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