**#258 General model of information spreading in complex networks**

*Authors: Guilherme Ferraz de Arruda, Emanuele Cozzo, Pablo Martín Rodríiguez, Yamir Moreno and Francisco A. Rodrigues*We propose a general information-spreading model based on discrete time Markov chains. Our model covers not only the traditional models of rumor and epidemic spreading, but also include some properties of recent models, such as apathy, forgetting, lost of interest and recovering of interest. The model is evaluated analytically to obtain the spreading threshold for the contact and reactive processes for several models. The comparison with Monte Carlo simulation shows that the model is very accurate. Our theoretical framework addresses data from Twitter and email networks and precise results are obtained when compared with simulations. This study may contribute to the analysis of disease and rumor spreading under the same theoretical framework.

**#261 A DATA DRIVEN NETWORK APPROACH TO RANK COUNTRIES PRODUCTION DIVERSITY AND FOOD SPECIALIZATION**

*Authors: Chengyi Tu, Joel Carr and Samir Suweis*The easy access to large data sets has allowed for leveraging methodology in network physics and complexity science to disentangle patterns and processes directly from the data, leading to key insights in the behavior of systems. Here we use to country specific food production data to study binary and weighted topological properties of the bipartite country-food production matrix. This country-food production matrix can be: 1) transformed into overlap matrices which embed information regarding shared production of products among countries, and or shared countries for individual products, 2) identify subsets of countries which produce similar commodities or subsets of commodities shared by a given country allowing for visualization of correlations in large networks, and 3) used to rank country’s fitness (the ability to produce a diverse array of products weighted on the type of food commodities) and food specialization (quantified on the number of countries producing that food product weighted on their fitness). Our results show that, on average, countries with high fitness producing highly specialized food commodities also produce low specialization goods, while nations with low fitness producing a small basket of diverse food products, typically produce low specialized food commodities.

**#271 Correlations in word length sequences from large texts**

*Authors: J.A. Quezada-González, D. Aguilar-Velázquez, Bibiana Obregón-Quintana and Lev Guzmán-Vargas*We present a study of the fractal behavior of word lengths sequences from 30 literary books in the English language. We obtained this data set from the Gutenberg Project (www.gutenberg.org). First, the word length sequence is considered as a point process, and the Fano and Allan factors are calculated to determine a scaling region characterized by a correlation exponent. Second, we use the natural visibility graph method NVG to convert the word length sequence into a graph to construct the degree distribution. We show that the Fano and Allan statistics exhibit a power law behavior (at large scales) with mean exponents for Fano δ_F=0.308 ± 0.196, and for Allan δ_A=0.373 ± 0.195, which indicate the presence of positive correlations. Particularly, for some literary books, the distributions of events (word spacing) are quite different compared to the homogeneous Poisson process, whereas for others the statistics resemble a white noise process. We also find that the degree distribution of the network follows a power law, P(k)~k^{-γ}, with two regimes, which are characterized by the exponents γs ≈ 1.7 (at short degree scales) and γl ≈ 1.3 (at large degree scales). This suggests that word lengths are much more strongly correlated at large distances between words than at short distances between words. Thus, all three methods find that the lack of correlation in word lengths at small scales is replaced by a positive correlation in word lengths over large separations between words. The large-scale linguistic structures in these books are different, in an important way, compared to the small-scale structures. We hope that these new findings will serve as the basis for a linguistic or semantic interpretation of what they tell us about language or, more specifically, about written language

**#278 On the maximum number of diﬀerent dynamics in elementary cellular automata**

*Authors: Marco Montalva Medel, Pedro P.B. de Oliveira and Eric Goles*

Given a Boolean network (BN) with n nodes, that models some phenomenon, a complete description of all the diﬀerent dynamics obtained from its evolution, out of each and every possible deterministic update schedule, lead us to a knowledge of all the possible dynamics and allows us, among other important things, to deﬁne good measures for determining how robust the model is. Since both the number of deterministic update schedules and the number of possible initial conﬁgurations for the BN grow exponentially as n increases, this renders the process computationally very intense; let alone the further task of ﬁltering out the distinct dynamics that should be eﬀectively considered. Nevertheless, in [1] an upper bound U(G) is established for the number of diﬀerent dynamics D(G), that depends only on the network connection graph G. In this context, it is an open problem to determine a mathematical expression for D(G). In order to gain some insights on the latter general problem, here we focus on elementary cellular automata (ECA) of n cells, which can be regarded as a special family of 256 BNs, that share the same circular graph H of n nodes, and where the local functions are the well studied synchronously updated rules deﬁned upon the local states of each node and its two next-nearest neighbours. We show by means of simulations that, by allowing an ECA to evolve with any deterministic update schedule – i.e., not only the synchronous one – 146 out the 256 possible ECAs have exactly D(H)=U(H)=3^n −2^{n+1} + 2 diﬀerent dynamics, a result that also constitutes an evidence that U(G) is sharp for this kind of BNs.

[1] J. Aracena, E. Fanchon, M. Montalva, M. Noual, Combinatorics on update digraphs in boolean networks, Discrete Applied Mathematics 159 (6) (2011) 401– 409.

**#279 Estimating topological properties of weighted and directed networks from limited information**

*Authors: Andrea Gabrielli, Giulio Cimini, Diego Garlaschelli and Tiziano Squartini*

A problem typically encountered when studying complex systems is the limitedness of the information available on their topology, which hinders our understanding of their structure and of the dynamical processes taking place on them. A paramount example is provided by financial networks, whose data are privacy protected: Banks publicly disclose only their aggregate exposure towards other banks, keeping individual exposures towards each single bank secret. Yet, the estimation of systemic risk strongly depends on the detailed structure of the interbank network. The resulting challenge is that of using aggregate information to statistically reconstruct a network and correctly predict its higher-order properties. Standard approaches either generate unrealistically dense networks, or fail to reproduce the observed topology by assigning homogeneous link weights. Here, we develop a reconstruction method, based on statistical mechanics concepts, that makes use of the empirical link density in a highly nontrivial way. Technically, our approach consists in the preliminary estimation of node degrees from empirical node strengths and link density, followed by a maximum-entropy inference based on a combination of empirical strengths and estimated degrees. Our method [1] is successfully tested on the international trade network and the interbank money market, and represents a valuable tool for gaining insights on privacy-protected or partially accessible systems. We then extend the method [2] to directed weighted networks making use of an optimized gravity model and test its validity in the context of the financial risk context.

[1] G. Cimini, T. Squartini, A. Gabrielli, D. Garlaschelli, Phys. Rev E, 92, 040802(R) (2015)

[2] G. Cimini, T. Squartini, D. Garlaschelli, A. Gabrielli, Sci. Rep. 5, 15758 (2015)

## Home |
## Calls |
## Programme |
## Registration |
## Contact |

Copyright CCS © 2016