Search Results (1,169)

The sign of the maximal almost sure Lyapunov exponent determines the stability of stochastic systems, while its numerical computation for three-dimensional linear Stratonovich stochastic differential equations remains challenging due to the failure of classical two-dimensional strategies. The spherical angular motion of 3D systems produces a Fokker–Planck equation with intractable mixed partial derivatives, preventing conventional analytical solutions. This paper develops a unified computational framework for three-dimensional linear Stratonovich stochastic systems using analytical derivation for degenerate cases and physics-informed neural network (PINN) approximation for general non-degenerate scenarios. For degenerate systems, we reduce the coefficient matrix to a lower triangular form via orthogonal transformation and establish tight upper bounds based on the logarithmic growth property of the Wiener process, yielding closed-form expressions for the maximal almost sure Lyapunov exponent under all parameter sign configurations. For non-degenerate systems, we reformulate the Fokker–Planck equation in spherical coordinates and construct a customized PINN with trigonometric encoding to enforce periodic boundary conditions. The network is trained by joint loss functions of equation residuals, boundary constraints and normalization consistency, and the converged stationary density is substituted into the Furstenberg–Khasminskii formula to calculate the exponent via Gauss–Legendre quadrature. Monte Carlo simulations confirm the accuracy and robustness of the proposed method, which reliably identifies the sign of the maximal almost sure Lyapunov exponent even in near-critical regimes. Numerical experiments on a 3D stochastic Hopf bifurcation model show that noise negatively shifts the bifurcation point, with the offset linearly proportional to the squared noise intensity. This work extends Lyapunov stability analysis from two-dimensional to three-dimensional linear Stratonovich stochastic systems, offering an effective tool for stability evaluation of general three-dimensional stochastic dynamical models. Full article

Curvature-based descriptors are increasingly used in surface metrology for the characterization of complex geometries. However, their sensitivity to measurement uncertainty remains insufficiently understood, particularly in comparison with conventional deviation-based metrics. This study investigates the propagation of coordinate measurement noise into curvature estimation using a numerical framework combining differential geometry, local quadratic surface fitting, and Monte Carlo simulation. A set of nominal surfaces, including spherical, cylindrical, and free-form geometries, was analyzed under controlled stochastic perturbations. The results show that curvature uncertainty increases nonlinearly with coordinate noise and is significantly more sensitive to measurement errors than point-wise deviations. Even small perturbations in measured coordinates lead to amplified variability in curvature due to its dependence on second-order derivatives. The analysis further reveals the presence of systematic bias in curvature estimation and demonstrates that the resulting distributions deviate from normality, despite Gaussian input noise. This finding highlights the limitations of classical uncertainty evaluation approaches based on linear propagation and normality assumptions. In addition, the study shows that increasing sampling density does not necessarily improve estimation reliability, while the size of the local fitting window plays a key role in stabilizing curvature estimation, acting as an implicit regularization parameter. The comparison with conventional form deviation metrics confirms that curvature-based analysis provides complementary information about local geometric stability, which is not captured by global measures. The proposed simulation-based approach offers a practical framework for evaluating uncertainty in nonlinear geometric measurements and supports the integration of curvature-based descriptors into advanced metrological applications. The proposed framework can support uncertainty-aware evaluation of free-form surfaces in practical measurement tasks, including coordinate measurement of turbine blades and aerodynamic components in the aerospace industry, as well as optical scanning and verification of patient-specific biomedical implants, where accurate curvature characterization is essential for quality assessment. Full article

Stock index price series are composed of superimposed multi-frequency components, including long-term trends, cyclical fluctuations, and stochastic noise. Effectively decoupling these heterogeneous components and modeling them separately is key to improving forecasting accuracy. Existing methods under the “decomposition–prediction” paradigm mostly employ fixed-scale decomposition, and the forecasting models are not specifically adapted to the non-stationary and high-noise characteristics of financial data, resulting in limitations in adaptivity and local dynamic capture. This paper proposes a frequency-aware adaptive multi-scale decomposition Transformer hybrid model (FAMS-Transformer). At the decomposition level, the fast Fourier transform is used to dynamically identify dominant cycles, thereby adaptively decoupling trends and fluctuations, overcoming the limitations of fixed-scale decomposition. At the forecasting level, a lightweight depthwise separable convolution is embedded between the self-attention and feedforward network of the Transformer encoder, enhancing the model’s ability to capture local temporal dynamics and achieving collaborative modeling of global dependencies and local information. Comparative experiments with 15 baseline models including LSTM, Transformer, TimesNet, and FreTS on three representative Chinese market indices—Shanghai Composite Index, Shenzhen Component Index, and Small and Medium Enterprises 100 Index—across four prediction horizons from one step to 15 steps demonstrate that FAMS-Transformer achieves the best forecasting accuracy in all scenarios. The coefficient of determination for 15-step prediction remains stably between 0.730 and 0.928. Moreover, the model still performs well on the S & P 500 dataset. Ablation studies and significance tests further validate the effectiveness of each core module and the statistical significance of the performance improvements. Full article

The seamless integration of real-time operational technology (OT) with big data architectures remains a critical bottleneck in developing robust robotic Digital Twins. Furthermore, evaluating stochastic motion planners strictly within pristine simulations obscures vital real-world challenges such as sensor noise, communication latency, and mechanical stress. This study presents a high-throughput, real-time Hardware-in-the-Loop (HIL) pipeline integrating ROS 2, Apache Kafka, and Functional Mock-up Units (FMUs). Using a UR10e manipulator in a constrained industrial environment, we conducted extensive physical benchmarking of 11 Open Motion Planning Library (OMPL) algorithms across 10 repetitions, generating a comprehensive dataset of 785,192 samples. The proposed IT/OT architecture achieved deterministic millisecond-level synchronization, bounding end-to-end communication latency between 0.09 and 15.51 ms. Physical executions revealed a macroscopic “topological divergence” between simulation and reality, with spatial deviations peaking at 457.65 mm due to real-world point-cloud noise. While algorithms like EST and KPIECE demonstrated optimal geometric efficiency (e.g., a mean path length of 14.57 m) and hardware-friendly dynamics, traditional planners like RRT generated severe inertial spikes of up to 100 N, demonstrating substantial unsuitability for continuous industrial deployment. The primary contribution is a methodologically novel, rigorously validated big data pipeline and the release of an open-source, 50 Hz multimodal dataset (spatial, temporal, and dynamic forces), bridging the sim-to-real gap and providing a foundational benchmark for future data-driven robotic applications. Full article

Liquid storage tanks are widely used in sectors such as water treatment, oil and gas, food processing, and chemical manufacturing. Knowing the exact amount of liquid in a tank is essential for ensuring safety, preventing spills, and optimizing process control; therefore, the liquid level in a tank must be maintained at a precise reference point. This is where liquid level control for tanks becomes crucial and constitutes a fundamental problem in the industrial sector due to nonlinearities, multivariable coupling, and stochastic disturbances. Given the drawbacks of available control methods, such as classical Model Predictive Control (MPC), which are highly dependent on model accuracy and struggle to reject complex stochastic noise, predicting random disturbances represents a major technological challenge. A new approach is proposed to specifically address the problem and challenge of the four-tank system, where water levels in two lower tanks must be controlled by two pumps, often with varying delays and significant parameter disturbances. To establish a relationship between expected performance and MPC parameters, this approach uses a novel hybrid nonlinear MPC, Extended State Observer, and Physics-Informed Neural State Estimation (NMPC-ESO-PINSE) architecture. A Physics-Informed Neural State Estimation (PINSE) layer, chosen for its learning capacity, is designed to filter sensor noise by applying Bernoulli’s physical laws, while an Extended State Observer (ESO) is integrated to capture and compensate for unmodeled uncertainties in the process. Finally, a proposed hybrid (NMPC-ESO-PINSE) strategy leverages these clean, physically consistent state estimations to solve a non-convex optimization problem via Sequential Quadratic Programming (SQP), computing optimal pump voltages. Extensive numerical simulations demonstrate the superior resilience of this decoupled framework against parametric drifts and continuous noise sequences, yielding a +27.36% reduction in global Root Mean Square Error (RMSE) compared to standard NMPC, accelerating the closed-loop settling time to 15.2 s, and restricting transient overshoot to just 0.18%. Full article

Transcriptional bursting, the stochastic production of mRNA in episodic pulses, is a fundamental source of cell-to-cell heterogeneity. In pluripotent stem cells (PSCs), these bursting dynamics at core pluripotency loci are not just noise but critical determinants of identity maintenance and lineage commitment. This review synthesizes current quantitative frameworks for dissecting bursting kinetics and elaborates on the multilayered regulatory hierarchy that governs them, ranging from promoter-intrinsic features and 3D genome architecture to the formation of transcriptional condensates via liquid–liquid phase separation (LLPS). By integrating findings from genomic profiling and live-cell imaging, we highlight how the integrated action between super-enhancers and epigenetic states shapes the unique bursting dynamics in PSCs. Furthermore, we explore the functional consequences of these kinetics in pluripotency surveillance and cell fate decisions. Collectively, this review establishes a unified regulatory framework, providing novel insights for understanding stem cell heterogeneity and offering key insights for regenerative medicine. Full article

Cold-chain supply systems depend on a sequence of linked production and logistics decisions. In prepared-food cold chains, quality may deteriorate not because one visible failure occurs, but because testing, traceability records, temperature monitoring, and abnormal-condition reporting are gradually weakened under cost pressure. Once such hidden effort reduction accumulates, external disturbances may push the system from strict assurance to weakened governance. To explain this nonlinear process, an asymmetric evolutionary game is built between prepared-food producers and cold-chain logistics providers, each choosing between strict and weakened quality assurance. White Gaussian noise is introduced to represent random operating shocks, and the two-population strategy system is projected onto a system-level quality-governance coordinate, q. This projection is used as a transparent baseline coordinate rather than as an assumption of linear system evolution. The reduced system is then transformed into a stochastic cusp catastrophe model, with a resilience indicator used to measure the distance from critical transition conditions. Numerical simulations show that quality assurance costs and short-term cost-saving benefits move the system toward a weakened-governance basin, whereas external incentives, coordination degree, and credible accountability mechanisms support recovery toward strict collaboration. The framework offers a scenario-based resilience diagnosis approach for identifying threshold effects in cold-chain quality governance. Digital traceability, temperature-data sharing, incentive alignment, and accountability rules are further interpreted as operational innovations that improve resilience and reduce avoidable quality losses in sustainable cold-chain operations. Full article

Methane source-rate inversion from remote-sensing plume imagery is essential for emissions monitoring, but its accuracy is often limited by uncertainty in ancillary wind information. This study examines how physical knowledge can be integrated into a deep-learning inversion model when the available wind input is imperfect. Using a controlled large-eddy-simulation (LES) benchmark designed for EnMAP/PRISMA-style imaging-spectrometer methane quantification, we compare six models that span image-only regression, flexible wind conditioning, simplified hard integrated-mass-enhancement (IME) coupling, and soft physics-guided learning under clean inputs, deterministic wind bias, stochastic Gaussian wind noise, and source-rate-stratified tests. Under clean benchmark conditions, flexible wind conditioning provides the best scalar accuracy, with FiLM reaching a mean absolute percentage error (MAPE) of 6.19% and a root mean squared error (RMSE) of 1323.36, followed closely by Concat (MAPE 6.37%, RMSE 1325.69). The simplified hard-coupling model is sensitive to wind perturbations: DIN-hard rises from MAPE 8.44% under clean inputs to 31.39% and 26.89% under deterministic wind-bias multipliers α = 0.7 and α = 1.3, respectively, and becomes unstable under stronger Gaussian wind noise in the tested protocol. By contrast, DIN-soft-v2 remains competitive under clean conditions (MAPE 6.39%, RMSE 1360.94), follows smoother degradation under biased or noisy wind, and improves plume spatial diagnostics relative to DIN-soft (center-of-mass shift 3.92 versus 4.07 pixels; plume alignment degree 2.60 versus 2.72 degrees). The calibrated IME-style physical baseline reaches a clean MAPE 24.45%, indicating that the learning-based models substantially outperform this benchmark physical proxy. Within this LES-based benchmark and the tested wind-perturbation protocols, the results suggest that IME-inspired physical knowledge is more robustly incorporated as a calibratable soft prior than as the simplified hard log-additive forward coupling considered here; however, transfer to real satellite scenes still requires validation. Full article

Urban low-altitude unmanned aerial vehicle (UAV) logistics networks face critical operational bottlenecks due to complex three-dimensional spatial blockages, continuous communication diffraction, and severe vulnerability to information-layer threats such as Automatic Dependent Surveillance—Broadcast (ADS-B) signal anomalies. To address these interconnected challenges, this paper proposes an event-driven, cloud–edge collaborative digital twin framework to guarantee continuous multi-link communication and flight safety. The architecture operates through a dual-tier “Teacher–Student” paradigm. Under secure conditions, a cloud digital twin acts as a high-capacity “Teacher,” employing Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to partition heterogeneous user topologies. It then utilizes an energy-guided stochastic diffusion sampling (EGSDS) method to refine initial macroscopic routing, generating precise, outage-free global trajectories by systematically minimizing non-line-of-sight (NLoS) observation penalties and kinematic regularization costs. To counteract signal anomalies, a distributed Time Difference of Arrival (TDOA) anchor network continuously validates UAV coordinate integrity. If a threshold is breached, control authority is instantly transferred to the UAV’s edge digital twin. This resource-constrained edge tier relies on a localized “Student” network trained via progressive distillation. By compressing the computationally heavy iterative diffusion process into a rapid one-step inference model, the UAV autonomously generates a secure, short-range emergency path that strictly adheres to minimum communication thresholds. Once interference clears, the cloud seamlessly regains control to complete the logistics mission. Experimental results demonstrate that the proposed scheme significantly outperforms conventional heuristic routing methods in cloud-based scenarios. Furthermore, the edge-based distillation mechanism substantially improves the overall trajectory survival rate under signal anomalies, ensuring resilient and continuous logistics operations. Full article

Magnetic anomaly detection is vulnerable to environmental noise and insufficient prior target information, making non-periodic anomaly signals difficult to detect at low-signal-to-noise-ratio (SNR) conditions. This paper proposes a detection method based on a multi-parameter-constrained mirror dual-branch biased monostable stochastic resonance (SR) system. Nonlinear odd-order bias terms are introduced into the conventional biased monostable potential function to build a multi-parameter-controllable SR model. This improves regulation of potential-well width, depth, and wall morphology, enhancing noise-energy utilization and responses to non-periodic features. Considering peak-type, valley-type, and bipolar anomaly morphologies, a mirror dual-branch SR structure is developed to cooperatively detect features with different polarities. To preserve temporal waveforms and time–frequency structures during parameter optimization, a composite metric combining the correlation coefficient and wavelet-domain image structural similarity index is constructed. Multi-fidelity robust Bayesian optimization is used to obtain a unified robust parameter set for the magnetic anomaly signal family. Experiments with simulated colored noise and measured geomagnetic noise show that the proposed method effectively recovers magnetic anomaly features under strong noise. At −19 dB SNR, its detection probability remains above 80%. Compared with orthogonal basis function decomposition, empirical mode decomposition, and complete ensemble empirical mode decomposition with adaptive noise, the method achieves better noise suppression, feature preservation, and detection performance under low-SNR conditions. Full article

Reliable spatial georeferencing of mobile mapping platforms is a fundamental prerequisite for high-fidelity urban remote sensing products such as 3D point clouds and digital twins. However, in deep urban canyons, severe signal occlusion and multipath effects reduce visible GNSS satellites, causing ambiguity resolution (AR) failure and degraded observation geometry for UGV-borne systems. Conventional Vehicle-to-Vehicle (V2V) cooperation offers limited improvement due to symmetric ground-level occlusion. To overcome this, we propose an asymmetric GNSS/UWB fusion method that introduces Unmanned Aerial Vehicles (UAVs) as high-altitude dynamic spatial anchors to reconstruct the 3D observation geometry. Two contributions are presented: (i) an asymmetric heterogeneous stochastic model coupling carrier-to-noise ratio (C/N0) and elevation angle to handle the quality disparity between air and ground sensor links, preventing multipath contamination of high-fidelity UAV observations; and (ii) a dynamic baseline constrained least-squares algorithm integrating Ultra-Wideband (UWB) ranging to stabilize GNSS positioning under high-dynamic relative motion. Validated through high-fidelity simulations and field experiments, the method achieves a 98.2% AR success rate and sub-decimeter 3D accuracy under extreme occlusion (≤3 visible satellites), while urban-canyon tests demonstrate 100% positioning availability across all evaluated epochs and reduce the 95th-percentile 3D error from 7.25 m to 0.19 m under the tested single-UAV/single-UGV configuration. The framework supports smart city modeling, 3D reconstruction, and infrastructure monitoring. Full article

We analyze the standard multi-particle particle swarm optimization (PSO) algorithm with global-best (all-to-all) topology and constant hyperparameters on smooth strongly convex objectives. By rewriting the PSO velocity recursion as a stochastic heavy-ball method acting on a time-varying quadratic surrogate defined by the personal and global bests, and by applying a Lyapunov drift argument in the style of stochastic momentum analyses, we obtain mean-square convergence of particle positions to the unique minimizer and convergence of the best-so-far objective gaps. The deterministic PSO obtained by fixing the random coefficients at their mean values appears as a noise-free special case of the same Lyapunov framework. Full article

The well-known effect of stabilization by noise for Ito’s scalar linear stochastic differential equation was proven by R.Z. Khasminskii more than 50 years ago. Here, a similar statement is obtained for a system of linear stochastic differential equations. The obtained result is illustrated on the system of two linear stochastic differential equations via several special examples with numerical simulations and figures. Full article

Accurate Unmanned Aerial Vehicle (UAV) position estimation is the cornerstone of urban low-altitude safety management systems. Time Difference of Arrival (TDOA) and Remote Identification (Remote ID) are widely used surveillance technologies with complementary characteristics. TDOA provides high-rate updates but suffers from geometry-induced horizontal–vertical anisotropy and multipath effects, while Remote ID supplies absolute state information yet struggles with intermittent sampling and packet loss. Existing fusion schemes typically address these issues in isolation: sequential filtering manages asynchrony but assumes Gaussian noise, robust estimators suppress outliers at the cost of discarding valid data, and coupled-filter architectures allow vertical anomalies to contaminate horizontal estimates through the Kalman gain cross-coupling. No prior framework jointly handles structural TDOA altitude jumps, stochastic Remote ID timing jitter, and the geometric anisotropy between estimation subspaces within a single coherent pipeline. To bridge this gap, we propose a Hybrid Conditional Kalman Filter (HCKF) framework comprising three integrated modules. First, a kinematics-based temporal alignment module maps asynchronous measurements onto a uniform timeline and predicts missing samples, resolving cross-modal time mismatches. Second, a measurement quality evaluation mechanism detects TDOA altitude steps via robust two-layer stratification and scores Remote ID timing irregularity through a confidence mapping, converting these anomalies into dynamic covariance adjustments and weight caps without discarding observations. Third, a Subspace-Decoupled Fusion strategy exploits the physical insight that TDOA horizontal precision derives from hyperbolic intersection geometry, whereas its vertical estimates suffer from weak observability due to near-coplanar ground-station deployment. By applying entropy-guided weighting in the horizontal plane and a conditional Remote ID-dominant rule in the vertical axis, this design prevents cross-dimensional error propagation. The framework was validated using three real-world flight missions at distinct altitudes (255 m, 345 m, and 440 m) totaling 13.51 km of flight distance, with RTK serving as ground truth. HCKF reduces the Root Mean Square Error by over 40% relative to single-source baselines (95% bootstrap confidence interval: [35.2%, 48.7%]), and paired Wilcoxon signed-rank tests confirm statistically significant improvement ($p<0.01$) over standard EKF, Covariance Intersection, and Iterative CI across all three tracks. Full article

We develop a systematic framework for incorporating perturbative correction terms into classical finite difference schemes for Allen–Cahn type stochastic partial differential equations. Three distinct correction approaches are introduced, conceptually motivated by perturbative quantum field theory, quantum coherent state evolution, and WKB (Wentzel–Kramers–Brillouin) barrier penetration theory. These quantum-inspired perturbative method (QIPM) corrections function as classical perturbations executing entirely on conventional hardware; quantum-mechanical formalism serves only as a design principle for constructing specific functional forms of correction terms. The primary novelty of this work lies in (i) a generic convergence-preservation theorem establishing sufficient conditions on correction magnitude for any perturbative correction to maintain the base scheme’s accuracy order, and (ii) a systematic translation methodology from quantum-mechanical analogies to explicit, implementable finite difference corrections with rigorous parameter bounds. Through convergence analysis, we demonstrate that appropriately parametrized corrections preserve the accuracy of the underlying numerical scheme, provided the solution possesses sufficient regularity and the parabolic scaling constraint $\Delta t=\mathcal{O}\left(h^2\right)$ holds. Numerical experiments on a spatially discretized domain over a finite time horizon using spatially correlated noise reveal that the anharmonic oscillator correction achieves exceptional accuracy with modest computational overhead, while the amplitude encoding correction provides intermediate accuracy with negligible timing cost. The tunneling-inspired correction exhibits higher error for smooth initial conditions, indicating strong problem-dependence. While these methods enhance accuracy in specific scenarios, genuine speedups on classical hardware are not achieved. The primary value lies in establishing systematic methodologies for perturbative correction design and developing theoretical foundations for future hybrid computational approaches. Full article