Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Griffiths phases and localization in hierarchical modular networks   We study variants of hierarchical modular network models suggested by Kaiser
and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional
brain connectivity, using extensive simulations and quenched mean-field theory
(QMF), focusing on structures with a connection probability that decays
exponentially with the level index. Such networks can be embedded in
two-dimensional Euclidean space. We explore the dynamic behavior of the contact
process (CP) and threshold models on networks of this kind, including
hierarchical trees. While in the small-world networks originally proposed to
model brain connectivity, the topological heterogeneities are not strong enough
to induce deviations from mean-field behavior, we show that a Griffiths phase
can emerge under reduced connection probabilities, approaching the percolation
threshold. In this case the topological dimension of the networks is finite,
and extended regions of bursty, power-law dynamics are observed. Localization
in the steady state is also shown via QMF. We investigate the effects of link
asymmetry and coupling disorder, and show that localization can occur even in
small-world networks with high connectivity in case of link disorder.

20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org