Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The "weak" interdependence of infrastructure systems produces mixed
  percolation transitions in multilayer networks   In this work, we propose an interdependent, multilayer network model and
percolation process that matches infrastructures better than previous models by
allowing some nodes to survive when their interdependent neighbors fail. We
consider a node-to-link failure propagation mechanism and establish "weak"
interdependence across layers via a tolerance parameter $\alpha$ which
quantifies the likelihood that a node survives when one of its interdependent
neighbors fails. We measure the robustness of any individual layer by the final
size of its giant component. Analytical and numerical results show that weak
interdependence produces a striking phenomenon: layers at different positions
within the multilayer system experience distinct percolation transitions.
Especially, layers with high super degree values percolate in an abrupt manner,
while those with low super degree values exhibit both continuous and abrupt
transitions. This novel phenomenon we call \emph{mixed percolation transitions}
has significant implications for network robustness. Previous results that do
not consider cascade tolerance and layer super degree may be under- or
over-estimating the vulnerability of real systems. Moreover, since $\alpha$
represents a generic measure of various risk management strategies used to
buffer infrastructure assets from cascades, our model reveals how nodal
protection activities influence failure dynamics in interdependent, multilayer
systems.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org