Abstract: Attacks by drones (i.e., unmanned combat air vehicles) continue to generate heated political and ethical debates. Here we examine the quantitative nature of drone attacks, focusing on how their intensity and frequency compare with that of other forms of human conflict. Instead of the power-law distribution found recently for insurgent and terrorist attacks, the severity of attacks is more akin to lognormal and exponential distributions, suggesting that the dynamics underlying drone attacks lie beyond these other forms of human conflict. We find that the pattern in the timing of attacks is consistent with one side having almost complete control, an important if expected result. We show that these novel features can be reproduced and understood using a generative mathematical model in which resource allocation to the dominant side is regulated through a feedback loop.
Abstract: Over the past two decades, school shootings within the United States have repeatedly devastated communities and shaken public opinion. Many of these attacks appear to be `lone wolf' ones driven by specific individual motivations, and the identification of precursor signals and hence actionable policy measures would thus seem highly unlikely. Here, we take a system wide view and investigate the timing of school attacks and the dynamical feedback with social media. We identify a trend divergence in which college attacks have continued to accelerate over the last 25 years while those carried out on K-12 schools have slowed down. We establish the copycat effect in school shootings and uncover a statistical association between social media chatter and the probability of an attack in the following days. While hinting at causality, this relationship may also help mitigate the frequency and intensity of future attacks.
Abstract: Society's techno-social systems are becoming ever faster and more computer-orientated. However, far from simply generating faster versions of existing behaviour, we show that this speed-up can generate a new behavioural regime as humans lose the ability to intervene in real time. Analyzing millisecond-scale data for the world's largest and most powerful techno-social system, the global financial market, we uncover an abrupt transition to a new all-machine phase characterized by large numbers of subsecond extreme events. The proliferation of these subsecond events shows an intriguing correlation with the onset of the system-wide financial collapse in 2008. Our findings are consistent with an emerging ecology of competitive machines featuring ‘crowds’ of predatory algorithms, and highlight the need for a new scientific theory of subsecond financial phenomena.
Abstract: Rare but potentially catastrophic real-world phenomena such as stock market crashes, are often referred to as rare or extreme ‘events’ on the assumption that they have a well-defined change (eg price-change) in some macroscopically measurable quantity (eg stock price) occurring at a particular point in space (eg Dow Jones) and time (eg at 10am), over a specific time-interval (eg 1 hour). If this idealization is indeed the case, then histograms can be obtained using historical data and, assuming the system is stationary, approximate point probabilities deduced to quantify the likelihood of future occurrence--albeit subject to the usual inaccuracies associated with performing sparse number statistics. However, as emphasized by Sornette, extreme'behaviors' such as the mysterious 2010 flash crash in stock prices shown in Fig. 1 in principle invoke an entirely different layer of difficulty, because (1) they do not have a well-defined duration, and hence may be missed when evaluating histograms of changes for a particular fixed, pre-defined time increment (eg 1 minute, 1 hour or 1 day); and (2) even if their duration and maximum size are well defined, they can take on an effectively infinite number of possible temporal profiles during that period, ie has its own characteristic time-dependence during. Hence for a given maximum drop size and duration, there are a priori myriad possible temporal forms of versus. This chapter takes a step toward examining whether these temporal profiles (ie vs. during) exhibit particular classes of behavior–and shows, for the case of a nontrivial toy model of a complex system, that there is indeed a taxonomy of such rare and extreme behaviors.
Abstract: We analyze the mechanistic origins of the extreme behaviors that arise in an idealized model of a population of competing agents, such as traders in a market. These extreme behaviors exhibit the defining characteristics of ‘dragon-kings’. Our model comprises heterogeneous agents who repeatedly compete for some limited resource, making binary choices based on the strategies that they have in their possession. It generalizes the well-known Minority Game by allowing agents whose strategies have not made accurate recent predictions, to step out of the competition until their strategies improve. This generates a complex dynamical interplay between the number V of active agents (mimicking market volume) and the imbalance D between the decisions made (mimicking excess demand). The wide spectrum of extreme behaviors which emerge, helps to explain why no unique relationship has been identified between the price and volume during real market crashes and rallies.
Abstract: Society's drive toward ever faster socio-technical systems, means that there is an urgent need to understand the threat from'black swan'extreme events that might emerge. 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. However, little is known about what lies ahead in the crucial sub-second regime where humans become unable to respond or intervene sufficiently quickly. 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.
Abstract: 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.
Abstract: 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 (eg insurgency) sporadically edges ahead of a Blue King (eg 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 formula 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 the physics of correlated walks.