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One of the core risk management tasks is to identify hidden high-risky states that may lead to system breakdown, which can provide valuable early warning knowledge. However, due to high dimensionality and nonlinear interaction embedded in large-scale complex systems like urban traffic, it remains challenging to identify hidden high-risky states from huge system state space where over 99% of possible system states are not yet visited in empirical data. Based on maximum entropy model, we infer the underlying interaction network from complicated dynamical processes of urban traffic, and construct system energy landscape. In this way, we can locate hidden high-risky states that have never been observed from real data. These states can serve as risk signals with high probability of entering hazardous minima in energy landscape, which lead to huge recovery cost. Our finding might provide insights for complex system risk management.

Counterfactual thinking is a critical yet challenging topic for artificial intelligence to learn knowledge from data and ultimately improve their performances for new scenarios. Many research works, including Potential Outcome Model and Structural Causal Model, have been proposed to realize it. However, their modelings, theoretical foundations and application approaches are usually different. Moreover, there is a lack of graphical approach to infer spatio-temporal counterfactuals, that considers spatial and temporal interactions between multiple units. Thus, in this work, our aim is to investigate a survey to compare and discuss different counterfactual models, theories and approaches, and further build a unified graphical causal frameworks to infer the spatio-temporal counterfactuals.

Large Language Models (LLMs), originally shown to ace various text comprehension tasks have also remarkably been shown to tackle table comprehension tasks without specific training. While previous research has explored LLM capabilities with tabular dataset tasks, our study assesses the influence of $\textit{in-context learning}$,$ \textit{model scale}$, $\textit{instruction tuning}$, and $\textit{domain biases}$ on Tabular Question Answering (TQA). We evaluate the robustness of LLMs on Wikipedia-based $\textbf{WTQ}$ and financial report-based $\textbf{TAT-QA}$ TQA datasets, focusing on their ability to robustly interpret tabular data under various augmentations and perturbations. Our findings indicate that instructions significantly enhance performance, with recent models like Llama3 exhibiting greater robustness over earlier versions. However, data contamination and practical reliability issues persist, especially with WTQ. We highlight the need for improved methodologies, including structure-aware self-attention mechanisms and better handling of domain-specific tabular data, to develop more reliable LLMs for table comprehension.

Understanding the interplay between egocentric preference and urban structure in shaping human mobility has profound implications for improving epidemic intervention, social equity, and urban resilience. However, numerous existing studies either solely identify the egocentric preferences -- the anchoring effects from home -- or the impact of hierarchical urban structures. Here, we propose a network-based approach to present human mobility in both spatial and topological aspects within the urban system, using cell phone trajectory data from millions of users across three countries. By segmenting mobility trajectories into modules and examining their overlap with urban scales, we have observed the inflation law that the geospatial extent of these modules increases sub-linearly with their distance from home. Moreover, the egocentric preference for higher urban levels leads to this increase. This universal finding indicates that home-based preferences distort the hierarchical scales of human mobility in the urban environment, regardless of demographics or geography., Comment: 15 pages, 6 figures

Neural architecture search (NAS) enables the automatic design of neural network models. However, training the candidates generated by the search algorithm for performance evaluation incurs considerable computational overhead. Our method, dubbed nasgraph, remarkably reduces the computational costs by converting neural architectures to graphs and using the average degree, a graph measure, as the proxy in lieu of the evaluation metric. Our training-free NAS method is data-agnostic and light-weight. It can find the best architecture among 200 randomly sampled architectures from NAS-Bench201 in 217 CPU seconds. Besides, our method is able to achieve competitive performance on various datasets including NASBench-101, NASBench-201, and NDS search spaces. We also demonstrate that nasgraph generalizes to more challenging tasks on Micro TransNAS-Bench-101.

The advancement of large-scale quantum technologies necessitates a deeper understanding of the quantum network (QN) design from first principles. Pioneering studies, however, do not fully capture the origin of the stronger connectivity in QN that surpasses classical percolation predictions. Here, we apply statistical physics to identify the origin of this stronger connectivity -- known as concurrence percolation. Our finding is demonstrated on hierarchical scale-free networks, the ($U,V$) flowers, which allow full analytical control over path connectivity by adjusting the two distinct path length scales, $U \leq V$. This advantage enables us to analytically determine the critical exponents for infinite systems well beyond the current simulation limits. Our analysis reveals for the first time that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from their different methods for how to ``superpose'' parallel, non-shortest path contributions into overall connectivity. Notably, we find that concurrence percolation relies on non-shortest paths and shows a higher resilience to detouring when these paths are rerouted and extended. This increased resilience is also evident in real-world hierarchical, scale-free Internet networks. Our findings highlight a critical principle for QN design: non-shortest paths contribute significantly to QN connectivity compared to classical percolation -- as long as they are abundant., Comment: 23 pages, 8 figures. Supplementary Information added

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called ``concurrence percolation,'' which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from theoretically analyzing them. Recently, the dimension-reduction approaches reduced the system's size by mapping the original system to a one-dimensional system such that only one effective representative can capture its macroscopic dynamics. However, the approaches dramatically fail as the network becomes heterogeneous and has multiple community structures. Here, we bridge the gap by developing a generalized dimension reduction approach, which enables us to map the original system to a $m$-dimensional system that consists of $m$ interacting components. Notably, by validating it on various dynamical models, this approach accurately predicts the original system state and the tipping point, if any. Furthermore, the numerical results demonstrate that this approach approximates the system evolution and identifies the critical points for complex networks with time delay., Comment: 26 pages, 11 figures

The progressive amplification of fluctuations in demand as the demand travels upstream the supply chains is known as the bullwhip effect. We first analytically characterize the bullwhip effect in general supply chain networks in two cases: (i) all suppliers have a unique layer position, where our method is founded on the control-theoretic approach, and (ii) not all suppliers have a unique layer position due to the presence of intra-layer links or inter-layer links between suppliers that are not positioned in consecutive layers, where we use both the absorbing Markov chain and the control-theoretic approach. We then investigate how network structures impact the BWE of supply chain networks. In particular, we analytically show that (i) if the market demand is generated from the same stationary process, the structure of supply networks does not affect the layer-wise bullwhip effect of supply networks, and (ii) if the market demand is generated from different stationary or non-stationary market processes, wider supply networks lead to a lower level of layer-wise bullwhip effect. Finally, numerical simulations are used to validate our propositions.

Network structure provides critical information for understanding the dynamic behavior of networks. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a more complete structure of networks. In this paper, we integrate the configuration model for generating random networks into an Expectation-Maximization-Aggregation (EMA) framework to reconstruct the complete structure of multiplex networks. We validate the proposed EMA framework against the random model on several real-world multiplex networks, including both covert and overt ones. It is found that the EMA framework generally achieves the best predictive accuracy compared to the EM framework and the random model. As the number of layers increases, the performance improvement of EMA over EM decreases. The inferred multiplex networks can be leveraged to inform the decision-making on monitoring covert networks as well as allocating limited resources for collecting additional information to improve reconstruction accuracy. For law enforcement agencies, the inferred complete network structure can be used to develop more effective strategies for covert network interdiction.

Efficient model selection for identifying a suitable pre-trained neural network to a downstream task is a fundamental yet challenging task in deep learning. Current practice requires expensive computational costs in model training for performance prediction. In this paper, we propose a novel framework for neural network selection by analyzing the governing dynamics over synaptic connections (edges) during training. Our framework is built on the fact that back-propagation during neural network training is equivalent to the dynamical evolution of synaptic connections. Therefore, a converged neural network is associated with an equilibrium state of a networked system composed of those edges. To this end, we construct a network mapping $\phi$, converting a neural network $G_A$ to a directed line graph $G_B$ that is defined on those edges in $G_A$. Next, we derive a neural capacitance metric $\beta_{\rm eff}$ as a predictive measure universally capturing the generalization capability of $G_A$ on the downstream task using only a handful of early training results. We carried out extensive experiments using 17 popular pre-trained ImageNet models and five benchmark datasets, including CIFAR10, CIFAR100, SVHN, Fashion MNIST and Birds, to evaluate the fine-tuning performance of our framework. Our neural capacitance metric is shown to be a powerful indicator for model selection based only on early training results and is more efficient than state-of-the-art methods., Comment: 19 pages, 7 figures, neural architecture search, mean-field

Neural architecture search enables automation of architecture design. Despite its success, it is computationally costly and does not provide an insight on how to design a desirable architecture. Here we propose a new way of searching neural network where we search neural architecture by rewiring the corresponding graph and predict the architecture performance by graph properties. Because we do not perform machine learning over the entire graph space and use predicted architecture performance to search architecture, the searching process is remarkably efficient. We find graph based search can give a reasonably good prediction of desirable architecture. In addition, we find graph properties that are effective to predict architecture performance. Our work proposes a new way of searching neural architecture and provides insights on neural architecture design., Comment: 12 pages

The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled bipartite pure states is generally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies a new and more effective mapping of a QN, referred to as concurrence percolation theory (ConPT), that suggests using deterministic rather than probabilistic protocols for scalably improving on CEP across arbitrary QN topologies. More precisely, we implement ConPT via a deterministic entanglement transmission (DET) scheme that is fully analogous to resistor network analysis, with the corresponding series and parallel rules represented by deterministic entanglement swapping and concentration protocols, respectively. The main contribution of this paper is to establish a powerful mathematical framework, which is applicable to arbitrary d-dimensional information carriers (qudits), that provides different natural optimality metrics in terms of generalized k-concurrences (a family of fundamental entanglement measures) for different QN topology. In particular, we conclude that the introduced DET scheme (a) is optimal over the well-known nested repeater protocol for distilling entanglement from partially entangled qubits and (b) leads to higher success probabilities of obtaining a maximally entangled state than using CEP. The implementation of the DET scheme is experimentally feasible as tested on IBM's quantum computation platform., Comment: 18 pages, 6 figures. Final version

Human mobility is crucial to understand the transmission pattern of COVID-19 on spatially embedded geographic networks. This pattern seems unpredictable, and the propagation appears unstoppable, resulting in over 350,000 death tolls in the U.S. by the end of 2020. Here, we create the spatiotemporal inter-county mobility network using 10 TB (Terabytes) trajectory data of 30 million smart devices in the U.S. in the first six months of 2020. We investigate its bound percolation by removing the weakly connected edges. The mobility network becomes vulnerable and prone to reach its criticality and thus experience surprisingly abrupt phase transitions. Despite the complex behaviors of the mobility network, we devised a novel approach to identify a small, manageable set of recurrent critical bridges, connecting the giant component and the second-largest component. These adaptive links, located across the United States, played a key role as valves connecting components in divisions and regions during the pandemic. Beyond, our numerical results unveil that network characteristics determine the critical thresholds and the bridge locations. The findings provide new insights into managing and controlling the connectivity of mobility networks during unprecedented disruptions. The work can also potentially offer practical future infectious diseases both globally and locally.

Establishing long-distance quantum entanglement, i.e., entanglement transmission, in quantum networks (QN) is a key and timely challenge for developing efficient quantum communication. Traditional comprehension based on classical percolation assumes a necessary condition for successful entanglement transmission between any two infinitely distant nodes: they must be connected by at least a path of perfectly entangled states (singlets). Here, we relax this condition by explicitly showing that one can focus not on optimally converting singlets but on establishing concurrence -- a key measure of bipartite entanglement. We thereby introduce a new statistical theory, concurrence percolation theory (ConPT), remotely analogous to classical percolation but fundamentally different, built by generalizing bond percolation in terms of "sponge-crossing" paths instead of clusters. Inspired by resistance network analysis, we determine the path connectivity by series/parallel rules and approximate higher-order rules via star-mesh transforms. Interestingly, we find that the entanglement transmission threshold predicted by ConPT is lower than the known classical-percolation-based results and is readily achievable on any series-parallel networks such as the Bethe lattice. ConPT promotes our understanding of how well quantum communication can be further systematically improved versus classical statistical predictions under the limitation of QN locality -- a "quantum advantage" that is more general and efficient than expected. ConPT also shows a percolation-like universal critical behavior derived by finite-size analysis on the Bethe lattice and regular two-dimensional lattices, offering new perspectives for a theory of criticality in entanglement statistics., Comment: Phys. Rev. Lett. 126, 170501 (2021)

From mass extinction to cell death, complex networked systems often exhibit abrupt dynamic transitions between desirable and undesirable states. Such transitions are often caused by topological perturbations, such as node or link removal, or decreasing link strengths. The problem is that reversing the topological damage, namely retrieving the lost nodes or links, or reinforcing the weakened interactions, does not guarantee the spontaneous recovery to the desired functional state. Indeed, many of the relevant systems exhibit a hysteresis phenomenon, remaining in the dysfunctional state, despite reconstructing their damaged topology. To address this challenge, we develop a two-step recovery scheme: first - topological reconstruction to the point where the system can be revived, then dynamic interventions, to reignite the system's lost functionality. Applying this method to a range of nonlinear network dynamics, we identify the recoverable phase of a complex system, a state in which the system can be reignited by microscopic interventions, for instance, controlling just a single node. Mapping the boundaries of this dynamical phase, we obtain guidelines for our two-step recovery.

Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of spatially-extended systems and the required time to recover to their desired states under stochastic environmental conditions. While mean-field approaches may guide recovery strategies by indicating the conditions needed to destabilize undesired states, these approaches are not accurately capturing the transition process toward the desired state of spatially-extended systems in stochastic environments. The difficulty is rooted in the lack of mathematical tools to analyze systems with high dimensionality, nonlinearity, and stochastic effects. We bridge this gap by developing new mathematical tools that employ nucleation theory in spatially-embedded systems to advance resilience restoration. We examine our approach on systems following mutualistic dynamics and diffusion models, finding that systems may exhibit single-cluster or multi-cluster phases depending on their sizes and noise strengths, and also construct a new scaling law governing the restoration time for arbitrary system size and noise strength in two-dimensional systems. This approach is not limited to ecosystems and has applications in various dynamical systems, from biology to infrastructural systems., Comment: 31 pages, 7 figures

Data-driven risk networks describe many complex system dynamics arising in fields such as epidemiology and ecology. They lack explicit dynamics and have multiple sources of cost, both of which are beyond the current scope of traditional control theory. We construct the global risk network by combining the consensus of experts from the World Economic Forum with risk activation data to define its topology and interactions. Many of these risks, including extreme weather, pose significant economic costs when active. We introduce a method for converting network interaction data into continuous dynamics to which we apply optimal control. We contribute the first method for constructing and controlling risk network dynamics based on empirically collected data. We identify seven risks commonly used by governments to control COVID-19 spread and show that many alternative driver risk sets exist with potentially lower cost of control., Comment: 15 pages, 3 figures

Major disasters such as extreme weather events can magnify and exacerbate pre-existing social disparities, with disadvantaged populations bearing disproportionate costs. Despite the implications for equity and emergency planning, we lack a quantitative understanding of how these social fault lines translate to different behaviors in large-scale emergency contexts. Here we investigate this problem in the context of Hurricane Harvey, using over 30 million anonymized GPS records from over 150,000 opted-in users in the Greater Houston Area to quantify patterns of disaster-inflicted relocation activities before, during, and after the shock. We show that evacuation distance is highly homogenous across individuals from different types of neighborhoods classified by race and wealth, obeying a truncated power-law distribution. Yet here the similarities end: we find that both race and wealth strongly impact evacuation patterns, with disadvantaged minority populations less likely to evacuate than wealthier white residents. Finally, there are considerable discrepancies in terms of departure and return times by race and wealth, with strong social cohesion among evacuees from advantaged neighborhoods in their destination choices. These empirical findings bring new insights into mobility and evacuations, providing policy recommendations for residents, decision makers, and disaster managers alike., Comment: 17 pages, 4 figures. The manuscript has been submitted to Scientific Reports

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability., Comment: Review chapter

Knowledge of time-variant functionality of real-world physical, social, and engineered networks is critical to the understanding of the resilience of networks facing external perturbations. The majority of existing studies, however, focus only on the topological properties of networks for resilience assessment, which does not fully capture their dynamical resilience. In this study, we evaluate and quantify network resilience based both on the functionality states of links and on topology. We propose three independent measures---the failure scaling index (FSI), the weighted degree scaling index (WDSI), and the link functionality irregularity index (LFII)---that capture macroscopic, microscopic, and temporal performance characteristics of networks. Accordingly, an integrated general resilience (GR) metric is used to assess performance loss and recovery speed in networks with time-variant functionality. We test the proposed methods in the study of traffic networks under urban flooding impacts in the context of Harris County, Texas, during Hurricane Harvey using a high-resolution dataset, which contains temporal speed of 20,000 roads every 5 minutes for 5 months. Our results show that link weights and node weighted degrees with perturbed functionality in the traffic network during flooding follow a scale-free distribution. Hence, three proposed measures capture clear resilience curves of the network as well as identify the irregularity of links. Accordingly, network performance measures and the methodology for resilience quantification reveal insights into the extent of network performance loss and recovery speed, suggesting possible improvements in network resilience in the face of external perturbations such as urban flooding., Comment: 14 pages, 10 figures

Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks. Prior studies usually focus on the structure-based estimation to infer network sizes, degree distributions, average degrees, and more. Little effort attempted to estimate the specific degree of each vertex from a sampled induced graph, which prevents us from measuring the lethality of nodes in protein networks and influencers in social networks. The current approaches dramatically fail for a tiny sampled induced graph and require a specific sampling method and a large sample size. These approaches neglect information of the vertex state, representing the dynamical behavior of the networked system, such as the biomass of species or expression of a gene, which is useful for degree estimation. We fill this gap by developing a framework to infer individual vertex degrees using both information of the sampled topology and vertex state. We combine the mean-field theory with combinatorial optimization to learn vertex degrees. Experimental results on real networks with a variety of dynamics demonstrate that our framework can produce reliable degree estimates and dramatically improve existing link prediction methods by replacing the sampled degrees with our estimated degrees., Comment: IJCAI 2020, 7 pages, 4 figures, network inference, incomplete network

Network reconstruction is fundamental to understanding the dynamical behaviors of the networked systems. Many systems, modeled by multiplex networks with various types of interactions, display an entirely different dynamical behavior compared to the corresponding aggregated network. In many cases, unfortunately, only the aggregated topology and partial observations of the network layers are available, raising an urgent demand for reconstructing multiplex networks. We fill this gap by developing a mathematical and computational tool based on the Expectation-Maximization framework to reconstruct multiplex layer structures. The reconstruction accuracy depends on the various factors, such as partial observation and network characteristics, limiting our ability to predict and allocate observations. Surprisingly, by using a mean-field approximation, we discovered that a discrimination indicator that integrates all these factors universally determines the accuracy of reconstruction. This discovery enables us to design the optimal strategies to allocate the fixed budget for deriving the partial observations, promoting the optimal reconstruction of multiplex networks. To further evaluate the performance of our method, we predict beside structure also dynamical behaviors on the multiplex networks, including percolation, random walk, and spreading processes. Finally, applying our method on empirical multiplex networks drawn from biological, transportation, and social domains, corroborate the theoretical analysis.

We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the network, without knowing the full network. A naive approach and the current state-of-the-art is to follow the dynamics of the observed partial network to local equilibrium. This dramatically fails to extract the true steady state. We use a mean-field approach to map the dynamics of the unseen part of the network to a single node, which allows us to recover accurate estimates of steady-state on as few as 5 observed vertices in domains ranging from ecology to social networks to gene regulation. Incomplete networks are the norm in practice, and we offer new ways to think about nonlinear dynamics when only sparse information is available., Comment: AAAI 2020, 9 pages, 5 figures

Increasing evidence demonstrates that in many places language coexistence has become ubiquitous and essential for supporting language and cultural diversity and associated with its financial and economic benefits. The competitive evolution among multiple languages determines the evolution outcome, either coexistence, decline, or extinction. Here, we extend the Abrams-Strogatz model of language competition to multiple languages and then validate it by analyzing the behavioral transitions of language usage over the recent several decades in Singapore and Hong Kong. In each case, we estimate from data the model parameters that measure each language utility for its speakers and the strength of two biases, the majority preference for their language, and the minority aversion to it. The values of these two biases decide which language is the fastest growing in the competition and what would be the stable state of the system. We also study the system convergence time to stable states and discover the existence of tipping points with multiple attractors. Moreover, the critical slowdown of convergence to the stable fractions of language users appears near and peaks at the tipping points, signaling when the system approaches them. Our analysis furthers our understanding of multiple language evolution and the role of tipping points in behavioral transitions. These insights may help to protect languages from extinction and retain the language and cultural diversity., Comment: 13 pages, 6 figures

The polarization of political opinions among members of the U.S. legislative chambers measured by their voting records is greater today than it was thirty years ago. Previous research efforts to find causes of such increase have suggested diverse contributors, like growth of online media, echo chamber effects, media biases, or disinformation propagation. Yet, we lack theoretic tools to understand, quantify, and predict the emergence of high political polarization among voters and their legislators. Here, we analyze millions of roll-call votes cast in the U.S. Congress over the past six decades. Our analysis reveals the critical change of polarization patterns that started at the end of 1980's. In earlier decades, polarization within each Congress tended to decrease with time. In contrast, in the recent decades, the polarization has been likely to grow within each term. To shed light on the reasons for this change, we introduce here a formal model for competitive dynamics to quantify the evolution of polarization patterns in the legislative branch of the U.S. government. Our model represents dynamics of polarization, enabling us to successfully predict the direction of polarization changes in 28 out of 30 U.S. Congresses elected in the past six decades. From the evolution of polarization level as measured by the Rice index, our model extracts a hidden parameter - polarization utility which determines the convergence point of the polarization evolution. The increase in the polarization utility implied by the model strongly correlates with two current trends: growing polarization of voters and increasing influence of election campaign funders. Two largest peaks of the model's polarization utility correlate with significant political or legislative changes happening at the same time.

Rapid expansions of their size and frequent changes of their topology make it difficult to observe and analyze complex networks. We explore the properties of the Hankel matrix and propose an algorithm for calculating the final synchronization state that uses a local observation of a single node for a time period significantly shorter than the synchronization process. We find that synchronization can be achieved more quickly than the routine rhythm. This finding refines our understanding of the abundant ultrafast synchronization phenomena observed in nature, and it enables the efficient design of self-aligned robots., Comment: 6 pages, 3 figures, 2 tables