Multiplexity-facilitated cascades in networks

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [D. J. Watts, Proc. Natl. Acad. Sci. U.S.A. 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recognizing distinct kinds of interactions) facilitate cascades. Notably, layers unsusceptible to global cascades can cooperatively achieve them if coupled. On one hand, this suggests fundamental limitations on predicting cascades without full knowledge of a system's multiplexity; on the other hand, it offers feasible means to control cascades by introducing or removing sparse layers in an existing network.Comment: Final version 4/30/12: 5 pages, 5 figure

Assessing the Cost of Global Biodiversity and Conservation Knowledge

Knowledge products comprise assessments of authoritative information supported by standards, governance, quality control, data, tools, and capacity building mechanisms. Considerable resources are dedicated to developing and maintaining knowledge products for biodiversity conservation, and they are widely used to inform policy and advise decision makers and practitioners. However, the financial cost of delivering this information is largely undocumented. We evaluated the costs and funding sources for developing and maintaining four global biodiversity and conservation knowledge products: The IUCN Red List of Threatened Species, the IUCN Red List of Ecosystems, Protected Planet, and the World Database of Key Biodiversity Areas. These are secondary data sets, built on primary data collected by extensive networks of expert contributors worldwide. We estimate that US$160 million (range: US$116–204 million), plus 293 person-years of volunteer time (range: 278–308 person-years) valued at US$14 million (range US$12–16 million), were invested in these four knowledge products between 1979 and 2013. More than half of this financing was provided through philanthropy, and nearly three-quarters was spent on personnel costs. The estimated annual cost of maintaining data and platforms for three of these knowledge products (excluding the IUCN Red List of Ecosystems for which annual costs were not possible to estimate for 2013) is US$6.5 million in total (range: US$6.2–6.7 million). We estimated that an additional US$114 million will be needed to reach pre-defined baselines of data coverage for all the four knowledge products, and that once achieved, annual maintenance costs will be approximately US$12 million. These costs are much lower than those to maintain many other, similarly important, global knowledge products. Ensuring that biodiversity and conservation knowledge products are sufficiently up to date, comprehensive and accurate is fundamental to inform decision-making for biodiversity conservation and sustainable development. Thus, the development and implementation of plans for sustainable long-term financing for them is critical

The extreme vulnerability of interdependent spatially embedded networks

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.Comment: 13 pages, 5 figure

Avoiding catastrophic failure in correlated networks of networks

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in abrupt failures. This theoretical finding bares an intrinsic paradox: If natural systems organize in interconnected networks, how can they be so stable? Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if network inter-connections are provided by hubs of the network and if there is a moderate degree of convergence of inter-network connection the systems of network are stable and robust to failure. We test this theoretical prediction in two independent experiments of functional brain networks (in task- and resting states) which show that brain networks are connected with a topology that maximizes stability according to the theory.Comment: 40 pages, 7 figure

Maximising Influence in Non-blocking Cascades of Interacting Concepts

Abstract. In large populations of autonomous individuals, the propa-gation of ideas, strategies or infections is determined by the composite effect of interactions between individuals. The propagation of concepts in a population is a form of influence spread and can be modelled as a cascade from a set of initial individuals through the population. Un-derstanding influence spread and information cascades has many appli-cations, from informing epidemic control and viral marketing strategies to understanding the emergence of conventions in multi-agent systems. Existing work on influence spread has mainly considered single concepts, or small numbers of blocking (exclusive) concepts. In this paper we focus on non-blocking cascades, and propose a new model for characterising concept interaction in an independent cascade. Furthermore, we propose two heuristics, Concept Aware Single Discount and Expected Infected, for identifying the individuals that will maximise the spread of a partic-ular concept, and show that in the non-blocking multi-concept setting our heuristics out-perform existing methods.

Green Plants in the Red: A Baseline Global Assessment for the IUCN Sampled Red List Index for Plants

Plants provide fundamental support systems for life on Earth and are the basis for all terrestrial ecosystems; a decline in plant diversity will be detrimental to all other groups of organisms including humans. Decline in plant diversity has been hard to quantify, due to the huge numbers of known and yet to be discovered species and the lack of an adequate baseline assessment of extinction risk against which to track changes. The biodiversity of many remote parts of the world remains poorly known, and the rate of new assessments of extinction risk for individual plant species approximates the rate at which new plant species are described. Thus the question ‘How threatened are plants?’ is still very difficult to answer accurately. While completing assessments for each species of plant remains a distant prospect, by assessing a randomly selected sample of species the Sampled Red List Index for Plants gives, for the first time, an accurate view of how threatened plants are across the world. It represents the first key phase of ongoing efforts to monitor the status of the world’s plants. More than 20% of plant species assessed are threatened with extinction, and the habitat with the most threatened species is overwhelmingly tropical rain forest, where the greatest threat to plants is anthropogenic habitat conversion, for arable and livestock agriculture, and harvesting of natural resources. Gymnosperms (e.g. conifers and cycads) are the most threatened group, while a third of plant species included in this study have yet to receive an assessment or are so poorly known that we cannot yet ascertain whether they are threatened or not. This study provides a baseline assessment from which trends in the status of plant biodiversity can be measured and periodically reassessed

Assessing the cost of global biodiversity and conservation knowledge

Knowledge products comprise assessments of authoritative information supported by stan-dards, governance, quality control, data, tools, and capacity building mechanisms. Considerable resources are dedicated to developing and maintaining knowledge productsfor biodiversity conservation, and they are widely used to inform policy and advise decisionmakers and practitioners. However, the financial cost of delivering this information is largelyundocumented. We evaluated the costs and funding sources for developing and maintain-ing four global biodiversity and conservation knowledge products: The IUCN Red List ofThreatened Species, the IUCN Red List of Ecosystems, Protected Planet, and the WorldDatabase of Key Biodiversity Areas. These are secondary data sets, built on primary datacollected by extensive networks of expert contributors worldwide. We estimate that US$160million (range: US$116–204 million), plus 293 person-years of volunteer time (range: 278–308 person-years) valued at US$14 million (range US$12–16 million), were invested inthese four knowledge products between 1979 and 2013. More than half of this financingwas provided through philanthropy, and nearly three-quarters was spent on personnelcosts. The estimated annual cost of maintaining data and platforms for three of these knowl-edge products (excluding the IUCN Red List of Ecosystems for which annual costs were notpossible to estimate for 2013) is US$6.5 million in total (range: US$6.2–6.7 million). We esti-mated that an additional US$114 million will be needed to reach pre-defined baselines ofdata coverage for all the four knowledge products, and that once achieved, annual mainte-nance costs will be approximately US$12 million. These costs are much lower than those tomaintain many other, similarly important, global knowledge products. Ensuring that biodi-versity and conservation knowledge products are sufficiently up to date, comprehensiveand accurate is fundamental to inform decision-making for biodiversity conservation andsustainable development. Thus, the development and implementation of plans for sustain-able long-term financing for them is critical