http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

J. Appl. Cryst.の発刊に際して

https://deim.urv.cat/~alexandre.arenas/publicacions/pdf/review.pdf

Synchronization in complex networks

The origin of large but rare cascades that are triggered by small initial shocks is a phenomenon that manifests itself as diversely as cultural fads, collective action, the diffusion of norms and innovations, and cascading failures in infrastructure and organizational networks. This paper presents a possible explanation of this phenomenon in terms of a sparse, random network of interacting agents whose decisions are determined by the actions of their neighbors according to a simple threshold rule. Two regimes are identified in which the network is susceptible to very large cascades—herein called global cascades—that occur very rarely. When cascade propagation is limited by the connectivity of the network, a power law distribution of cascade sizes is observed, analogous to the cluster size distribution in standard percolation theory and avalanches in self-organized criticality. But when the network is highly connected, cascade propagation is limited instead by the local stability of the nodes themselves, and the size distribution of cascades is bimodal, implying a more extreme kind of instability that is correspondingly harder to anticipate. In the first regime, where the distribution of network neighbors is highly skewed, it is found that the most connected nodes are far more likely than average nodes to trigger cascades, but not in the second regime. Finally, it is shown that heterogeneity plays an ambiguous role in determining a system's stability: increasingly heterogeneous thresholds make the system more vulnerable to global cascades; but an increasingly heterogeneous degree distribution makes it less vulnerable.

/pdf/a-simple-model-of-global-cascades-on-random-networks-zv4xfy8ajb.pdf

A simple model of global cascades on random networks

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Electric power transmission systems are a key infrastructure, and blackouts of these systems have major consequences for the economy and national security. Analyses of blackout data suggest that blackout size distributions have a power law form over much of their range. This result is an indication that blackouts behave as a complex dynamical system. We use a simulation of an upgrading power transmission system to investigate how these complex system dynamics impact the assessment and mitigation of blackout risk. The mitigation of failures in complex systems needs to be approached with care. The mitigation efforts can move the system to a new dynamic equilibrium while remaining near criticality and preserving the power law region. Thus, while the absolute frequency of blackouts of all sizes may be reduced, the underlying forces can still cause the relative frequency of large blackouts to small blackouts to remain the same. Moreover, in some cases, efforts to mitigate small blackouts can even increase the frequency of large blackouts. This result occurs because the large and small blackouts are not mutually independent, but are strongly coupled by the complex dynamics.

/pdf/exploring-complex-systems-aspects-of-blackout-risk-and-30qv5wa7uh.pdf

Exploring Complex Systems Aspects of Blackout Risk and Mitigation

Electric power transmission systems are a key infrastructure and blackouts of these systems have major direct and indirect consequences on the economy and national security. Analysis of North American Electrical Reliability Council blackout data suggests the existence of blackout size distributions with power tails. This is an indication that blackout dynamics behave as a complex dynamical system. Here, we investigate how these complex system dynamics impact the assessment and mitigation of blackout risk. The mitigation of failures in complex systems needs to be approached with care. The mitigation efforts can move the system to a new dynamic equilibrium while remaining near criticality and preserving the power tails. Thus, while the absolute frequency of disruptions of all sizes may be reduced, the underlying forces can still cause the relative frequency of large disruptions to small disruptions to remain the same. Moreover, in some cases, efforts to mitigate small disruptions can even increase the frequency of large disruptions. This occurs because the large and small disruptions are not independent but are strongly coupled by the dynamics.

/pdf/blackout-mitigation-assessment-in-power-transmission-systems-zooshm6wa0.pdf

Blackout mitigation assessment in power transmission systems

Numerical calculations using the full MHD equations in toroidal geometry

Critical infrastructures have some of the characteristic properties of complex systems. They exhibit infrequent large failures events. These events, though infrequent, often obey a power law distribution in their probability versus size. This power law behavior suggests that ordinary risk analysis might not apply to these systems. It is thought that some of this behavior comes from different parts of the systems interacting with each other both in space and time. While these complex infrastructure systems can exhibit these characteristics on their own, in reality these individual infrastructure systems interact with each other in even more complex ways. This interaction can lead to increased or decreased risk of failure in the individual systems. To investigate this and to formulate appropriate risk assessment tools for such systems, a set of models are used to study to impact of coupling complex systems. A probabilistic model and a dynamical model that have been used to study blackout dynamics in the power transmission grid are used as paradigms. In this paper, we investigate changes in the risk models based on the power law event probability distributions, when complex systems are coupled.

/pdf/risk-assessment-in-complex-interacting-infrastructure-2pyatww61r.pdf

Risk Assessment in Complex Interacting Infrastructure Systems

The intensity of single-crystal Bragg peaks obtained by mapping neutron time-of-flight event data into reciprocal space and integrating in various ways is compared. These methods include spherical integration with a fixed radius, ellipsoid fitting and integration of the peak intensity, and one-dimensional peak profile fitting. In comparison to intensities obtained by integrating in real detector histogram space, the data integrated in reciprocal space result in better agreement factors and more accurate atomic parameters. Furthermore, structure refinement using integrated intensities from one-dimensional profile fitting is demonstrated to be more accurate than simple peak-minus-background integration.

Vickie E. Lynch

Papers

Exploring Complex Systems Aspects of Blackout Risk and Mitigation

Blackout mitigation assessment in power transmission systems

Numerical calculations using the full MHD equations in toroidal geometry

Risk Assessment in Complex Interacting Infrastructure Systems

Integration of neutron time-of-flight single-crystal Bragg peaks in reciprocal space