Search Results (407)

In this paper, a controlled Picard semi-analytical technique is improved for a branch of nonlinear fractional stochastic delay differential equations since the nonlinear terms always prevent the establishment of closed-form solutions. The proposed approach extends the known Picard iteration by embedding a convergence-control parameter that improves the flexibility and stability of the iterative scheme while keeping the original mathematical formulation. A careful theoretical analysis is presented to establish the existence of the iterative sequence, its mean-square boundedness, convergence, and an explicit error estimate under standard Lipschitz continuity and linear growth assumptions. Moreover, a Numerical Picard implementation is updated to rebuild stochastic sample trajectories and to give an independent illustration through comparison with a predictor–corrector scheme. The presented methodology is applied to fractional stochastic models of human postural sway and logistic population models. The numerical results illustrate that the semi-analytical framework evaluates the expectation of and variance in the stochastic response for various fractional orders accurately. Although the semi-analytical controlled Picard method is incapable of performing a lot of iterations, it generates statistical moments that agree with those obtained using both the Numerical Picard and predictor–corrector methods, while explicit semi-analytical representations of the solution. These results show that the presented technique gives an accurate and effective approach for examining nonlinear fractional stochastic delay systems from biological, ecological, and engineering applications. Full article

This paper develops a unified asymptotic theory for inverse-probability-weighted conditional U-statistics of arbitrary fixed order in the presence of missing-at-random responses and infinite-dimensional functional covariates. The target is a conditional higher-order functional generated by a measurable response kernel and evaluated locally on a separable Banach space. Localization is formulated through delta sequences, providing a common framework for kernel, partition, regressogram, orthogonal series, and related smoothing procedures without recourse to finite-dimensional density arguments. For bounded kernels, we establish uniform almost-complete convergence over pseudo-compact functional domains and obtain a sharp decomposition into deterministic localization bias and stochastic fluctuation. The latter is governed by the localized-kernel variance, the envelope of the delta sequence, the metric complexity of the indexing domain, and the small-ball concentration of the functional covariate. Unbounded kernels are treated under explicit weighted moment, truncation, and summability conditions. The feasible theory quantifies the additional perturbation induced by estimating the propensity score and identifies conditions under which this first-stage uncertainty is asymptotically negligible. Pointwise distributional theory is derived through a denominator linearization combined with the Hoeffding decomposition of the centered localized kernel. The Gaussian limit is driven by the first projection, while the higher-order canonical components are shown to be negligible under explicit local-mass, moment, and noncancellation assumptions. This yields oracle-equivalent feasible inference, a consistent first-projection variance estimator, and asymptotically valid studentized confidence intervals. A finite-grid adaptive comparison principle is also developed for data-driven resolution selection. The scope of the theory is illustrated through conditional rank functionals, discrimination with incomplete labels, metric-learning criteria, and functional prediction. Synthetic and semi-synthetic studies based on functional classification, phoneme log-periodograms, and growth trajectories document the finite-sample interaction between covariate-dependent label observation, local information loss, propensity estimation, and inverse-weighting variance. Full article

The Guangdong–Hong Kong–Macao Greater Bay Area has high building density and diverse project types, and building disaster governance features cross-regional, multi-stakeholder and strongly uncertain characteristics. To reveal the multi-agent strategic interactions after embedding AI digital technologies into the governance process, this paper constructs a three-party stochastic evolutionary game model among public regulators, construction firms and AI technology providers, and introduces multiplicative Gaussian white noise with boundary degradation into the replicator dynamics. The study finds that (1) under baseline parameters, the system evolves toward the state “coordinated strong regulation–AI-compliant governance–high-quality supply”; noise below the local mean-square stability threshold does not change the direction of recovery near the equilibrium but enlarges short-term fluctuations of stochastic trajectories; (2) there is synergistic transmission in the initial strategies of the three parties, with firms’ compliance probability linking both the regulatory and technology sides; (3) governance performance benefits, cross-regional coordination gains, firms’ digitalization gains and high-quality technology subsidies each form positive incentives at different links, while firms’ AI retrofit costs directly depress compliance returns; (4) the mechanism shown on the original parameter surface indicates that higher AI retrofit costs first suppress firms’ AI-compliant governance and, via firms’ demand transmission, affect high-quality technology supply, whereas the response of public regulators is relatively weak. The findings provide mechanism-level hypotheses for phased incentives, cross jurisdictional data collaboration, technology quality assurance, and adaptive regulation. Because the parameters are dimensionless and uncalibrated, project or jurisdiction specific policy magnitudes require empirical estimation and validation. Full article

Accurate dynamic parameters are required for model-based control of lower-limb exoskeletons, but limited excitation, transmission friction, and assembly-dependent uncertainty can degrade conventional estimates. This study examines a two-stage method that combines recursive least squares (RLS) with an adaptive grey wolf optimizer (AGWO). Offline RLS tracks the base-parameter trajectory and expands its post-convergence extrema to construct a finite search space; a non-smooth friction severity index then modulates the GWO convergence schedule. The method was evaluated on a pedestal-mounted, single-degree-of-freedom hip mechanism using a 5 s calibration trajectory and a separate 7 s validation trajectory. Deterministic least squares (LS) and bound-constrained least squares (BCLS) were compared with standard PSO, RLS–PSO, RLS–GA, RLS–GWO, and RLS–AGWO. Each stochastic method used a population of 30, with 80 iterations (2400 fitness evaluations) and 30 independent seeds. On the independent trajectory, BCLS obtained an RMSE of 0.1152 Nm. Median validation RMSEs were 0.1152, 0.1152, 0.1562, and 0.1516 Nm for RLS–PSO, RLS–GA, RLS–GWO, and RLS–AGWO, respectively. Thus, the adaptive schedule improved median GWO error by 3.0%, but deterministic BCLS was both more accurate and faster for the present linear-in-parameters model. AGWO is therefore not mathematically necessary for the current convex objective; its potential advantage should be tested with genuinely nonlinear friction parameterizations. The conclusions remain limited to a single-axis pedestal experiment and do not establish performance during human-worn gait. Full article

Load Frequency Control (LFC) is critical for maintaining stability in smart grids (SGs) against complex hybrid (deterministic and/or stochastic) cyber-deception attacks. This paper presents a new approach to handle such a complicated problem via trajectory tracking of the response of a pre-designed ideal attack-free model. This method guarantees robust tracking in LFC and desired transient behavior (e.g., rising time, settling time). More precisely, the optimal attack-free model’s response is controlled by the chosen control strategy as a result of load variations. The output of such a model is used online to clean up the cyber-deception attacked output of the system. The cleaned output is then used to estimate the states of the system using the recently developed Regularized Least Squares (RLS) observer. Then, a control strategy is proposed to ensure a trajectory tracking mechanism where the cyber-attacked system is forced to follow the trajectories of an ideal attack-free reference model. Unlike other approaches, which attenuate the effect of cyber-attacks, the present approach eliminates the distortions created by these attacks completely. The stability of the proposed scheme is rigorously analyzed, and its efficacy is validated through the application of an isolated power system. Full article

Many natural and engineered systems evolve under constraints that restrict the set of admissible states. Classical frameworks study invariant sets, viability regions, survival probabilities, and exit-time events, while the explicit treatment of threshold-defined admissible subsets induced by sampled finite-horizon persistence is not usually isolated as a primary state-space object. This paper formulates a finite-horizon framework for Persistence Under Declared Constraints (PSUC). For a fixed constraint set, sampling step, persistence horizon, and tolerance level, the associated survival domain is the set of initial conditions whose sampled trajectories remain inside the declared constraint set with probability of at least $1-\alpha$. Under explicit regularity assumptions, survival domains are closed superlevel sets of the persistence field and form a nested filtration as the persistence horizon increases. This filtration admits a canonical intrinsic representation through a maximal admissible sampled-horizon field whose sampled superlevel sets recover it exactly. The same field also induces a canonical admissibility preorder; after quotienting by horizon-indistinguishability, this yields a partial order and its associated Alexandrov topology, in which the sampled survival filtration is represented as an upper-set filtration. The Alexandrov construction itself is classical; the contribution lies in the canonical order induced by the sampled admissibility-depth field and in the resulting canonical order-theoretic representation of the filtration. A secondary scalar ordering is also obtained for any lower-bounded auxiliary scalar function. Under an additional continuity assumption, the framework further yields boundary localization at the threshold level and an inheritance relation for connected components along the filtration. Finally, the paper shows that sampled survival domains need not coincide with continuous-time survival sets, thereby clarifying the intrinsically protocol-dependent nature of the object studied. The contribution is therefore a restricted but explicit analysis of threshold-defined admissible-state filtrations induced by sampled finite-horizon persistence, together with a canonical order-theoretic representation of the same filtration, formulated in a way that remains compatible with existing work on viability, stochastic survival, and exit-time analysis. Full article

End-effector obstacle-avoidance trajectory planning is essential for improving the autonomy, safety, and executability of industrial robotic manipulators in constrained workspaces. Conventional Rapidly Exploring Random Tree (RRT) planners provide effective exploration capability but often suffer from stochastic tree expansion, redundant trajectories, and insufficient directional guidance near obstacle regions, which limits planning efficiency and trajectory quality. This study proposes a clearance-field-guided RRT framework with behavior-cloning-assisted refinement for end-effector obstacle-avoidance trajectory planning of industrial robotic manipulators. The proposed method formulates the planning problem in Cartesian space based on an end-effector kinematic model and introduces local clearance-field guidance into the RRT sampling process. Candidate samples are evaluated by considering obstacle clearance, reference-line deviation, and goal distance, enabling the search tree to preferentially expand toward effective traversable regions while maintaining the exploration capability of conventional RRT. Behavior cloning is further introduced as an offline auxiliary strategy to investigate the influence of expert trajectories on local motion-direction learning and trajectory continuity. A Python–Unity joint simulation–verification framework and a physical manipulator experimental platform are established to evaluate the feasibility and practical executability of the generated trajectories. Python is used for offline trajectory generation, expert dataset construction, behavior-cloning training, and performance evaluation, while Unity is employed for three-dimensional manipulator modeling and trajectory reproduction. The experimental results demonstrate that the proposed Field-guided RRT achieves a better balance among path efficiency, planning time, obstacle-clearance maintenance, and trajectory execution capability compared with conventional RRT-based methods. The proposed framework provides an effective solution for collision-free end-effector trajectory planning in industrial applications such as assembly, welding, component placement, and robotic inspection. Full article

In signalized urban road networks, periodic signal phase switching is a key factor influencing traffic-flow stability and operational efficiency. With the rapid development of Connected and Automated Vehicle (CAV) technologies, exploiting their enhanced perception, communication, and cooperative control capabilities has become an important research topic. To characterize the acceleration, deceleration, queueing, and discharge disturbances induced by signal phase transitions, this study proposes a Signal-Constrained Optimal Velocity Model (SC-OVM). By introducing a continuous signal decision function, the proposed model dynamically couples traffic signal states with vehicle-following behavior, including preceding-vehicle following and stop-line tracking within a unified optimal-velocity framework. Furthermore, linear stability analysis, boundary critical condition analysis, and disturbance probability modeling are integrated to reveal the instability mechanism caused by abrupt signal phase transitions, with extensions to stochastic prediction errors and adaptive Signal Phase and Timing (SPaT) inputs. Numerical simulations show that SC-OVM-controlled CAVs can smooth vehicle trajectories, reduce average delay, improve end-of-green passing performance, and achieve a balanced performance in efficiency, stability, and safety compared with the Full Velocity Difference Model (FVDM), Virtual Leading Vehicle model (VLV), and Intelligent Driver Model (IDM). The findings provide theoretical support and practical insights for stability modeling and cooperative control of mixed-traffic flow at signalized intersections. Full article

Growing Neural Cellular Automata (GNCA) are capable of robust self-maintenance and self-repair, yet the internal dynamical mechanisms that support these capabilities remain poorly understood. Here, we investigate the role of internal fluctuations—temporal micro-variability of hidden channel states—in a trained GNCA model, hypothesizing that they constitute a functional component of the dynamics rather than merely residual stochastic noise. We analyzed the trained model through dynamical-systems analysis (low-dimensional embedding and recurrence analysis of collective state trajectories) and information-theoretic analysis (transfer entropy and partial information decomposition), including its response to localized damage and to suppression of small-magnitude updates. These analyses show that internal fluctuations are spatially structured, dynamically coupled to an attracting collective state, and associated with distributed small-magnitude updates that contribute to damage recovery. Damage induces a global deviation in latent state space followed by gradual re-convergence, and suppressing distributed small-magnitude updates associated with baseline fluctuation dynamics outside a permissive radius that encompasses the majority of the cells significantly impairs recovery. Transfer entropy analysis characterizes a spatially differentiated repair response: corrective inward flow near the damage site coexists with outward perturbation propagation at greater distances. Partial information decomposition further suggests a regime shift from synergy-dominant resting computation to redundancy-increased coordination during recovery. These findings indicate that GNCA self-maintenance and self-repair emerge from high-dimensional nonlinear collective dynamics in which internal fluctuations serve as a functional component supporting information flow, coordination, and return toward an attracting recurrent state. Full article

This study examines how misinformation can persist when broadcast exposure and social feedback reinforce one another under stochastic platform conditions. Text classifiers and single-layer cascade models omit latent exposure, reply-driven amplification, random attention shocks, and uncertainty in intervention response. A stochastic duplex SEIR model is developed on heterogeneous networks, with an information exposure layer for broadcast and recommendation channels and a social feedback layer for replies, discussion, and amplification. The analysis combines degree-weighted mean-field equations, next-generation threshold calculations, Lyapunov stability arguments, Fokker–Planck linear noise approximation, Milstein simulation, and Wasserstein distributionally robust control. Theoretical results provide positivity, stochastic threshold conditions, extinction and persistence regimes, and sufficient conditions for stationary behavior and robust control stability. Numerical simulations show extinction–persistence transitions, cross-layer resonance, noise-induced threshold shifts, stationary bands, control cost–safety trade-offs, and sensitivity to unidentifiable stochastic parameters. A CoAID tweet–reply case study maps public interaction traces to observable duplex indicators, including tweet–reply densities, propagation elasticities, coupling proxies, and classifier features. Duplex observable features improve over a single-layer public data baseline, while model-assisted stochastic features add modest gains in the available public projection. Structural fitting of the stochastic duplex process would require time-stamped user-level multiplex trajectories, recommendation exposures, and intervention logs. The case study also clarifies the data granularity needed for future platform-level calibration and operational readiness. The framework supports data-informed platform governance by linking propagation thresholds, algorithmic down-ranking, reply thread moderation, intervention cost, and robustness bounds within a common threshold control language for practical settings. Full article

Large Language Model (LLM) agents in long-horizon planning often exhibit Semantic-Execution Drift (SED), where executed actions progressively deviate from original language constraints. To formalize this phenomenon, we model SED as a stochastic drift process, expressed by the recurrence D(t+1) = alpha D(t) + epsilon(t) + beta P(t), and show that policies with an alpha below one induce semantic contraction. We propose ReflectiChain, a framework integrating Retrospective Reflection, a Latent World Model, and Double-Loop Policy Adaptation to preserve semantic consistency during long trajectories. To evaluate SED, we introduce Sema-Sim, a multi-agent supply chain benchmark containing 10 policy constraints, six adversarial perturbations, and 30-step planning horizons. We further propose the Semantic Fidelity Index (SFI) for measuring instruction adherence. Experiments on DeepSeek-V3.2 across seven reasoning strategies show that ReflectiChain achieves the highest SFI (88.7) and stable semantic contraction (alpha = 0.823, below one). The results are consistently validated on Qwen3.5-122B and Qwen2.5-72B. Ablation studies demonstrate that Retrospective Reflection contributes most to performance gains. Additional analyses on scalability, failure modes, and cost efficiency further verify the robustness and practicality of the proposed framework. All code and evaluation resources are publicly released. Full article

Fractional Brownian motion (fBm) provides a powerful stochastic framework for modeling long-range temporal dependence that cannot be represented by classical Brownian motion. This study presents a numerical and theoretical investigation of constrained fractional Brownian motion with applications to stochastic financial systems. An efficient simulation framework combining Fast Fourier Transform (FFT)-based circulant embedding and Markov Chain Monte Carlo (MCMC) sampling is developed to generate long correlated trajectories under absorbing boundary conditions. The proposed algorithm enables simulations with trajectory lengths up to L = 10⁷ while reducing the computational complexity from O (L³) for direct covariance decomposition to approximately O(L log L). Numerical results accurately reproduce the theoretical autocorrelation function of fBm and confirm the expected persistence behavior governed by the Hurst exponent. Super-diffusive regimes (H > 0.5) exhibit persistent long-range correlations and enhanced survival probabilities, whereas sub-diffusive regimes (H < 0.5) display anti-persistent dynamics and increased boundary absorption. The fractional stochastic volatility formulation captures important characteristics associated with long-memory financial systems, including persistent volatility dynamics and implied-volatility structures. The proposed biophysical-based FFT–MCMC methodology provides an accurate, scalable, and computationally efficient framework for studying constrained fractional stochastic processes and offers a foundation for future investigations of fractional volatility models and related financial applications. A conceptual Adaptive Hurst Momentum framework is briefly discussed as a possible direction for future research. Full article

Accurate vehicle trajectory prediction is essential for autonomous driving safety. However, existing data-driven models often ignore kinematic constraints, causing lateral jitter and trajectory distortion, while purely kinematics-based models lack flexibility in complex interactions. To address this, this paper presents a multimodal trajectory prediction method combining kinematics with dynamic interaction features. Operating in the Frenet coordinate system, the proposed model extracts historical features via a Bidirectional Gated Recurrent Unit (Bi-GRU) and utilizes an Adaptive Social Gating Network (ASGN) with multi-head attention to filter irrelevant interaction noise. This paper introduces a Stochastic Gating Decoder for multimodal latent variable sampling, adaptively fusing kinematics and data-driven paths to capture driver intention uncertainty while maintaining kinematic consistency. The model is trained using a composite loss function (Focal Loss and Best-of-K) to mitigate dataset long-tail distribution and trajectory divergence. Experiments on the HighD dataset show the proposed model achieves a minADE of 0.425 m and a minFDE of 0.955 m, outperforming baselines and reducing Lat-ADE by 53.9% compared to Social-GAN. These results confirm the model generates smoother, kinematically interpretable trajectories with higher accuracy in long-tail lane-changing scenarios. Full article

This paper presents a generic stochastic simulation framework for evaluating the operational feasibility of solar-powered unmanned aerial vehicles (UAVs) executing an invariant trajectory in high-variability climates. Unlike conventional approaches relying on idealised irradiance conditions, the proposed framework combines a modified ASHRAE radiation model corrected for local bias and variability with a semi-Markov process modelling stochastic transitions between cloud and sunlight states using parametrised state duration times. The environmental model is further extended with diurnal temperature variation and standard atmosphere effects. UAV motion is represented using a rigid body flight dynamics model combined with a cascaded trajectory tracking controller and an energy subsystem incorporating a lithium-ion battery model. Warsaw (Dfb climate) is used as a representative Central European test case characterised by frequent radiation deficits and highly variable atmospheric conditions. The simulations quantify the influence of environmental uncertainty and selected battery capacities on mission success probability across different solar-to-wing area ratios, with the mission entry at 70% initial battery state of charge and no additional manoeuvre losses or external atmospheric perturbations. The evaluations were conducted for a fixed mission start at solar noon on 15 July and were supplemented by an optimised mission scheduling analysis to establish upper flight-time limits. The results demonstrate the strong sensitivity of solar-assisted UAV operations to stochastic cloud conditions and support the design and mission planning for low-altitude long-endurance aircraft. Full article

With the widespread integration of renewable energy sources and distributed energy storage systems, intraday dispatch of distribution networks (DNs) has gradually evolved into a multistage sequential decision-making problem with intertemporal state coupling and progressively revealed uncertainty. Stochastic optimization under the stagewise independence assumption and limited horizon prediction cannot adequately capture temporal transition characteristics, which may lead to biased future cost estimation and myopic decisions. To address this obstacle, this paper proposes a conditional-cut-enhanced Markov chain stochastic dual dynamic programming strategy (MC-SDDP-CC) for multistage intraday dispatch of DNs. Feature encoding and scenario-lattice-driven trajectory sampling with Markovian path dependence are introduced to accurately characterize the temporal dependence in DNs. To improve computational efficiency, a node-wise conditional cut management scheme is developed to accelerate the recursion and tighten the conditional value function approximation. Numerical studies on modified IEEE 33-bus and 123-bus networks, as well as a practical system in a southwestern province of China, verify the effectiveness of the proposed method in terms of optimality, scalability and ablation performance. Full article