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.
The escalating computational demands of deep learning have raised serious energy concerns, calling for urgent solutions in green artificial intelligence (AI). In this paper, we introduce the Colloidal Boltzmann Machine (CBM), a computing architecture based on an ensemble of nearly independent colloidal particles that can switch between binary active and inactive states. This architecture builds on a key insight from colloid science that the Gibbs factor N! remains essential even for classically distinguishable particles. Specifically, by incorporating this factor into the entropy formulation of colloidal particles, we derive an irreducible baseline energy in the classical regime, which is inherent to the presence of thermal fluctuations. We show that, under thermal fluctuations, the CBM spontaneously evolves toward its global energy minimum, thereby overcoming a limitation of certain conventional models, which can become trapped in local optima. Crucially, this baseline energy prevents complete system shutdown, enabling the potential for self-sustaining computational operation. The CBM thus offers a potential pathway toward energy-efficient, always-on natural computing hardware.
For non-cooperative swarms, such as unidentified unmanned aerial vehicles, implementing guidance methods through invasive take over control poses significant operational challenges. To address this issue, we propose a non-invasive guidance mechanism that leverages statistical properties of noise-disturbed swarms. This mechanism is inspired by the observation that Vicsek swarms exhibit directional selectivity when passing through regions of spatial noises. By configuring the shape of the noisy regions, we can guide the swarm along prespecified motion direction in both 2-dimensional and 3-dimensional spaces. Simulation results demonstrate that the proposed guidance mechanism can effectively guide non-cooperative swarms to desired positions and enable them to move away from specific areas under the influence of spatial noise.
Connected Automated Vehicle (CAV) platoons, while promising significant improvements in traffic systems, are vulnerable to cyberattacks, yet the quantitative safety impacts of diverse attack modalities remain poorly understood. This paper investigates the underlying mechanisms of how various cyberattack types compromise the cooperative car-following dynamics and safety of CAV platoons. We introduce a generic car-following model that explicitly embeds a bidirectional communication topology and instantiate it via the Intelligent Driver Model (IDM). A dedicated dynamic simulation framework is then constructed to systematically quantify and compare the safety impacts of six cyberattack types manipulating vehicle kinematics (speed, position, acceleration). The platoon's safety performance was rigorously evaluated by categorizing and analyzing various cyberattack types, and assessing their impacts across different platoon sizes, attack durations, and targeting schemes, including both single and coordinated multi-vehicle attacks. Results demonstrate that deceleration attacks most severely degrade platoon stability, while acceleration attacks precipitate the most acute collision risks. Coordinated attacks on intermediate vehicles were found to dramatically escalate collision probability. The influence of platoon size and attack duration on risk propagation is complex, with system adaptability showing potential for risk mitigation in specific contexts. Critically, the findings reveal a decoupling of string stability from collision risk and show that systemic threats from coordinated attacks significantly outweigh those from single-point intrusions. These insights provide a theoretical basis for designing differentiated cybersecurity defenses and lay the groundwork for developing robust detection and control strategies resilient to high-risk, coordinated cyberphysical threats in CAV platoons.
In recent years, resistor networks have found wide applications. However, existing methods for dynamic problems often suffer from slow convergence and low computational efficiency. The torus structure, characterized by periodic closure, is a super structured quadrilateral mesh ubiquitous in engineering and scientific systems and increasingly relevant to robot path planning. To address these issues, a New Neural Network (NNN) algorithm is proposed to solve the node potential of the Torus Super Structured Quadrilateral (TSSQ) Dynamic Resistor Networks. First, a model is constructed to solve the voltage-current relationship in torus resistor networks. By exploiting the structural properties of the Laplacian matrix, an optimized computational scheme is developed, significantly improving computational efficiency. Second, integrating the inherent natural decline characteristic of the node potential of the resistor network into the core layer of the design for the intelligent robot's path-finding algorithm, an innovative and effective algorithm for the path planning of the intelligent robot has been presented. The algorithm efficiently generates collision-free paths in static environments and demonstrates superior efficiency compared with classical methods, while also exhibiting robust performance in dynamic environments. Finally, a conjecture is presented that the natural descent of electric potential corresponds to the fastest path.
This paper investigates the coupled interplay among public opinion, mass media, and epidemic spreading through a co-evolutionary multilayer network framework. We develop a Susceptible-Alert-Infected-Susceptible (SAIS) model on the physical layer, coupled with a dynamic opinion layer that captures groups' perceived severity of the epidemic. A key feature of the model is a parameter-level coupling mechanism, whereby opinions-shaped by mass media and social interactions-directly modulate infection and recovery rates. The opinion dynamics evolve on a directed signed graph, incorporating both cooperative and antagonistic inter-group interactions as well as media influence. We rigorously establish the well-posedness of the system and derive opinion-dependent reproduction numbers to characterize epidemic thresholds. Analytical and numerical results reveal that the interaction between media-driven alertness and social influence generates rich dynamical behaviors, leading to multiple stable equilibria. By examining different regimes of the reproduction numbers, we identify diverse epidemic-opinion scenarios and discuss their potential strategic implications.
Traditional complexity measurement commonly emphasizes pattern structure and density estimation. Although the emergence of patterns inherently stems from the intrinsic autocorrelation and inter-correlations within signals, complexity measurements do not specifically cope with these correlations, leading to limited performance on multivariate time series. To address this limitation, we introduce time-delay embedding and singular value decomposition to permutation entropy (denoted as HES), which comprehensively characterizes the complexity of multichannel signals from multiple perspectives while reducing the impact of correlations. Our method achieves improved classification accuracy compared to state-of-the-art complexity metrics, and exhibits enhanced sensitivity to intrinsic mode memory changes. Furthermore, we combine HES with random forest or support vector machine classifiers and a surrogate optimization algorithm on three benchmark datasets. This combination method achieves higher accuracy which smoothly varies with embedding parameters. Moreover, HES excels in binary classification problem and is highly effective for short vibration signals.
Directed network dynamics are inherently asymmetric, yet node-level spectral sensitivity often does not explicitly distinguish perturbation direction. Here we formulate an incoming-link-based nodal Fiedler contribution as a direction-aware node-level aggregation of Laplacian spectral sensitivity, measuring the first-order response of the real part of the relevant nonzero directed-Laplacian eigenvalue to a structured perturbation of all incoming links of a node. Building on first-order non-Hermitian perturbation theory, the formulation is defined under explicit assumptions of strong connectivity and spectral simplicity. Across motifs, synthetic ensembles, and empirical directed networks, we show that this incoming-link-based quantity is systematically associated with nodal relaxation and synchronization times, although the strength of the association depends strongly on topology. More importantly, comparison with the corresponding outgoing-link perturbation reveals a pronounced directional asymmetry: the two nodal sensitivities are generally not equivalent and can exhibit qualitatively different relations to nodal timescales. These results support direction-dependent node-level spectral sensitivity as a useful diagnostic feature of directed network dynamics and clarify both its explanatory value and its limitations.
Discrete systems with spatially inhomogeneous occupation are analyzed using triangular and square elementary cells, in which the occupation probability depends on the position of the central site. As a first approximation, a first order parameterization is introduced for both geometries, assigning different probabilities to the central site and its nearest neighbors. Subsequently, in the case of the square lattice, the formulation is extended to the second order by incorporating the contribution of the corner sites, allowing for a more detailed description of the spatial structure of connectivity. Based on an exact classification of percolating configurations, a master equation is constructed for each geometry, whose derivative enables the determination of the percolation threshold via the Rosowsky method, correctly recovering the homogeneous case as a particular limit. The results show that the percolation threshold depends strongly on the spatial distribution of occupation and on the lattice geometry, revealing a hierarchy in the contribution of different types of sites. In particular, critical frontiers are identified in the parameter space, separating regions where percolation is accessible. In contrast, other regions correspond to regimes in which global connectivity can only be achieved in the limit of near total occupation (p -> 1). Finally, the model is reinterpreted in terms of infection spreading on a discrete lattice, where site occupation represents the probability of infection in a structured medium. In this context, the percolation threshold may be interpreted as a qualitative effective epidemic threshold associated with the ability of the infection to propagate through the system. The spatial heterogeneity introduced in the model controls the transmission efficiency between different types of sites, giving rise to an alternative, simple, and semi-analytical framework that allows exploration of how tissue structure and the spatial distribution of contacts may influence spreading processes.
This study explores cross-national emotional differences in media consumption by analyzing Netflix movie trailers. Emotional scores were extracted from the top 10 trailers per month across 28 countries in 2022 using facial recognition and machine learning. Each country's emotional profile was constructed, and emotional distance between countries was measured. These emotional distances were then compared with six socio-cultural indicators: language, culture, religion, genetics, geography, and economy. A gravity model framework was employed to assess how these factors influence emotional distance across country pairs. Results show that religious, genetic, and geographic distances significantly predict emotional distance, whereas language, cultural distance, and GDP per capita do not. However, subsequent mediation analyses reveal that genre distance significantly mediates the relationship between linguistic and cultural distances and emotional distance, indicating that their influence operates indirectly through differences in genre composition rather than through direct emotional alignment. This suggests that emotional similarity between nations is more closely linked to deep-rooted historical and social factors than to economic or linguistic proximity. By introducing emotional distance as a novel metric, the study offers a new framework for understanding global media engagement beyond conventional cultural and economic analyses.
The occurrence of crowd pushing significantly reduces evacuation efficiency and increases the risk of casualties. To quantify the impact of pushing behavior on the evacuation process, this paper develops a ship pedestrians evacuation model based on the Social Force Model. The improved social force model uses a Sigmoid function to describe how the panic coefficient influences the intensity of the pushing force. It also introduces the conditions of pedestrian spacing and movement direction to determine when pushing forces occur, allowing for dynamic evaluation of the pushing force during the evacuation process. The simulation results show that as the panic coefficient increases, evacuation time exhibits a nonlinear growth trend, with evacuation efficiency dropping sharply under high panic conditions; the greater the pushing force, the longer the evacuation time. A comparative analysis with typical tests from MSC.1/Circ.1533 guidelines and simulation results from the Pathfinder evacuation software shows that the model proposed in this study effectively simulates the pushing behavior between pedestrians in a panic state and can accurately assess the impact of panic on the evacuation process. The model can be used to evaluate the evacuation capacity of a ship's pedestrians in panic situations.
Infectious disease dynamics modeling demands accurate and efficient numerical solvers for nonlinear stiff systems, while traditional compartmental models oversimplify population heterogeneity and intervention effects. To address these issues, this work develops a refined SITR model that distinguishes two susceptible subgroups (S1, S2), infected (I), treated (T), and recovered (R) populations, incorporating natural demography, transmission heterogeneity, and therapeutic interventions. To solve the resulting high-dimensional nonlinear ordinary differential equations, we propose a time-domain piecewise physics-informed random neural network (PIRNN) with algebraic constraints. The method constructs trial functions that exactly satisfy initial conditions, randomly initializes and freezes hidden-weights, and converts the differential system into a set of nonlinear algebraic equations over segmented time subintervals, which are solved sequentially via MATLAB's fsolve. Compared with the standard physics-informed neural network (PINN), which suffers from slow gradient descent convergence, local minima trapping, and error accumulation in long-time simulations, the proposed PIRNN avoids iterative backpropagation, reduces optimization dimensionality, and mitigates stiffness-induced numerical instability. Numerical experiments on two representative epidemic scenarios demonstrate that the PIRNN achieves 10-8-10-9 level accuracy, significantly outperforming PINN (with errors at 10-3-10-2) and the reference Runge-Kutta (ode45) solver in both solution precision and computational efficiency. The proposed framework provides a robust and scalable tool for dynamic simulation, parameter calibration, and intervention strategy optimization of complex infectious disease systems.
Quasi-static shear in granular sphere packing have been reported with intermittent peaks in the unbalanced force (UBF) index, which is attributed to the release of stored elastic energy, but the microscopic mechanisms underlying these events have remained unclear. In this work, we examine these events using a network-based analysis of particle interactions. The granular system is represented as a contact network, and modularity-based community detection is applied to identify groups of interacting particles at discrete time steps, without using predefined thresholds or labels. By following the evolution of these communities, we observe that large UBF peaks tend to follow the changes in local community organization. The study aims to perform data-driven analysis of UBF peak anomaly linking community-level dynamics to the UBF fluctuations. These results suggest that modularity-based community analysis can be a useful tool for studying collective effects in quasi-static granular systems.
Heterogeneous hypergraphs can better reflect real events, and heterogeneous hyperlink prediction is an effective way to discover hidden events. Most existing methods embed heterogeneous hypergraphs in Euclidean space for representation learning. However, distortion occurs when embedding graph-structured data in Euclidean space, which affects prediction performance. To tackle these challenges, we introduce hyperbolic hypergraph embedding to reduce distortion. In this paper, we propose a novel Heterogeneous Hyperlink Prediction method based on Hyperbolic Hypergraph Attention Networks (HeHLP-HHAN). First, the feature spaces of different types of nodes are aligned. Next, the hypergraph convolution operation in hyperbolic space is designed to obtain the hyperbolic embedding of nodes. Finally, a hyperlink scoring function is designed based on the hyperbolic embedding to measure the likelihood of the hyperlink existence. In addition, we design two attention mechanisms, type-level and node-level, to improve the expression ability of the HeHLP-HHAN model. In experiments on five real-world network event datasets, HeHLP-HHAN outperforms baselines in terms of Average Precision (AP) and Area Under Curve (AUC) indicators, achieving the best prediction performance.
In the context of urban road networks, intelligent and connected vehicles (ICVs) leverage cooperative sensing, real-time communication, and intelligent decision-making, making them central to future intelligent transportation systems. However, the parallel movement and unpredictable trajectory disturbances of non-motorised vehicles on urban roads often force mainline vehicles to accelerate or decelerate abruptly, severely impacting ride comfort. Concurrently, ICVs' heavy reliance on open communications renders them vulnerable to cyberattacks such as false data injection and data tampering, posing direct challenges to cooperative efficiency and driving safety. To systematically investigate the coupled dynamics of malicious cyberattacks and traffic jerk effects on vehicle coordination, we develop a novel 2-D lattice-based hydrodynamic approach that includes a multi-phase optimal velocity function to emulate intermittent acceleration patterns observed in empirical traffic. Linear stability analysis establishes the stability condition and reveals a critical dependency: the order of phase transition is intrinsically governed by the number of turning points in the optimal velocity function. Moreover, the imposed malicious cyberattack intensity and traffic jerk factor profoundly degrade traffic flow stability, thereby widening the instability basin in phase space. Through a nonlinear perturbation approach, we derive the modified Korteweg-de Vries (mKdV) equation for the new model and analytically obtain its kink-antikink soliton solution, which elucidates the evolution of clustered congestion and flow deceleration near the critical stability region. Computational experiments under periodic boundary conditions validate the theoretical results. This work provides insights into the destabilisation mechanics of urban networks under cyber threats and supports the subsequent design of emergency management and control strategies.
Cascading failures have been widely used to assess vulnerability in urban rail transit networks (URTNs), yet most existing models rely on assumptions that are misaligned with timetable-based rail operations. In particular, they often equate congestion with functional failure, assume that station failures disable line operations, and allow unrestricted passenger redistribution, which may artificially amplify disturbance propagation. This study revisits cascading failures in URTNs from an operational perspective and develops a simulation framework that integrates (i) timetable-based batch service with explicit boarding/alighting and dwell-time dynamics, (ii) destination-oriented and time-dependent passenger demand, and (iii) passenger responses to service inaccessibility within a multi-layer network representation. Numerical experiments in the Shanghai URTN show that isolated station disruptions rarely trigger large-scale cascading failures under realistic parameters. More pronounced propagation emerges under consecutive train cancellations, but remains spatially localized and temporally bounded. Comparative experiments further show that stronger propagation arises mainly when passenger exit is suppressed and service continuity at failed stations is removed, highlighting the buffering roles of realistic accessibility limits and the multilayer service representation. Sensitivity analyses demonstrate the buffering role of residual capacity. These findings imply that large-scale cascades reported for URTNs appear to be sensitive to modeling assumptions, especially continuous flow redistribution, enforced topological disconnection, and the treatment of congestion as failure, rather than an inherent property of timetable-based rail operations.
