Aaron Clauset, Barbara F. Walter, Lars-Erik Cederman, Kristian Skrede Gleditsch

Although very large wars remain an enduring threat in global politics, we lack a clear understanding of how some wars become large and costly, while most do not. There are three possibilities: large conflicts start with and maintain intense fighting, they persist over a long duration, or they escalate in intensity over time. Using detailed within-conflict data on civil and interstate wars 1946–2008, we show that escalation dynamics — variations in fighting intensity within an armed conflict — play a fundamental role in producing large conflicts and are a generic feature of both civil and interstate wars. However, civil wars tend to deescalate when they become very large, limiting their overall severity, while interstate wars exhibit a persistent risk of continual escalation. A non-parametric model demonstrates that this distinction in escalation dynamics can explain the differences in the historical sizes of civil vs. interstate wars, and explain Richardson’s Law governing the frequency and severity of interstate conflicts over the past 200 years. Escalation dynamics also drive enormous uncertainty in forecasting the eventual sizes of both hypothetical and ongoing civil wars, indicating a need to better understand the causes of escalation and deescalation within conflicts. The close relationship between the size, and hence the cost, of an armed conflict and its potential for escalation has broad implications for theories of conflict onset or termination and for risk assessment in international relations.

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Tiago P. Peixoto

Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same observation. Nevertheless, the vast majority of statistical methods proposed for this task — formulated as the inference of a graphical generative model — can only produce a “point estimate,” i.e. a single network considered the most likely. In general, this can give only a limited characterization of the reconstruction, since uncertainties and competing answers cannot be conveyed, even if their probabilities are comparable, while being structurally different. In this work we present an efficient MCMC algorithm for sampling from posterior distributions of reconstructed networks, which is able to reveal the full population of answers for a given reconstruction problem, weighted according to their plausibilities. Our algorithm is general, since it does not rely on specific properties of particular generative models, and is specially suited for the inference of large and sparse networks, since in this case an iteration can be performed in time O(Nlog2N) for a network of N nodes, instead of O(N2), as would be the case for a more naive approach. We demonstrate the suitability of our method in providing uncertainties and consensus of solutions (which provably increases the reconstruction accuracy) in a variety of synthetic and empirical cases.

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Xingyu Pan, Zerong Guo

Chaos, Solitons & Fractals
Volume 196, July 2025, 116369

Many real-world systems comprise fundamental elements that exhibit mutual exclusion and alternating activation. Here, we develop a framework for the evolution of network structures that captures the behaviors of such systems. We define the dynamic resilience of temporal networks using variational rates to measure how the evolutionary trajectories of network structures diverge under perturbations. We show that perturbations to specific edges and states of mutually exclusive elements can cause evolutionary trajectories of network structures to deviate significantly from the original path. Furthermore, we demonstrate that traditional resilience factors do not affect dynamic resilience, which is instead governed by mutual exclusion within our framework. Our results advance the study of network resilience, particularly for networks with evolving structures, offering a novel perspective for identifying crucial perturbations within the context of the states of mutually exclusive elements.

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Chengbin Sun, Alfonso de Miguel-Arribas, Chaoqian Wang, Haoxiang Xia, Yamir Moreno

In real-life complex systems, individuals often encounter multiple social dilemmas that cannot be effectively captured using a single-game model. Furthermore, the environment and limited resources both play a crucial role in shaping individuals’ decision-making behaviors. In this study, we employ an adaptive control mechanism by which agents may benefit from their environment, thus redefining their individual fitness. Under this setting, a detailed examination of the co-evolution of individual strategies and resource allocation is carried. Through extensive simulations, we find that the advantageous environment mechanism not only significantly increases the proportion of cooperators in the system but also influences the resource distribution among individuals. Additionally, limited resources reinforce cooperative behaviors within the system while shaping the evolutionary dynamics and strategic interactions across different dilemmas. Once the system reaches equilibrium, resource distribution becomes highly imbalanced. To promote fairer resource allocation, we introduce a minimum resource guarantee mechanism. Our results show that this mechanism not only reduces disparities in resource distribution across the entire system and among individuals in different dilemmas but also significantly enhances cooperative behavior in higher resource intervals. Finally, to assess the robustness of our model, we further examine the influence of the advantageous environment on system-wide cooperation in small-world and random graph network models.

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Matthew R. DeVerna, Francesco Pierri, Yong-Yeol Ahn, Santo Fortunato, Alessandro Flammini & Filippo Menczer
npj Complexity volume 2, Article number: 11 (2025)

Understanding how misinformation affects the spread of disease is crucial for public health, especially given recent research indicating that misinformation can increase vaccine hesitancy and discourage vaccine uptake. However, it is difficult to investigate the interaction between misinformation and epidemic outcomes due to the dearth of data-informed holistic epidemic models. Here, we employ an epidemic model that incorporates a large, mobility-informed physical contact network as well as the distribution of misinformed individuals across counties derived from social media data. The model allows us to simulate various scenarios to understand how epidemic spreading can be affected by misinformation spreading through one particular social media platform. Using this model, we compare a worst-case scenario, in which individuals become misinformed after a single exposure to low-credibility content, to a best-case scenario where the population is highly resilient to misinformation. We estimate the additional portion of the U.S. population that would become infected over the course of the COVID-19 epidemic in the worst-case scenario. This work can provide policymakers with insights about the potential harms of exposure to online vaccine misinformation.

Read the full article at: www.nature.com