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A systematic quantitative investigation into whether the mechanisms of large earthquakes are unique could significantly deepen our understanding of fault rupture and seismicity patterns. This research holds the potential to advance our ability to predict large earthquakes and enhance the effectiveness of disaster prevention and mitigation strategies. In 2009, one of us introduced the dragon-king theory, offering a quantitative framework for identifying and testing extreme outliers-referred to as dragon-king events-that are endogenously generated. This theory provides valuable tools for explaining, predicting, and managing the risks associated with these rare but highly impactful events. The present paper discusses the feasibility of applying this theory to seismology, proposing that dragon-king earthquake events can be identified as outliers to the Gutenberg-Richter law. It also examines several seismological mechanisms that may contribute to the occurrence of these extraordinary events. Although applying the dragon-king theory to seismology presents practical challenges, it offers the potential to significantly enrich statistical seismology. By reexamining the classification of earthquake rupture types through a statistical testing lens and integrating these insights with underlying physical mechanisms, this approach can greatly enhance the analytical tools and depth of research in the field of statistical seismology., Comment: 21 pages, 2 figures

Emotions are essential for guiding human behavior, particularly in social interactions. In modern societies, a growing share of human interactions are taking place online which has been shown to amplify and distort the expression and perception of emotions. However, the entanglement across different emotions is not fully understood. We use a multivariate Hawkes self-excited point process to model and calibrate the temporal expressions of six basic emotions in YouTube live chats. This allows us to understand interdependencies among emotions, but also to disentangle the influence from the video content and social interactions with peers. Positive emotions are found to be more contagious, while negative emotions tend to leave a longer-lasting impression on users' memories. Furthermore, we quantify the endogeneity of online emotion dynamics and find that peer interactions drive user emotional expressions 3-5 times more than passive content consumption. This underscores the powerful incentives of social interactions and the potential risk of emotional manipulation through the use of modern chatbots.

To ensure optimal survival of the neonate, the biological timing of parturition must be tightly controlled. Medical studies show that a variety of endocrine systems play the role of a control system, establishing a dynamic balance between the forces that cause uterine quiescence during pregnancy and the forces that produce coordinated uterine contractility at parturition. These control mechanism, and the factors that affect their performance, are still poorly understood. To help fill this gap, we propose a model of the pregnant uterus as a network of FitzHugh-Nagumo oscillators, with each cell symbolizing the electrical activity of a myocyte. The model is augmented with sparse adaptive control mechanisms representing the regulating endocrine functions. The control system is characterized by the fraction of controlled sites, and strength of control. We quantitatively find the conditions for which the control system exhibit a balance between robustness (resilience against perturbations) and flexibility (ability to switch function with minimal cost) crucial for optimal neonatal survival. Specifically, we show that Braxton-Hicks and Alvarez contractions, which are observed sporadic contractions of the uterine muscle, serve as a safety valve against over-controlling, strategically suppressed yet retained to optimize the control system's efficiency. Preterm birth is suggested to be understood as a mis-identification of the control boundaries. These insights contribute to advancing our understanding of maternal-fetal health.

The Log-Periodic Power Law Singularity (LPPLS) model offers a general framework for capturing dynamics and predicting transition points in diverse natural and social systems. In this work, we present two calibration techniques for the LPPLS model using deep learning. First, we introduce the Mono-LPPLS-NN (M-LNN) model; for any given empirical time series, a unique M-LNN model is trained and shown to outperform state-of-the-art techniques in estimating the nonlinear parameters $(t_c, m, \omega)$ of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Second, we extend the M-LNN model to a more general model architecture, the Poly-LPPLS-NN (P-LNN), which is able to quickly estimate the nonlinear parameters of the LPPLS model for any given time-series of a fixed length, including previously unseen time-series during training. The Poly class of models train on many synthetic LPPLS time-series augmented with various noise structures in a supervised manner. Given enough training examples, the P-LNN models also outperform state-of-the-art techniques for estimating the parameters of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Additionally, this class of models is shown to substantially reduce the time to obtain parameter estimates. Finally, we present applications to the diagnostic and prediction of two financial bubble peaks (followed by their crash) and of a famous rockslide. These contributions provide a bridge between deep learning and the study of the prediction of transition times in complex time series., Comment: 10 pages, 6 figures

The Epidemic-Type Aftershock Sequences (ETAS) model and its variants effectively capture the space-time clustering of seismicity, setting the standard for earthquake forecasting. Accurate unbiased ETAS calibration is thus crucial. But we identify three sources of bias, (i) boundary effects, (ii) finite-size effects, and (iii) censorship, which are often overlooked or misinterpreted, causing errors in seismic analysis and predictions. By employing an ETAS model variant with variable spatial background rates, we propose a method to correct for these biases, focusing on the branching ratio n, a key indicator of earthquake triggering potential. Our approach quantifies the variation in the apparent branching ratio (napp) with increased cut-off magnitude (Mco) above the optimal cut-off (Mcobest). The napp(Mco) function yields insights superior to traditional point estimates. We validate our method using synthetic earthquake catalogs, accurately recovering the true branching ratio (ntrue) after correcting biases with napp(Mco). Additionally, our method introduces a refined estimation of the minimum triggering magnitude (m0), a crucial parameter in the ETAS model. Applying our framework to the earthquake catalogs of California, New Zealand, and the China Seismic Experimental Site (CSES) in Sichuan and Yunnan provinces, we find that seismicity hovers away from the critical point, nc = 1, remaining distinctly subcritical, however with values tending to be larger than recent reports that do not consider the above biases. It is interesting that, m0 is found around 4 for California, 3 for New Zealand and 2 for CSES, suggesting that many small triggered earthquakes may not be fertile. Understanding seismicity's critical state significantly enhances our comprehension of seismic patterns, aftershock predictability, and informs earthquake risk mitigation and management strategies., Comment: 36 pages, 7 figures, 5 tables

Landslides exhibit intermittent gravity-driven downslope movements developing over days to years before a possible major collapse, commonly boosted by external events like precipitations and earthquakes. The reasons behind these episodic movements and how they relate to the final instability remain poorly understood. Here, we develop a novel 'endo-exo' theory to quantitatively diagnose landslide dynamics, capturing the interplay between exogenous stressors such as rainfall and endogenous damage/healing processes. We predict four distinct types of episodic landslide dynamics (endogenous/exogenous-subcritical/critical), characterized by power law relaxations with different exponents, all related to a single parameter $\vartheta$. These predictions are tested on the dataset of the Preonzo landslide, which exhibited multi-year episodic movements prior to a catastrophic collapse. All its episodic activities can be accounted for within this classification with $\vartheta \approx 0.45\pm0.1$, providing strong support for our parsimonious theory. We find that the final collapse of this landslide is clearly preceded over 1-2 months by an increased frequency of medium/large velocities, signaling the transition into a catastrophic regime with amplifying positive feedbacks., Comment: 5 figures

We develop a statistical thermodynamic approach for understanding earthquake nucleation on homogeneous faults, explaining the occurrence of both self-arresting and run-away unstable ruptures (subshear and supershear events) previously observed in numerical simulations. Our theory identifies the conditions under which self-arresting earthquakes occur, based on critical sliding distance and dynamical stress drop. We also derive the Gutenberg-Richter distribution for these earthquakes, linking the fractal nature of faulting with the nucleation physics through the critical size's dependence on dynamical stress drop. Furthermore, we connect our findings to the dragon-king theory, which suggests that the largest earthquakes differ significantly in physical and statistical properties from smaller ones, offering new insights for earthquake prediction and risk assessment., Comment: 5 pages, 1 figure

We study the temporal evolution of the holding-time distribution of bitcoins and find that the average distribution of holding-time is a heavy-tailed power law extending from one day to over at least $200$ weeks with an exponent approximately equal to $0.9$, indicating very long memory effects. We also report significant sample-to-sample variations of the distribution of holding times, which can be best characterized as multiscaling, with power-law exponents varying between $0.3$ and $2.5$ depending on bitcoin price regimes. We document significant differences between the distributions of book-to-market and of realized returns, showing that traders obtain far from optimal performance. We also report strong direct qualitative and quantitative evidence of the disposition effect in the Bitcoin Blockchain data. Defining age-dependent transaction flows as the fraction of bitcoins that are traded at a given time and that were born (last traded) at some specific earlier time, we document that the time-averaged transaction flow fraction has a power law dependence as a function of age, with an exponent close to $-1.5$, a value compatible with priority queuing theory. We document the existence of multifractality on the measure defined as the normalized number of bitcoins exchanged at a given time.

We present a standard form of master equations (ME) for general one-dimensional non-Markovian (history-dependent) jump processes, complemented by an asymptotic solution derived from an expanded system-size approach. The ME is obtained by developing a general Markovian embedding using a suitable set of auxiliary field variables. This Markovian embedding uses a Laplace-convolution operation applied to the velocity trajectory. We introduce an asymptotic method tailored for this ME standard, generalising the system-size expansion for these jump processes. Under specific stability conditions tied to a single noise source, upon coarse-graining, the Generalized Langevin Equation (GLE) emerges as a universal approximate model for point processes in the weak-coupling limit. This methodology offers a unified analytical toolset for general non-Markovian processes, reinforcing the universal applicability of the GLE founded in microdynamics and the principles of statistical physics., Comment: 29 pages, 8 figures

We propose a formulation to construct new classes of financial price processes based on the insight that the key variable driving prices $P$ is the earning-over-price ratio $\gamma \simeq 1/P$, which we refer to as the earning yield and is analogous to the yield-to-maturity of an equivalent perpetual bond. This modeling strategy is illustrated with the choice for real-time $\gamma$ in the form of the Cox-Ingersoll-Ross (CIR) process, which allows us to derive analytically many stylised facts of financial prices and returns, such as the power law distribution of returns, transient super-exponential bubble behavior, and the fat-tailed distribution of prices before bubbles burst. Our model sheds new light on rationalizing the excess volatility and the equity premium puzzles. The model is calibrated to five well-known historical bubbles in the US and China stock markets via a quasi-maximum likelihood method with the L-BFGS-B optimization algorithm. Using $\phi$-divergence statistics adapted to models prescribed in terms of stochastic differential equations, we show the superiority of the CIR process for $\gamma_t$ against three alternative models.

The processes of ecological interactions, dispersal and mutations shape the dynamics of biological communities, and analogous eco-evolutionary processes acting upon economic entities have been proposed to explain economic change. This hypothesis is compelling because it explains economic change through endogenous mechanisms, but it has not been quantitatively tested at the global economy level. Here, we use an inverse modelling technique and 59 years of economic data covering 77 countries to test whether the collective dynamics of national economic activities can be characterised by eco-evolutionary processes. We estimate the statistical support of dynamic community models in which the dynamics of economic activities are coupled with positive and negative interactions between the activities, the spatial dispersal of the activities, and their transformations into other economic activities. We find strong support for the models capturing positive interactions between economic activities and spatial dispersal of the activities across countries. These results suggest that processes akin to those occurring in ecosystems play a significant role in the dynamics of economic systems. The strength-of-evidence obtained for each model varies across countries and may be caused by differences in the distance between countries, specific institutional contexts, and historical contingencies. Overall, our study provides a new quantitative, biologically inspired framework to study the forces shaping economic change., Comment: 23 pages

The new broadband seismic network in China will increase the number of stations from approximately 950 to 2000. The higher-resolution monitoring of the frequent smaller earthquakes expected inside Mainland China can be quantified via the completeness magnitude (Mc) metric. Using the Bayesian Magnitude of Completeness (BMC) method, we generate the spatial distribution of Mc predicted for the new network, based on the prior model calibrated on the current earthquake catalog (2012 to 2021) and network configuration. If 99% of Mainland China is at present covered down to Mc = 2.7, this threshold will soon fall to Mc = 2.0. This means approximately 3 times more earthquakes available per year. Based on the observation that seismic precursors are most likely to be observed at least at 3 units below the mainshock magnitude, the new seismic network shall achieve the goal of almost total coverage for optimal seismic-based earthquake prediction research., Comment: 20 pages, 5 figures, 1 table

The China Earthquake Administration (CEA) has launched an ambitious nationwide earthquake early warning (EEW) system project currently under development, which will include approximately 15,000 seismic stations and be the largest EEW system in the world. The new EEW system is planned to go online at the end of 2023. In approximately 50%, 30% and 20% of Chinese mainland, the inter-station distance will soon be smaller than 50 km, 25 km and 15 km, respectively. The expected effectiveness of this EEW system can be quantified via the metric determined from the radius of the blind zone, which refers to the area near the epicenter where there is insufficient time to issue a warning before the arrival of strong S- and surface waves. This study uses a theoretical network-based method together with Monte Carlo simulation to obtain the spatial distribution of the blind zone radii and their associated uncertainties for the new seismic network based on its configuration. We find that the densified new seismic network is expected to have excellent EEW performance as the area covered by small blind zones with radius less than 30 km increases dramatically from approximately 2% to 22%, that is by 2.4 million km2 inside Chinese mainland. We also find that every 1,000,000 RMB (about 146,000 USD) invested to densify the planned network will lead to an areal increase of 3,000 km2 of small blind zones. Continuing to increase the density of stations in some key regions with blind zone radii ranging from 15 to 40 km is still necessary to control the unexpected expansion of blind zones due to possible (and common) stations failure. Our work provides insights into the expected performance of the upcoming EEW network in Chinese mainland, and our proposed evaluation approach is broadly applicable for predicting the performance of EEW systems during their planning, design, and implementation stages., Comment: 41 pages, 14 figures, 1 table

Motivated by learning from experience and exploiting existing knowledge in civil nuclear operations, we have developed in-house generic PSA models for pressurized and boiling water reactors. The models are computationally light, handy, transparent, user-friendly, and easily adaptable to account for major plant-specific differences. They cover the common internal initiating events, frontline and support systems reliability and dependencies, human-factors, common-cause failures, and account for new factors typically overlooked in many developed PSAs. For quantification, the models use generic US reliability data, precursor analysis reports and studies, the ETHZ Curated Nuclear Events Database, and experts' opinions. Moreover, uncertainties in the most influential basic events are addressed. The generated results show good agreement with assessments available in the literature with detailed PSAs. We envision the models as an unbiased framework to measure nuclear operational risk with the same "ruler", and hence support inter-plant risk comparisons that are usually not possible due to differences in plant-specific PSA assumptions and scopes. The models can be used for initial risk screening, order-of-magnitude precursor analysis, and other research and pedagogic applications especially when no plant-specific PSAs are available. Finally, we are using the generic models for large-scale precursor analysis that will generate big picture trends, lessons, and insights., Comment: 21 pages, 9 figures, 10 tables

Hawkes point processes are first-order non-Markovian stochastic models of intermittent bursty dynamics with applications to physical, seismic, epidemic, biological, financial, and social systems. While accounting for positive feedback loops that may lead to critical phenomena in complex systems, the standard linear Hawkes process only describes excitative phenomena. To describe the co-existence of excitatory and inhibitory effects (or negative feedbacks), extensions involving nonlinear dependences of the intensity as a function of past activity are needed. However, such nonlinear Hawkes processes have been found hitherto to be analytically intractable due to the interplay between their non-Markovian and nonlinear characteristics, with no analytical solutions available. Here, we present various exact and robust asymptotic solutions to nonlinear Hawkes processes using the field master equation approach. We report explicit power law formulas for the steady state intensity distributions $P_{\mathrm{ss}}(\lambda)\propto \lambda^{-1-a}$, where the tail exponent $a$ is expressed analytically as a function of parameters of the nonlinear Hawkes models. We present three robust interesting characteristics of the nonlinear Hawkes process: (i) for one-sided positive marks (i.e., in the absence of inhibitory effects), the nonlinear Hawkes process can exhibit any power law relation either as intermediate asymptotics ($a\leq 0$) or as true asymptotics ($a>0$) by appropriate model selection; (ii) for distribution of marks with zero mean (i.e., for balanced excitatory and inhibitory effects), the Zipf law ($a\approx 1$) is universally observed for a wide class of nonlinear Hawkes processes with fast-accelerating intensity map; (iii) for marks with a negative mean, the asymptotic power law tail becomes lighter with an exponent increasing above 1 ($a>1$) as the mean mark becomes more negative., Comment: 63 pages, 12 figures, 1 table

Fundamentally related to the UV divergence problem in Physics, conventional wisdom in seismology is that the smallest earthquakes, which are numerous and often go undetected, dominate the triggering of major earthquakes, making the prediction of the latter difficult if not inherently impossible. By developing a rigorous validation procedure, we show that, in fact, large earthquakes (above magnitude 6.3 in California) are preferentially triggered by large events. Because of the magnitude correlations intrinsic in the validated model, we further rationalize the existence of earthquake doublets. These findings have far-reaching implications for short-term and medium-term seismic risk assessment, as well as for the development of a deeper theory without UV cut-off that is locally self-similar.

The origin(s) of the ubiquity of probability distribution functions (PDF) 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 PDF 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 non-positive 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., Comment: To appear in Phys. Rev. Lett. (5 pages, 2 figures + Appendices)

Multi criteria decision analysis (MCDA) has been used to provide a holistic evaluation of the quality of 13 electricity generation technologies in use today. A group of 19 energy experts cast scores on a scale of 1 to 10 using 12 quality criteria, based around the pillars of sustainability (society, environment and economy), with the aim of quantifying each criterion for each technology. The total mean score is employed as a holistic measure of system quality. The top three technologies to emerge in rank order are nuclear, combined cycle gas and hydroelectric. The bottom three are solar PV, biomass and tidal lagoon. All seven new renewable technologies fared badly, perceived to be expensive, unreliable, and not as environmentally friendly as is often assumed. We validate our approach by 1) comparing scores for pairs of criteria where we expect a correlation to exist; 2) comparing our qualitative scores with quantitative data; and; 3) comparing our qualitative scores with NEEDS project baseline costs. In many cases, R2>0.8 suggests that the structured hierarchy of our approach has led to scores that may be used in a semi-quantitative way. Adopting the results of this survey would lead to a very different set of energy policy priorities in the OECD and throughout the world., Comment: 84 pages, 41 figures

We study two-dimensional tensorial elastic wave transport in densely fractured media and document transitions from propagation to diffusion and to localization/delocalization. For large fracture stiffness, waves are propagative at the scale of the system. For small stiffness, multiple scattering prevails, such that waves are diffusive in disconnected fracture networks, and localized in connected ones with a strong multifractality of the intensity field. A reentrant delocalization is found in well-connected networks due to energy leakage via evanescent waves and cascades of mode conversion., Comment: 5 pages, 5 figures

Seismicity and faulting within the Earth crust are characterized by many scaling laws that are usually interpreted as qualifying the existence of underlying physical mechanisms associated with some kind of criticality in the sense of phase transitions. Using an augmented Epidemic-Type Aftershock Sequence (ETAS) model that accounts for the spatial variability of the background rates $\mu(x,y)$, we present a direct quantitative test of criticality. We calibrate the model to the ANSS catalog of the entire globe, the region around California, and the Geonet catalog for the region around New Zealand using an extended Expectation-Maximization (EM) algorithm including the determination of $\mu(x,y)$. We demonstrate that the criticality reported in previous studies is spurious and can be attributed to a systematic upward bias in the calibration of the branching ratio of the ETAS model, when not accounting correctly for spatial variability. We validate the version of the ETAS model which possesses a space varying background rate $\mu(x,y)$ by performing pseudo prospective forecasting tests. The non-criticality of seismicity has major implications for the prediction of large events.

With the unfolding of the COVID-19 pandemic, mathematical modeling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long term predictions were extremely challenging to address. Moreover, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modeling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitigation strategies. In this study, we propose a Markovian stochastic framework designed to describe the evolution of entropy during the COVID-19 pandemic and the instantaneous reproductive ratio. We then introduce and use entropy-based metrics of global transmission to measure the impact and temporal evolution of a pandemic event. In the formulation of the model, the temporal evolution of the outbreak is modeled by the master equation of a nonlinear Markov process for a statistically averaged individual, leading to a clear physical interpretation. We also provide a full Bayesian inversion scheme for calibration. The time evolution of the entropy rate, the absolute change in the system entropy, and the instantaneous reproductive ratio are natural and transparent outputs of this framework. The framework has the appealing property of being applicable to any compartmental epidemic model. As an illustration, we apply the proposed approach to a simple modification of the Susceptible-Exposed-Infected-Removed (SEIR) model. Applying the model to the Hubei region, South Korean, Italian, Spanish, German, and French COVID-19 data-sets, we discover a significant difference in the absolute change of entropy but highly regular trends for both the entropy evolution and the instantaneous reproductive ratio.

Bitcoin represents one of the most interesting technological breakthroughs and socio-economic experiments of the last decades. In this paper, we examine the role of speculative bubbles in the process of Bitcoin's technological adoption by analyzing its social dynamics. We trace Bitcoin's genesis and dissect the nature of its techno-economic innovation. In particular, we present an analysis of the techno-economic feedback loops that drive Bitcoin's price and network effects. Based on our analysis of Bitcoin, we test and further refine the Social Bubble Hypothesis, which holds that bubbles constitute an essential component in the process of technological innovation. We argue that a hierarchy of repeating and exponentially increasing series of bubbles and hype cycles, which has occurred over the past decade since its inception, has bootstrapped Bitcoin into existence.

We simulate a simplified version of the price process including bubbles and crashes proposed in Kreuser and Sornette (2018). The price process is defined as a geometric random walk combined with jumps modelled by separate, discrete distributions associated with positive (and negative) bubbles. The key ingredient of the model is to assume that the sizes of the jumps are proportional to the bubble size. Thus, the jumps tend to efficiently bring back excess bubble prices close to a normal or fundamental value (efficient crashes). This is different from existing processes studied that assume jumps that are independent of the mispricing. The present model is simplified compared to Kreuser and Sornette (2018) in that we ignore the possibility of a change of the probability of a crash as the price accelerates above the normal price. We study the behaviour of investment strategies that maximize the expected log of wealth (Kelly criterion) for the risky asset and a risk-free asset. We show that the method behaves similarly to Kelly on Geometric Brownian Motion in that it outperforms other methods in the long-term and it beats classical Kelly. As a primary source of outperformance, we determine knowledge about the presence of crashes, but interestingly find that knowledge of only the size, and not the time of occurrence, already provides a significant and robust edge. We then perform an error analysis to show that the method is robust with respect to variations in the parameters. The method is most sensitive to errors in the expected return.

Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infected cases for the whole of China, 29 provinces in China, and 33 countries and regions that have been or are undergoing major outbreaks. We dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province. We quantitatively document four phases of the outbreak in China with a detailed analysis on the heterogeneous situations across provinces. The extreme containment measures implemented by China were very effective with some instructive variations across provinces. Borrowing from the experience of China, we made scenario projections on the development of the outbreak in other countries. We identified that outbreaks in 14 countries (mostly in western Europe) have ended, while resurgences of cases have been identified in several among them. The modeling results clearly show longer after-peak trajectories in western countries, in contrast to most provinces in China where the after-peak trajectory is characterized by a much faster decay. We identified three groups of countries in different level of outbreak progress, and provide informative implications for the current global pandemic.

We analyse the compiled set of precursory data that were reported to be available in real time before the Ms 7.5 Haicheng earthquake in Feb. 1975 and the Ms 7.6-7.8 Tangshan earthquake in July 1976. We propose a robust and simple coarse-graining method consisting in aggregating and counting how all the anomalies together (geodesy, levelling, geomagnetism, soil resistivity, Earth currents, gravity, Earth stress, well water radon, well water level) develop as a function of time. We demonstrate a strong evidence for the existence of an acceleration of the number of anomalies leading up to the major Haicheng and Tangshan earthquakes. In particular for the Tangshan earthquake, the frequency of occurrence of anomalies is found to be well described by the log-periodic power law singularity (LPPLS) model, previously proposed for the prediction of engineering failures and later adapted to the prediction of financial crashes. Based on a mock real-time prediction experiment, and simulation study, we show the potential for an early warning system with lead-time of a few days, based on this methodology of monitoring accelerated rates of anomalies., Comment: 18 pages, 13 figures, 3 tables

A field theoretical framework is developed for the Hawkes self-excited point process with arbitrary memory kernels by embedding the original non-Markovian one-dimensional dynamics onto a Markovian infinite-dimensional one. The corresponding Langevin dynamics of the field variables is given by stochastic partial differential equations that are Markovian. This is in contrast to the Hawkes process, which is non-Markovian (in general) by construction as a result of its (long) memory kernel. We derive the exact solutions of the Lagrange-Charpit equations for the hyperbolic master equations in the Laplace representation in the steady state, close to the critical point of the Hawkes process. The critical condition of the original Hawkes process is found to correspond to a transcritical bifurcation in the Lagrange-Charpit equations. We predict a power law scaling of the PDF of the intensities in an intermediate asymptotics regime, which crosses over to an asymptotic exponential function beyond a characteristic intensity that diverges as the critical condition is approached. We also discuss the formal relationship between quantum field theories and our formulation. Our field theoretical framework provides a way to tackle complex generalisation of the Hawkes process, such as nonlinear Hawkes processes previously proposed to describe the multifractal properties of earthquake seismicity and of financial volatility., Comment: 39 pages, 7 figures

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 (PDF) of the intensities close to the critical point $n=1$ of the Hawkes process, with a non-universal exponent, function of the background intensity $\nu_0$ of the Hawkes intensity, the average time scale of the memory kernel and the branching ratio $n$. Our theoretical predictions are confirmed by numerical simulations., Comment: 6 pages, 3 figures

We introduce the first fully self-consistent model combining the seismic micro-ruptures occurring within a generalized Burridge-Knopoff spring-block model with the nucleation and propagation of electric charge pulses within a coupled mechano-electrokinetic system. This model provides a general theoretical framework for modeling and analyzing geoelectric precursors to earthquakes. In particular, it can reproduce the unipolar pulses that have often been reported before large seismic events, as well as various observed anomalies in the statistical moments of the ambient electric fields and the power-law exponent transition of the power spectra of electric fields.

We examine the precursory behavior of geoelectric signals before large earthquakes by means of an algorithm including an alarm-based model and binary classification. This algorithm, introduced originally by Chen and Chen [Nat. Hazards., 84, 2016], is improved by removing a time parameter for coarse-graining of earthquake occurrences, as well as by extending the single station method into a joint stations method. We also determine the optimal frequency bands of earthquake-related geoelectric signals with the highest signal-to-noise ratio. Using significance tests, we also provide evidence of an underlying seismoelectric relationship. It is appropriate for machine learning to extract this underlying relationship, which could be used to quantify probabilistic forecasts of impending earthquakes, and to get closer to operational earthquake prediction.

Empirical investor networks (EIN) proposed by \cite{Ozsoylev-Walden-Yavuz-Bildik-2014-RFS} are assumed to capture the information spreading path among investors. Here, we perform a comparative analysis between the EIN and the cellphone communication networks (CN) to test whether EIN is an information exchanging network from the perspective of the layer structures of ego networks. We employ two clustering algorithms ($k$-means algorithm and $H/T$ break algorithm) to detect the layer structures for each node in both networks. We find that the nodes in both networks can be clustered into two groups, one that has a layer structure similar to the theoretical Dunbar Circle corresponding to that the alters in ego networks exhibit a four-layer hierarchical structure with the cumulative number of 5, 15, 50 and 150 from the inner layer to the outer layer, and the other one having an additional inner layer with about 2 alters compared with the Dunbar Circle. We also find that the scale ratios, which are estimated based on the unique parameters in the theoretical model of layer structures \citep{Tamarit-Cuesta-Dunbar-Sanchez-2018-PNAS}, conform to a log-normal distribution for both networks. Our results not only deepen our understanding on the topological structures of EIN, but also provide empirical evidence of the channels of information diffusion among investors., Comment: 9 pages, 9 figues, 3 tables

Hierarchical structures are ubiquitous in human and animal societies, but a fundamental understanding of their raison d'\^etre 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.