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Using detailed statistical analyses of the size distribution of a universe of equity exchange-traded funds (ETFs), we discover a discrete hierarchy of sizes, which imprints a log-periodic structure on the probability distribution of ETF sizes that dominates the details of the asymptotic tail. This allows us to propose a classification of the studied universe of ETFs into seven size layers approximately organized according to a multiplicative ratio of 3.5 in their total market capitalization. Introducing a similarity metric generalising the Herfindhal index, we find that the largest ETFs exhibit a significantly stronger intra-layer and inter-layer similarity compared with the smaller ETFs. Comparing the performance across the seven discerned ETF size layers, we find an inverse size effect, namely large ETFs perform significantly better than the small ones both in 2014 and 2015.

Organizations exist because they provide additional production gains, in comparison to horizontal ways of allocating resources, such as markets, and the open source movement is deemed to be a new kind of peer-production organization somehow in between hierarchically organized firms and markets. However, to strive as a new kind of organization, open source must provide production gains, which in turn should be measurable. The open source movement is particularly interesting to study for this reason. Here, we confront and discuss two contrasting views, which were reported in the literature recently. On the one hand, Sornette et al. uncovered a superlinear production mechanism, which quantifies Aristotle adage: `the whole is more than the sum of its parts'. On the other hand, Scholtes et al. found opposite results, and referred to Maximilien Ringelmann, a French agricultural engineer (1861-1931), who discovered the tendency for individual members of a group to become increasingly less productive as the size of their group increases. Since Ringelmann, the topic of collective intelligence has interested numbers of researchers in social sciences and social psychology, as well as practitioners in management aiming at improving the performance of their team. In most research and practice case studies, the Ringelmann effect has been found to hold, while, in contrast, the superlinear effect found by Sornette et al.is novel and may challenge common wisdom. Here, we compare these two theories, weigh their strengths and weaknesses, and discuss how they have been tested with empirical data. We find that they may not contradict each other as much as was claimed by Scholtes et al., Comment: 22 pages, published in Physica A

We contribute to the understanding of social relationships within cultural contexts by proposing a connection between a social theory, relational models theory (RMT: Fiske 1991, 1992) and a social and political one, cultural or plural rationality theory (PRT: Douglas, 1982, Thompson et al., 1990). Drawing examples from the literature of both theories, we argue that each relational model of RMT may be implemented in ways compatible with each cultural bias of PRT. A cultural bias restrains the range of congruent implementations of relational models, but does not preclude any relational model altogether. This stands in contrast to earlier reconciliation attempts between PRT and RMT. Based on hypothetical one-to-one mappings, these attempts expect each cultural setting to be significantly associated with some, but not all, relational models. The framework we develop helps explain the findings of these previous attempts and provides insights into empirical research by clarifying which associations to expect between relationships and cultural contexts. We discuss the theoretical basis of our framework, including the idea that RMT and PRT apply to different levels of analysis: RMT's relational models are tied to relationships between two actors and PRT's cultural biases to structures of social networks.

A likely source of earthquake clustering is static stress transfer between individual events. Previous attempts to quantify the role of static stress for earthquake triggering generally considered only the stress changes caused by large events, and often discarded data uncertainties. We conducted a robust two-fold empirical test of the static stress change hypothesis by accounting for all events of magnitude M>=2.5 and their location and focal mechanism uncertainties provided by catalogs for Southern California between 1981 and 2010, first after resolving the focal plane ambiguity and second after randomly choosing one of the two nodal planes. For both cases, we find compelling evidence supporting the static triggering with stronger evidence after resolving the focal plane ambiguity above significantly small (about 10 Pa) but consistently observed stress thresholds. The evidence for the static triggering hypothesis is robust with respect to the choice of the friction coefficient, Skempton's coefficient and magnitude threshold. Weak correlations between the Coulomb Index (fraction of earthquakes that received positive Coulomb stress change) and the coefficient of friction indicate that the role of normal stress in triggering is rather limited. Last but not the least, we determined that the characteristic time for the loss of the stress change memory of a single event is nearly independent of the amplitude of the Coulomb stress change and varies between ~95 and ~180 days implying that forecasts based on static stress changes will have poor predictive skills beyond times that are larger than a few hundred days on average.

We present a detailed methodological study of the application of the modified profile likelihood method for the calibration of nonlinear financial models characterised by a large number of parameters. We apply the general approach to the Log-Periodic Power Law Singularity (LPPLS) model of financial bubbles. This model is particularly relevant because one of its parameters, the critical time $t_c$ signalling the burst of the bubble, is arguably the target of choice for dynamical risk management. However, previous calibrations of the LPPLS model have shown that the estimation of $t_c$ is in general quite unstable. Here, we provide a rigorous likelihood inference approach to determine $t_c$, which takes into account the impact of the other nonlinear (so-called "nuisance") parameters for the correct adjustment of the uncertainty on $t_c$. This provides a rigorous interval estimation for the critical time, rather than a point estimation in previous approaches. As a bonus, the interval estimations can also be obtained for the nuisance parameters ($m,\omega$, damping), which can be used to improve filtering of the calibration results. We show that the use of the modified profile likelihood method dramatically reduces the number of local extrema by constructing much simpler smoother log-likelihood landscapes. The remaining distinct solutions can be interpreted as genuine scenarios that unfold as the time of the analysis flows, which can be compared directly via their likelihood ratio. Finally, we develop a multi-scale profile likelihood analysis to visualize the structure of the financial data at different scales (typically from 100 to 750 days). We test the methodology successfully on synthetic price time series and on three well-known historical financial bubbles., Comment: 40 pages, 10 figures

We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power sa (with a > 1) of the cluster sizes s, similarly to a generalized percolation susceptibility. The power sa of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite-time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold pc. Realistic dynamics are generated by modelling the density of traders on the percolation network by an Ornstein-Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes., Comment: 14 pages, 6 figures

We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita growth at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. Our main finding is that the distribution of GDP growth rates can be well approximated by a bimodal function associated to a series of switches between regimes of strong growth rate $\rho_\text{high}$ and regimes of low growth rate $\rho_\text{low}$. The succession of such two regimes compounds to produce a remarkably stable long term average real annualized growth rate of 1.6\% from 1800 to 2010 and $\approx 2.0\%$ since 1950, which is the result of a subtle compensation between the high and low growth regimes that alternate continuously. Thus, the overall growth dynamics of the US economy is punctuated, with phases of strong growth that are intrinsically unsustainable, followed by corrections or consolidation until the next boom starts. We interpret these findings within the theory of "social bubbles" and argue as a consequence that estimations of the cost of the 2008 crisis may be misleading. We also interpret the absence of strong recovery since 2008 as a protracted low growth regime $\rho_\text{low}$ associated with the exceptional nature of the preceding large growth regime.

A macroeconomic model based on the economic variables (i) assets, (ii) leverage (defined as debt over asset) and (iii) trust (defined as the maximum sustainable leverage) is proposed to investigate the role of credit in the dynamics of economic growth, and how credit may be associated with both economic performance and confidence. Our first notable finding is the mechanism of reward/penalty associated with patience, as quantified by the return on assets. In regular economies where the EBITA/Assets ratio is larger than the cost of debt, starting with a trust higher than leverage results in the highest long-term return on assets (which can be seen as a proxy for economic growth). Our second main finding concerns a recommendation for the reaction of a central bank to an external shock that affects negatively the economic growth. We find that late policy intervention in the model economy results in the highest long-term return on assets and largest asset value. But this comes at the cost of suffering longer from the crisis until the intervention occurs. The phenomenon can be ascribed to the fact that postponing intervention allows trust to increase first, and it is most effective to intervene when trust is high. These results derive from two fundamental assumptions underlying our model: (a) trust tends to increase when it is above leverage; (b) economic agents learn optimally to adjust debt for a given level of trust and amount of assets. Using a Markov Switching Model for the EBITA/Assets ratio, we have successfully calibrated our model to the empirical data of the return on equity of the EURO STOXX 50 for the time period 2000-2013. We find that dynamics of leverage and trust can be highly non-monotonous with curved trajectories, as a result of the nonlinear coupling between the variables., Comment: 32 pages with 10 figures

We introduce the Speculative Influence Network (SIN) to decipher the causal relationships between sectors (and/or firms) during financial bubbles. The SIN is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of regime-switching between a normal market phase represented by a geometric Brownian motion (GBM) and a bubble regime represented by the stochastic super-exponential Sornette-Andersen (2002) bubble model. The calibration of the HMM provides the probability at each time for a given security to be in the bubble regime. Conditional on two assets being qualified in the bubble regime, we then use the transfer entropy to quantify the influence of the returns of one asset $i$ onto another asset $j$, from which we introduce the adjacency matrix of the SIN among securities. We apply our technology to the Chinese stock market during the period 2005-2008, during which a normal phase was followed by a spectacular bubble ending in a massive correction. We introduce the Net Speculative Influence Intensity (NSII) variable as the difference between the transfer entropies from $i$ to $j$ and from $j$ to $i$, which is used in a series of rank ordered regressions to predict the maximum loss (\%{MaxLoss}) endured during the crash. The sectors that influenced other sectors the most are found to have the largest losses. There is a clear prediction skill obtained by using the transfer entropy involving industrial sectors to explain the \%{MaxLoss} of financial institutions but not vice versa. We also show that the bubble state variable calibrated on the Chinese market data corresponds well to the regimes when the market exhibits a strong price acceleration followed by clear change of price regimes. Our results suggest that SIN may contribute significant skill to the development of general linkage-based systemic risks measures and early warning metrics.

Humans are heterogenous and the behaviors of individuals could be different from that at the population level. We conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73'339 anonymous cellphone users with the same truncated Weibull distribution of inter-call durations. We find that the individual call events exhibit a pattern of bursts, in which high activity periods are alternated with low activity periods. Surprisingly, the number of events in high activity periods are found to conform to a power-law distribution at the population level, but follow an exponential distribution at the individual level, which is a hallmark of absence of memory in individual call activities. Such exponential distribution is also observed for the number of events in low activity periods. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain giving very good agreement with the empirical distributions using the parameters estimated from real data for about half of the individuals in our sample. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we explain the difference with previous population level studies, purporting the existence of power-law distributions, via the "Superposition of Distributions" mechanism: The superposition of many exponential distributions of activities with a power-law distribution of their characteristic scales leads to a power-law distribution of the activities at the population level., Comment: 16 pages, 7 figures

We generalise the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number of particles in the inner layer and its change per unit time, where the inner layer is revealed by the correlations between price velocity and change in the number of particles (limit orders). This allows us to introduce the Knudsen number of the financial Brownian particle motion and its asymmetric version (on the buy and sell sides). Not being considered previously, the asymmetric Knudsen numbers are crucial in finance in order to detect asymmetric price changes. The Knudsen numbers allows us to characterise the conditions for the market dynamics to be correctly described by a continuous stochastic process. Not questioned until now for large liquid markets such as the USD/JPY and EUR/USD exchange rates, we show that there are regimes when the Knudsen numbers are so high that discrete particle effects dominate, such as during market stresses and crashes. We document the presence of imbalances of particles depletion rates on the buy and sell sides that are associated with high Knudsen numbers and violent directional price changes. This indicator can detect the direction of the price motion at the early stage while the usual volatility risk measure is blind to the price direction.

We study the performance of the euro/Swiss franc exchange rate in the extraordinary period from September 6, 2011 and January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Non-parametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics are incorrect. The clue is to realise that the random walk nature of financial prices results from the continuous anticipations of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank stated commitment to enforce the barrier, traders's anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. We give direct quantitative empirical evidence that this effect is well described by Krugman's target zone model [P.R. Krugman. The Quarterly Journal of Economics, 106(3):669-682, 1991]. Motivated by the insights from this economical model, we revise the initial economics-physics analogy and show that, within the context of hindered diffusion, the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient.

We introduce two ratio-based robust test statistics, max-robust-sum (MRS) and sum-robust-sum (SRS), designed to enhance the robustness of outlier detection in samples with exponential or Pareto tails. We also reintroduce the inward sequential testing method -- formerly relegated since the introduction of outward testing -- and show that MRS and SRS tests reduce susceptibility of the inward approach to masking, making the inward test as powerful as, and potentially less error-prone than, outward tests. Moreover, inward testing does not require the complicated type I error control of outward tests. A comprehensive comparison of the test statistics is done, considering performance of the proposed tests in both block and sequential tests, and contrasting their performance with classical test statistics across various data scenarios. In five case studies -- financial crashes, nuclear power generation accidents, stock market returns, epidemic fatalities, and city sizes -- significant outliers are detected and related to the concept of `Dragon King' events, defined as meaningful outliers that arise from a unique generating mechanism., Comment: 32 pages with 9 figures

Tomasetti and Vogelstein recently proposed that the majority of variation in cancer risk among tissues is due to "bad luck," that is, random mutations arising during DNA replication in normal noncancerous stem cells. They generalize this finding to cancer overall, claiming that "the stochastic effects of DNA replication appear to be the major contributor to cancer in humans." We show that this conclusion results from a logical fallacy based on ignoring the influence of population heterogeneity in correlations exhibited at the level of the whole population. Because environmental and genetic factors cannot explain the huge differences in cancer rates between different organs, it is wrong to conclude that these factors play a minor role in cancer rates. In contrast, we show that one can indeed measure huge differences in cancer rates between different organs and, at the same time, observe a strong effect of environmental and genetic factors in cancer rates.

Buyer--seller relationships among firms can be regarded as a longitudinal network in which the connectivity pattern evolves as each firm receives productivity shocks. Based on a data set describing the evolution of buyer--seller links among 55,608 firms over a decade and structural equation modeling, we find some evidence that interfirm networks evolve reflecting a firm's local decisions to mitigate adverse effects from neighbor firms through interfirm linkage, while enjoying positive effects from them. As a result, link renewal tends to have a positive impact on the growth rates of firms. We also investigate the role of networks in aggregate fluctuations.

Personal data breaches from organisations, enabling mass identity fraud, constitute an \emph{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 \emph{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., Comment: 16 pages, 3 sets of figures, and 4 tables

We provide, and perform a risk theoretic statistical analysis of, a dataset that is 75 percent larger than the previous best dataset on nuclear incidents and accidents, comparing three measures of severity: INES (International Nuclear Event Scale), radiation released, and damage dollar losses. The annual rate of nuclear accidents, with size above 20 Million US$, per plant, decreased from the 1950s until dropping significantly after Chernobyl (April, 1986). The rate is now roughly stable at 0.002 to 0.003, i.e., around 1 event per year across the current fleet. The distribution of damage values changed after Three Mile Island (TMI; March, 1979), where moderate damages were suppressed but the tail became very heavy, being described by a Pareto distribution with tail index 0.55. Further, there is a runaway disaster regime, associated with the "dragon-king" phenomenon, amplifying the risk of extreme damage. In fact, the damage of the largest event (Fukushima; March, 2011) is equal to 60 percent of the total damage of all 174 accidents in our database since 1946. In dollar losses we compute a 50% chance that (i) a Fukushima event (or larger) occurs in the next 50 years, (ii) a Chernobyl event (or larger) occurs in the next 27 years and (iii) a TMI event (or larger) occurs in the next 10 years. Finally, we find that the INES scale is inconsistent. To be consistent with damage, the Fukushima disaster would need to have an INES level of 11, rather than the maximum of 7.

We present the symmetric thermal optimal path (TOPS) method to determine the time-dependent lead-lag relationship between two stochastic time series. This novel version of the previously introduced TOP method alleviates some inconsistencies by imposing that the lead-lag relationship should be invariant with respect to a time reversal of the time series after a change of sign. This means that, if `$X$ comes before $Y$', this transforms into `$Y$ comes before $X$' under a time reversal. We show that previously proposed bootstrap test lacks power and leads too often to a lack of rejection of the null that there is no lead-lag correlation when it is present. We introduce instead two novel tests. The first the free energy p-value $\rho$ criterion quantifies the probability that a given lead-lag structure could be obtained from random time series with similar characteristics except for the lead-lag information. The second self-consistent test embodies the idea that, for the lead-lag path to be significant, synchronizing the two time series using the time varying lead-lag path should lead to a statistically significant correlation. We perform intensive synthetic tests to demonstrate their performance and limitations. Finally, we apply the TOPS method with the two new tests to the time dependent lead-lag structures of house price and monetary policy of the United Kingdom (UK) and United States (US) from 1991 to 2011. The TOPS approach stresses the importance of accounting for change of regimes, so that similar pieces of information or policies may have drastically different impacts and developments, conditional on the economic, financial and geopolitical conditions. This study reinforces the view that the hypothesis of statistical stationarity is highly questionable.

We introduce the Hawkes process with renewal immigration and make its statistical estimation possible with two Expectation Maximization (EM) algorithms. The standard Hawkes process introduces immigrant points via a Poisson process, and each immigrant has a subsequent cluster of associated offspring of multiple generations. We generalize the immigration to come from a Renewal process; introducing dependence between neighbouring clusters, and allowing for over/under dispersion in cluster locations. This complicates evaluation of the likelihood since one needs to know which subset of the observed points are immigrants. Two EM algorithms enable estimation here: The first is an extension of an existing algorithm that treats the entire branching structure - which points are immigrants, and which point is the parent of each offspring - as missing data. The second considers only if a point is an immigrant or not as missing data and can be implemented with linear time complexity. Both algorithms are found to be consistent in simulation studies. Further, we show that misspecifying the immigration process introduces signficant bias into model estimation-- especially the branching ratio, which quantifies the strength of self excitation. Thus, this extended model provides a valuable alternative model in practice.

We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which investors are arguably the most concerned with. Similarly to the distribution of returns, we find that the distributions of epsilon-drawdowns and epsilon-drawups exhibit power law tails, albeit with exponents significantly larger than those for the return distributions. This paradoxical result can be attributed to (i) the existence of significant transient dependence between returns and (ii) the presence of large outliers (dragon-kings) characterizing the extreme tail of the drawdown/drawup distributions deviating from the power law. The study of the tail dependence between the sizes, speeds and durations of drawdown/drawup indicates a clear relationship between size and speed but none between size and duration. This implies that the most extreme drawdown/drawup tend to occur fast and are dominated by a few very large returns. We discuss both the endogenous and exogenous origins of these extreme events.

We present a new Monte-Carlo methodology to forecast the crude oil production of Norway and the U.K. based on a two-step process, (i) the nonlinear extrapolation of the current/past performances of individual oil fields and (ii) a stochastic model of the frequency of future oil field discoveries. Compared with the standard methodology that tends to underestimate remaining oil reserves, our method gives a better description of future oil production, as validated by our back-tests starting in 2008. Specifically, we predict remaining reserves extractable until 2030 to be 188 +/- 10 million barrels for Norway and 98 +/- 10 million barrels for the UK, which are respectively 45% and 66% above the predictions using the standard methodology.

We present a mechanism design, coupling an online collaboration software and a prediction market, which allows tracking down the very roots of individual incentives, actions and how these behaviors influence collective intelligence in terms of knowledge production as a public good. We show that the incentive mechanism efficiently engages users without further governance structure, and doesn't crowd out intrinsic motivation. Furthermore, it enables a powerful and robust creative destruction process, which helps quickly filter out irrelevant knowledge. While still at an early stage, this mechanism design can not only bring insights for knowledge production organization design, but also has the potential to illuminate the fundamental mechanisms underlying the emergence of collective intelligence.

In a variety of open source software projects, we document a superlinear growth of production ($R \sim c^\beta$) as a function of the number of active developers $c$, with $\beta \simeq 4/3$ with large dispersions. For a typical project in this class, doubling of the group size multiplies typically the output by a factor $2^\beta=2.5$, 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, {\it interaction-based} and {\it 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, in the sense of a subtle balance between order and disorder. 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., Comment: 29 pages, 8 figures

We define a financial bubble as a period of unsustainable growth, when the price of an asset increases ever more quickly, in a series of accelerating phases of corrections and rebounds. More technically, during a bubble phase, the price follows a faster-than-exponential power law growth process, often accompanied by log-periodic oscillations. This dynamic ends abruptly in a change of regime that may be a crash or a substantial correction. Because they leave such specific traces, bubbles may be recognised in advance, that is, before they burst. In this paper, we will explain the mechanism behind financial bubbles in an intuitive way. We will show how the log-periodic power law emerges spontaneously from the complex system that financial markets are, as a consequence of feedback mechanisms, hierarchical structure and specific trading dynamics and investment styles. We argue that the risk of a major correction, or even a crash, becomes substantial when a bubble develops towards maturity, and that it is therefore very important to find evidence of bubbles and to follow their development from as early a stage as possible. The tools that are explained in this paper actually serve that purpose. They are at the core of the Financial Crisis Observatory at the ETH Zurich, where tens of thousands of assets are monitored on a daily basis. This allow us to have a continuous overview of emerging bubbles in the global financial markets. The companion report available as part of the Notenstein white paper series (2014) with the title ``Financial bubbles: mechanism, diagnostic and state of the World (Feb. 2014)'' presents a practical application of the methodology outlines in this article and describes our view of the status concerning positive and negative bubbles in the financial markets, as of the end of January 2014., Comment: 24 pages, 10 figures. Notenstein white paper series (2014)

We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase transitions in complex systems., Comment: 5 pages, 4 figures (main text) + 14 figures and 8 figures (supplementary materials). Accepted for publication by Physical Review Letters

Humans are fundamentally social. They have progressively dominated their environment by the strength and creativity provided by and within their grouping. It is well recognised that human groups are highly structured, and the anthropological literature has loosely classified them according to their size and function, such as support cliques, sympathy groups, bands, cognitive groups, tribes, linguistic groups and so on. Recently, combining data on human grouping patterns in a comprehensive and systematic study, Zhou et al. identified a quantitative discrete hierarchy of group sizes with a preferred scaling ratio close to $3$, which was later confirmed for hunter-gatherer groups and for other mammalian societies. Using high precision large scale Internet-based social network data, we extend these early findings on a very large data set. We analyse the organisational structure of a complete, multi-relational, large social multiplex network of a human society consisting of about 400,000 odd players of a massive multiplayer online game for which we know all about the group memberships of every player. Remarkably, the online players exhibit the same type of structured hierarchical layers as the societies studied by anthropologists, where each of these layers is three to four times the size of the lower layer. Our findings suggest that the hierarchical organisation of human society is deeply nested in human psychology., Comment: 9 pages, 3 figures