We study the effect of clustering on the organization of cooperation, by analyzing the evolutionary dynamics of the Prisoner's Dilemma on scale-free networks with a tunable value of clustering. We find that a high value of the clustering coefficient produces an overall enhancement of cooperation in the network, even for a very high temptation to defect. On the other hand, high clustering homogeneizes the process of invasion of degree classes by defectors, decreasing the chances of survival of low densities of cooperator strategists in the network.PACS numbers: 87.23.Ge, 02.50. Le, 89.75.Fb Cooperative phenomena are essential in natural and human systems and have been the subject of intense research during decades [1,2,3,4,5,6]. Evolutionary game theory is concerned with systems of replicating agents programmed to use some strategy in their interactions with other agents, which ultimately yields a feedback loop that drives the evolution of the strategies composition of the population [6,7,8]. To understand the observed survival of cooperation among unrelated individuals in populations when selfish actions provide a short-term higher benefit, a lot of attention has been paid to the analysis of evolutionary dynamics of the Prisoner's Dilemma (PD) game. In this simple two-players game, individuals adopt one of the two available strategies, cooperation (C) or defection (D); both receive R under mutual cooperation and P under mutual defection, while a cooperator receives S when confronted to a defector, which in turn receives T , where T > R > P > S. Under these conditions in a one-shot game it is better to defect, regardless of the opponent strategy, and the proportion of cooperators asymptotically vanishes in a well-mixed population. On the other hand, the structure of interactions among individuals in real societies are seen to be described by complex networks of contacts rather than by a set of agents connected all-to-all [9,10]. Therefore, it is necessary to abandon the panmixia hypothesis to study how cooperative behavior appear in the social context.Several studies [11,12,13,14,15,16,17,18,19] have reported the asymptotic survival of cooperation on different kinds of networks. Notably, cooperation even dominates over defection in non-homogeneous, scale-free (SF) networks, i.e. in graphs where the number k of neighbors of an individual (the node degree) is distributed as a power law [12,15], P (k) ∼ k −γ , with 2 < γ ≤ 3. Networks with such a distribution are ubiquitous: scale-free topologies appear as the backbone of many social, biological, technological complex systems. However, in the context of social systems, other topological features, such as the presence of degree-degree correlations and of high clustering coefficients, are relevant ingredients to take into account in a complete description of the networks. The studies of the PD game on SF networks have considered so far networks with no degree correlations and nearly zero clustering coefficient, with the remarkable exception of Ref. [20] where high ...

Synchronization is a collective phenomenon occurring in systems of interacting units, and is ubiquitous in nature, society and technology. Recent studies have enlightened the important role played by the interaction topology on the emergence of synchronized states. However, most of these studies neglect that real world systems change their interaction patterns in time. Here, we analyze synchronization features in networks in which structural and dynamical features co-evolve. The feedback of the node dynamics on the interaction pattern is ruled by the competition of two mechanisms: homophily (reinforcing those interactions with other correlated units in the graph) and homeostasis (preserving the value of the input strength received by each unit). The competition between these two adaptive principles leads to the emergence of key structural properties observed in real world networks, such as modular and scale–free structures, together with a striking enhancement of local synchronization in systems with no global order.

Type of publicationArticle (peer-reviewed)Link to publisher's version https://journals.aps.org/prl/abstract

We perform a simulation study of the diffusion of small solutes in the confined domains imposed by inverse bicontinuous cubic phases for the primitive, diamond, and gyroid symmetries common to many lipid/water mesophase systems employed in experiments. For large diffusing domains, the long-time diffusion coefficient shows universal features when the size of the confining domain is renormalized by the Gaussian curvature of the triply periodic minimal surface. When bottlenecks are widely present, they become the most relevant factor for transport, regardless of the connectivity of the cubic phase.

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