contagion dynamics analysis and tipping-point detection

Existing models of complex contagion struggle to capture the interplay among individual preferences, local social influence, and global sentiment, and offer limited insight into the critical thresholds governing phase transitions in viral spread. This work proposes a unified cascade model that embeds both ideas and network nodes into a shared high-dimensional feature space. Node state updates are driven by a decision function integrating transmission affinity, local reinforcement, and global activation, yielding an efficiently samplable Markovian cascade process. The model reveals, for the first time, how the dynamic balance between local and global influences critically determines cascade success or failure, and demonstrates that early-stage growth patterns can effectively predict phase transitions. Comprehensive experiments analyze cascade distributions, latent dynamics, parameter sensitivity, and critical behavior, establishing a new paradigm for studying complex contagion mechanisms.

Distinguishing simple contagion (e.g., independent cascade) from complex contagion (e.g., threshold-based activation) solely from observed diffusion data remains challenging due to reliance on strong parametric assumptions and sensitivity to noise and partial observability. Method: We propose the first topological classification framework based on Extended Persistent Homology (EPH), which captures the multiscale evolution of loop structures throughout the diffusion process—without assuming specific activation mechanisms or functional forms. Our approach integrates Topological Data Analysis (TDA), graph neural network–based diffusion simulation, and supervised learning. Contribution/Results: Evaluated on three real-world networks, the framework achieves high-accuracy contagion-type classification (average accuracy >92%) and accurate regression of key parameters (e.g., threshold values). It significantly improves robustness against observational noise, parameter uncertainty, and incomplete observations compared to conventional methods, establishing a novel model-agnostic paradigm for inferring contagion mechanisms from empirical data.

This study characterizes the extinction–persistence phase transition boundary of complex contagion models with recovery mechanisms on random networks. Focusing on the Watts threshold SIS model, the authors perform over 180,000 Monte Carlo simulations on Erdős–Rényi and Barabási–Albert networks, combining adaptive Delaunay sampling with weighted logistic regression to quantitatively reconstruct— for the first time—the phase boundary in the joint parameter space of transmission rate, adoption threshold, and infectious duration. The results reveal an exceptionally sharp transition, with the 10%–90% extinction probability bandwidth spanning only 0.005–0.008, and a phase boundary structure invariant across network topologies. The adoption threshold dominates the transition, while transmission rate and infectious duration play secondary, asymmetric roles. This work establishes a benchmark analogous to the classical SIS epidemic threshold for complex contagion and develops a high-precision six-parameter interaction model.

This study addresses the problem of algorithmic sycophancy induced by large language models, which can trap populations in spirals of erroneous collective beliefs. To counteract this cognitive bias, the authors construct a networked stochastic dynamical system incorporating a minority of topologically central “teacher” nodes designed to correct group-level misperceptions. By employing degree-weighted mean-field approximation, they reduce the high-dimensional Langevin equations to a macroscopic drift equation, thereby offering the first analytical framework that integrates statistical physics with social network theory to elucidate AI-induced sycophancy. Key contributions include an analytical solution for the critical tipping time based on saddle-node bifurcation, a proof that centralized rapid intervention outperforms distributed slow strategies, and demonstration of universal data collapse and theoretical bounds across diverse network topologies. Under strict budget constraints, the work further derives an optimal intervention policy.

This study addresses the formidable challenge of providing ultra-early warnings for irreversible critical transitions in complex dynamical systems subjected to parameter drift and stochastic perturbations. The authors propose a model-free framework that, for the first time, integrates reservoir computing with established stability indicators—such as the dominant eigenvalue of the Jacobian, the maximal Floquet multiplier, and Lyapunov exponents—to learn local dynamics and extrapolate trends solely from observed time series. This approach enables prediction significantly ahead of the actual tipping point. The method demonstrates robust performance across multiple synthetic systems, eight real-world datasets, and the Atlantic Meridional Overturning Circulation, exhibiting strong interpretability, resilience to noise, and exceptional capability for ultra-early warning.

This study addresses a key limitation in existing dynamic network change-point detection methods, which typically assume abrupt and stationary regime shifts, thereby failing to capture the continuous nature of real-world mechanistic transitions. The authors conceptualize a “mechanism” as a coherent evolutionary trajectory along a geodesic in graph space and propose detecting changes by measuring the cumulative deviation of an observed graph sequence from an ideal geodesic path. This approach is the first to model and identify transitions between continuously evolving mechanisms in graph space, moving beyond conventional assumptions of abrupt stationarity. By integrating graph regression with geodesic modeling and embedding it within a change-point detection framework, the method significantly outperforms existing approaches on both synthetic data and real-world mobility networks during the COVID-19 pandemic, yielding change points that align more closely with major external events.

This study investigates how AI-generated content interacting with social network dynamics can induce systematic distortions in collective knowledge. The work proposes a novel dual-feedback mechanism—comprising an “AI contagion channel” and a “social distortion amplifier”—by modeling agents that disseminate information influenced by AI, while the AI itself is retrained on socially generated data already contaminated by its prior outputs. Leveraging dynamical systems theory, spectral radius analysis, and network science, the authors reduce the high-dimensional system to a tractable two-dimensional representation, rigorously characterizing conditions for system stability. They identify the minimal regulatory filtering threshold required to maintain stability and quantify how network topology modulates informational risk.

This study investigates how local mobility, bounded memory, and network structure jointly shape the critical conditions and time scales under which committed minorities drive shifts in group conventions. To this end, we develop a transparent agent-based model that simulates the dynamics of individuals switching between two behavioral states. Departing from prior work focused solely on whether convention change occurs, this paper systematically links structural and behavioral factors to the temporal dynamics of convention shift and introduces a unified predictive model that quantifies their influence on the time required for full adoption. Simulation results demonstrate that convention change ultimately occurs across most configurations, with mobility acting as the dominant accelerator of convergence; memory length and network connectivity further modulate convergence speed in predictable ways, enabling the model to accurately forecast the time to full adoption.

This study addresses the critical challenge of identifying plausible epidemic scenarios from disease transmission cascades. It introduces, for the first time, “boundary degree”—defined as the number of uninfected neighbors of an infected node in a contact network—as an explicit node feature for scenario identification, complemented by edge features and evaluated through systematic ablation experiments. Leveraging agent-based simulations on real-world social contact networks, graph neural representation learning, and theoretical distinguishability analysis, the work demonstrates that certain epidemic scenarios become indistinguishable in the absence of boundary or edge information. Incorporating boundary degree alone improves identification accuracy by 19%, and it exhibits complementary value with edge features, underscoring the importance of tracking contacts involving non-infected individuals for accurate scenario inference.

Existing methods struggle to effectively detect structural breaks in dynamical systems driven by nonlinear, nonstationary trajectories arising from external interventions or environmental shifts. This work proposes a unified framework that, for the first time, jointly models residual discrepancies and normalized parameter drifts to construct a test statistic. By integrating a multi-scale seeded narrowest-over-threshold algorithm, order-preserving segmentation, and symmetric contrastive calibration, the method achieves precise localization of structural changes in ordinary differential equation–driven systems. It simultaneously accounts for model fit and evidence of parameter variation, demonstrating robustness under both stable and divergent trajectories while attaining near-minimax localization accuracy and effective false discovery rate (FDR) control. Experiments show significant improvements over state-of-the-art approaches in detection accuracy and FDR management, with successful applications to modeling COVID-19 transmission dynamics and global temperature trends.