Dynamics of large-scale network processes underlies crucial phenomena ranging
across all sciences. Forward simulation of large network models is often
computationally prohibitive. Yet, most networks have intrinsic community
structure. We exploit these communities and propose a fast simulation algorithm
for network dynamics. In particular, aggregating the inputs a node receives
constitutes the limiting factor in numerically simulating large-scale network
dynamics. We develop community integration algorithms (CIAs) significantly
reducing function-evaluations. We obtain a substantial reduction from
polynomial to linear computational complexity. We illustrate our results in
multiple applications including classical and higher-order Kuramoto-type
systems for synchronisation and Cucker--Smale systems exhibiting flocking
behaviour on synthetic as well as real-world networks. Numerical comparison and
theoretical analysis confirm the robustness and efficiency of CIAs.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat