Search Results (4,230)

This article shows the geometric decay rate of the Euler–Maruyama scheme for a one-dimensional stochastic differential equation towards its invariant probability measure under total variation distance. Firstly, the existence and uniqueness of invariant probability measure and the uniform geometric ergodicity of the chain are studied through the introduction of non-atomic Markov chains. Secondly, the equivalent conditions for uniform geometric ergodicity of the chain are discovered by constructing a split Markov chain based on the original Euler–Maruyama scheme. Full article

The rapid proliferation of cloud data centers has intensified concerns over carbon emissions, energy efficiency, and sustainability. Virtual machine (VM) placement is a pivotal control lever, yet existing methods rarely couple carbon intensity signals with computationally tractable multi-objective optimization. In this paper, we propose CASO (Carbon-Aware Surrogate-Guided Optimization), a novel framework that integrates an online adaptive Radial Basis Function (RBF) surrogate model with a self-adaptive hybrid PSO-DE swarm optimizer for real-time VM placement in geo-distributed edge cloud environments. CASO simultaneously minimizes carbon emissions, energy consumption, SLA violation rate, and network latency under strict host capacity and Quality-of-Service (QoS) constraints. Three key innovations differentiate CASO: (i) an online surrogate update mechanism that refines fitness approximations incrementally as workload patterns evolve; (ii) a carbon intensity weighting scheme anchored to real-time Grid Emission Factor (GEF) signals; and (iii) an adaptive parameter controller that autonomously tunes swarm exploration–exploitation trade-offs without hand-crafting. Experiments on the publicly available Alibaba Cluster Trace (cluster-trace-v2026-GenAI) dataset within a CloudSim-Plus environment show that CASO reduces carbon emissions by up to 31.4%, energy consumption by 27.9%, and SLA violations by 18.8% compared to the strongest baseline while converging 3.8× faster than the strongest baseline (ADEDL). Full article

We study positive–negative guarded systems of language equations over a fixed finite alphabet. The ambient space is the complete ultrametric space of all formal languages equipped with a length-based distance, where two languages are close whenever they agree on all words up to a sufficiently large length. The systems considered here contain both positive recursive dependencies and negative dependencies expressed through language complements. To handle this mixed structure, we introduce a suitable product order on pairs of languages and prove that the associated system operator has the weak monotone property. We show that the complement is an isometry for the length-based ultrametric and establish a signed wrapping estimate for guarded positive and negative language terms. These estimates lead to an ordered contraction principle for comparable pairs. As a consequence, the canonical lower and upper Picard iterations converge to the same limit, which is the unique fixed pair of the system. We also derive an explicit convergence rate and a finite-depth certification result: after a prescribed number of iterations, the approximants agree with the fixed-point semantics on all words below a given length. Additional symmetry assumptions are shown to force the unique fixed pair to be diagonal, reducing the system to a single language equation. Finally, we discuss an application to trace-based policies for tool-using AI agents. In this interpretation, finite executions of an agent are represented as words over an alphabet of observable tool-events, and the two components of the fixed point provide a stable semantics for policy-defined admissible and risky trace classes. The resulting framework gives a mathematically certified method for finite-depth analysis of recursive trace-based policies based on ultrametric fixed-point techniques. Full article

This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three major sources of complexity in modern functional data analysis: infinite-dimensional covariates, smoothly time-varying stochastic dynamics, and incomplete response observations. The methodology is based on a class of kernel-type estimators combining temporal localization, functional single-index smoothing, and inverse-propensity correction. Temporal localization captures the gradual evolution of the underlying regression structure, the single-index projection provides an effective dimension-reduction mechanism for functional covariates, and the propensity adjustment restores the target conditional functional under the MAR sampling scheme. The principal contribution of the paper is the establishment of weak convergence, in a suitable space of bounded functions, for the resulting propensity-adjusted conditional U-process indexed by a general class of measurable kernels. Under absolute regularity conditions, local stationarity assumptions, small-ball probability requirements, entropy restrictions of VC type, and uniform consistency of the propensity-score estimator, the normalized process is shown to converge weakly to a tight centered Gaussian process. The limiting covariance structure explicitly reflects the interaction between temporal smoothing, functional concentration, dependence, and the random loss of responses. In parallel, uniform convergence rates are derived for the associated conditional single-index U-statistic estimators, thereby quantifying the respective contributions of smoothing bias, stochastic fluctuation, local-stationarity approximation error, and missingness-induced variance inflation. A substantial part of the analysis is devoted to the technical difficulties created by the simultaneous presence of dependence, nonstationarity, functional covariates, and incomplete observations. The proofs combine Hoeffding-type decompositions adapted to weighted incomplete data, blocking and coupling arguments for absolutely regular triangular arrays, refined entropy bounds for kernel-indexed function classes, and small-ball probability techniques for functional covariates. The MAR mechanism is incorporated via inverse-propensity weighting, and its effects on the effective sample size, asymptotic variance, and bias structure are made explicit. The theory also provides a rigorous foundation for bandwidth selection through blocked, propensity-adjusted cross-validation and clarifies its relation to the corresponding oracle risk. The proposed framework encompasses a broad class of statistical learning and inference problems involving pairwise or higher-order functionals of functional time series. In particular, it applies to conditional Kendall-type functionals, discrimination problems, metric learning with incomplete labels, and conditional independence testing under local stationarity. A simulation study illustrates the finite-sample behavior of the proposed estimators and supports the theoretical findings across varying regimes of temporal nonstationarity, serial dependence, functional concentration, and response missingness. Overall, the results provide a mathematically rigorous and methodologically flexible foundation for inference from evolving functional data when dependence, infinite dimensionality, and incomplete observation are present simultaneously. Full article

This paper develops a boundary-sensitive asymptotic theory for nonparametric conditional U-statistics smoothed by support-adapted asymmetric kernels when the response variable is subject to Missing-at-Random observation. The problem lies at the intersection of three well-established but traditionally separate lines of research: conditional U-statistics, asymmetric smoothing on constrained supports, and incomplete-data inference under MAR sampling. The contribution of the paper is not a novelty claim concerning any of these components in isolation. Rather, it consists in deriving a kernel-specific and MAR-aware limit theory for their simultaneous occurrence, where the estimators are nonlinear complete-case ratios of localized U-statistics and the localization devices are point-dependent approximate identities adapted to the geometry of the covariate support. The analysis covers three principal classes of support-respecting smoothers: Dirichlet kernels on the simplex, Bernstein polynomial smoothers, and multivariate beta kernels on hypercubes, with an additional extension to mixed continuous–categorical regressors. These smoothing schemes are not translation-invariant, and their local moments, effective support, normalizing constants and $L^2$-masses vary with the evaluation point, especially near the boundary. Consequently, their incorporation into conditional U-statistics requires more than a direct transfer of ordinary asymmetric-kernel regression theory. The numerator and denominator of the estimators are localized U-statistics whose stochastic expansions are governed by Hoeffding projections, including canonical components that must be controlled uniformly over the conditioning domain. Under regularity, smoothness and positivity assumptions adapted to the MAR setting, we establish uniform consistency, weak and strong uniform convergence rates, stochastic expansions and asymptotic normality. The results are obtained both on fixed compact subsets and on interior regions approaching the boundary, thereby identifying how support geometry enters the bias and stochastic normalizations. A central feature of the theory is the separation between the deterministic effect of complete-case sampling and its stochastic effect. For the complete-case estimator, the natural deterministic equivalent is obtained by replacing the design density f with the effective complete-case density $pf$, where p is the propensity score. Thus, the MAR mechanism may enter higher-order deterministic bias constants through the local design tilt, whereas the leading stochastic dispersion reflects the loss of effective information through propensity score factors. The precise variance constants and normalizing rates remain kernel-specific, depending on the local $L^2$-structure of the Dirichlet, Bernstein or beta smoothing device. The paper should therefore be viewed as a MAR extension and refinement of the complete-data asymmetric-kernel conditional U-statistic theory. It provides a common probabilistic architecture for several boundary-adapted smoothing schemes while retaining the kernel-dependent bias operators, variance constants, boundary regimes and Hoeffding-projection structures required for sharp asymptotic interpretation. Numerical experiments illustrate the finite-sample behavior predicted by the theory and highlight the interaction between support-adapted smoothing, boundary effects and incomplete response observation. Full article

In this paper, we propose a new three-step iterative scheme to approximate fixed points of contraction operators in Banach spaces. Under standard Lipschitz conditions, we establish the existence, uniqueness, and strong convergence of the iterative sequence. The convergence rate and data dependence of the method are also investigated. A comparative analysis with Noor, Picard–S, Abbas–Nazir, SP, and NIP iterative methods is presented. As an application, the proposed scheme is employed to solve a fractional viscoelastic model involving a Caputo derivative of order $0<\alpha <1$, which is reformulated as a Volterra integral equation. The numerical results, including error analysis and graphical illustrations, demonstrate that the proposed method achieves faster convergence and a higher accuracy. Full article

To address the problems of false negatives, false positives, and delayed response in traditional fire detection systems, this paper proposes a warehouse fire detection scheme based on multi-sensor information fusion. By constructing a ZigBee wireless sensor network and integrating temperature, CO concentration and smoke sensors, fire simulation data are collected in the warehouse. At the data processing level, an improved Grubbs criterion is innovatively adopted to eliminate outliers, and the median is used instead of the average to effectively suppress the same-side shielding effect. At the feature layer fusion stage, a BP neural network model optimized by the cosine decreasing inertia weight particle swarm optimization algorithm (CIW-PSO) is designed. By dynamically adjusting the learning factors (c₁, c₂) and inertia weight (w), the convergence speed and global optimization ability are significantly improved. At the decision-making level, a fuzzy logic reasoning mechanism is introduced to integrate multi-parameter membership functions, thereby reducing the probability of misjudgment. Field tests have verified that the system can achieve early fire warning in a 50 m × 100 m warehouse environment, with a false alarm rate reduced by 42% compared to a single sensor and a response time shortened by 35%, providing an efficient and reliable intelligent solution for warehouse fire safety. Full article

Hot forging of Ti-6Al-4V is extensively utilized in the manufacture of orthopedic implants; however, the coupled influence of strain rate and temperature on ductile damage evolution during the forging of femoral stems remains insufficiently quantified. In this study, a finite element framework is developed to analyze and optimize the hot forging process, incorporating strain rate- and temperature-dependent plasticity, as well as the Johnson–Cook damage criterion. Mesh convergence is established, and the assumption of quasi-adiabatic conditions is substantiated via Péclet number analysis. A full factorial design is implemented by varying the ram velocity (0.1–0.5 m/s) and initial billet temperature (850–950 °C) to evaluate the forging load, stress triaxiality, equivalent plastic strain, and damage accumulation. Results indicate that process kinetics govern the mechanical response: increasing the ram velocity enhances strain-rate hardening, resulting in higher peak loads, while explicitly reducing stress triaxiality and suppressing ductile damage evolution. Conversely, temperature exhibits a secondary influence within the investigated domain. Validation of the damage criterion confirms safe operating windows, identifying low-velocity forging as a high-risk condition for localized defect formation. These findings provide practical guidelines for the strain-rate-based optimization of thermomechanical processing parameters for Ti-6Al-4V femoral stems. Full article

Traditional permanent magnet synchronous motor (PMSM) control systems rely on mechanical position sensors for high-precision rotor position and speed information, which increases hardware complexity, raises system cost, reduces reliability, and limits adaptability to harsh environments. To overcome the above limitations, this paper proposes a novel high-performance sensorless speed control strategy for PMSMs, which is constructed based on a non-singular terminal sliding mode observer (NTSMO) and a non-singular terminal sliding mode controller (NTSMC). First, an improved fast power reaching law (IFPRL) is proposed, which consists of a variable exponential reaching term and a power reaching term. Specifically, the gain of the exponential reaching term is dynamically adjusted by the absolute value of the sliding mode switching function, enabling the reaching law to operate in two different modes throughout the entire convergence process of the system state. Moreover, the introduction of scaling coefficient c compensates for the performance degradation caused by variations in the range of sliding mode surfaces (SMSs) in different systems. The proposed IFPRL not only effectively mitigates the inherent chattering issue, it also expedites the rate at which the system state converges to its SMS. On this basis, both the NTSMO for rotor position observation and the NTSMC for speed closed-loop control are designed by embedding the proposed IFPRL into the framework of non-singular terminal sliding mode control theory. Finally, the effectiveness of the proposed method is validated through numerical simulations and experimental tests. Experimental results demonstrate that the proposed IFPRL-based NTSMC + NTSMO scheme reduces the root mean square error (RMSE) of speed control by 2.7% relative to the traditional SMC + SMO method. The proposed method realizes reliable sensorless speed control for PMSMs and exhibits superior dynamic response, higher control accuracy, and stronger robustness against disturbances. Full article

The contact force between the ultrasound probe and human skin directly affects image quality, patient safety, and comfort. In infant developmental dysplasia of the hip (DDH) ultrasound examinations, higher force control precision is required, as infants have thin skin and soft cartilage that are easily deformed under excessive probe pressure. This paper proposes a comprehensive force control method for DDH ultrasound robots. Firstly, an online gravity calibration approach is employed to estimate the installation tilt, sensor zero offset, and probe center of gravity, thereby improving force measurement accuracy. Then, a torque-based pose control algorithm is adopted to achieve conformal probe–skin contact. Finally, a variable admittance control strategy based on fuzzy neural network (FNN) is proposed, which adaptively regulates the damping coefficient based on the force error and its rate, enabling stable force control without explicit soft-tissue modeling. Experiments on an infant phantom and human skin show that the proposed method achieves force fluctuation amplitudes of 0.0984 ± 0.0012 N and 0.0976 ± 0.0014 N, respectively, with absolute steady-state force errors below 0.01 N. Compared with conventional admittance control, it significantly reduces force oscillations and improves tracking accuracy. In infant experiments, the method enables smooth convergence to the desired force and maintains relatively stable probe–skin interaction, which contributes to consistent ultrasound image acquisition and reduces tissue deformation. These results suggest that the proposed method can provide a feasible force control basis for stable and gentle robotic DDH ultrasound scanning. Full article

Estimating dependency relationships between variables is an important issue in statistics. Mutual information (MI) is a measure of dependency which quantifies the amount of shared information between two variables. It is free of distribution assumption and captures both linear and non-linear dependencies. MI estimation methods were primarily developed for datasets with exclusively discrete variables, exclusively continuous variables, or a mixture of both. In practice, complex variables containing both discrete and continuous values (discrete-continuous variables), specifically continuous censored variables, are often present in real datasets (e.g., biological measures from analytical tools with lower detection limit). Methods have been developed to handle discrete-continuous data, but their effectiveness on the specific case of continuous censored data has not yet been evaluated. We propose a new estimation method based on the decomposition of the MI formula, with a first part handling the censoring status of the data, and a second part handling its continuous section. This estimation method works as a correction, as it takes in parameter one MI estimator for continuous data, and makes it able to handling censoring. We constructed different simulation scenarios of pairs of correlated censored log-normal variables, by varying the censoring rate, correlation, and sample size. We evaluated our correction on a few existing estimators previously developed for continuous, mixed or discrete-continuous data. We compared the selected estimators, with and without the correction, on these different scenarios. We found that the correction globally enables to reduce bias, and allows convergence towards the true MI value as the number of observations increases. Full article

Most UAV missions currently require visiting multiple checkpoints to perform field tasks in environments with varying levels of obstacle complexity. These missions become more challenging because UAVs have limited onboard resources, particularly in terms of energy, making it necessary to determine a safe and efficient path that enables all required visits to be completed while minimizing both travel distance and energy consumption. To address these challenges, this study proposes a hybrid fuzzy metaheuristic approach that integrates Cuckoo Search and Tabu Search for multi-objective UAV path planning. The proposed approach generates collision-free paths in environments with static obstacles and employs fuzzy logic to construct a unified evaluation function, in which distance and energy values are mapped to membership functions and combined into a single fitness score to guide the optimization process. Cuckoo Search drives global exploration of the solution space, while Tabu Search refines solutions locally. Together, they improve path quality and avoid premature convergence. Experimental results across two scenarios with varying obstacle densities and checkpoint counts demonstrate the efficacy of the proposed hybrid approach. Compared with two baseline algorithms, the hybrid approach achieves reductions in path length ranging from 0.01% to 42.11% and in energy consumption ranging from 0.08% to 27.91%, depending on scenario complexity. Moreover, it maintains a high success rate of 96–100% as both checkpoint counts and obstacle density increase, whereas the baseline algorithms drop to 3–13% in more complex environments. These results highlight the effectiveness and scalability of the approach for multi-checkpoint UAV path planning in obstacle-rich environments. Full article

Multivariate time-series anomaly detection on physical sensor networks faces three challenges that generic deep learning models inadequately addressed: heterogeneous sensor reliability, context-dependent anomaly scoring, and inactionable binary outputs lacking per sensor attribution. We propose an uncertainty-aware Temporal Convolutional Network (TCN) framework built on two tightly integrated uncertainty-driven components: (i) an Adaptive Uncertainty-Aware Attention (AUAA) mechanism that gates temporal attention weights by per sensor predictive uncertainty obtained from Monte Carlo dropout; and (ii) a Dynamic Weight Adapter that learns context-sensitive blending of reconstruction error and uncertainty via a GRU over weight history. The architecture also includes an exploratory per sensor attribution head, which we audit rather than claim: a controlled-perturbation test shows it is not yet causally faithful. We complement the empirical architecture with two distribution-free theoretical results: a Chebyshev-type false-positive bound on the hybrid anomaly score, and a Monte Carlo posterior moment convergence result at rate $O\left(M^{-1/2}\right)$. Evaluated on four-month indoor air quality sensor data, the Full Enhanced model achieves $R^2=0.9988$ and MSE $1.65\times {10}^{-4}$, a $25.2\%$ MSE reduction over the Base TCN ($R^2=0.9984$, MSE $2.20\times {10}^{-4}$). Because the IAQ stream is unlabeled, the primary quantitative detection evaluation uses the labeled Skoltech Anomaly Benchmark (SKAB), a publicly available industrial water-circulation corpus disjoint from the IAQ training distribution; it yields an 8.8 × F1 advantage ($0.477$ vs. $0.054$) and a 14.4 × recall advantage ($0.418$ vs. $0.029$) for the proposed model configuration over the Base TCN at a validation-calibrated threshold applied without retuning. Against twelve established detectors under a unified protocol, the proposed model attains the best F1 and recall, while the strongest reconstruction baselines retain higher precision and a marginally higher ROC-AUC, a recall-driven trade-off. Ablation isolates each component’s contribution, the detector degrades gracefully under channel masking and noise, and the distribution-free false-positive bound is empirically respected. The framework retains a low inference cost ($0.16$ ms per window at $M=20$ Monte Carlo samples, including the uncertainty pass). Full article

Discrete diffusion models have become an important class of generative models for categorical data, yet their theoretical understanding remains largely limited to time-homogeneous noise schedules. In this work, we study uniform-rate discrete diffusion models with time-inhomogeneous continuous-time Markov chain forward processes. We establish convergence guarantees for practical reverse-time samplers by directly controlling the total variation distance, avoiding the indirect route of first bounding KL divergence and then applying Pinsker’s inequality. Our analysis decomposes the sampling error into initialization, score-estimation, discretization, and early-stopping errors, and explicitly characterizes how each term depends on the accumulated noise, the local noise rate, and the smoothness of the noise schedule. Under suitable regularity conditions on the noise schedule, we further derive step-complexity guarantees that match the order of existing results for homogeneous samplers. Full article

Blind image watermarking models such as HiDDeN have laid an important foundation for end-to-end watermarking. Nevertheless, they still suffer from three major limitations: single-scale feature extraction, fixed fusion weights, and slow training convergence. To address these issues, this paper proposes an adaptive multi-scale watermarking algorithm based on collaborative dual-attention mechanisms. The algorithm designs an adaptive multi-scale feature fusion module (MA-FFM) with a dynamic gating network in the encoder, which flexibly combines local multi-scale textures with global contextual information, overcoming the limitation of fixed fusion weights. In the decoder, a multi-level channel attention module is embedded to strengthen the extraction of watermark signals. The two attention modules work synergistically: the encoder focuses on adaptive feature fusion while the decoder leverages channel attention to selectively enhance watermark-related features, forming a dual-attention synergy that balances robustness and imperceptibility. Moreover, the dynamic gating network adaptively adjusts the contribution of local versus global features via learnable weights, whose evolution from approximately 0.51 to about 0.89 improves model interpretability. Experiments are conducted on the COCO 2017 dataset. Compared with HiDDeN, the proposed algorithm reduces the bit error rate (BER) from 0.1696 to 0.1538 under no attack with a relative reduction of 9.3%, increases PSNR by 0.61 dB, and improves SSIM from 0.9058 to 0.9077. Under various attacks—including JPEG compression, Gaussian noise, salt-and-pepper noise, and brightness/contrast adjustments—the BER remains consistently lower than that of HiDDeN. Ablation studies confirm the effectiveness of each module. Overall, the proposed algorithm preserves visual quality, improves the accuracy of watermark embedding and extraction, and exhibits strong generalization robustness against common image distortions. Full article