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What genotypic features explain the evolvability of organisms that have to accomplish many different tasks? The genotype of behaviorally complex organisms may be more likely to encode modular neural architectures because neural modules dedicated to distinct tasks avoid neural interference, i.e., the arrival of conflicting messages for changing the value of connection weights during learning. However, if the connection weights for the various modules are genetically inherited, this raises the problem of genetic linkage: favorable mutations may fall on one portion of the genotype encoding one neural module and unfavorable mutations on another portion encoding another module. We show that this can prevent the genotype from reaching an adaptive optimum. This effect is different from other linkage effects described in the literature and we argue that it represents a new class of genetic constraints. Using simulations we show that sexual reproduction can alleviate the problem of genetic linkage by recombining separate modules all of which incorporate either favorable or unfavorable mutations. We speculate that this effect may contribute to the taxonomic prevalence of sexual reproduction among higher organisms. In addition to sexual recombination, the problem of genetic linkage for behaviorally complex organisms may be mitigated by entrusting evolution with the task of finding appropriate modular architectures and learning with the task of finding the appropriate connection weights for these architectures.

We study numerically the ordering process of two very simple dynamical models for a two-state variable on several topologies with increasing levels of heterogeneity in the degree distribution. We find that the zero-temperature Glauber dynamics for the Ising model may get trapped in sets of partially ordered metastable states even for finite system size, and this becomes more probable as the size increases. Voter dynamics instead always converges to full order on finite networks, even if this does not occur via coherent growth of domains. The time needed for order to be reached diverges with the system size. In both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale-free., Comment: 12 pages, 12 figures

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic, cellular or protein networks) or technological problems (optimization of large infrastructures). Several types of algorithm exist for revealing the community structure in networks, but a general and quantitative definition of community is still lacking, leading to an intrinsic difficulty in the interpretation of the results of the algorithms without any additional non-topological information. In this paper we face this problem by introducing two quantitative definitions of community and by showing how they are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a new local algorithm to detect communities which outperforms the existing algorithms with respect to the computational cost, keeping the same level of reliability. The new algorithm is tested on artificial and real-world graphs. In particular we show the application of the new algorithm to a network of scientific collaborations, which, for its size, can not be attacked with the usual methods. This new class of local algorithms could open the way to applications to large-scale technological and biological applications., Comment: Revtex, final form, 14 pages, 6 figures