Random walks in directed modular networks

Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently directed. In the case of undirected diffusion, it can be shown that the steady-state probability of the random walk dynamics is fully correlated with the degree, which no longer holds for directed networks. We investigate the relationship between such probability and the inward node degree, which we call efficiency, in modular networks. Our findings show that the efficiency of a given community depends mostly on the balance between its ingoing and outgoing connections. In addition, we derive analytical expressions to show that the internal degree of the nodes do not play a crucial role in their efficiency, when considering the Erd\H{o}s-R\'enyi and Barab\'asi-Albert models. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communication systems

Complementary action of chemical and electrical synapses to perception

Acknowledgements This study was possible by partial financial support from the following agencies: Fundação Araucária, EPSRC-EP/I032606/1, CNPq No. 441553/2014-1, CAPES No. 17656-12-5 and Science Without Borders Program— Process Nos. 17656125, 99999.010583/2013-00 and 245377/2012-3.Peer reviewedPostprin

Local Spin Glass Order in 1D

We study the behavior of one dimensional Kac spin glasses as function of the interaction range. We verify by Montecarlo numerical simulations the crossover from local mean field behavior to global paramagnetism. We investigate the behavior of correlations and find that in the low temperature phase correlations grow at a faster rate then the interaction range. We completely characterize the growth of correlations in the vicinity of the mean-field critical region

The complex channel networks of bone structure

Bone structure in mammals involves a complex network of channels (Havers and Volkmann channels) required to nourish the bone marrow cells. This work describes how three-dimensional reconstructions of such systems can be obtained and represented in terms of complex networks. Three important findings are reported: (i) the fact that the channel branching density resembles a power law implies the existence of distribution hubs; (ii) the conditional node degree density indicates a clear tendency of connection between nodes with degrees 2 and 4; and (iii) the application of the recently introduced concept of hierarchical clustering coefficient allows the identification of typical scales of channel redistribution. A series of important biological insights is drawn and discussedComment: 3 pages, 1 figure, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org