Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Susceptible-infected-susceptible model on networks with eigenvector
  localization   It is a longstanding debate on the absence of threshold for
susceptible-infected-susceptible (SIS) model on networks with finite second
order moment of degree distribution. The eigenvector localization of the
adjacency matrix for a network gives rise to the inactive Griffiths phase
featuring slow decay of the activity localized around highly connected nodes
due to the dynamical fluctuation. We show how it dramatically changes our
understanding of SIS model, opening up new possibilities for the debate. We
derive the critical condition for Griffiths to active phase transition: on
average, an infected node can further infect another one in the characteristic
lifespan of the star subgraph composed of the node and its nearest neighbors.
The system approaches the critical point of avoiding the irreversible dynamical
fluctuation and the trap of absorbing state. As a signature of the phase
transition, the infection density of a node is not only proportional to its
degree, but also proportional to the exponentially growing lifespan of the
star. And the divergence of the average lifespan of the stars is responsible
for the vanishing threshold in the thermodynamic limit. The eigenvector
localization exponentially reinforces the infection of highly connected nodes,
while it inversely suppresses the infection of small-degree nodes.

33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat