Zipf's power law is a ubiquitous empirical regularity found in many systems, thought to result from proportional growth. Here, we establish empirically the usually assumed ingredients of stochastic growth models that have been previously conjectured to be at the origin of Zipf's law. We use exceptionally detailed data on the evolution of open source software projects in Linux distributions, which offer a remarkable example of a growing complex self-organizing adaptive system, exhibiting Zipf's law over four full decades.

With the development of the Internet, new kinds of massive epidemics, distributed attacks, virtual conflicts and criminality have emerged. We present a study of some striking statistical properties of cyber-risks that quantify the distribution and time evolution of information risks on the Internet, to understand their mechanisms, and create opportunities to mitigate, control, predict and insure them at a global scale. First, we report an exceptionnaly stable power-law tail distribution of personal identity losses per event, Pr(ID lossThis result is robust against a surprising strong non-stationary growth of ID losses culminating in July 2006 followed by a more stationary phase. Moreover, this distribution is identical for different types and sizes of targeted organizations. Since b < 1, the cumulative number of all losses over all events up to time t increases faster-than-linear with time according to ≃ t 1/b , suggesting that privacy, characterized by personal identities, is necessarily becoming more and more insecure. We also show the existence of a size effect, such that the largest possible ID losses per event grow faster-than-linearly as ∼ S 1.3 with the organization size S. The small value b ≃ 0.7 of the power law distribution of ID losses is explained by the interplay between Zipf's law and the size effect.We also infer that compromised entities exhibit basically the same probability to incur a small or large loss. * Electronic address: tmaillart@ethz.ch † Electronic address: dsornette@ethz.ch 1

Personal data breaches from organisations, enabling mass identity fraud, constitute an extreme risk. This risk worsens daily as an ever-growing amount of personal data are stored by organisations and on-line, and the attack surface surrounding this data becomes larger and harder to secure. Further, breached information is distributed and accumulates in the hands of cyber criminals, thus driving a cumulative erosion of privacy. Statistical modeling of breach data from 2000 through 2015 provides insights into this risk: A current maximum breach size of about 200 million is detected, and is expected to grow by fifty percent over the next five years. The breach sizes are found to be well modeled by an extremely heavy tailed truncated Pareto distribution, with tail exponent parameter decreasing linearly from 0.57 in 2007 to 0.37 in 2015. With this current model, given a breach contains above fifty thousand items, there is a ten percent probability of exceeding ten million. A size effect is unearthed where both the frequency and severity of breaches scale with organisation size like s 0.6 . Projections indicate that the total amount of breached information is expected to double from two to four billion items within the next five years, eclipsing the population of users of the Internet. This massive and uncontrolled dissemination of personal identities raises fundamental concerns about privacy.

In a variety of open source software projects, we document a superlinear growth of production intensity () as a function of the number of active developers , with a median value of the exponent , with large dispersions of from slightly less than up to . For a typical project in this class, doubling of the group size multiplies typically the output by a factor , explaining the title. This superlinear law is found to hold for group sizes ranging from 5 to a few hundred developers. We propose two classes of mechanisms, interaction-based and large deviation, along with a cascade model of productive activity, which unifies them. In this common framework, superlinear productivity requires that the involved social groups function at or close to criticality, or in a “superradiance” mode, in the sense of the appearance of a cooperative process and order involving a collective mode of developers defined by the build up of correlation between the contributions of developers. In addition, we report the first empirical test of the renormalization of the exponent of the distribution of the sizes of first generation events into the renormalized exponent of the distribution of clusters resulting from the cascade of triggering over all generation in a critical branching process in the non-meanfield regime. Finally, we document a size effect in the strength and variability of the superlinear effect, with smaller groups exhibiting widely distributed superlinear exponents, some of them characterizing highly productive teams. In contrast, large groups tend to have a smaller superlinearity and less variability.

Clinical research in autism has recently witnessed promising digital phenotyping results, mainly focused on single feature extraction, such as gaze, head turn on name-calling or visual tracking of the moving object. The main drawback of these studies is the focus on relatively isolated behaviors elicited by largely controlled prompts. We recognize that while the diagnosis process understands the indexing of the specific behaviors, ASD also comes with broad impairments that often transcend single behavioral acts. For instance, the atypical nonverbal behaviors manifest through global patterns of atypical postures and movements, fewer gestures used and often decoupled from visual contact, facial affect, speech. Here, we tested the hypothesis that a deep neural network trained on the non-verbal aspects of social interaction can effectively differentiate between children with ASD and their typically developing peers. Our model achieves an accuracy of 80.9% (F1 score: 0.818; precision: 0.784; recall: 0.854) with the prediction probability positively correlated to the overall level of symptoms of autism in social affect and repetitive and restricted behaviors domain. Provided the non-invasive and affordable nature of computer vision, our approach carries reasonable promises that a reliable machine-learning-based ASD screening may become a reality not too far in the future.