The emergence of social conventions in multi-agent systems has been analyzed mainly in settings where every agent may interact either with every other agent or with nearest neighbours, according to some regular underlying topology. In this note we argue that these topologies are too simple if we take into account recent discoveries on real networks. These networks, one of the main examples being the Internet, are what is called complex, that is, either graphs with the small-world property or scale-free graphs. In this note we study the efficiency of the emergence of social conventions in complex networks, that is, how fast conventions are reached. Our main result is that complex graphs make the system much more efficient than regular graphs with the same average number of links per node. Furthermore, we find out that scale-free graphs make the system as efficient as fully connected graphs.

We study direct products of free-abelian and free groups with special emphasis on algorithmic problems. After giving natural extensions of standard notions into that family, we find an explicit expression for an arbitrary endomorphism of Zm×Fn. These tools are used to solve several algorithmic problems for Zm×Fn: the membership problem, the isomorphism problem, the finite index problem, the subgroup and coset intersection problems, the fixed point problem, and the Whitehead problem.Peer ReviewedPostprint (author’s final draft

We propose an algorithm to find the community structure in complex networks based on the combination of spectral analysis and modularity optimization. The clustering produced by our algorithm is as accurate as the best algorithms on the literature of modularity optimization; however, the main asset of the algorithm is its efficiency. The best match for our algorithm is Newman's fast algorithm, which is the reference algorithm for clustering in large networks due to its efficiency. When both algorithms are compared, our algorithm outperforms the fast algorithm both in efficiency and accuracy of the clustering, in terms of modularity. Thus, the results suggest that the proposed algorithm is a good choice to analyze the community structure of medium and large networks in the range of tens and hundreds of thousand vertices.

The problem of calculating a degree of reputation for agents acting as assistants to the members of an electronic community is discussed and a solution presented. Usual reputation mechanisms rely on feedback after interaction between agents. An alternative way to establish reputation is related with the position of each member of a community within the corresponding social network. We propose a method based on this idea, which is also used by well-known ranking algorithms, discuss its properties as well as experimental results and compare them to other reputation mechanisms for electronic communities supported by agents. The method proposed uses only local information in order to extract reputation and it is able to adapt automatically to the topology of the network or graph.

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Army ant colonies display complex foraging raid patterns involving thousands of individuals communicating through chemical trails. In this article we explore, by means of a simple search algorithm, the properties of these trails in order to test the hypothesis that their structure reflects an optimized mechanism for exploring and exploiting food resources. The raid patterns of three army ant species, Eciton hamatum, Eciton burchelli, and Eciton rapax, are analyzed. The respective diets of these species involve large but rare, small but common, and a combination of large but rare and small but common food sources. Using a model proposed by Deneubourg et al. [4], we simulate the formation of raid patterns in response to different food distributions. Our results indicate that the empirically observed raid patterns maximize return on investment, that is, the amount of food brought back to the nest per unit of energy expended, for each of the diets. Moreover, the values of the parameters that characterize the three optimal pattern-generating mechanisms are strikingly similar. Therefore the same behavioral rules at the individual level can produce optimal colony-level patterns. The evolutionary implications of these findings are discussed.

Computational methods in statistical physics and nonlinear dynamics. PACS. 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion.Abstract. -We analyze the propagation of activity in a system of mobile automata. A number ρL d of elements move as random walkers on a lattice of dimension d, while with a small probability p they can jump to any empty site in the system. We show that this system behaves as a Dynamic Small-World (DSW) and present analytic and numerical results for several quantities. Our analysis shows that the persistence time T * (equivalent to the persistence size L * of small-world networks) scales as T * ∼ (ρp) −τ , with τ = 1/(d + 1).c EDP Sciences

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