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Concept: Network topology


Short-term memory in the brain cannot in general be explained the way long-term memory can - as a gradual modification of synaptic weights - since it takes place too quickly. Theories based on some form of cellular bistability, however, do not seem able to account for the fact that noisy neurons can collectively store information in a robust manner. We show how a sufficiently clustered network of simple model neurons can be instantly induced into metastable states capable of retaining information for a short time (a few seconds). The mechanism is robust to different network topologies and kinds of neural model. This could constitute a viable means available to the brain for sensory and/or short-term memory with no need of synaptic learning. Relevant phenomena described by neurobiology and psychology, such as local synchronization of synaptic inputs and power-law statistics of forgetting avalanches, emerge naturally from this mechanism, and we suggest possible experiments to test its viability in more biological settings.

Concepts: Nervous system, Psychology, Neuron, Brain, Human brain, Hippocampus, Long-term memory, Network topology


A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Concepts: Algorithm, Real number, Graph theory, Networks, Computational complexity theory, Social network, Centrality, Network topology


Topological networks lie at the heart of our cities and social milieu. However, it remains unclear how and when the brain processes topological structures to guide future behaviour during everyday life. Using fMRI in humans and a simulation of London (UK), here we show that, specifically when new streets are entered during navigation of the city, right posterior hippocampal activity indexes the change in the number of local topological connections available for future travel and right anterior hippocampal activity reflects global properties of the street entered. When forced detours require re-planning of the route to the goal, bilateral inferior lateral prefrontal activity scales with the planning demands of a breadth-first search of future paths. These results help shape models of how hippocampal and prefrontal regions support navigation, planning and future simulation.

Concepts: Brain, Topology, Manifold, Graph theory, Topological space, Metric space, Open set, Network topology


The theoretically proven security of quantum key distribution (QKD) could revolutionize the way in which information exchange is protected in the future. Several field tests of QKD have proven it to be a reliable technology for cryptographic key exchange and have demonstrated nodal networks of point-to-point links. However, until now no convincing answer has been given to the question of how to extend the scope of QKD beyond niche applications in dedicated high security networks. Here we introduce and experimentally demonstrate the concept of a ‘quantum access network’: based on simple and cost-effective telecommunication technologies, the scheme can greatly expand the number of users in quantum networks and therefore vastly broaden their appeal. We show that a high-speed single-photon detector positioned at a network node can be shared between up to 64 users for exchanging secret keys with the node, thereby significantly reducing the hardware requirements for each user added to the network. This point-to-multipoint architecture removes one of the main obstacles restricting the widespread application of QKD. It presents a viable method for realizing multi-user QKD networks with efficient use of resources, and brings QKD closer to becoming a widespread technology.

Concepts: Quantum mechanics, Quantum information science, Key, Network topology, Quantum entanglement, Quantum cryptography, Cryptography, One-time pad


The cheapest and thus widespread way to add new generators to a high-voltage power grid is by a simple tree-like connection scheme. However, it is not entirely clear how such locally cost-minimizing connection schemes affect overall system performance, in particular the stability against blackouts. Here we investigate how local patterns in the network topology influence a power grid’s ability to withstand blackout-prone large perturbations. Employing basin stability, a nonlinear concept, we find in numerical simulations of artificially generated power grids that tree-like connection schemes-so-called dead ends and dead trees-strongly diminish stability. A case study of the Northern European power system confirms this result and demonstrates that the inverse is also true: repairing dead ends by addition of a few transmission lines substantially enhances stability. This may indicate a topological design principle for future power grids: avoid dead ends.

Concepts: Mathematics, Real number, Electrical engineering, Nikola Tesla, Network topology, Electric power transmission, Electricity distribution, Power outage


The human brain is a topologically complex network embedded in anatomical space. Here, we systematically explored relationships between functional connectivity, complex network topology, and anatomical (Euclidean) distance between connected brain regions, in the resting-state functional magnetic resonance imaging brain networks of 20 healthy volunteers and 19 patients with childhood-onset schizophrenia (COS). Normal between-subject differences in average distance of connected edges in brain graphs were strongly associated with variation in topological properties of functional networks. In addition, a club or subset of connector hubs was identified, in lateral temporal, parietal, dorsal prefrontal, and medial prefrontal/cingulate cortical regions. In COS, there was reduced strength of functional connectivity over short distances especially, and therefore, global mean connection distance of thresholded graphs was significantly greater than normal. As predicted from relationships between spatial and topological properties of normal networks, this disorder-related proportional increase in connection distance was associated with reduced clustering and modularity and increased global efficiency of COS networks. Between-group differences in connection distance were localized specifically to connector hubs of multimodal association cortex. In relation to the neurodevelopmental pathogenesis of schizophrenia, we argue that the data are consistent with the interpretation that spatial and topological disturbances of functional network organization could arise from excessive “pruning” of short-distance functional connections in schizophrenia.

Concepts: Brain, Magnetic resonance imaging, Cerebral cortex, Topology, Graph theory, Frontal lobe, Metric space, Network topology


There is growing interest in the complex topology of human brain functional networks, often measured using resting-state functional MRI (fMRI). Here, we used a meta-analysis of the large primary literature that used fMRI or PET to measure task-related activation (>1,600 studies; 1985-2010). We estimated the similarity (Jaccard index) of the activation patterns across experimental tasks between each pair of 638 brain regions. This continuous coactivation matrix was used to build a weighted graph to characterize network topology. The coactivation network was modular, with occipital, central, and default-mode modules predominantly coactivated by specific cognitive domains (perception, action, and emotion, respectively). It also included a rich club of hub nodes, located in parietal and prefrontal cortex and often connected over long distances, which were coactivated by a diverse range of experimental tasks. Investigating the topological role of edges between a deactivated and an activated node, we found that such competitive interactions were most frequent between nodes in different modules or between an activated rich-club node and a deactivated peripheral node. Many aspects of the coactivation network were convergent with a connectivity network derived from resting state fMRI data (n = 27, healthy volunteers); although the connectivity network was more parsimoniously connected and differed in the anatomical locations of some hubs. We conclude that the community structure of human brain networks is relevant to cognitive function. Deactivations may play a role in flexible reconfiguration of the network according to cognitive demand, varying the integration between modules, and between the periphery and a central rich club.

Concepts: Psychology, Brain, Human brain, Cerebral cortex, Cerebrum, Frontal lobe, Occipital lobe, Network topology


The balance of global integration and functional specialization is a critical feature of efficient brain networks, but the relationship of global topology, local node dynamics and information flow across networks has yet to be identified. One critical step in elucidating this relationship is the identification of governing principles underlying the directionality of interactions between nodes. Here, we demonstrate such principles through analytical solutions based on the phase lead/lag relationships of general oscillator models in networks. We confirm analytical results with computational simulations using general model networks and anatomical brain networks, as well as high-density electroencephalography collected from humans in the conscious and anesthetized states. Analytical, computational, and empirical results demonstrate that network nodes with more connections (i.e., higher degrees) have larger amplitudes and are directional targets (phase lag) rather than sources (phase lead). The relationship of node degree and directionality therefore appears to be a fundamental property of networks, with direct applicability to brain function. These results provide a foundation for a principled understanding of information transfer across networks and also demonstrate that changes in directionality patterns across states of human consciousness are driven by alterations of brain network topology.

Concepts: Mathematics, Philosophy of mind, Mind, Consciousness, Human anatomy, Computer network, Network topology, Degree of a continuous mapping


The 2007-2008 financial crisis solidified the consensus among policymakers that a macro-prudential approach to regulation and supervision should be adopted. The currently preferred policy option is the regulation of capital requirements, with the main focus on combating procyclicality and on identifying the banks that have a high systemic importance, those that are “too big to fail”. Here we argue that the concept of systemic risk should include the analysis of the system as a whole and we explore systematically the most important properties for policy purposes of networks topology on resistance to shocks. In a thorough study going from analytical models to empirical data, we show two sharp transitions from safe to risky regimes: 1) diversification becomes harmful with just a small fraction (~2%) of the shocks sampled from a fat tailed shock distributions and 2) when large shocks are present a critical link density exists where an effective giant cluster forms and most firms become vulnerable. This threshold depends on the network topology, especially on modularity. Firm size heterogeneity has important but diverse effects that are heavily dependent on shock characteristics. Similarly, degree heterogeneity increases vulnerability only when shocks are directed at the most connected firms. Furthermore, by studying the structure of the core of the transnational corporation network from real data, we show that its stability could be clearly increased by removing some of the links with highest centrality betweeness. Our results provide a novel insight and arguments for policy makers to focus surveillance on the connections between firms, in addition to capital requirements directed at the nodes.

Concepts: Risk, Policy, Computer network, Bank run, Subprime mortgage crisis, Network topology, Systemic risk, Modern portfolio theory


Information flow during catastrophic events is a critical aspect of disaster management. Modern communication platforms, in particular online social networks, provide an opportunity to study such flow and derive early-warning sensors, thus improving emergency preparedness and response. Performance of the social networks sensor method, based on topological and behavioral properties derived from the “friendship paradox”, is studied here for over 50 million Twitter messages posted before, during, and after Hurricane Sandy. We find that differences in users' network centrality effectively translate into moderate awareness advantage (up to 26 hours); and that geo-location of users within or outside of the hurricane-affected area plays a significant role in determining the scale of such an advantage. Emotional response appears to be universal regardless of the position in the network topology, and displays characteristic, easily detectable patterns, opening a possibility to implement a simple “sentiment sensing” technique that can detect and locate disasters.

Concepts: Sociology, Graph theory, Networks, Emergency management, Social network, Network theory, Centrality, Network topology