Localized shocks arising from climate extremes, geopolitical conflicts, and trade protectionism cascade through trade networks, triggering global food crises. Cross-product substitution, a critical response strategy, induces cross-product cascading effects that remain underexplored. Here, we develop a multilayer network model that simulates the short-term response to food supply shocks. When applied to cereal trade networks, comparisons with and without substitution, as well as with increased substitute layers, reveal that substitution mitigates risks in the shocked layer but induces derived risks in substitute layers, causing the network system to present four response regimes ranging from resilient to systemic crisis. These regimes' boundaries and magnitudes emerge from the interplay of four critical factors: shock intensity, substitution extent, supply capacity of substitute layers, and inter-layer substitution structure. Scenario simulations of three real-world shocks further reveal country-level heterogeneity in substitution effectiveness. Our framework provides a quantitative tool for designing response strategies and resilient food systems.

Peer review shapes which scientific claims enter the published record, but its internal dynamics are hard to measure at scale because reviewer criticism and author revision are usually embedded in long, unstructured correspondence. Here we use a fixed-prompt large language model pipeline to convert the review correspondence of Nature Communications papers published from 2017 to 2024 into structured reviewer–author interactions. We find that review pressure is concentrated in the first round and focused disproportionately on core claims rather than peripheral presentation. Higher average opinion strength is also associated with more reviewer disagreement, while review patterns vary little with broad team attributes, consistent with relatively impartial evaluation. Contrary to the intuition that stronger papers should pass review more smoothly, with greater reviewer–author agreement and less extensive revision, we find that stronger criticism, higher-quality comments, and greater revision burden are associated with higher later citation impact within accepted papers. We finally show that fields differ more in review style than in review length, pointing to disciplinary variation in how criticism is negotiated and resolved. These findings position open peer review not just as a gatekeeping mechanism but as a measurable record of how influential scientific claims are challenged, defended, and revised before entering the published record.

Accurately capturing nonlinear dependencies and causal interactions in multivariate time series remains a fundamental challenge in complex systems analysis. Traditional deep learning models, though effective in sequence modeling, often overlook causality and offer limited interpretability. To address this limitation, we propose the Multivariate Transfer Entropy-guided Self-Attention (MTESA) mechanism, which integrates multivariate transfer entropy (MTE) as a causality-informed prior into the self-attention framework. In this design, the pre-estimated MTE values are incorporated as learnable bias terms that guide the attention mechanism toward causally relevant dependencies while maintaining full model trainability. Rather than altering the core architecture of attention-based models, MTESA provides a flexible integration route for embedding external causal priors into deep learning systems. The proposed framework is evaluated on representative energy forecasting tasks, including coal-fired power plant fuel consumption and wind power generation. Experimental results demonstrate that MTESA consistently improves forecasting accuracy and robustness and yields attention patterns that align with the causal structures revealed by MTE analysis. Overall, this work contributes an effective engineering integration of information-theoretic causality with attention mechanisms, offering a practical pathway toward causality-aware deep learning in multivariate time series forecasting.

Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have emerged as a research hotspot due to their ability to express interactions among multiple nodes. This study proposes an iterative generation model for higher-order fractal networks. The iteration is controlled by three parameters: the dimension K of the simplicial complex, the multiplier m, and the iteration count t. The constructed network is a pure simplicial complex. Theoretical analysis using the similarity dimension and experimental verification using the box-counting dimension demonstrate that the generated networks exhibit fractal characteristics. When the multiplier m is large, the generalized degree distribution of the generated networks exhibits scale-free properties.

Both structural and functional failures in infrastructure systems can trigger cascading failures. However, existing models typically address these two dimensions separately, overlooking their coupling effects. We propose a coupled load-threshold cascading failure model based on simplicial complexes, which integrates higher-order structural disintegration and functional overload mechanisms within a unified dynamical framework. Nodes are classified into critical hubs and ordinary nodes according to the second-order generalized degree, where hubs are subject to dual constraints of load capacity and structural thresholds. Our results show that the coupled system exhibits hybrid phase transition behavior, transitioning from continuous degradation to abrupt collapse, along with a temporal propagation pattern in which structural failures precede and trigger functional failures. Under targeted attacks, the two mechanisms display early-stage mutual reinforcement, significantly accelerating cascading destruction. To enhance system robustness, we design two control strategies: critical higher-order structure protection and risk-aware path blocking. Empirical analysis on nine real-world power grids demonstrates that both strategies effectively improve network robustness. Notably, in certain scenarios, these strategies can transform abrupt first-order phase transitions into progressive second-order phase transitions. This study advances the understanding of coupled failure mechanisms in higher-order networks and provides guidance for the resilient design of critical infrastructures.

Mentoring is a key component of scientific achievements, contributing to overall measures of career success for mentees and mentors. Within the scientific community, possessing a large research group is often perceived as an indicator of exceptional mentorship and high-quality research. However, such large, competitive groups may also escalate dropout rates, particularly among early-career researchers. Overly high dropout rates of young researchers may lead to severe postdoc shortage and loss of top-tier academics in contemporary academia. In this context, we collect longitudinal genealogical data on mentor-mentee relations and their publications, and analyse the influence of a mentor's group size on the future academic longevity and performance of their mentees. Our findings indicate that mentees trained in larger groups tend to exhibit superior academic performance compared with those from smaller groups, provided they remain in academia post graduation. However, we also observe two surprising patterns: academic survival rate is significantly lower for (1) mentees from larger groups and for (2) mentees with more productive mentors. The trend is verified in institutions of different prestige levels. These findings highlight a negative correlation between a mentor's success and the academic survival rate of their mentees, prompting a rethinking of effective mentorship and offering actionable insights for career advancement.

Link prediction on multiplexed networks has wide applications in various fields such as social networks and recommendation systems. Some algorithms have been proposed to solve link prediction on multiplexed networks, which often rely on single-layer node characteristics, inter-layer similarity, and layer fusion. In this paper, we attempt to address this issue from the perspective of the local structure that can be constructed by two nodes. We propose a motifs-based naïve Bayes model for link prediction in multiplex networks, which considers the number of motif predictors and the role of nodes in the motif composition of different network layers. We apply this method to multiple empirical networks, and the results show that our method not only outperforms other existing algorithms in link prediction but also has high prediction accuracy. In addition, the role functions of the nodes included in the model can, indeed, help improve the performance of link prediction methods based solely on motifs. The motifs-based link prediction method effectively leverages the heterogeneity of edges and provides ideas for a more in-depth study of multiplexed networks.

Citations in the scientific literature system do not simply reflect relationships between knowledge but are influenced by non-objective and societal factors. Citation bias, irresponsible citation, and citation manipulation are widespread and have become a serious and growing problem. However, it has been difficult to assess the consequences of mixing societal factors into the literature system because there was no observable literature system unmixed with societal factors for comparison. In this paper, we construct a mathematical theorem network, representing a logic-based and objective knowledge system, to address this problem. By comparing the mathematical theorem network and the scientific citation networks, we find that these two types of networks are significantly different in their structure and function. In particular, the reward function in citation networks is impaired: The scientific citation network fails to provide more recognition for more disruptive results, while the mathematical theorem network can achieve. We develop a network generation model that can create two types of linksx2014logical and societalx2014to account for these differences. The model parameter q, which we call the human influence factor, can control the number of societal links and thus regulate the degree of mixing of societal factors in the networks. Under this design, the model successfully reproduces the differences among real networks. These results suggest that the presence of societal factors undermines the function of the scientific reward system. To improve the status quo, we advocate for reforming the reference list format in papers, urging journals to require authors to separately disclose logical references and social references.

The study of spreading in networks presents a fascinating topic with a wide array of practical applications. Various strategies have been proposed to attack or immunize networks. However, it is often not feasible or necessary to consider the entire network in the context of real-world systems. Here, we focus on a certain group of target nodes with the aim of disconnecting them from the global network structure. For instance, it becomes possible to effectively prevent the transmission of the disease to vulnerable populations, such as infants and the elderly, by isolating some specific nodes such as their caretakers during the epidemic. From this perspective of targeted avoidance, we introduce a series of target centrality indicators and apply them to segment the target nodes from the giant component of the network. Additionally, we propose a more effective iterative graph-segmentation method for targeted immunization. Our experimental findings reveal that our proposed method can substantially reduce the number of nodes required for removal when compared with the methods based on target centrality, which implies a significant cost effectiveness in isolating target nodes from the rest of the network. Finally, we verify our method on a large mobility network in the scenario of the COVID-19 pandemic, and find that our method can effectively protect the elderly by immunizing or isolating a very small group of nodes.

The Kuramoto model is one of the most profound and classical models of coupled phase oscillators.Because of the global couplings between oscillators,its precise critical exponents can be obtained using the mean-field approximation(MFA),where the time average of the modulus of the mean-field is defined as the order parameter.Here,we further study the phase fluctuations of oscillators from the mean-field using the eigen microstate theory(EMT),which was recently developed.The synchronization of phase fluctuations is identified by the condensation and criticality of eigen microstates with finite eigenvalues,which follow the finite-size scaling with the same critical exponents as those of the MFA in the critical regime.Then,we obtain the complete critical behaviors of phase oscillators in the Kuramoto model.We anticipate that the critical behaviors of general phase oscillators can be investigated by using the EMT and different critical exponents from those of the MFA will be obtained.

Signed social networks are a special type of social network with positive and negative relationships. It can provide a powerful framework for studying information spreading in light of opposite user relationships. Currently, static immunization strategies have been constructed to control the spread of disinformation on signed social networks. Here, we focus on dynamic immunization that can be real-time immune to the spread of disinformation on signed social networks, which is vital for shaping public discourse and opinion formation. Accordingly, we proposed the signed contact-tracing (SCT) considering the opposite attitudes of users toward information. Experiments with synthetic and empirical signed networks explore the impact of signed network structure with positive and negative edges on dynamic immunity and confirm the necessity of considering signs in the dynamic immune process. Then, the effectiveness of SCT was verified by two evaluation indicators, and find that targeting individuals with the same ideological group has a smaller spreading range and lower spreading speed than those without differentiated attitudes. Furthermore, the signed backward-contact-tracing (SBCT) based on SCT optimization offers optimal regulatory recommendations for enhancing immunity against disinformation in signed social networks. The study demonstrates how negative relationships impact the dynamic immunity of disinformation, and improves the application of dynamic immunity strategies in signed networks.

The unique structure of signed networks,characterized by positive and negative edges,poses significant challenges for analyzing network topology.In recent years,various statistical algorithms have been developed to address this issue.However,there remains a lack of a unified framework to uncover the nontrivial properties inherent in signed network structures.To support developers,researchers,and practitioners in this field,we introduce a Python library named SNSAlib(Signed Network Structure Analysis),specifically designed to meet these analytical requirements.This library encompasses empirical signed network datasets,signed null model algorithms,signed statistics algorithms,and evaluation indicators.The primary objective of SNSAlib is to facilitate the systematic analysis of micro-and meso-structure features within signed networks,including node popularity,clustering,assortativity,embeddedness,and community structure by employing more accurate signed null models.Ultimately,it provides a robust paradigm for structure analysis of signed networks that enhances our understanding and application of signed networks.

The fractal property widely exists in various complex self-organized systems, so a comprehensive analysis of the robustness of fractal networks is of great significance for the construction of resilient real-world systems. Previous studies have mainly focused on the structural robustness analysis of fractal networks, while this study considers the network functionality to investigate the robustness of fractal scale-free networks to catastrophic cascades and their relationship with the fractal dimension. The hierarchical multiplicative growth model with shortcuts is first created to generate scale-free networks capable of large-scale cascading failures. These networks have the same number of nodes, number of links, degree exponent, and clustering coefficient, but different fractal dimensions. Then, the cascades triggered by two targeted attack strategies within three types of cascade models are analyzed. The results on model networks indicate that the fractal topology can expand the range of load distribution and reduce the load disparity among nodes (or links). As a result of this effect, cascading failures in fractal scale-free networks are more predictable and controllable than their non-fractal counterparts. Notably, the smaller the fractal dimension, the more robust the network is to cascading failures. Finally, numerical results on four types of real-world networks confirm that the above conclusions are considered reliable. This study contributes to a deeper understanding of the evolutionary advantages of fractal topology from the perspective of network functionality, and may provide insight into the prevention, prediction, and control of cascading failures in real-world networks.

Purpose Ranking scientific papers is an important issue for all disciplines. Although this research problem has been intensively studied, the best ranking algorithm is still to be discovered. Some existing studies have proposed evaluation algorithms based on heterogeneous scholarly networks to measure the influence of papers. However, these algorithms have not fully considered the weighted characteristics of different scholarly networks, which can lead to biased ranking results. Evaluation algorithms based on weighted heterogeneous scholarly networks need to be further developed to address this limitation.Design/methodology/approach We propose a weighted heterogeneous network-based ranking algorithm to evaluate the impact of scientific papers, considering the mutual reinforcement relationship among the influences of different academic entities. The weighted heterogeneous scholarly network we constructed considers factors such as the similarity between papers, the number of authors in the papers, and the number of papers published by the authors, which can effectively reflect the relationships among papers, authors, and journals.Findings We applied the proposed algorithm to the American Physical Society (APS) dataset and verified the effectiveness of this method. The empirical results indicate that, compared with other mutual enhancement algorithms, our proposed algorithm can better identify recognized high-impact papers and perform well in evaluating both author and journal impacts.Research limitations The proposed algorithm has only been verified in the domain of physics, and further validation of the algorithm's effectiveness is needed in other disciplines.Practical implications This research can deepen our understanding of impact evaluation and help propose better evaluation methods. The proposed algorithm can be applied to identify important papers in the field of physics and recommend them to relevant scientists.Originality/value This study considers the weighted characteristics of different academic networks more comprehensively and, on this basis, proposes a paper impact evaluation algorithm based on weighted heterogeneous networks by leveraging the mutual reinforcement relationship of the influence of different academic entities.

CONTEXT: As the global population increases and the per capita demand for resource-intensive diets rises, the resulting surge in food demand places greater pressure on the global food system, intensifying its reliance on trade. While much of the existing literature has primarily focused on bilateral trade relationships between countries-many of which are over a decade old-with limited recent contributions. OBJECTIVE: This study presents a novel framework for analyzing global food trade dynamics by conceptualizing food trade in terms of net caloric content. Unlike previous approaches that focus primarily on trade volume, our method accounts for the net caloric value of food exchanges, providing deeper insights into the nutritional balance and food security of countries. METHODS: Using directed, weighted networks to model net caloric flows between countries from 1986 to 2023, we highlight the significant role of nutritional considerations in food security and trade policy. We further employ network metrics-such as connectivity, heterogeneity, modularity, and node correlation similarity-to explore the structural dynamics of global net food calorie trade networks. RESULTS AND CONCLUSIONS: The analysis reveals substantial heterogeneity in trade patterns, with specific countries emerging as key exporters and importers of calories. Our findings also show that the global food trade network has become increasingly integrated, with growing connectivity facilitating the redistribution of food calories, yet also increasing vulnerability to global disruptions. SIGNIFICANCE: The study underscores the importance of incorporating nutritional balance into the discussion of food security, offering a more holistic understanding of global food trade dynamics and highlighting the need for more robust policies to ensure food security in an increasingly interconnected world.

Disruptive innovation is an important feature of scientific research. However, increasing evidence in recent years shows that highly disruptive papers are not necessarily milestone works in science and may even receive very few citations. To understand the mechanisms leading to such phenomena, we develop a link disruption metric that quantifies the disruptiveness of each citation link. This metric allows us to investigate disruption at both the reference and citation levels, enabling the development of a two-dimensional framework to evaluate the persistence of disruption caused by a given paper. Surprisingly, we find that papers with high reference disruption can have high citation disruption, meaning that a paper that disrupts previous papers may itself be further disrupted by its later citing papers. We find that persistently disruptive papers (disruptive papers that are not disrupted by citing papers) are more likely to be recognized as award-winning papers and receive high numbers of citations. Finally, we find that papers of larger teams and papers in recent years, though found to have weaker disruption, are more likely to have stronger persistent disruption once they disrupt previous papers.

Higher-order networks are capable of capturing higher-order interactions among individuals that go beyond simple binary relationships. Networks with high robustness can effectively resist internal interference and external attacks. Therefore, developing strategies to improve the robustness of higher-order networks is very necessary and important. Meanwhile, the community structures of higher-order networks can have a significant impact on the robustness of these networks. However, the robustness enhancement mechanism of higher-order networks with community structures remains unexplored. In this paper, we propose network regulation strategies to enhance the robustness of higher-order networks with community structure through the strategic placement of higher-order structures at distinct topological positions. We also employ the load redistribution model for higher-order networks with community structures to simulate cascading failure processes. By observing the changes in the critical behavior of higher-order synthetic networks and real-world networks under different enhancement strategies, we find that for networks with clear community structures, adding higher-order structures among communities is more effective in enhancing network robustness, whereas for networks with ambiguous community structures, adding them within communities yields better outcomes. Additionally, a mixed higher-order structures addition strategy can be superior to a single-position addition strategy in certain networks. We also compare the results of the strategies of adding higher-order structures with the strategies of randomly adding edges and find that adding higher-order structures can more efficiently improve network robustness. This study contributes to a deeper understanding of the structure and cascading failure dynamics of high-order networks and lays the foundation for developing better robustness enhancement strategies.

An in-depth analysis of the attack vulnerability of fractal scale-free networks is of great significance for designing robust networks. Previous studies have mainly focused on the impact of fractal property on attack vulnerability of scale-free networks under static node attacks, while we extend the study to the cases of various types of targeted attacks, and explore the relationship between the attack vulnerability of fractal scale-free networks and the fractal dimension. A hierarchical multiplicative growth model is first proposed to generate scale-free networks with the same structural properties except for the fractal dimension. Furthermore, the fractal dimension of the network is calculated using two methods, namely, the box-covering method and the cluster-growing method, to exclude the possibility of differences in conclusions caused by the methods of calculating the fractal dimension for the subsequent relationship analysis. Finally, four attack strategies are used to attack the network, and the network performance is quantitatively measured by three structural indicators. Results on model networks show that compared to non-fractal modular networks, fractal scale-free networks are more robust to both static and dynamic targeted attacks on nodes and links, and the robustness of the network increases as the fractal dimension decreases. However, there is a cost in that as the fractal dimension decreases, the network becomes less efficient and more vulnerable to random failures on links. These findings contribute to a deeper understanding of the impact of fractal property on scale-free network performance and may be useful for designing resilient infrastructures.

Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the number of variables, but most existing methods do not account for networked systems with separable coupling-dynamics, where the interaction between nodes can be decomposed into a function of the node state and a function of the neighbor state. Here, we present a novel dimensionality reduction framework that can effectively capture the global dynamics of these networks by projecting them onto a low-dimensional system. We derive the reduced system's equation and stability conditions, and propose an error metric to quantify the reduction accuracy. We demonstrate our framework on two examples of networked systems with separable coupling-dynamics: a modified susceptible-infected-susceptible model with direct infection and a modified Michaelis-Menten model with activation and inhibition. We conduct numerical experiments on synthetic and empirical networks to validate and evaluate our framework, and find a good agreement between the original and reduced systems. We also investigate the effects of different network structures and parameters on the system dynamics and the reduction error. Our framework offers a general and powerful tool for studying complex dynamical networks with separable coupling-dynamics.

Link prediction has a wide range of applications in the study of complex networks, and the current research on link prediction based on single-layer networks has achieved fruitful results, while link prediction methods for multilayer networks have to be further developed. Existing research on link prediction for multilayer networks mainly focuses on multiplexed networks with homogeneous nodes and heterogeneous edges, while there are relatively few studies on general multilayer networks with heterogeneous nodes and edges. In this context, this paper proposes a method for heterogeneous multilayer networks based on motifs for link prediction. The method considers not only the effect of heterogeneity of edges on network links but also the effect of heterogeneous and homogeneous nodes on the existence of links between nodes. In addition, we use the role function of nodes to measure the contribution of nodes to form the motifs with links in different layers of the network, thus enabling the prediction of intra- and inter-layer links on heterogeneous multilayer networks. Finally, we apply the method to several empirical networks and find that our method has better link prediction performance than several other link prediction methods on multilayer networks.