We characterize the multifractal scaling of Bitcoin returns using approximately 774,000 fiveminute observations spanning August 2017 to December 2024. Three methodological innovations distinguish this study from prior multifractal analyses of cryptocurrency markets. First, we adopt the q-Gaussian rescaling framework recently developed by Kluszczy & nacute;ski et al. (2025) to disentangle genuine from spurious multifractality, replacing the conventional but mathematically problematic decomposition that treats temporal correlations and fat tails as additive sources. Second, we identify and characterize a statistically significant scaling crossover at approximately twenty-five days, separating a near-efficient short-time regime from an anti-persistent long-time regime while singularity spectrum width remains essentially invariant across the two regimes. Third, we contrast pre-and post-ETF market behavior to provide quantitative evidence for adaptive efficiency: the Market Deficiency Measure declines by more than half following the January 2024 spot ETF approval, accompanied by a substantial reduction in long-range dependence. The observed Bitcoin multifractality is genuine in the sense of Kluszczy & nacute;ski et al. (2023): nonlinear temporal correlations are necessary, while fat tails play an amplifying role conditional on those correlations. Across the rolling-window panel of estimates, realized volatility and multifractal complexity are negatively coupled at high statistical significance, consistent with regime-dependent multiplicative cascades in which high-volatility episodes are dominated by a single class of large fluctuations and therefore display narrower singularity spectra. Together, these results offer a coherent multifractal characterization of Bitcoin price formation that aligns with the Adaptive Markets Hypothesis and with the broader statistical-physics framework of price scaling complexity.
With the increasing complexity of urban systems, link weight prediction in transportation has become a key issue for understanding system behavior and optimizing resource allocation. As a typical dynamic complex network, transportation systems exhibit highly nonlinear and multi-scale characteristics, where link strengths dynamically evolve over time and space. Traditional methods based on static graph structures or fixed time windows are insufficient for effectively modeling the dynamic evolution of link weights, particularly when it comes to distinguishing between node inherent patterns (non-diffusive) and state propagation (diffusive). To tackle these challenges, this paper presents a Multi-Scale Adaptive Spatio-Temporal Network (MA-STNet) for traffic flow prediction, which systematically models the complex spatio-temporal dependence of link weights in dynamic networks. In the temporal dimension, the model incorporates periodic temporal embeddings and a multi-scale causal temporal attention mechanism, effectively capturing hierarchical temporal dependencies ranging from local fluctuations to long-term trends. For spatial modeling, an adaptive dynamic graph spatial fusion encoder is designed to explicitly distinguish and integrate non-diffusive structural features and dynamically diffusive propagation information, enabling dynamic modeling and prediction of link strength. Experimental results on four real-world large-scale traffic datasets (PEMS03, PEMS04, PEMS07 and PEMS08) show that MA-STNet achieves lower MAE, RMSE and MAPE compared with mainstream methods, effectively capturing both short-term fluctuations and long-term trends in traffic flow, and demonstrating consistency and reliability in link weight prediction tasks within dynamic complex networks.
We study a coupled two-layer opinion dynamics model in which agents simultaneously hold binary opinions on an online and an offline layer. The dynamics combine same-layer social imitation with a symmetric intra-agent cross-layer reconciliation process: with probability p, one layer of an agent is updated to match the other layer. Thus p quantifies the rate of internal cross-layer coordination, rather than a directed preference for either the online or offline state. Monte Carlo simulations reveal an observation-window-dependent crossover from a rapid-consensus regime to a long-lived polarized regime as p increases, with effective crossover centers p close to unity for both network types. The crossover depends on network topology: Erd & odblac;s-R & eacute;nyi networks show a mean-field-like connectivity dependence, whereas Barab & aacute;si-Albert scale-free networks exhibit a much weaker and more scattered dependence, consistent with stabilization by topological heterogeneity. Under periodic external driving with frequency f, both topologies display hysteresis loops whose enclosed area A scales as A similar to f1/2 over the simulated range. The central analytical result is that the leading mean-field driven dynamics admits an exact cancellation of the internal coupling p from the total-magnetization equation. This cancellation leads to a square-root hysteresis scaling that is independent of p at leading order and only weakly dependent on topology, thereby separating topology-sensitive finite-time consensus stability from a comparatively topology-insensitive nonlinear response.
Driving risks during the merging process are complex and highly dynamic, with vehicle interactions serving as the fundamental driver of risk evolution. Existing vehicle interaction models predominantly rely on the discrete classification of interaction patterns, resulting in a lack of temporal analysis regarding the evolution of driving risk. To address this limitation, this study constructs a vehicle interaction model for merging zones employing kinematic approaches, characterizing the dynamic competition-cooperation relationship by quantifying interaction strength (IS). Subsequently, an explanatory framework employing locally weighted SHAP is established to investigate the mechanisms through which kinematic features drive IS. Finally, the Granger causality test is utilized to uncover the influence patterns of interaction strength on the evolution of merging risk. Validation results using trajectory data from merging zones demonstrate that: (1) the proposed vehicle interaction model successfully quantifies interaction strength, with its validity corroborated by statistical test results; (2) THW serves as the optimal parameter for regulating the competition-cooperation phase transition, and the adoption of a decisive and accelerated merging strategy by the merging vehicle facilitates the occurrence of cooperative merging; and (3) IS is statistically confirmed to Granger-cause merging risk. The merging risk generally lags behind variations in IS while maintaining a consistent directional trend, exhibiting a more rapid response under high-intensity interaction conditions. The proposed model provides a methodological reference for analyzing the evolution of merging risk, and the findings offer an empirical basis for optimizing the interactive merging decision-making of autonomous vehicles (AVs).
This paper proposes an approximate analytical expression for the steady-state probability density function (PDF) of a nonlinear stochastic vibration system using neural networks. First, the PDF is expressed in exponential form based on the maximum entropy principle. By leveraging dimensional analysis, the exponential representation is rewritten as a linear combination of dimensionless clusters of system variables (e.g., excitation intensity, system states, and parameters). The approximate PDF is then derived by training two neural networks: the first learns the steady-state PDF, while the second optimizes the weight coefficients of the dimensionless clusters. Unlike existing case-by-case neural network approaches for solving the Fokker-Planck-Kolmogorov (FPK) equation, the proposed method generates a generalizable approximate expression applicable to diverse system parameters. To validate the method, we apply it to the Duffing oscillator, demonstrating close agreement with the exact solution. Further testing on a nonlinear damping system confirms high solution accuracy across a broad parameter range.
