The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as ...diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of materials. In this book, Didier Sornette boldly applies his varied experience in these areas to propose a simple, powerful, and general theory of how, why, and when stock markets crash. Most attempts to explain market failures seek to pinpoint triggering mechanisms that occur hours, days, or weeks before the collapse. Sornette proposes a radically different view: the underlying cause can be sought months and even years before the abrupt, catastrophic event in the build-up of cooperative speculation, which often translates into an accelerating rise of the market price, otherwise known as a "bubble." Anchoring his sophisticated, step-by-step analysis in leading-edge physical and statistical modeling techniques, he unearths remarkable insights and some predictions—among them, that the "end of the growth era" will occur around 2050.
We study the relaxation response of a social system after endogenous and exogenous bursts of activity using the time series of daily views for nearly 5 million videos on YouTube. We find that most ...activity can be described accurately as a Poisson process. However, we also find hundreds of thousands of examples in which a burst of activity is followed by an ubiquitous power-law relaxation governing the timing of views. We find that these relaxation exponents cluster into three distinct classes and allow for the classification of collective human dynamics. This is consistent with an epidemic model on a social network containing two ingredients: a power-law distribution of waiting times between cause and action and an epidemic cascade of actions becoming the cause of future actions. This model is a conceptual extension of the fluctuation-dissipation theorem to social systems Ruelle, D (2004) Phys Today 57:48-53 and Roehner BM, et al., (2004) Int J Mod Phys C 15:809-834, and provides a unique framework for the investigation of timing in complex systems.
We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS) structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we ...introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially) the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the "S&P 500 1987" bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs.
The origin(s) of the ubiquity of probability distribution functions with power law tails is still a matter of fascination and investigation in many scientific fields from linguistic, social, ...economic, computer sciences to essentially all natural sciences. In parallel, self-excited dynamics is a prevalent characteristic of many systems, from the physics of shot noise and intermittent processes, to seismicity, financial and social systems. Motivated by activation processes of the Arrhenius form, we bring the two threads together by introducing a general class of nonlinear self-excited point processes with fast-accelerating intensities as a function of "tension." Solving the corresponding master equations, we find that a wide class of such nonlinear Hawkes processes have the probability distribution functions of their intensities described by a power law on the condition that (i) the intensity is a fast-accelerating function of tension, (ii) the distribution of marks is two sided with nonpositive mean, and (iii) it has fast-decaying tails. In particular, Zipf's scaling is obtained in the limit where the average mark is vanishing. This unearths a novel mechanism for power laws including Zipf's law, providing a new understanding of their ubiquity.
The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological, and economic systems. By expressing the ...probability for the next event per unit time (called "intensity"), say of an earthquake, as a sum over all past events of (possibly) long-memory kernels, the Hawkes model is non-Markovian. By mapping the Hawkes model onto stochastic partial differential equations that are Markovian, we develop a field theoretical approach in terms of probability density functionals. Solving the steady-state equations, we predict a power law scaling of the probability density function of the intensities close to the critical point n = 1 of the Hawkes process, with a nonuniversal exponent, function of the background intensity ν0 of the Hawkes intensity, the average timescale of the memory kernel and the branching ratio n. Our theoretical predictions are confirmed by numerical simulations.
We propose a stochastic dynamical model to simulate slope secondary and tertiary creep phenomena. The slope secondary creep is represented by the Kesten process defined as a stochastic affine ...auto‐regressive process involving both multiplicative and additive random variables. The Kesten process can realistically capture the co‐existence of a background deformation and intermittent displacement bursts, which are together well characterized by an inverse gamma velocity distribution. The slope tertiary creep is modeled by a nonlinear stochastic dynamical equation embodying a nonlinear feedback mechanism and a nonlinear random effect, which can mimic the development of slow or catastrophic landslides. For catastrophic landslides, the probability density function of slope velocities tends to deviate from the inverse gamma distribution by populating the “dragon‐king” regime, although sometimes they may grow undetectably in the “black‐swan” regime. Our model provides a quantitative framework to understand, simulate, and interpret complex landslide displacement time series.
Plain Language Summary
Landslides that threaten life and property often exhibit complex temporal evolutions. Some landslides may creep slowly over a long period of time, while others can accelerate rapidly or even collapse catastrophically. It remains difficult to understand and/or predict their behavior. In this work, we develop a novel stochastic dynamical formulation that can realistically reproduce the displacement time series of landslides in natural systems. It can simulate the progressive deformation of a slowly creeping slope as well as mimic its rapid acceleration with/without catastrophic failure. The ever‐present fluctuations in natural systems can also be captured in this stochastic modeling framework. By conducting synthetic numerical simulations capable of resembling many of the observed essential features of real landslides, we develop quantitative insights into the mechanisms that drive their complex temporal evolutions. Recommendations for landslide hazard forecasting and mitigation are further provided.
Key Points
A slope approaching failure tends to exhibit a phase transition from secondary to tertiary creep
The stochastic Kesten process reproduces the phenomenology of intermittent bursts and inverse gamma velocity distribution of secondary creep
A nonlinear stochastic dynamical process captures the tertiary creep of a slope evolving into a slow or catastrophic landslide
In the first quarter of 2020, the COVID-19 pandemic brought the world to a state of paralysis. During this period, humanity saw by far the largest organized travel restrictions and unprecedented ...efforts and global coordination to contain the spread of the SARS-CoV-2 virus. Using large scale human mobility and fine grained epidemic incidence data, we develop a framework to understand and quantify the effectiveness of the interventions implemented by various countries to control epidemic growth. Our analysis reveals the importance of timing and implementation of strategic policy in controlling the epidemic. We also unearth significant spatial diffusion of the epidemic before and during the lockdown measures in several countries, casting doubt on the effectiveness or on the implementation quality of the proposed Governmental policies.
The arguably most important paradox of financial economics-the excess volatility puzzle-first identified by Robert Shiller in 1981 states that asset prices fluctuate much more than information about ...their fundamental value. We show that this phenomenon is associated with an intrinsic propensity for financial markets to evolve towards instabilities. These properties, exemplified for two major financial markets, the foreign exchange and equity futures markets, can be expected to be generic in other complex systems where excess fluctuations result from the interplay between exogenous driving and endogenous feedback. Using an exact mapping of the key property (volatility/variance) of the price diffusion process onto that of a point process (arrival intensity of price changes), together with a self-excited epidemic model, we introduce a novel decomposition of the volatility of price fluctuations into an exogenous (i.e. efficient) component and an endogenous (i.e. inefficient) excess component. The endogenous excess volatility is found to be substantial, largely stable at longer time scales and thus provides a plausible explanation for the excess volatility puzzle. Our theory rationalises the remarkable fact that small stochastic exogenous fluctuations at the micro-scale of milliseconds to seconds are renormalised into long-term excess volatility with an amplification factor of around 5 for equity futures and 2 for exchange rates, in line with models including economic fundamentals explicitly.
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.
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