In military planning, it is important to be able to estimate not only the number of fatalities but how often attacks that result in fatalities will take place. We uncovered a simple dynamical pattern that may be used to estimate the escalation rate and timing of fatal attacks. The time difference between fatal attacks by insurgent groups within individual provinces in both Afghanistan and Iraq, and by terrorist groups operating worldwide, gives a potent indicator of the later pace of lethal activity.
Society's drive toward ever faster socio-technical systems [1][2][3] , means that there is an urgent need to understand the threat from 'black swan' extreme events that might emerge [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . On 6 May 2010, it took just five minutes for a spontaneous mix of human and machine interactions in the global trading cyberspace to generate an unprecedented system-wide Flash Crash 4 . However, little is known about what lies ahead in the crucial sub-second regime where humans become unable to respond or intervene sufficiently quickly 20,21 . Here we analyze a set of 18,520 ultrafast black swan events that we have uncovered in stock-price movements between 2006 and 2011. We provide empirical evidence for, and an accompanying theory of, an abrupt system-wide transition from a mixed human-machine phase to a new all-machine phase characterized by frequent black swan events with ultrafast durations (<650ms for crashes, <950ms for spikes). Our theory quantifies the systemic fluctuations in these two distinct phases in terms of the diversity of the system's internal ecology and the amount of global information being processed. Our finding that the ten most susceptible entities are major international banks, hints at a hidden relationship between these ultrafast 'fractures' and the slow 'breaking' of the global financial system post-2006. More generally, our work provides tools to help predict and mitigate the systemic risk developing in any complex socio-technical system that attempts to operate at, or beyond, the limits of human response times.
We develop a new population-scale model incorporating diapause induction and termination that allows multi-year predictions of pest dynamics. In addition to predicting phenology and voltinism, the model also allows us to study the degree of overlapping among the life-stages across time; a quantity not generally predicted by previous models yet a key determinant of how frequently management must be done to maintain control. The model is a physiological, stage-structured population model that includes temperature-dependent vital rates, diapause processes, and plasticity in development. The model is statistically fitted with a 33-year long weekly term time series of Cydia pomonella adults captured in pheromone-baited traps from a research orchard in southern Pennsylvania. The multiannual model allows investigation of both within season control strategies, as well as the likely consequences of climate change for this important agricultural pest. The model predicts that warming temperatures will cause earlier spring emergence, additional generations, and increased overall abundance. Most importantly, by calculating the circular variance, we find that warmer temperatures are associated with an increase in overlap among life-stages especially at the beginning of the growing season. Our findings highlight the importance of modeling diapause to fully understand C. pomonella lifecycle and to better inform management for effectively controlling this pest in a warmer future.
The Red Queen's notion "It takes all the running you can do, to keep in the same place" has been applied within evolutionary biology, politics and economics. We find that a generalized version in which an adaptive Red Queen (e.g. insurgency) sporadically edges ahead of a Blue King (e.g. military), explains the progress curves for fatal insurgent attacks against the coalition military within individual provinces in Afghanistan and Iraq. Remarkably regular mathematical relations emerge which suggest a prediction τ n = τ 1 n − m log 10 τ 1 +c [ ] for the timing of the n'th future fatal day, and provide a common framework for understanding how insurgents fight in different regions. Our findings are consistent with a Darwinian selection hypothesis which favors a weak species which can adapt rapidly, and establish an unexpected conceptual connection to Physics through correlated walks.
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