Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares.

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equations to compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

Predicting multiple observations in complex systems through low-dimensional embeddings.

Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and then sets the low-dimensional feature manifold as a generalized predictor to achieve predictions of all components. The substantial potential of FRMM is shown for both representative models and real-world data involving Indian monsoon, electroencephalogram (EEG) signals, foreign exchange market, and traffic speed in Los Angeles Country. FRMM overcomes the curse of dimensionality and finds a generalized predictor, and thus has potential for applications in many other real-world systems.

Percolation Theories for Quantum Networks.

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.

Reconstructing Sparse Multiplex Networks with Application to Covert Networks.

Network structure provides critical information for understanding the dynamic behavior of complex systems. 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 Expectation-Maximization (EM) framework and 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.

An influential node identification method considering multi-attribute decision fusion and dependency.

It is essential to study the robustness and centrality of interdependent networks for building reliable interdependent systems. Here, we consider a nonlinear load-capacity cascading failure model on interdependent networks, where the initial load distribution is not random, as usually assumed, but determined by the influence of each node in the interdependent network. The node influence is measured by an automated entropy-weighted multi-attribute algorithm that takes into account both different centrality measures of nodes and the interdependence of node pairs, then averaging for not only the node itself but also its nearest neighbors and next-nearest neighbors. The resilience of interdependent networks under such a more practical and accurate setting is thoroughly investigated for various network parameters, as well as how nodes from different layers are coupled and the corresponding coupling strength. The results thereby can help better monitoring interdependent systems.

A spatiotemporal decay model of human mobility when facing large-scale crises.

A common feature of large-scale extreme events, such as pandemics, wildfires, and major storms is that, despite their differences in etiology and duration, they significantly change routine human movement patterns. Such changes, which can be major or minor in size and duration and which differ across contexts, affect both the consequences of the events and the ability of governments to mount effective responses. Based on naturally tracked, anonymized mobility behavior from over 90 million people in the United States, we document these mobility differences in space and over time in six large-scale crises, including wildfires, major tropical storms, winter freeze and pandemics. We introduce a model that effectively captures the high-dimensional heterogeneity in human mobility changes following large-scale extreme events. Across five different metrics and regardless of spatial resolution, the changes in human mobility behavior exhibit a consistent hyperbolic decline, a pattern we characterize as "spatiotemporal decay." When applied to the case of COVID-19, our model also uncovers significant disparities in mobility changes-individuals from wealthy areas not only reduce their mobility at higher rates at the start of the pandemic but also maintain the change longer. Residents from lower-income regions show a faster and greater hyperbolic decay, which we suggest may help account for different COVID-19 rates. Our model represents a powerful tool to understand and forecast mobility patterns post emergency, and thus to help produce more effective responses.

Estimating comparable distances to tipping points across mutualistic systems by scaled recovery rates.

Mutualistic systems can experience abrupt and irreversible regime shifts caused by local or global stressors. Despite decades of efforts to understand ecosystem dynamics and determine whether a tipping point could occur, there are no current approaches to estimate distances (in state/parameter space) to tipping points and compare the distances across various mutualistic systems. Here we develop a general dimension-reduction approach that simultaneously compresses the natural control and state parameters of high-dimensional complex systems and introduces a scaling factor for recovery rates. Our theoretical framework places various systems with entirely different dynamical parameters, network structure and state perturbations on the same scale. More importantly, it compares distances to tipping points across different systems on the basis of data on abundance and topology. By applying the method to 54 real-world mutualistic networks, our analytical results unveil the network characteristics and system parameters that control a system's resilience. We contribute to the ongoing efforts in developing a general framework for mapping and predicting distance to tipping points of ecological and potentially other systems.

Discrimination reveals reconstructability of multiplex networks from partial observations.

An excellent method for predicting links in multiplex networks is reflected in its ability to reconstruct them accurately. Although link prediction methods perform well on estimating the existence probability of each potential link in monoplex networks by the set of partially observed links, we lack a mathematical tool to reconstruct the multiplex network from the observed aggregate topology and partially observed links in multiplex networks. Here, we fill this gap by developing a theoretical and computational framework that builds a probability space containing possible structures with a maximum likelihood estimation. Then, we discovered that the discrimination, an indicator quantifying differences between layers from an entropy perspective, determines the reconstructability, i.e., the accuracy of such reconstruction. This finding enables us to design the optimal strategy to allocate the set of observed links in different layers for promoting the optimal reconstruction of multiplex networks. Finally, the theoretical analyses are corroborated by empirical results from biological, social, engineered systems, and a large volume of synthetic networks.

Identifying the shifting sources to predict the dynamics of COVID-19 in the U.S.

Mobility restriction is a crucial measure to control the transmission of the COVID-19. Research has shown that effective distance measured by the number of travelers instead of physical distance can capture and predict the transmission of the deadly virus. However, these efforts have been limited mainly to a single source of disease. Also, they have not been tested on finer spatial scales. Based on prior work of effective distances on the country level, we propose the multiple-source effective distance, a metric that captures the distance for the virus to propagate through the mobility network on the county level in the U.S. Then, we estimate how the change in the number of sources impacts the global mobility rate. Based on the findings, a new method is proposed to locate sources and estimate the arrival time of the virus. The new metric outperforms the original single-source effective distance in predicting the arrival time. Last, we select two potential sources and quantify the arrival time delay caused by the national emergency declaration. In doing so, we provide quantitative answers on the effectiveness of the national emergency declaration.

Data science approaches to confronting the COVID-19 pandemic: a narrative review.

During the COVID-19 pandemic, more than ever, data science has become a powerful weapon in combating an infectious disease epidemic and arguably any future infectious disease epidemic. Computer scientists, data scientists, physicists and mathematicians have joined public health professionals and virologists to confront the largest pandemic in the century by capitalizing on the large-scale 'big data' generated and harnessed for combating the COVID-19 pandemic. In this paper, we review the newly born data science approaches to confronting COVID-19, including the estimation of epidemiological parameters, digital contact tracing, diagnosis, policy-making, resource allocation, risk assessment, mental health surveillance, social media analytics, drug repurposing and drug development. We compare the new approaches with conventional epidemiological studies, discuss lessons we learned from the COVID-19 pandemic, and highlight opportunities and challenges of data science approaches to confronting future infectious disease epidemics. This article is part of the theme issue 'Data science approaches to infectious disease surveillance'.

Percolation of temporal hierarchical mobility networks during COVID-19.

Percolation theory is essential for understanding disease transmission patterns on the temporal mobility networks. However, the traditional approach of the percolation process can be inefficient when analysing a large-scale, dynamic network for an extended period. Not only is it time-consuming but it is also hard to identify the connected components. Recent studies demonstrate that spatial containers restrict mobility behaviour, described by a hierarchical topology of mobility networks. Here, we leverage crowd-sourced, large-scale human mobility data to construct temporal hierarchical networks composed of over 175 000 block groups in the USA. Each daily network contains mobility between block groups within a Metropolitan Statistical Area (MSA), and long-distance travels across the MSAs. We examine percolation on both levels and demonstrate the changes of network metrics and the connected components under the influence of COVID-19. The research reveals the presence of functional subunits even with high thresholds of mobility. Finally, we locate a set of recurrent critical links that divide components resulting in the separation of core MSAs. Our findings provide novel insights into understanding the dynamical community structure of mobility networks during disruptions and could contribute to more effective infectious disease control at multiple scales. This article is part of the theme issue 'Data science approaches to infectious disease surveillance'.

Polarization and tipping points.

Research has documented increasing partisan division and extremist positions that are more pronounced among political elites than among voters. Attention has now begun to focus on how polarization might be attenuated. We use a general model of opinion change to see if the self-reinforcing dynamics of influence and homophily may be characterized by tipping points that make reversibility problematic. The model applies to a legislative body or other small, densely connected organization, but does not assume country-specific institutional arrangements that would obscure the identification of fundamental regularities in the phase transitions. Agents in the model have initially random locations in a multidimensional issue space consisting of membership in one of two equal-sized parties and positions on 10 issues. Agents then update their issue positions by moving closer to nearby neighbors and farther from those with whom they disagree, depending on the agents' tolerance of disagreement and strength of party identification compared to their ideological commitment to the issues. We conducted computational experiments in which we manipulated agents' tolerance for disagreement and strength of party identification. Importantly, we also introduced exogenous shocks corresponding to events that create a shared interest against a common threat (e.g., a global pandemic). Phase diagrams of political polarization reveal difficult-to-predict transitions that can be irreversible due to asymmetric hysteresis trajectories. We conclude that future empirical research needs to pay much closer attention to the identification of tipping points and the effectiveness of possible countermeasures.

Network percolation reveals adaptive bridges of the mobility network response to COVID-19.

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 the bond percolation process by removing the weakly connected edges. As we increase the threshold, the mobility network nodes become less interconnected 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.

Vaccination intentions generate racial disparities in the societal persistence of COVID-19.

We combined survey, mobility, and infections data in greater Boston, MA to simulate the effects of racial disparities in the inclination to become vaccinated on continued infection rates and the attainment of herd immunity. The simulation projected marked inequities, with communities of color experiencing infection rates 3 times higher than predominantly White communities and reaching herd immunity 45 days later on average. Persuasion of individuals uncertain about vaccination was crucial to preventing the worst inequities but could only narrow them so far because 1/5th of Black and Latinx individuals said that they would never vaccinate. The results point to a need for well-crafted, compassionate messaging that reaches out to those most resistant to the vaccine.

From data to complex network control of airline flight delays.

Many critical complex systems and networks are continuously monitored, creating vast volumes of data describing their dynamics. To understand and optimize their performance, we need to discover and formalize their dynamics to enable their control. Here, we introduce a multidisciplinary framework using network science and control theory to accomplish these goals. We demonstrate its use on a meaningful example of a complex network of U.S. domestic passenger airlines aiming to control flight delays. Using the real data on such delays, we build a flight delay network for each airline. Analyzing these networks, we uncover and formalize their dynamics. We use this formalization to design the optimal control for the flight delay networks. The results of applying this control to the ground truth data on flight delays demonstrate the low costs of the optimal control and significant reduction of delay times, while the costs of the delays unabated by control are high. Thus, the introduced here framework benefits the passengers, the airline companies and the airports.

Concurrence Percolation in Quantum Networks.

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 and 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 percolationlike 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.

Heuristic assessment of choices for risk network control.

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 economy 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 and drastic inflation, 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 simulate applying this method to control the spread of COVID-19 and show that the choice of risks through which the network is controlled has significant influence on both the cost of control and the total cost of keeping network stable. We additionally describe a heuristic for choosing the risks trough which the network is controlled, given a general risk network.

The impact of non-pharmaceutical interventions on the prevention and control of COVID-19 in New York City.

The emergence of coronavirus disease 2019 (COVID-19) has infected more than 62 million people worldwide. Control responses varied across countries with different outcomes in terms of epidemic size and social disruption. This study presents an age-specific susceptible-exposed-infected-recovery-death model that considers the unique characteristics of COVID-19 to examine the effectiveness of various non-pharmaceutical interventions (NPIs) in New York City (NYC). Numerical experiments from our model show that the control policies implemented in NYC reduced the number of infections by 72% [interquartile range (IQR) 53-95] and the number of deceased cases by 76% (IQR 58-96) by the end of 2020. Among all the NPIs, social distancing for the entire population and protection for the elderly in public facilities is the most effective control measure in reducing severe infections and deceased cases. School closure policy may not work as effectively as one might expect in terms of reducing the number of deceased cases. Our simulation results provide novel insights into the city-specific implementation of NPIs with minimal social disruption considering the locations and population characteristics.

A quantification method of non-failure cascading spreading in a network of networks.

The cascading spreading process in social and economic networks is more complicated than that in physical systems. These networks' multiple nodes and edges increase their structural complexity and recoverability, enabling the system to lose partial functionality rather than completely fail. However, these phenomena in social and economic networks introduce challenges to the existing network robustness models, where a node is either in a functional state or a failed state. This research uses a network of networks (NoN) to simulate multiple types of nodes and edges. A non-failure cascading process is utilized to model the nodes' self-adaptation and recoverability. The main contribution of this research is proposing a spreading model to extend the non-failure cascading process to the NoN, which can be used in predicting real-world system damage suffering from special events. The case study of this research evaluated the effect degree of crude oil trade changes on each sector from 2015 to 2016.

Robustness and lethality in multilayer biological molecular networks.

Robustness is a prominent feature of most biological systems. Most previous related studies have been focused on homogeneous molecular networks. Here we propose a comprehensive framework for understanding how the interactions between genes, proteins and metabolites contribute to the determinants of robustness in a heterogeneous biological network. We integrate heterogeneous sources of data to construct a multilayer interaction network composed of a gene regulatory layer, a protein-protein interaction layer, and a metabolic layer. We design a simulated perturbation process to characterize the contribution of each gene to the overall system's robustness, and find that influential genes are enriched in essential and cancer genes. We show that the proposed mechanism predicts a higher vulnerability of the metabolic layer to perturbations applied to genes associated with metabolic diseases. Furthermore, we find that the real network is comparably or more robust than expected in multiple random realizations. Finally, we analytically derive the expected robustness of multilayer biological networks starting from the degree distributions within and between layers. These results provide insights into the non-trivial dynamics occurring in the cell after a genetic perturbation is applied, confirming the importance of including the coupling between different layers of interaction in models of complex biological systems.