Understanding the process by which the individuals of a society make up their minds and reach opinions about different issues can be of fundamental importance. In this work we propose an idealized model for competitive cluster growth in complex networks. Each cluster can be thought as a fraction of a community that shares some common opinion. Our results show that the cluster size distribution depends on the particular choice for the topology of the network of contacts among the agents. As an application, we show that the cluster size distributions obtained when the growth process is performed on hierarchical networks, e.g., the Apollonian network, have a scaling form similar to what has been observed for the distribution of number of votes in an electoral process. We suggest that this similarity is due to the fact that social networks involved in the electoral process may also posses an underlining hierarchical structure.

IntroductionIndependent component analysis (ICA) has been extensively used for reducing task‐free BOLD fMRI recordings into spatial maps and their associated time‐courses. The spatially identified independent components can be considered as intrinsic connectivity networks (ICNs) of non‐contiguous regions. To date, the spatial patterns of the networks have been analyzed with techniques developed for volumetric data.ObjectiveHere, we detail a graph building technique that allows these ICNs to be analyzed with graph theory.MethodsFirst, ICA was performed at the single‐subject level in 15 healthy volunteers using a 3T MRI scanner. The identification of nine networks was performed by a multiple‐template matching procedure and a subsequent component classification based on the network “neuronal” properties. Second, for each of the identified networks, the nodes were defined as 1,015 anatomically parcellated regions. Third, between‐node functional connectivity was established by building edge weights for each networks. Group‐level graph analysis was finally performed for each network and compared to the classical network.ResultsNetwork graph comparison between the classically constructed network and the nine networks showed significant differences in the auditory and visual medial networks with regard to the average degree and the number of edges, while the visual lateral network showed a significant difference in the small‐worldness.ConclusionsThis novel approach permits us to take advantage of the well‐recognized power of ICA in BOLD signal decomposition and, at the same time, to make use of well‐established graph measures to evaluate connectivity differences. Moreover, by providing a graph for each separate network, it can offer the possibility to extract graph measures in a specific way for each network. This increased specificity could be relevant for studying pathological brain activity or altered states of consciousness as induced by anesthesia or sleep, where specific networks are known to be altered in different strength.

No abstract

After experiences are encoded, post‐encoding reactivations during sleep have been proposed to mediate long‐term memory consolidation. Spindle–slow oscillation coupling during NREM sleep is a candidate mechanism through which a hippocampal‐cortical dialogue may strengthen a newly formed memory engram. Here, we investigated the role of fast spindle‐ and slow spindle–slow oscillation coupling in the consolidation of spatial memory in humans with a virtual watermaze task involving allocentric and egocentric learning strategies. Furthermore, we analyzed how resting‐state functional connectivity evolved across learning, consolidation, and retrieval of this task using a data‐driven approach. Our results show task‐related connectivity changes in the executive control network, the default mode network, and the hippocampal network at post‐task rest. The hippocampal network could further be divided into two subnetworks of which only one showed modulation by sleep. Decreased functional connectivity in this subnetwork was associated with higher spindle–slow oscillation coupling power, which was also related to better memory performance at test. Overall, this study contributes to a more holistic understanding of the functional resting‐state networks and the mechanisms during sleep associated to spatial memory consolidation.