River landscapes and optimal channel networks.

We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for every [Formula: see text] Results extend our capabilities in environmental statistical mechanics.

How to Estimate Epidemic Risk from Incomplete Contact Diaries Data?

Social interactions shape the patterns of spreading processes in a population. Techniques such as diaries or proximity sensors allow to collect data about encounters and to build networks of contacts between individuals. The contact networks obtained from these different techniques are however quantitatively different. Here, we first show how these discrepancies affect the prediction of the epidemic risk when these data are fed to numerical models of epidemic spread: low participation rate, under-reporting of contacts and overestimation of contact durations in contact diaries with respect to sensor data determine indeed important differences in the outcomes of the corresponding simulations with for instance an enhanced sensitivity to initial conditions. Most importantly, we investigate if and how information gathered from contact diaries can be used in such simulations in order to yield an accurate description of the epidemic risk, assuming that data from sensors represent the ground truth. The contact networks built from contact sensors and diaries present indeed several structural similarities: this suggests the possibility to construct, using only the contact diary network information, a surrogate contact network such that simulations using this surrogate network give the same estimation of the epidemic risk as simulations using the contact sensor network. We present and compare several methods to build such surrogate data, and show that it is indeed possible to obtain a good agreement between the outcomes of simulations using surrogate and sensor data, as long as the contact diary information is complemented by publicly available data describing the heterogeneity of the durations of human contacts.

Tracing two decades of carbon emissions using a network approach.

According to the guidelines of the Intergovernmental Panel on Climate Change, carbon emissions are attributed to the producers of goods and services. This approach has been challenged by recent literature, advocating an attribution criterion based on consumers, i.e. accounting for the carbon embedded into the goods imported by each country. Quantifying the effectiveness of such a consumption-based accounting requires understanding the complex structure of the graph induced by the flows of emissions between world countries. To this aim, we have considered a balanced panel of a hundred of countries and constructed the corresponding Carbon Trade Network for each of the past twenty years. Our analysis highlights the tendency of each country to behave either as a 'net producer'-or 'net exporter'-of emissions or as a 'net consumer'-or 'net importer'-of emissions; besides, it reveals the presence of an unexpected, positive feedback: despite individual exchanges having become less carbon-intensive, the increasing trade activity has ultimately risen the amount of emissions directed from 'net exporters' towards 'net importers'. Adopting a consumption-aware accounting would re-distribute responsibility between these two groups, possibly reducing disparities.

Information load dynamically modulates functional brain connectivity during narrative listening.

Narratives are paradigmatic examples of natural language, where nouns represent a proxy of information. Functional magnetic resonance imaging (fMRI) studies revealed the recruitment of temporal cortices during noun processing and the existence of a noun-specific network at rest. Yet, it is unclear whether, in narratives, changes in noun density influence the brain functional connectivity, so that the coupling between regions correlates with information load. We acquired fMRI activity in healthy individuals listening to a narrative with noun density changing over time and measured whole-network and node-specific degree and betweenness centrality. Network measures were correlated with information magnitude with a time-varying approach. Noun density correlated positively with the across-regions average number of connections and negatively with the average betweenness centrality, suggesting the pruning of peripheral connections as information decreased. Locally, the degree of the bilateral anterior superior temporal sulcus (aSTS) was positively associated with nouns. Importantly, aSTS connectivity cannot be explained by changes in other parts of speech (e.g., verbs) or syllable density. Our results indicate that the brain recalibrates its global connectivity as a function of the information conveyed by nouns in natural language. Also, using naturalistic stimulation and network metrics, we corroborate the role of aSTS in noun processing.

The unbalanced reorganization of weaker functional connections induces the altered brain network topology in schizophrenia.

Network neuroscience shed some light on the functional and structural modifications occurring to the brain associated with the phenomenology of schizophrenia. In particular, resting-state functional networks have helped our understanding of the illness by highlighting the global and local alterations within the cerebral organization. We investigated the robustness of the brain functional architecture in 44 medicated schizophrenic patients and 40 healthy comparators through an advanced network analysis of resting-state functional magnetic resonance imaging data. The networks in patients showed more resistance to disconnection than in healthy controls, with an evident discrepancy between the two groups in the node degree distribution computed along a percolation process. Despite a substantial similarity of the basal functional organization between the two groups, the expected hierarchy of healthy brains' modular organization is crumbled in schizophrenia, showing a peculiar arrangement of the functional connections, characterized by several topologically equivalent backbones. Thus, the manifold nature of the functional organization's basal scheme, together with its altered hierarchical modularity, may be crucial in the pathogenesis of schizophrenia. This result fits the disconnection hypothesis that describes schizophrenia as a brain disorder characterized by an abnormal functional integration among brain regions.

Grand canonical ensemble of weighted networks.

The cornerstone of statistical mechanics of complex networks is the idea that the links, and not the nodes, are the effective particles of the system. Here, we formulate a mapping between weighted networks and lattice gases, making the conceptual step forward of interpreting weighted links as particles with a generalized coordinate. This leads to the definition of the grand canonical ensemble of weighted complex networks. We derive exact expressions for the partition function and thermodynamic quantities, both in the cases of global and local (i.e., node-specific) constraints on the density and mean energy of particles. We further show that, when modeling real cases of networks, the binary and weighted statistics of the ensemble can be disentangled, leading to a simplified framework for a range of practical applications.

Spatio-Temporal Patterns of the International Merger and Acquisition Network.

This paper analyses the world web of mergers and acquisitions (M&As) using a complex network approach. We use data of M&As to build a temporal sequence of binary and weighted-directed networks for the period 1995-2010 and 224 countries (nodes) connected according to their M&As flows (links). We study different geographical and temporal aspects of the international M&A network (IMAN), building sequences of filtered sub-networks whose links belong to specific intervals of distance or time. Given that M&As and trade are complementary ways of reaching foreign markets, we perform our analysis using statistics employed for the study of the international trade network (ITN), highlighting the similarities and differences between the ITN and the IMAN. In contrast to the ITN, the IMAN is a low density network characterized by a persistent giant component with many external nodes and low reciprocity. Clustering patterns are very heterogeneous and dynamic. High-income economies are the main acquirers and are characterized by high connectivity, implying that most countries are targets of a few acquirers. Like in the ITN, geographical distance strongly impacts the structure of the IMAN: link-weights and node degrees have a non-linear relation with distance, and an assortative pattern is present at short distances.

Organization and hierarchy of the human functional brain network lead to a chain-like core.

The brain is a paradigmatic example of a complex system: its functionality emerges as a global property of local mesoscopic and microscopic interactions. Complex network theory allows to elicit the functional architecture of the brain in terms of links (correlations) between nodes (grey matter regions) and to extract information out of the noise. Here we present the analysis of functional magnetic resonance imaging data from forty healthy humans at rest for the investigation of the basal scaffold of the functional brain network organization. We show how brain regions tend to coordinate by forming a highly hierarchical chain-like structure of homogeneously clustered anatomical areas. A maximum spanning tree approach revealed the centrality of the occipital cortex and the peculiar aggregation of cerebellar regions to form a closed core. We also report the hierarchy of network segregation and the level of clusters integration as a function of the connectivity strength between brain regions.

Contact Patterns in a High School: A Comparison between Data Collected Using Wearable Sensors, Contact Diaries and Friendship Surveys.

Given their importance in shaping social networks and determining how information or transmissible diseases propagate in a population, interactions between individuals are the subject of many data collection efforts. To this aim, different methods are commonly used, ranging from diaries and surveys to decentralised infrastructures based on wearable sensors. These methods have each advantages and limitations but are rarely compared in a given setting. Moreover, as surveys targeting friendship relations might suffer less from memory biases than contact diaries, it is interesting to explore how actual contact patterns occurring in day-to-day life compare with friendship relations and with online social links. Here we make progresses in these directions by leveraging data collected in a French high school and concerning (i) face-to-face contacts measured by two concurrent methods, namely wearable sensors and contact diaries, (ii) self-reported friendship surveys, and (iii) online social links. We compare the resulting data sets and find that most short contacts are not reported in diaries while long contacts have a large reporting probability, and that the durations of contacts tend to be overestimated in the diaries. Moreover, measured contacts corresponding to reported friendship can have durations of any length but all long contacts do correspond to a reported friendship. On the contrary, online links that are not also reported in the friendship survey correspond to short face-to-face contacts, highlighting the difference of nature between reported friendships and online links. Diaries and surveys suffer moreover from a low sampling rate, as many students did not fill them, showing that the sensor-based platform had a higher acceptability. We also show that, despite the biases of diaries and surveys, the overall structure of the contact network, as quantified by the mixing patterns between classes, is correctly captured by both networks of self-reported contacts and of friendships, and we investigate the correlations between the number of neighbors of individuals in the three networks. Overall, diaries and surveys tend to yield a correct picture of the global structural organization of the contact network, albeit with much less links, and give access to a sort of backbone of the contact network corresponding to the strongest links, i.e., the contacts of longest cumulative durations.

Enhancing the evaluation of pathogen transmission risk in a hospital by merging hand-hygiene compliance and contact data: a proof-of-concept study.

BACKGROUND: Hand-hygiene compliance and contacts of health-care workers largely determine the potential paths of pathogen transmission in hospital wards. We explored how the combination of data collected by two automated infrastructures based on wearable sensors and recording (1) use of hydro-alcoholic solution and (2) contacts of health-care workers provide an enhanced view of the risk of transmission events in the ward. METHODS: We perform a proof-of-concept observational study. Detailed data on contact patterns and hand-hygiene compliance of health-care workers were collected by wearable sensors over 12 days in an infectious disease unit of a hospital in Marseilles, France. RESULTS: 10,837 contact events among 10 doctors, 4 nurses, 4 nurses' aids and 4 housekeeping staff were recorded during the study. Most contacts took place among medical doctors. Aggregate contact durations were highly heterogeneous and the resulting contact network was highly structured. 510 visits of health-care workers to patients' rooms were recorded, with a low rate of hand-hygiene compliance. Both data sets were used to construct histories and statistics of contacts informed by the use of hydro-alcoholic solution, or lack thereof, of the involved health-care workers. CONCLUSIONS: Hand-hygiene compliance data strongly enrich the information concerning contacts among health-care workers, by assigning a 'safe' or 'at-risk' value to each contact. The global contact network can thus be divided into 'at-risk' and 'safe' contact networks. The combined data could be of high relevance for outbreak investigation and to inform data-driven models of nosocomial disease spread.

Reconstructing the world trade multiplex: the role of intensive and extensive biases.

In economic and financial networks, the strength of each node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown. However, several studies have proved that real economic networks and multiplexes topologically differ from configurations inferred only from node strengths. Here we provide a detailed analysis of the world trade multiplex by comparing it to an enhanced null model that simultaneously reproduces the strength and the degree of each node. We study several temporal snapshots and almost 100 layers (commodity classes) of the multiplex and find that the observed properties are systematically well reproduced by our model. Our formalism allows us to introduce the (static) concept of extensive and intensive bias, defined as a measurable tendency of the network to prefer either the formation of extra links or the reinforcement of link weights, with respect to a reference case where only strengths are enforced. Our findings complement the existing economic literature on (dynamic) intensive and extensive trade margins. More generally, they show that real-world multiplexes can be strongly shaped by layer-specific local constraints.