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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