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Abstract Traditional neural network models of associative memories were used to store and retrieve static patterns. We develop reservoir-computing based memories for complex dynamical attractors, under two common recalling scenarios in neuropsychology: location-addressable with an index channel and content-addressable without such a channel. We demonstrate that, for location-addressable retrieval, a single reservoir computing machine can memorize a large number of periodic and chaotic attractors, each retrievable with a specific index value. We articulate control strategies to achieve successful switching among the attractors, unveil the mechanism behind failed switching, and uncover various scaling behaviors between the number of stored attractors and the reservoir network size. For content-addressable retrieval, we exploit multistability with cue signals, where the stored attractors coexist in the high-dimensional phase space of the reservoir network. As the length of the cue signal increases through a critical value, a high success rate can be achieved. The work provides foundational insights into developing long-term memories and itinerancy for complex dynamical patterns.

Abstract The initial transient phase of an emerging epidemic is of critical importance for data-driven model building, model-based prediction of the epidemic trend, and articulation of control/prevention strategies. Quantitative models for real-world epidemics need to be memory-dependent or non-Markovian, but this presents difficulties for data collection, parameter estimation, computation, and analyses. In contrast, such difficulties do not arise in the traditional Markovian models. To uncover the conditions under which Markovian and non-Markovian models are equivalent, we develop a comprehensive computational and analytic framework. We show that the transient-state equivalence holds when the average generation time matches the average removal time, resulting in minimal Markovian estimation errors in the basic reproduction number, epidemic forecasting, and evaluation of control strategy. The errors depend primarily on the generation-to-removal time ratio, while rarely on the specific values and distributions of these times. Overall, our study provides a general criterion for modeling memory-dependent processes using Markovian frameworks.

Abstract Global climate change has been shown to cause longer, more intense, and frequent heatwaves, of which anthropogenic stressors concentrated in urban areas are a critical contributor. In this study, we investigate the causal interactions during heatwaves across 520 urban sites in the U.S. combining complex network and causal analysis. The presence of regional mediators is manifest in the constructed causal networks, together with long-range teleconnections. More importantly, megacities, such as New York City and Chicago, are causally connected with most of other cities and mediate the structure of urban networks during heatwaves. We also identified a significantly positive correlation between the causality strength and the total populations in megacities. These findings corroborate the contribution of human activities e.g., anthropogenic emissions of greenhouse gases or waste heat, to urban heatwaves. The emergence of teleconnections and supernodes are informative for the prediction and adaptation to heatwaves under global climate change.

Reinforcement learning (RL) has been employed to devise the best course of actions in defending the critical infrastructures, such as power networks against cyberattacks. Nonetheless, even in the case of the smallest power grids, the action space of RL experiences exponential growth, rendering efficient exploration by the RL agent practically unattainable. The current RL algorithms tailored to power grids are generally not suited when the state-action space size becomes large, despite trade-offs. We address the large action-space problem for power grid security by exploiting temporal graph convolutional neural networks (TGCNs) to develop a parallel but heterogeneous RL framework. In particular, we divide the action space into smaller subspaces, each explored by an RL agent. How to efficiently organize the spatiotemporal action sequences then becomes a great challenge. We invoke TGCN to meet this challenge by accurately predicting the performance of each individual RL agent in the event of an attack. The top performing agent is selected, resulting in the optimal sequence of actions. First, we investigate the action-space size comparison for IEEE 5-bus and 14-bus systems. Furthermore, we use IEEE 14-bus and IEEE 118-bus systems coupled with the Grid2Op platform to illustrate the performance and action division influence on training times and grid survival rates using both deep Q-learning and Soft Actor Critic trained agents and Grid2Op default greedy agents. Our TGCN framework provides a computationally reasonable approach for generating the best course of actions to defend cyber physical systems against attacks.

It has been recently demonstrated that two machine-learning architectures, reservoir computing and time-delayed feed-forward neural networks, can be exploited for detecting the Earth’s anomaly magnetic field immersed in overwhelming complex signals for magnetic navigation in a GPS-denied environment. The accuracy of the detected anomaly field corresponds to a positioning accuracy in the range of 10–40 m. To increase the accuracy and reduce the uncertainty of weak signal detection as well as to directly obtain the position information, we exploit the machine-learning model of random forests that combines the output of multiple decision trees to give optimal values of the physical quantities of interest. In particular, from time-series data gathered from the cockpit of a flying airplane during various maneuvering stages, where strong background complex signals are caused by other elements of the Earth’s magnetic field and the fields produced by the electronic systems in the cockpit, we demonstrate that the random-forest algorithm performs remarkably well in detecting the weak anomaly field and in filtering the position of the aircraft. With the aid of the conventional inertial navigation system, the positioning error can be reduced to less than 10 m. We also find that, contrary to the conventional wisdom, the classic Tolles–Lawson model for calibrating and removing the magnetic field generated by the body of the aircraft is not necessary and may even be detrimental for the success of the random-forest method.

Abstract In our modern time, travel has become one of the most significant factors contributing to global epidemic spreading. A deficiency in the literature is that travel has largely been treated as a Markovian process: it occurs instantaneously without any memory effect. To provide informed policies such as determining the mandatory quarantine time, the non-Markovian nature of real-world traveling must be taken into account. We address this fundamental problem by constructing a network model in which travel takes a finite time and infections can occur during the travel. We find that the epidemic threshold can be maximized by a proper level of travel, implying that travel infections do not necessarily promote spreading. More importantly, the epidemic threshold can exhibit a two-threshold phenomenon in that it can increase abruptly and significantly as the travel time exceeds a critical value. This may provide a quantitative estimation of the minimally required quarantine time in a pandemic.

Abstract Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian, and spatiotemporal nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.

Data-driven recovery of topology is challenging for networks beyond pairwise interactions. The authors propose a framework to reconstruct complex networks with higher-order interactions from time series, focusing on networks with 2-simplexes where social contagion and Ising dynamics generate binary data.

Abstract Identifying regions that mediate regional propagation of atmospheric perturbations is important to assessing the susceptibility and resilience of complex hydroclimate systems. Detecting the regional gateways through causal inference, can help unravel the interplay of physical processes and inform projections of future changes. In this study, we characterize the causal interactions among nine climate regions in the contiguous United States using long‐term (1901–2018) precipitation data. The constructed causal networks reveal the cross‐regional propagation of precipitation perturbations. Results show that the Ohio Valley region acts as an atmospheric gateway for precipitation and moisture transport in the U.S., which is largely regulated by the regional convective uplift. The findings have implications for improving predicative capacity of hydroclimate modeling of regional precipitation.

The benefits of noise to applications of nonlinear dynamical systems through mechanisms such as stochastic and coherence resonances have been well documented. Recent years have witnessed a growth of research in exploiting machine learning to predict nonlinear dynamical systems. It has been known that noise can act as a regularizer to improve the training performance of machine learning. Utilizing reservoir computing as a paradigm, we find that injecting noise to the training data can induce a resonance phenomenon with significant benefits to both short-term prediction of the state variables and long-term prediction of the attractor. The optimal noise level leading to the best performance in terms of the prediction accuracy, stability, and horizon can be identified by treating the noise amplitude as one of the hyperparameters for optimization. The resonance phenomenon is demonstrated using two prototypical high-dimensional chaotic systems.

In the field of quantum chaos, spectral statistics is one of the most extensively investigated characteristics. Despite a large body of existing literature, the effects of many-body interactions on the spectral statistics of relativistic quantum systems remain poorly understood. Treating electron-electron interactions through the one-orbital mean-field Hubbard model, we address this fundamental issue using graphene billiards with the geometric shape of a circular sector as prototypical systems. Our approach is to consider the two characteristically different cases where the statistics are Poisson and Gaussian orthogonal ensemble (GOE) so the corresponding classical dynamics are typically integrable and chaotic, respectively, and to systematically investigate how the statistics change as the Hubbard interaction strength increases from zero. We find that, for energies near the Dirac point, the Hubbard interactions have a significant effect on the spectral statistics. Regardless of the type of spectral statistics to begin with, increasing the Hubbard interaction strength up to a critical value causes the statistics to approach GOE, rendering more applicable the random matrix theory. As the interaction strength increases beyond the critical value, the statistics evolve toward Poisson, due to the emergence of an energy gap rendering the quasiparticles massive. We also find that the energy levels above and below the Dirac point can exhibit different statistics, and the many-body interactions have little effect on the statistics for levels far from the Dirac point. These results reveal the intriguing interplay between many-body interactions and the spectral statistics, which we develop a physical picture to understand.

Abstract Despite extensive investigation demonstrating that resource competition can significantly alter the deterministic behaviors of synthetic gene circuits, it remains unclear how resource competition contributes to the gene expression noise and how this noise can be controlled. Utilizing a two‐gene circuit as a prototypical system, a surprising double‐edged role of resource competition in gene expression noise is uncovered: competition decreases noise through introducing a resource constraint but generates its own type of noise which we name as “resource competitive noise.” Utilization of orthogonal resources enables retainment of the noise reduction conferred by resource constraint while removing the added resource competitive noise. The noise reduction effects are studied using three negative feedback types: negatively competitive regulation (NCR), local, and global controllers, each having four placement architectures in the protein biosynthesis pathway (mRNA or protein inhibition on transcription or translation). The results show that both local and NCR controllers with mRNA‐mediated inhibition are efficacious at reducing noise, with NCR controllers demonstrating a superior noise‐reduction capability. Combining feedback controllers with orthogonal resources can improve the local controllers. This work provides deep insights into the origin of stochasticity in gene circuits with resource competition and guidance for developing effective noise control strategies.

Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.

It is crucial yet challenging to identify cause-consequence relation in complex dynamical systems where direct causal links can mix with indirect ones. Leng et al. propose a data-driven model-independent method to distinguish direct from indirect causality and test its applicability to real-world data.

Understanding failure propagation dynamics in complex networks with recovery processes is vital to realizing networks that are resistant to large scale failures. Here, the authors report a model for general failure propagation dynamics in complex networks with non-Markovian recovery processes.

Predicting network dynamics based on data, a problem with broad applications, has been studied extensively in the past, but most existing approaches assume that the complete set of historical data from the whole network is available. This requirement presents a great challenge in applications, especially for large, distributed networks in the real world, where data collection is accomplished by many clients in a parallel fashion. Often, each client only has the time series data from a partial set of nodes, and the client has access to only partial time stamps of the whole set of time series data and the partial structure of the network. Due to privacy concerns or license-related issues, the data collected by different clients cannot be shared. Accurately predicting the network dynamics while protecting the privacy of different parties is a critical problem in modern times. Here, we propose a solution based on federated graph neural networks (FGNNs) that enables the training of a global dynamic model for all parties without data sharing. We validate the working of our FGNN framework through two types of simulations to predict a variety of network dynamics (four discrete and three continuous dynamics). As a significant real-world application, we demonstrate successful prediction of state-wise influenza spreading in the USA. Our FGNN scheme represents a general framework to predict diverse network dynamics through collaborative fusing of the data from different parties without disclosing their privacy.

It is evident that increasing the intensive-care-unit (ICU) capacity and giving priority to admitting and treating patients will reduce the number of COVID-19 deaths, but the quantitative assessment of these measures has remained inadequate. We develop a comprehensive, non-Markovian state transition model, which is validated through the accurate prediction of the daily death toll for two epicenters: Wuhan, China and Lombardy, Italy. The model enables prediction of COVID-19 deaths in various scenarios. For example, if appropriate treatment priorities had been used, the death toll in Wuhan and Lombardy would have been reduced by about 10% and 7%, respectively. The strategy depends on the epidemic scale and is more effective in countries with a younger population structure. Analyses of data from China, South Korea, Italy, and Spain suggest that countries with less per capita ICU medical resources should implement this strategy in the early stage of the pandemic to reduce mortalities. We emphasize that the results of this paper should be interpreted purely from a scientific and a quantitative-analysis point of view. No ethical implications are intended and meaningful.

Linear controllability theories have stimulated research on control of complex networks. Here the authors investigate the concordance between linear and nonlinear approaches in ranking the importance of nodes in nonlinear networks, and conclude that linear controllability may not be applicable.

When modelling epidemic spreading on complex networks, one useful simplification is to assume that the dynamics are Markovian, i.e. memoryless. Here the authors present a more general non-Markovian approach which is able to accurately reproduce the transient and stationary regime on different substrates.

We develop a framework based on the deep convolutional neural network (DCNN) for model-free prediction of the occurrence of extreme events both in time (“when”) and in space (“where”) in nonlinear physical systems of spatial dimension two. The measurements or data are a set of two-dimensional snapshots or images. For a desired time horizon of prediction, a proper labeling scheme can be designated to enable successful training of the DCNN and subsequent prediction of extreme events in time. Given that an extreme event has been predicted to occur within the time horizon, a space-based labeling scheme can be applied to predict, within certain resolution, the location at which the event will occur. We use synthetic data from the two-dimensional complex Ginzburg-Landau equation and empirical wind speed data from the North Atlantic Ocean to demonstrate and validate our machine-learning-based prediction framework. The trade-offs among the prediction horizon, spatial resolution, and accuracy are illustrated, and the detrimental effect of spatially biased occurrence of extreme events on prediction accuracy is discussed. The deep learning framework is viable for predicting extreme events in the real world.

Non-coding RNAs are fundamental to the competing endogenous RNA (CeRNA) hypothesis in oncology. Previous work focused on static CeRNA networks. We construct and analyze CeRNA networks for four sequential stages of lung adenocarcinoma (LUAD) based on multi-omics data of long non-coding RNAs (lncRNAs), microRNAs and mRNAs. We find that the networks possess a two-level bipartite structure: common competing endogenous network (CCEN) composed of an invariant set of microRNAs over all the stages and stage-dependent, unique competing endogenous networks (UCENs). A systematic enrichment analysis of the pathways of the mRNAs in CCEN reveals that they are strongly associated with cancer development. We also find that the microRNA-linked mRNAs from UCENs have a higher enrichment efficiency. A key finding is six microRNAs from CCEN that impact patient survival at all stages, and four microRNAs that affect the survival from a specific stage. The ten microRNAs can then serve as potential biomarkers and prognostic tools for LUAD.

Previous work in the field of relativistic quantum chaos has revealed initial evidence that the manifestations of classical chaos in relativistic quantum systems tend to be weakened as compared with those in nonrelativistic quantum systems. To place this finding on a firmer ground, we investigate the relativistic quantum fingerprints of classical chaos using the out-of-time-order correlator (OTOC). OTOC has recently been applied to a number of fields in physics and it holds special promises for the field of quantum chaos, but existing work focused exclusively on nonrelativistic quantum systems. Calculating and analyzing OTOC for relativistic quantum billiard systems described by the massless Dirac equation, we find that the signatures of classical chaos are indeed characteristically less pronounced in relativistic than in nonrelativistic quantum systems. The finding is substantiated by studying four different aspects of OTOC. Firstly, in the energy eigenspace, in the short time regime there is a complete lack of any signature of chaos associated with the evolution of OTOC in the Dirac billiard due to the relativistic quantum phenomenon of Zitterbewegung, in contrast to nonrelativistic quantum billiard systems where chaos leaves behind a quite distinct signature. Secondly, weakening of the relativistic quantum manifestations of classical chaos occurs in the long time regime as well. Thirdly, evolution of the wave packet based OTOC also reveals that the fingerprints of chaos are much less pronounced in the Dirac billiard systems as compared with the Schrödinger billiards. Fourthly, the level spacing statistics of the OTOC operators in systems with classically integrable and chaotic dynamics, which are characteristically distinct in the Schrödinger billiards, bear a strong similarity in the Dirac billiards, indicating again the dwindling effects of chaos. The OTOC based results suggest that the impacts of classical chaos are generally weaker in relativistic than in nonrelativistic quantum systems, a fundamental issue that warrants further investigation.

Abstract Data based source localization in complex networks has a broad range of applications. Despite recent progress, locating multiple diffusion sources in time varying networks remains to be an outstanding problem. Bridging structural observability and sparse signal reconstruction theories, we develop a general framework to locate diffusion sources in time varying networks based solely on sparse data from a small set of messenger nodes. A general finding is that large degree nodes produce more valuable information than small degree nodes, a result that contrasts that for static networks. Choosing large degree nodes as the messengers, we find that sparse observations from a few such nodes are often sufficient for any number of diffusion sources to be located for a variety of model and empirical networks. Counterintuitively, sources in more rapidly varying networks can be identified more readily with fewer required messenger nodes.

Abstract Previous studies of multilayer network robustness model cascading failures via a node-to-node percolation process that assumes “strong” interdependence across layers–once a node in any layer fails, its neighbors in other layers fail immediately and completely with all links removed. This assumption is not true of real interdependent infrastructures that have emergency procedures to buffer against cascades. In this work, we consider a node-to-link failure propagation mechanism and establish “weak” interdependence across layers via a tolerance parameter α which quantifies the likelihood that a node survives when one of its interdependent neighbors fails. Analytical and numerical results show that weak interdependence produces a striking phenomenon: layers at different positions within the multilayer system experience distinct percolation transitions. Especially, layers with high super degree values percolate in an abrupt manner, while those with low super degree values exhibit both continuous and discontinuous transitions. This novel phenomenon we call mixed percolation transitions has significant implications for network robustness. Previous results that do not consider cascade tolerance and layer super degree may be under- or over-estimating the vulnerability of real systems. Moreover, our model reveals how nodal protection activities influence failure dynamics in interdependent, multilayer systems.

Understanding and accurate prediction of human mobility is of increasing importance, but a universal framework is lacking. Here, the authors develop a unified model that accurately predicts both individual and population mobility and scaling behaviors on diverse spatial scales.

In transport of micro- or nanosized particles through a confined structure driven by thermal fluctuations and external forcing—a situation that arises commonly in a variety of fields in physical and biological sciences, efficient and controllable separation of particles of different sizes is an important but challenging problem. We study, numerically and analytically, the diffusion dynamics of Brownian particles through the biologically relevant setting of a spatially periodic structure, subject to static and temporally periodic forcing. Molecular dynamical simulations reveal that the mean velocity in general depends sensitively on the particle size. The phenomenon of current reversal is uncovered, where particles larger than or smaller than a critical size diffuse in exactly opposite directions. This striking behavior occurs in a wide range of the forcing amplitude and provides a mechanism to separate the Brownian particles of different sizes. Besides the forcing amplitude, other parametric quantities characterizing the forcing profile, such as the temporal asymmetry, can also be exploited to modulate or control the transport dynamics of particles of different sizes. To gain a theoretical understanding, we exploit the Fick-Jacobs approximation to obtain a one-dimensional description of the diffusion problem, which enables key quantities characterizing the diffusion process, such as the mean velocity, to be predicted. In the regime of weak forcing, a reasonable agreement between theory and numerical results is achieved. Beyond the weakly forcing regime, the diffusion approximation breaks down, causing the theoretical predictions to deviate from the numerical results, into which we provide physical insights. Our findings have potential applications in optimizing transport in microfluidic devices or through biological channels.

In realistic systems of coupled oscillators, it is desired to predict the onset of synchronization where the system equations are unknown, raising the need to develop a prediction framework that is model free and fully data driven. We show that this challenging problem can be addressed with machine learning. In particular, exploiting reservoir computing or echo state networks, we employ a “parameter-aware” scheme to train the neural machine using time series acquired from a small number of distinct asynchronous states in the parameter regime prior to the onset of synchronization. The trained machine can then be used to predict the synchronization transition through tuning the control parameter. We demonstrate the power of the machine learning-based framework using two types of synchronization behaviors: Complete synchronization in coupled identical chaotic oscillators and the phase synchronization in coupled nonidentical phase oscillators, which are representative of the collective dynamics in coupled systems. In addition, we design our numerical experiments such that two transition scenarios are covered: Smooth (second-order) and explosive (first-order) transitions that represent the generic types of phase transition in nonlinear physical systems. A remarkable feature is that, for the network systems exhibiting explosive (first-order) transition, the machine learning scheme is capable of predicting not only the locations of the transition points associated with the forward and backward transition paths but also the hysteresis between the two paths.

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian neural networks (HNNs) with physical constraints defined by Hamilton's equations of motion, which represent a major class of physics-enhanced neural networks. We introduce a class of HNNs capable of adaptable prediction of nonlinear physical systems: by training the neural network based on time series from a small number of bifurcation-parameter values of the target Hamiltonian system, the HNN can predict the dynamical states at other parameter values, where the network has not been exposed to any information about the system at these parameter values. The architecture of the HNN differs from the previous ones in that we incorporate an input parameter channel, rendering the HNN parameter-cognizant. We demonstrate, using paradigmatic Hamiltonian systems, that training the HNN using time series from as few as four parameter values bestows the neural machine with the ability to predict the state of the target system in an entire parameter interval. Utilizing the ensemble maximum Lyapunov exponent and the alignment index as indicators, we show that our parameter-cognizant HNN can successfully predict the route of transition to chaos. Physics-enhanced machine learning is a forefront area of research, and our adaptable HNNs provide an approach to understanding machine learning with broad applications.

Abstract Evolutionary games of cyclic competitions have been extensively studied to gain insights into one of the most fundamental phenomena in nature: biodiversity that seems to be excluded by the principle of natural selection. The Rock-Paper-Scissors (RPS) game of three species and its extensions [e.g., the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game] are paradigmatic models in this field. In all previous studies, the intrinsic symmetry associated with cyclic competitions imposes a limitation on the resulting coexistence states, leading to only selective types of such states. We investigate the effect of nonuniform intraspecific competitions on coexistence and find that a wider spectrum of coexistence states can emerge and persist. This surprising finding is substantiated using three classes of cyclic game models through stability analysis, Monte Carlo simulations and continuous spatiotemporal dynamical evolution from partial differential equations. Our finding indicates that intraspecific competitions or alternative symmetry-breaking mechanisms can promote biodiversity to a broader extent than previously thought.

Abstract Dynamical processes occurring on the edges in complex networks are relevant to a variety of real-world situations. Despite recent advances, a framework for edge controllability is still required for complex networks of arbitrary structure and interaction strength. Generalizing a previously introduced class of processes for edge dynamics, the switchboard dynamics, and exploit- ing the exact controllability theory, we develop a universal framework in which the controllability of any node is exclusively determined by its local weighted structure. This framework enables us to identify a unique set of critical nodes for control, to derive analytic formulas and articulate efficient algorithms to determine the exact upper and lower controllability bounds, and to evaluate strongly structural controllability of any given network. Applying our framework to a large number of model and real-world networks, we find that the interaction strength plays a more significant role in edge controllability than the network structure does, due to a vast range between the bounds determined mainly by the interaction strength. Moreover, transcriptional regulatory networks and electronic circuits are much more strongly structurally controllable (SSC) than other types of real-world networks, directed networks are more SSC than undirected networks, and sparse networks are typically more SSC than dense networks.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Localized surface plasmon and Klein tunneling resonances are two phenomena that were previously thought to be unrelated, where the former plays an important role in subwavelength optics while the latter is fundamental to relativistic quantum mechanics and physics of Dirac materials. We develop a rigorous theory for spin-1 Dirac-Weyl particles, which establishes a striking analogy between the two phenomena and unveils a deep connection between the distinct physical contexts, paving the way for gate-controlled surface plasmon mimetic electronics as well as for realizing localized spoof plasmons in a scope wider than previously thought. A possible experimental scheme is articulated.

A widely held belief in network epidemiology is that information diffusion makes individuals aware of the epidemic and thus drives them to seek protections from nonpharmaceutical or pharmaceutical resources, which can help suppress its spread. However, as the COVID-19 pandemic has revealed, excessive information diffusion can trigger irrational acquisition and hoarding behaviors, which can lead to shortages of resources even for those in urgent need, consequently, worsening disease spreading. To develop a quantitative understanding of the effect of information diffusion on epidemic spreading, subject to allocations of limited resources, has become an urgently important problem with broad implications. We construct a multiplex network framework to characterize the complex interplay among resource allocation, information diffusion, and epidemic spreading, and develop a microscopic Markov chain theory to analyze their coevolution dynamics. There are two main findings. Firstly, if infected individuals have a large recovery probability, information diffusion plays the expected “normal” role of suppressing the epidemic. However, if the recovery probability is low, information diffusion can anomalously worsen the spread, regardless of the available resources insofar as they are limited. Secondly, different types of resources can lead to distinct phase transitions underlying the epidemic outbreak when the recovery probability is low: with limited cure-focused resources, the phase transition is of the second order, but if resources are of the protection type, the transition becomes first order, and a hysteresis loop emerges. The generality of the findings is established through simulations of synthetic and empirical three-layer networks with results in agreement with the theoretical predictions.

According to the official report, the first case of COVID-19 and the first death in the United States occurred on January 20 and February 29, 2020, respectively. On April 21, California reported that the first death in the state occurred on February 6, implying that community spreading of COVID-19 might have started earlier than previously thought. Exactly what is time zero, i.e., when did COVID-19 emerge and begin to spread in the U.S. and other countries? We develop a comprehensive predictive modeling framework to address this question. Using available data of confirmed infections to obtain the optimal values of the key parameters, we validate the model and demonstrate its predictive power. We then carry out an inverse inference analysis to determine time zero for 10 representative states in the U.S., plus New York City, United Kingdom, Italy, and Spain. The main finding is that, in both the U.S. and Europe, COVID-19 started around the new year day.

To predict a critical transition due to parameter drift without relying on a model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system will be in a transient state preceding its collapse. We develop a model-free, machine-learning-based solution to both problems by exploiting reservoir computing to incorporate a parameter input channel. We demonstrate that, when the machine is trained in the normal functioning regime with a chaotic attractor (i.e., before the critical transition), the transition point can be predicted accurately. Remarkably, for a parameter drift through the critical point, the machine with the input parameter channel is able to predict not only that the system will be in a transient state, but also the distribution of the transient lifetimes and their average before the final collapse, revealing an important physical property of transient chaos.

Complex networks, including physical, biological and social systems are ubiquitous, but understanding of how to control them is elusive. Here Wang et al. develop a framework based on the concept of attractor networks to facilitate the study of controllability of nonlinear dynamics in complex systems.

The ability to manipulate pseudospin can find applications in Dirac-material based spintronics. Unlike the transport of real spin that can be modulated by a magnetic field, some form of magnetization, or a spin-transfer torque, pseudospin does not respond to a magnetic field, making modulating pseudospin transport a challenging task. We articulate an asymmetrically coupled cavity-waveguide configuration in graphene and uncover a phenomenon: making the classical dynamics of the cavity deformed can effectively modulate and enhance pseudospin polarization in the waveguide. The underlying mechanism of this remarkable phenomenon can be attributed to chaos-assisted tunneling, which has been well documented in nonrelativistic quantum systems but not yet in Dirac material systems. The finding establishes the feasibility to develop pseudospin modulators for graphene systems through externally applied electrical potential only, with fidelity over 10% at the effective distance of several cavity sizes along the waveguide.

The dynamical mechanism underlying the processes of anesthesia-induced loss of consciousness and recovery is key to gaining insights into the working of the nervous system. Previous experiments revealed an asymmetry between neural signals during the anesthesia and recovery processes. Here we obtain experimental evidence for the hysteresis loop and articulate the dynamical mechanism based on percolation on multilayer complex networks with self-similarity. Model analysis reveals that, during anesthesia, the network is able to maintain its neural pathways despite the loss of a substantial fraction of the edges. A predictive and potentially testable result is that, in the forward process of anesthesia, the average shortest path and the clustering coefficient of the neural network are markedly smaller than those associated with the recovery process. This suggests that the network strives to maintain certain neurological functions by adapting to a relatively more compact structure in response to anesthesia.

Quantum materials that host a flatband, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern insulating behaviors. We report a surprising class of electronic in-gap edge states in pseudospin-1 materials without the conventional need of band-inversion topological phase transitions or introducing magnetism via an external magnetic type of interactions. In particular, we find that, in two-dimensional gapped (insulating) Dirac systems of massive spin-1 quasiparticles, in-gap edge modes can emerge through only an electrostatic potential applied to a finite domain. Associated with these unconventional edge modes are spontaneous formation of pronounced domain-wall spin textures, which exhibit the feature of out-of-plane spin-angular momentum locking on both sides of the domain boundary and are quite robust against boundary deformations and impurities despite a lack of an explicit topological origin. The in-gap modes are formally three-component evanescent wave solutions, akin to the Jackiw-Rebbi type of bound states. Such modes belong to a distinct class due to the following physical reasons: three-component spinor wave function, unusual boundary conditions, and a shifted flatband induced by the external scalar potential. Not only is the finding of fundamental importance, but it also paves the way for generating highly controllable in-gap edge states with emergent spin textures using the traditional semiconductor gate technology. Results are validated using analytic calculations of a continuum Dirac-Weyl model and tight-binding simulations of realistic materials through characterizations of local density of state spectra and resonant tunneling conductance.

Chimera states arising in the classic Kuramoto system of two-dimensional phase-coupled oscillators are transient but they are “long” transients in the sense that the average transient lifetime grows exponentially with the system size. For reasonably large systems, e.g., those consisting of a few hundred oscillators, it is infeasible to numerically calculate or experimentally measure the average lifetime, so the chimera states are practically permanent. We find that small perturbations in the third dimension, which make system “slightly” three dimensional, will reduce dramatically the transient lifetime. In particular, under such a perturbation, the practically infinite average transient lifetime will become extremely short because it scales with the magnitude of the perturbation only logarithmically. Physically, this means that a reduction in the perturbation strength over many orders of magnitude, insofar as it is not zero, would result in only an incremental increase in the lifetime. The uncovered type of fragility of chimera states raises concerns about their observability in physical systems.

Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions and hystereses can arise, but a full picture of these behaviors in the parameter space is lacking. We develop a theory for interacting spreading dynamics on complex networks through spectral dimension reduction. In particular, we derive from the microscopic quenched mean-field equations a two-dimensional system in terms of the macroscopic variables, which enables a full phase diagram to be determined analytically. The diagram predicts critical phenomena that were known previously but only numerically, such as the interplay between discontinuous transition and hysteresis as well as the emergence and role of tricritical points.

We study electron scattering from a closed magnetic structure embedded in the top surface of a topological insulator. Outside the structure there is a uniform layer of ferromagnetic insulators, leading to a positive effective mass for the Dirac electrons. The mass inside the structure can be engineered to be negative, leading to a skyrmion structure. The geometric shape of the structure can be circular or deformed, leading to integrable or chaotic dynamics, respectively, in the classical limit. For a circular structure, the relativistic quantum scattering characteristics can be calculated analytically. For a deformed structure, we develop an efficient numerical method, the multiple-multipole method, to solve the scattering wave functions. We find that, for scattering from a skyrmion, an anomalous Hall effect, as characterized by strong skew scattering, can arise, which is robust against structural deformation due to the emergence of resonant modes. In the short- (long-)wavelength regime, the resonant modes manifest themselves as confined vortices (excited edge states). The origin of the resonant states is the spin phase factor of massive Dirac electrons at the skyrmion boundary. Further, in the short-wavelength regime, for a circular skyrmion, a large number of angular momentum channels contribute to the resonant modes. In this regime, in principle, classical dynamics is relevant, but we find that geometric deformations, even those as severe as leading to fully developed chaos, have little effect on the resonant modes. The vortex structure of the resonant states makes it possible to electrically charge the skyrmion, rendering feasible the electrical manipulation of its motion. In the long-wavelength regime, only the lowest angular momentum channels contribute to the resonant modes, making the skew scattering sharply directional. These phenomena can be exploited for applications in generating dynamic skyrmions for information storage and in Hall devices.

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has been about half dozen Lyapunov time. Is it possible to significantly extend the prediction time beyond what has been achieved so far? We articulate a scheme incorporating time-dependent but sparse data inputs into reservoir computing and demonstrate that such rare “updates” of the actual state practically enable an arbitrarily long prediction horizon for a variety of chaotic systems. A physical understanding based on the theory of temporal synchronization is developed.

An emergent class of two-dimensional Dirac materials is α-T_{3} lattices that can be realized by adding an atom at the center of each unit cell of a lattice with T_{3} symmetry. The interaction strength α between this atom and any of its nearest neighbors is a parameter that can be continuously tuned between zero and one to generate a spectrum of materials. We investigate the fundamentally important and practically relevant issue of quasiparticle confinement for the entire spectrum of α-T_{3} materials. Except for the two end points, i.e., α=0,1, which correspond to the graphene and pseudospin-1 lattices, respectively, the time-reversal symmetry is broken, leading to the removal of level degeneracy and facilitating confinement. Taking the approach of quantum scattering off an electrically generated potential cavity in the quantum-dot regime, we characterize confinement by identifying and examining the scattering resonances. We study a number of cavities with characteristically distinct classical dynamics: circular, annular, elliptical, and stadium cavities. For the circular and annular cavities with classically integrable and mixed dynamics, respectively, the scattering matrix can be analytically obtained, so the scattering cross sections and the Wigner-Smith time delay associated with the resonances can be calculated to quantify confinement. For the elliptical and stadium cavities with mixed and chaotic dynamics in the classical limit, respectively, the scattering-matrix approach is infeasible, so we adopt an efficient numerical method to calculate the scattering wave functions and experimentally accessible measures of confinement such as the magnetic moment. The main finding is that, for all the cases, the regime of small α values offers the best confinement possible among the spectrum of α-T_{3} materials, which is general and holds regardless of the nature of the corresponding classical dynamics.

We uncover an unexpected family of in-gap chiral edge states in noninverted spin-1 Dirac quantum dots. The system represents a topologically trivial confinement configuration where such edge states are not expected according to the conventional wisdom. In particular, for a massive type of confining potential, two distinct situations can arise: with or without mass sign change, corresponding to a quantum dot with or without band inversion, respectively. The former case is conventional, where topologically protected chiral edge modes can arise in the gap. For the latter, contrary to the belief that there should be no one-way current-carrying edge channels, we find the surprising emergence of such edge states and the spin-1 analog of Majorana modes. These states are strikingly robust and immune to backscattering. In the presence of a magnetic field, the edge states result in peculiar Fock-Darwin states originated from Landau-level confinement. The unexpected phenomenon is also validated in systems with bulk-topology regularization through (1) a properly regularized continuum model and (2) an experimentally accessible tight-binding dice lattice system.

Quantum scars constitute one of the fundamental pillars in the traditional field of nonrelativistic quantum chaos. In relativistic quantum systems, chiral scars have been discovered recently whose wave functions concentrate on odd periodic orbits and break the time-reversal symmetry. We develop a theoretical framework to unify the scarring phenomena in nonrelativistic and relativistic quantum systems, which were previously thought to be distinct. In particular, we exploit massive Dirac billiard systems and derive semiclassical quantization rules to bridge the two opposite limits: the massless Dirac case and the large mass regime where the system effectively degenerates into one governed by the Schrödinger equation. A nontrivial phase is uncovered, which depends on the mass, the wave number, and the angle of reflection, and we demonstrate that this phase plays a key role in transforming the chiral scars and in bridging the relativistic and nonrelativistic quantum scars. In the large-mass limit, time-reversal symmetry is restored, as evidenced by a spectral analysis.

A common difficulty in applications of machine learning is the lack of any general principle for guiding the choices of key parameters of the underlying neural network. Focusing on a class of recurrent neural networks—reservoir computing systems, which have recently been exploited for model-free prediction of nonlinear dynamical systems—we uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized. In a three-dimensional representation of the error versus the time and spectral radius, the interval corresponds to the bottom region of a “valley.” Such a valley arises for a variety of spatiotemporal dynamical systems described by nonlinear partial differential equations, regardless of the structure and the edge-weight distribution of the underlying reservoir network. We also find that, while the particular location and size of the valley depend on the details of the target system to be predicted, the interval tends to be larger for undirected than for directed networks. The valley phenomenon can be beneficial to the design of optimal reservoir computing, representing a small step forward in understanding these machine-learning systems.

The process of cell fate determination has been depicted intuitively as cells travelling and resting on a rugged landscape, which has been probed by various theoretical studies. However, few studies have experimentally demonstrated how underlying gene regulatory networks shape the landscape and hence orchestrate cellular decision-making in the presence of both signal and noise. Here we tested different topologies and verified a synthetic gene circuit with mutual inhibition and auto-activations to be quadrastable, which enables direct study of quadruple cell fate determination on an engineered landscape. We show that cells indeed gravitate towards local minima and signal inductions dictate cell fates through modulating the shape of the multistable landscape. Experiments, guided by model predictions, reveal that sequential inductions generate distinct cell fates by changing landscape in sequence and hence navigating cells to different final states. This work provides a synthetic biology framework to approach cell fate determination and suggests a landscape-based explanation of fixed induction sequences for targeted differentiation.