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. 1.

This paper describes a dynamic instrumentation tool for the Linux Kernel which allows a stock Linux kernel to be modi ed while in execution, with instruments implemented as kernel modules. The Intel x86 architecture poses a particular problem, due to variable length instructions, which this paper addresses for the rst time. Finally we present a short case study illustrating its use in understanding i/o behaviour in the kernel. The source code is freely available for download.

We analyze a 15-year time series of North American electric power transmission system blackouts for evidence of self-organized criticality.The probability distribution functions of various measures of blackout size have a power tail and R/S analysis of the time series shows moderate long time correlations.Moreover, the same analysis applied to a time series from a sandpile model known to be self-organized critical gives results of the same form.Thus the blackout data is consistent with self-organized criticality. A qualitative explanation of the complex dynamics observed in electric power system blackouts is suggested.

We give a comprehensive account of a complex systems approach to large blackouts caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data suggests that the frequency of large blackouts is governed by a power law. This result is consistent with the power system being a complex system designed and operated near criticality. The power law makes the risk of large blackouts consequential and implies the need for nonstandard risk analysis. Power system overall load relative to operating limits is a key factor affecting the risk of cascading failure. Blackout models and an abstract model of cascading failure show that there are critical transitions as load is increased. Power law behavior can be observed at these transitions. The critical loads at which blackout risk sharply increases are identifiable thresholds for cascading failure and we discuss approaches to computing the proximity to cascading failure using these thresholds. Approximating cascading failure as a branching process suggests ways to compute and monitor criticality by quantifying how much failures propagate. Inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near criticality and confirm this idea using a blackout model. Mitigation of blackout risk should take care to account for counter-intuitive effects in complex self-organized critical systems. For example, suppressing small blackouts could lead the system to be operated closer to the edge and ultimately increase the risk of large blackouts. 1

Few will argue that the epi-phenomena of biological systems and socio-economic systems are anything but complex. The purpose of this Feature is to examine critically and contribute to the burgeoning multi-disciplinary literature on markets as complex adaptive systems (CAS). The new sciences of complexity, the principles of self-organisation and emergence along with the methods of evolutionary computation and artificially intelligent agent models have been developed in a multi-disciplinary fashion. The cognoscenti here consider that complex systems whether natural or artificial, physical, biological or socio-economic can be characterised by a unifying set of principles. Further, it is held that these principles mark a paradigm shift from earlier ways of viewing such phenomenon. The articles in this Feature aim to provide detailed insights and examples of both the challenges and the prospects for economics that are offered by the new methods of the complexity sciences. The applicability or not of the optimisation framework of conventional economics depends on the domain of the problem and in particular the modern theories behind non-computability are outlined to explain why adaptive or emergent methods of computation and agent-based

... framework of cognitive psychology in favor of the framework of nonlinear dynamical systems theory. Van Orden et al. presented evidence that“purposive behavior originates in self-organized criticality ” (p. 333). Here, the authors show that Van Orden et al.’s analyses do not test their hypotheses. Further, the authors argue that a confirmation of Van Orden et al.’s hypotheses would not have constituted firm evidence in support of their framework. Finally, the absence of a specific model for how self-organized criticality produces the observed behavior makes it very difficult to derive testable predictions. The authors conclude that the proposed paradigm shift is presently unwarranted.

Abstract. The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high probability is also proven in 1-D. The results are relevant for self-organized critical behaviour of stochastic nonlinear diffusion equations with critical states.

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the dissipative sandpiles ’ correlation length exponent ν always equals 1/dw, where dw is the fractal dimension of the random walker. This leads to a new understanding of the known result that ν = 1/2 on any Euclidean lattice. Our result is however more general and as an example we also present exact data for finite Sierpinski gaskets which fully confirm our predictions. 1 Self organised criticality (SOC) [1, 2] is the phenomenon in which a slowly driven system with many interacting degrees of freedom evolves spontaneously into a critical state, characterised by long range correlations in space and time (for introductory reviews, see [3, 4]). This phenomenon has by now been recognised (or conjectured to exist) in many (models of) natural phenomena such as earthquakes [5], forest fires [6], speciation of life [7],...Moreover, the possible presence of SOC can be investigated in experimentally controlable phenomena

A new model ecosystem of many interacting species is introduced in which the species are connected through a random matrix with a given connectivity. The model is studied both analytically and by numerical simulations. A probability distribution derived from the model is in good agreement with simulations and #eld data. It is also shown that the connectivity, C, and the number of species, S, are linked through the scaling relation = k(C) -1+# , which is observed in real ecosystems. Our approach suggests a natural link between log-normal and power-law distributions of species abundances. c 2000 Elsevier Science B.V. All rights reserved.

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