arXiv subjects

Didier Sornette

Publications and source records attributed to Didier Sornette.

At least 91 records · Page 5Linked to original sources

arXiv2019

A Theory of Discrete Hierarchies as Optimal Cost-Adjusted Productivity Organisations

Hierarchical structures are ubiquitous in human and animal societies, but a fundamental understanding of their raison d'être has been lacking. Here, we present a general theory in which hierarchies are obtained as the optimal design that strikes a balance between the benefits of group productivity and the costs of communication for coordination. By maximising a generic representation of the output of a hierarchical organization with respect to its design, the optimal configuration of group sizes at different levels can be determined. With very few ingredients, a wide variety of hierarchically ordered complex organisational structures can be derived. Furthermore, our results rationalise the ubiquitous occurrence of triadic hierarchies, i.e., of the universal preferred scaling ratio between $3$ and $4$ found in many human and animal hierarchies, which should occur according to our theory when production is rather evenly contributed by all levels. We also provide a systematic approach for optimising team organisation, helping to address the question of the optimal `span of control'. The significantly larger number $\sim 3-20$ of subordinates a supervisor typically manages is rationalised to occur in organisations where the production is essentially done at the bottom level and in which the higher levels are only present to optimise coordination and control.

physics.soc-ph↗

arXiv2019

The fair reward problem: the illusion of success and how to solve it

Humanity has been fascinated by the pursuit of fortune since time immemorial, and many successful outcomes benefit from strokes of luck. But success is subject to complexity, uncertainty, and change - and at times becoming increasingly unequally distributed. This leads to tension and confusion over to what extent people actually get what they deserve (i.e., fairness/meritocracy). Moreover, in many fields, humans are over-confident and pervasively confuse luck for skill (I win, it's skill; I lose, it's bad luck). In some fields, there is too much risk taking; in others, not enough. Where success derives in large part from luck - and especially where bailouts skew the incentives (heads, I win; tails, you lose) - it follows that luck is rewarded too much. This incentivizes a culture of gambling, while downplaying the importance of productive effort. And, short term success is often rewarded, irrespective, and potentially at the detriment, of the long-term system fitness. However, much success is truly meritocratic, and the problem is to discern and reward based on merit. We call this the fair reward problem. To address this, we propose three different measures to assess merit: (i) raw outcome; (ii) risk adjusted outcome, and (iii) prospective. We emphasize the need, in many cases, for the deductive prospective approach, which considers the potential of a system to adapt and mutate in novel futures. This is formalized within an evolutionary system, comprised of five processes, inter alia handling the exploration-exploitation trade-off. Several human endeavors - including finance, politics, and science -are analyzed through these lenses, and concrete solutions are proposed to support a prosperous and meritocratic society.

econ.GN↗

arXiv2019

Aristotle vs. Ringelmann: On Superlinear Production in Open Source Software

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.

cs.SE↗

arXiv2019

Forecasting the full distribution of earthquake numbers is fair, robust and better

Forecasting the full distribution of the number of earthquakes is revealed to be inherently superior to forecasting their mean. Forecasting the full distribution of earthquake numbers is also shown to yield robust projections in the presence of "surprise" large earthquakes, which in the past have strongly deteriorated the scores of existing models. We show this with pseudo-prospective experiments on synthetic as well as real data from the Advanced National Seismic System (ANSS) database for California, with earthquakes with magnitude larger than 2.95 that occurred between the period 1971-2016. Our results call in question the testing methodology of the Collaboratory for the study of earthquake predictability (CSEP), which amounts to assuming a Poisson distribution of earthquake numbers, which is known to be a poor representation of the heavy-tailed distribution of earthquake numbers. Using a spatially varying ETAS model, we demonstrate a remarkable stability of the forecasting performance, when using the full distribution of earthquake numbers for the forecasts, even in the presence of large earthquakes such as Mw 7.1 Hector Mine, Mw 7.2 El Mayor-Cucapah, Mw 6.6 Sam Simeon earthquakes, or in the presence of intense swarm activity in Northwest Nevada in 2014. While our results have been derived for ETAS type models, we propose that all earthquake forecasting models of any type should embrace the full distribution of earthquake numbers, such that their true forecasting potential is revealed.

physics.geo-ph↗

arXiv2019

Forecasting the rates of future aftershocks of all generations is essential to develop better earthquake forecast models

Currently, one of the best performing and most popular earthquake forecasting models rely on the working hypothesis that: "locations of past background earthquakes reveal the probable location of future seismicity". As an alternative, we present a class of smoothed seismicity models (SSMs) based on the principles of the Epidemic Type Aftershock Sequence (ETAS) model, which forecast the location, time and magnitude of all future earthquakes using the estimates of the background seismicity rate and the rates of future aftershocks of all generations. Using the Californian earthquake catalog, we formulate six controlled pseudo-prospective experiments with different combination of three target magnitude thresholds: 2.95, 3.95 or 4.95 and two forecasting time horizons: 1 or 5 year. In these experiments, we compare the performance of:(1) ETAS model with spatially homogenous parameters or GETAS (2) ETAS model with spatially variable parameters or SVETAS (3) three declustering based SSMs (4) a simple SSM based on undeclustered data and (5) a model based on strain rate data, in forecasting the location and magnitude of all (undeclustered) target earthquakes during many testing periods. In all conducted experiments, the SVETAS model comes out with consistent superiority compared to all the competing models. Consistently better performance of SVETAS model with respect to declustering based SSMs highlights the importance of forecasting the future aftershocks of all generations for developing better earthquake forecasting models. Among the two ETAS models themselves, accounting for the optimal spatial variation of the parameters leads to strong and statistically significant improvements in forecasting performance.

physics.geo-ph↗

arXiv2019

Magnitude Of Earthquakes Controls The Size Distribution Of Their Triggered Events

The driving concept behind one of the most successful statistical forecasting models, the ETAS model, has been that the seismicity is driven by spontaneously occurring background earthquakes that cascade into multitudes of triggered earthquakes. In nearly all generalizations of the ETAS model, the magnitudes of the background and the triggered earthquakes are assumed to follow Gutenberg-Richter law with the same exponent (\b{eta}-value). Furthermore, the magnitudes of the triggered earthquakes are always assumed to be independent of the magnitude of the triggering earthquake. Using an EM algorithm applied to the Californian earthquake catalogue, we show that the distribution of earthquake magnitudes exhibits three distinct \b{eta}-values: \b{eta}_b for background events; \b{eta}_a-δ and \b{eta}_a+δ, respectively, for triggered events below and above the magnitude of the triggering earthquake; the two last values express a correlation between the magnitudes of triggered events with that of the triggering earthquake, a feature so far absent in all proposed operational generalizations of the ETAS model. The ETAS model incorporating this kinked magnitude distribution provides by far the best description of seismic catalogs and could thus have the best forecasting potential. We speculate that the kinked magnitude distribution may result from the system tending to restore the symmetry of the regional displacement gradient tensor that has been broken by the initiating event. The general emerging concept could be that while the background events occur primarily to accommodate the symmetric stress tensor at the boundaries of the system, the triggered earthquakes are quasi-Goldstone fluctuations of a self-organized critical deformation state.

physics.geo-ph↗

arXiv2018

Pattern phase diagram of spiking neurons on spatial networks

We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over networks with varying edge density and spatial embedded ness. For intermediate edge density and sufficiently strong spatial embeddedness, we observe a novel spatiotemporal pattern in the field of oscillator phases, visually resembling the surface of a frothing liquid. Increasing the edge density results in critical dynamics, with the distribution of neuronal avalanche sizes following a power law with exponent one. Further increase of the edge density results in metastable behaviour between pattern formation and synchronisation, before transitioning the system entirely into synchrony.

q-bio.NC↗

arXiv2018

The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform

This work revisits a class of biomimetically inspired log-periodic waveforms first introduced by R.A. Altes in the 1970s for generalized target description. It was later observed that there is a close connection between such sonar techniques and wavelet decomposition for multiresolution analysis. Motivated by this, we formalize the original Altes waveforms as a family of hyperbolic chirplets suitable for the detection of accelerating time-series oscillations. The formalism results in a remarkably flexible set of wavelets with desirable properties of admissibility, regularity, vanishing moments, and time-frequency localization. These "Altes wavelets" also facilitate efficient implementation of the scale invariant hyperbolic chirplet transform (HCT). From a practical perspective, log-periodic oscillations with an acceleration towards criticality can serve as indicators of an incipient bifurcation. Such signals abound in nature, often as precursors to phase transitions in the non-linear dynamics of complex systems. For example, the authors' interest lies in automatic detection of the well documented phenomenon of log-periodic price dynamics during financial bubbles and preceding market crashes. However, the methodology presented here is more widely applicable in such diverse domains as prediction of critical failures in mechanical systems, and fault detection in electrical networks. Examples beyond failure diagnostics include animal species identification via call recordings, commercial \& military radar, and there are many more. A synthetic application is presented in this report for illustrative purposes.

eess.SP↗

arXiv2018

The ARMA Point Process and its Estimation

We introduce the ARMA (autoregressive-moving-average) point process, which is a Hawkes process driven by a Neyman-Scott process with Poisson immigration. It contains both the Hawkes and Neyman-Scott process as special cases and naturally combines self-exciting and shot-noise cluster mechanisms, useful in a variety of applications. The name ARMA is used because the ARMA point process is an appropriate analogue of the ARMA time series model for integer-valued series. As such, the ARMA point process framework accommodates a flexible family of models sharing methodological and mathematical similarities with ARMA time series. We derive an estimation procedure for ARMA point processes, as well as the integer ARMA models, based on an MCEM (Monte Carlo Expectation Maximization) algorithm. This powerful framework for estimation accommodates trends in immigration, multiple parametric specifications of excitement functions, as well as cases where marks and immigrants are not observed.

math.ST↗

arXiv2018

Classification of cryptocurrency coins and tokens by the dynamics of their market capitalisations

We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simple proportional growth with birth & death model previously employed to describe the size distribution of firms, cities, webpages, etc. We empirically validate the model and its main predictions, in terms of proportional growth (Gibrat's law) of the coins and tokens. Estimating the main parameters of the model, the theoretical predictions for the power-law exponents of coin and token distributions are in remarkable agreement with the empirical estimations, given the simplicity of the model. Our results clearly characterize coins as being "entrenched incumbents" and tokens as an "explosive immature ecosystem", largely due to massive and exuberant Initial Coin Offering activity in the token space. The theory predicts that the exponent for tokens should converge to 1 in the future, reflecting a more reasonable rate of new entrants associated with genuine technological innovations.

physics.soc-ph↗

arXiv2018

Multifractal analysis of financial markets

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

q-fin.ST↗

arXiv2018

Time-dependent lead-lag relationship between the onshore and offshore Renminbi exchange rates

We employ the thermal optimal path method to explore both the long-term and short-term interaction patterns between the onshore CNY and offshore CNH exchange rates (2012-2015). For the daily data, the CNY and CNH exchange rates show a weak alternate lead-lag structure in most of the time periods. When CNY and CNH display a large disparity, the lead-lag relationship is uncertain and depends on the prevailing market factors. The minute-scale interaction pattern between the CNY and CNH exchange rates change over time according to different market situations. We find that US dollar appreciation is associated with a lead-lag relationship running from offshore to onshore, while a (contrarian) Renminbi appreciation is associated with a lead-lag relationship running from onshore to offshore. These results are robust with respect to different sub-sample analyses and variations of the key smoothing parameter of the TOP method.

q-fin.ST↗

arXiv2018

Are Bitcoin Bubbles Predictable? Combining a Generalized Metcalfe's Law and the LPPLS Model

We develop a strong diagnostic for bubbles and crashes in bitcoin, by analyzing the coincidence (and its absence) of fundamental and technical indicators. Using a generalized Metcalfe's law based on network properties, a fundamental value is quantified and shown to be heavily exceeded, on at least four occasions, by bubbles that grow and burst. In these bubbles, we detect a universal super-exponential unsustainable growth. We model this universal pattern with the Log-Periodic Power Law Singularity (LPPLS) model, which parsimoniously captures diverse positive feedback phenomena, such as herding and imitation. The LPPLS model is shown to provide an ex-ante warning of market instabilities, quantifying a high crash hazard and probabilistic bracket of the crash time consistent with the actual corrections; although, as always, the precise time and trigger (which straw breaks the camel's back) being exogenous and unpredictable. Looking forward, our analysis identifies a substantial but not unprecedented overvaluation in the price of bitcoin, suggesting many months of volatile sideways bitcoin prices ahead (from the time of writing, March 2018).

econ.EM↗

arXiv2018

Symmetric thermal optimal path and time-dependent lead-lag relationship: Novel statistical tests and application to UK and US real-estate and monetary policies

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 $ρ$ 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.

q-fin.ST↗

arXiv2018

Is there a housing bubble in China

There is a growing concern in recent years over the potential formation of bubbles in the Chinese real estate market. This paper aims to conduct a series of bubble diagnostic analysis over nine representative Chinese cities from two aspects. First, we investigate whether the prices had been significantly deviating from economic fundamentals by applying a standard Engle-Granger cointegration test. Second, we apply the Log-Periodic-Power-Law-Singularity (LPPLS) model to detect whether there is any evidence of unsustainable, self-reinforcing speculative behaviours amongst the price series. We propose that, given the heterogeneity that exists amongst cities with different types of bubble signatures, it is vital to conduct bubble diagnostic tests and implement relevant policies toward specific bubble characteristics, rather than enforcing one-that-fits-for-all type policy that does not take into account such heterogeneity.

q-fin.RM↗

arXiv2017

Controlling percolation with limited resources

Connectivity - or the lack thereof - is crucial for the function of many man-made systems, from financial and economic networks over epidemic spreading in social networks to technical infrastructure. Often, connections are deliberately established or removed to induce, maintain, or destroy global connectivity. Thus, there has been a great interest in understanding how to control percolation, the transition to large-scale connectivity. Previous work, however, studied control strategies assuming unlimited resources. Here, we depart from this unrealistic assumption and consider the effect of limited resources on the effectiveness of control. We show that, even for scarce resources, percolation can be controlled with an efficient intervention strategy. We derive this strategy and study its implications, revealing a discontinuous transition as an unintended side-effect of optimal control.

cond-mat.dis-nn↗

arXiv2017

Earthquake precursors in the light of peroxy defects theory: critical review of systematic observations

The starting point of the present review is to acknowledge that there are innumerable reports of non-seismic types of earthquake precursory phenomena that are intermittent and seem not to occur systematically, while associated reports are not widely accepted by the geoscience community at large because no one could explain their origins. We review a unifying theory for a solid-state mechanism, based on decades of research bridging semi-conductor physics, chemistry and rock physics. A synthesis has emerged that all pre-earthquake phenomena could trace back to one fundamental physical process: the activation of electronic charges (electrons and positive holes) in rocks subjected to ever-increasing tectonic stresses prior to any major seismic activity, via the rupture of peroxy bonds. In the second part of the review, we critically examine satellite and ground station data, recorded before past large earthquakes, as they have been claimed to provide evidence that precursory signals tend to become measurable days, sometimes weeks before the disasters. We review some of the various phenomena that can be directly predicted by the peroxy defect theory , namely, radon gas emanations, corona discharges, thermal infrared emissions, air ionization, ion and electron content in the ionosphere, and electro-magnetic anomalies. Our analysis demonstrates the need for further systematic investigations, in particular with strong continuous statistical testing of the relevance and confidence of the precursors. Only then, the scientific community will be able to assess and improve the performance of earthquake forecasts.

physics.geo-ph↗

arXiv2017

GDP growth rates as confined Lévy flights

A new model that combines economic growth rate fluctuations at the microscopic and macroscopic level is presented. At the microscopic level, firms are growing at different rates while also being exposed to idiosyncratic shocks at the firm and sector level. We describe such fluctuations as independent Lévy-stable fluctuations, varying over multiple orders of magnitude. These fluctuations are aggregated and measured at the macroscopic level in averaged economic output quantities such as GDP. A fundamental question is thereby to what extend individual firm size fluctuations can have a noticeable impact on the overall economy. We argue that this question can be answered by considering the Lévy fluctuations as embedded in a steep confining potential well, ensuring nonlinear mean-reversal behavior, without having to rely on microscopic details of the system. The steepness of the potential well directly controls the extend towards which idiosyncratic shocks to firms and sectors are damped at the level of the economy. Additionally, the theory naturally accounts for business cycles, represented in terms of a bimodal economic output distribution, and thus connects two so far unrelated fields in economics. By analyzing 200 years of US GDP growth rates, we find that the model is in good agreement with the data.

q-fin.GN↗