Spatial effects in real networks: measures, null models, and applications

Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two factors can be varied arbitrarily, it is much more difficult to disentangle these two architectural effects in real networks. Here we propose a solution to the problem by introducing global and local measures of spatial effects that, through a comparison with adequate null models, effectively filter out the spurious contribution of non-spatial constraints. Our filtering allows us to consistently compare different embedded networks or different historical snapshots of the same network. As a challenging application we analyse the World Trade Web, whose topology is expected to depend on geographic distances but is also strongly determined by non-spatial constraints (degree sequence or GDP). Remarkably, we are able to detect weak but significant spatial effects both locally and globally in the network, showing that our method succeeds in retrieving spatial information even when non-spatial factors dominate. We finally relate our results to the economic literature on gravity models and trade globalization

Reconciling long-term cultural diversity and short-term collective social behavior

An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and long-term cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are well understood, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a high-dimensional analysis of the scientific beliefs of thousands of Europeans. We find that inter-opinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space, a result unaccessible to one-dimensional analyses and in striking contrast with random assumptions. When empirical data are used as inputs in models, we find that ultrametricity has strong and counterintuitive effects, especially in the extreme case of long-range online-like interactions bypassing social ties. On short time-scales, it strongly facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long time-scales, it severely suppresses cultural convergence by restricting it within disjoint groups. We therefore find that, remarkably, the empirical distribution of individuals in cultural space appears to optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence

Cycling and reciprocity in weighted food webs and economic networks

Networks of mass flows describe the basic structure of ecosystems as food webs, and of economy as input–output tables. Matter leaving a node in these networks can return to it immediately as part of a reciprocal flow, or completing a longer, multi-node cycle. Previous research comparing cycling of matter in ecosystems and economy was limited by relying on unweighted or few networks. Overcoming this limitation, we study mass cycling in large datasets of weighted real-world networks: 169 mostly aquatic food webs and 155 economic networks. We quantify cycling as the portion of all flows that is due to cycles, known as the Finn Cycling Index (FCI). We find no correlation between FCI and the largest eigenvalues of unweighted adjacency matrices used as a cycling proxy in the past. Unweighted networks ignore the actual flow values that in reality can differ by even 10 orders of magnitude. FCI can be decomposed into a sum of contributions of individual nodes. This enables us to quantify how organisms recycling dead organic matter dominate mass cycling in weighted food webs. FCI of food webs has a geometric mean of 5%. We observe lower average mass cycling in the economic networks. The global production network had an FCI of 3.7% in 2011. Cycling in economic networks (input–output tables and trade relationships) and food webs strongly correlates with reciprocity. Encouraging reciprocity could enhance cycling in the economy by acting locally, without the need to perfectly know its global structure

ST segment depression in the inferior leads in Brugada Pattern: It's time to look for it

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How crude oil prices shape the global division of labor

Our work sheds new light on the role of oil prices in shaping the world economy by investigating flows of goods and services through global value chains between 1960 and 2011, by means of Markov Chain and network analysis. We show that over that time period the international division of labor and trade patterns are tightly linked to the price of oil. We observe a remarkably high negative correlation (−0.85) between the oil price and the share of cyclical value, i.e. the share of value embodied in raw materials and intermediate products that are conserved across direct and indirect relationships. We demonstrate that this correlation does not depend on the balance of payments nor on the nominal value of trade or trade agreements; it is instead linked to the way Global Value Chains (GVCs) shape global trade. The cycling indexes show two majors structural breaks in terms of distance and length of GVCs, hinting at two phases of the recent globalization dynamics, sustained by two major transport modes. Our study suggests that transport played an important structural role in shaping GVCs, unveiling the deep, long-term impact of energy costs on the structure and connectivity of the global economy. In more theoretical term, our results indicate that the production structure could be approached as an energy system, forged by the efficiency in the transport sector. Understanding the role of oil in a globalized economy is of paramount importance for decoupling of economic growth from energy growth and transitioning toward a de-carbonized economy. © 2016 Elsevier Lt

How crude oil prices shape the global division of labor

Our work sheds new light on the role of oil prices in shaping the world economy by investigating flows of goods and services through global value chains between 1960 and 2011, by means of Markov Chain and network analysis. We show that over that time period the international division of labor and trade patterns are tightly linked to the price of oil. We observe a remarkably high negative correlation (−0.85) between the oil price and the share of cyclical value, i.e. the share of value embodied in raw materials and intermediate products that are conserved across direct and indirect relationships. We demonstrate that this correlation does not depend on the balance of payments nor on the nominal value of trade or trade agreements; it is instead linked to the way Global Value Chains (GVCs) shape global trade. The cycling indexes show two majors structural breaks in terms of distance and length of GVCs, hinting at two phases of the recent globalization dynamics, sustained by two major transport modes. Our study suggests that transport played an important structural role in shaping GVCs, unveiling the deep, long-term impact of energy costs on the structure and connectivity of the global economy. In more theoretical term, our results indicate that the production structure could be approached as an energy system, forged by the efficiency in the transport sector. Understanding the role of oil in a globalized economy is of paramount importance for decoupling of economic growth from energy growth and transitioning toward a de-carbonized economy

Multiplexity and multireciprocity in directed multiplexes

Real-world multilayer networks feature nontrivial dependencies among links of different layers. Here we argue that if links are directed, then dependencies are twofold. Besides the ordinary tendency of links of different layers to align as the result of "multiplexity," there is also a tendency to antialign as a result of what we call "multireciprocity," i.e., the fact that links in one layer can be reciprocated by opposite links in a different layer. Multireciprocity generalizes the scalar definition of single-layer reciprocity to that of a square matrix involving all pairs of layers. We introduce multiplexity and multireciprocity matrices for both binary and weighted multiplexes and validate their statistical significance against maximum-entropy null models that filter out the effects of node heterogeneity. We then perform a detailed empirical analysis of the world trade multiplex (WTM), representing the import-export relationships between world countries in different commodities. We show that the WTM exhibits strong multiplexity and multireciprocity, an effect which is, however, largely encoded into the degree or strength sequences of individual layers. The residual effects are still significant and allow us to classify pairs of commodities according to their tendency to be traded together in the same direction and/or in opposite ones. We also find that the multireciprocity of the WTM is significantly lower than the usual reciprocity measured on the aggregate network. Moreover, layers with low (high) internal reciprocity are embedded within sets of layers with comparably low (high) mutual multireciprocity. This suggests that, in the WTM, reciprocity is inherent to groups of related commodities rather than to individual commodities. We discuss the implications for international trade research focusing on product taxonomies, the product space, and fitness and complexity metrics