1,088 research outputs found
Driving interconnected networks to supercriticality
Networks in the real world do not exist as isolated entities, but they are
often part of more complicated structures composed of many interconnected
network layers. Recent studies have shown that such mutual dependence makes
real networked systems potentially exposed to atypical structural and dynamical
behaviors, and thus there is a urgent necessity to better understand the
mechanisms at the basis of these anomalies. Previous research has mainly
focused on the emergence of atypical properties in relation with the moments of
the intra- and inter-layer degree distributions. In this paper, we show that an
additional ingredient plays a fundamental role for the possible scenario that
an interconnected network can face: the correlation between intra- and
inter-layer degrees. For sufficiently high amounts of correlation, an
interconnected network can be tuned, by varying the moments of the intra- and
inter-layer degree distributions, in distinct topological and dynamical
regimes. When instead the correlation between intra- and inter-layer degrees is
lower than a critical value, the system enters in a supercricritical regime
where dynamical and topological phases are not longer distinguishable.Comment: 7 pages, 4 figures + Supplementary Informatio
Decoding communities in networks
According to a recent information-theoretical proposal, the problem of
defining and identifying communities in networks can be interpreted as a
classical communication task over a noisy channel: memberships of nodes are
information bits erased by the channel, edges and non-edges in the network are
parity bits introduced by the encoder but degraded through the channel, and a
community identification algorithm is a decoder. The interpretation is
perfectly equivalent to the one at the basis of well-known statistical
inference algorithms for community detection. The only difference in the
interpretation is that a noisy channel replaces a stochastic network model.
However, the different perspective gives the opportunity to take advantage of
the rich set of tools of coding theory to generate novel insights on the
problem of community detection. In this paper, we illustrate two main
applications of standard coding-theoretical methods to community detection.
First, we leverage a state-of-the-art decoding technique to generate a family
of quasi-optimal community detection algorithms. Second and more important, we
show that the Shannon's noisy-channel coding theorem can be invoked to
establish a lower bound, here named as decodability bound, for the maximum
amount of noise tolerable by an ideal decoder to achieve perfect detection of
communities. When computed for well-established synthetic benchmarks, the
decodability bound explains accurately the performance achieved by the best
community detection algorithms existing on the market, telling us that only
little room for their improvement is still potentially left.Comment: 9 pages, 5 figures + Appendi
Evolution of optimal L\'evy-flight strategies in human mental searches
Recent analysis of empirical data [F. Radicchi, A. Baronchelli & L.A.N.
Amaral. PloS ONE 7, e029910 (2012)] showed that humans adopt L\'evy flight
strategies when exploring the bid space in on-line auctions. A game theoretical
model proved that the observed L\'evy exponents are nearly optimal, being close
to the exponent value that guarantees the maximal economical return to players.
Here, we rationalize these findings by adopting an evolutionary perspective. We
show that a simple evolutionary process is able to account for the empirical
measurements with the only assumption that the reproductive fitness of a player
is proportional to her search ability. Contrarily to previous modeling, our
approach describes the emergence of the observed exponent without resorting to
any strong assumptions on the initial searching strategies. Our results
generalize earlier research, and open novel questions in cognitive, behavioral
and evolutionary sciences.Comment: 8 pages, 4 figure
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