Search Results (914)

To address the insufficient parameter estimation accuracy and poor filtering convergence caused by noise in radar trajectory measurement data, this paper proposes a joint framework combining SW-STPSO adaptive wavelet denoising and an improved Unscented Kalman Filter (UKF). First, SW-STPSO preprocesses noisy data using a sliding-window strategy and improved particle swarm optimization to adapt wavelet parameters to local noise characteristics. Then, the improved UKF adopts exponential-decay adaptive Q adjustment and covariance matrix positive-definite regularization to achieve high-precision estimation of ballistic parameters, including position, velocity, and ballistic coefficient. Simulation results show that: (1) SW-STPSO denoising improves subsequent parameter-estimation accuracy by more than 60% compared with the case without denoising; (2) the improved UKF achieves 37% faster convergence and 42% higher stability than the traditional UKF; and (3) the joint scheme reduces the position RMSE, velocity RMSE, and ballistic-coefficient RMSE to 0.92 m, 0.256 m/s, and 0.023 m${}^2$/kg, respectively. These results indicate that the proposed method is effective for radar trajectory data processing under the adopted simulation conditions. Full article

Accurately and promptly acquiring the load history characteristics of impact events on composite aircraft structures is crucial for identifying impact-induced damage and developing high-fidelity digital twin models. To address this need, we propose a method for reconstructing the impact load history on composite structures, leveraging Generalized Cross-Validation (GCV) and a Fiber Bragg Grating (FBG) pattern. An equivalent expansion technique based on discretized time-domain sparse strain sampling is developed to mitigate the local distortion of impact response signals, a common issue arising from the low sampling rates of quasi-distributed FBG. By incorporating Tikhonov regularization, the ill-posed nature of the impact frequency response matrix is effectively managed. Furthermore, an adaptive optimization method based on the GCV criterion is introduced to overcome the limitations of manually selecting regularization parameters and the associated constraints on noise suppression. The results show that the proposed GCV-based reconstruction method achieves an average peak relative error of 11.4% and an average root mean square error of 0.36 N for the reconstructed impact load, demonstrating that the proposed method synergistically enhances both the reconstruction of the overall impact load waveform profile and the precise characterization of transient details, even with low-rate sampling. This provides robust technical support for health monitoring and condition-based maintenance of composite structures. Full article

This paper is devoted to the problem of identifying the mechanisms of hard excitation of oscillations in coupled systems of equilibrium neurons. In this study, a system of two coupled Chialvo neurons is used. For the deterministic model, we studied how increased coupling causes an abrupt transformation of the quiescent neurons into complex oscillations, both regular and chaotic. We show that even in the case when the deterministic system is in equilibrium, similar spike oscillations can be generated by noise. The important role of fractal basins of short and long deterministic transients is discussed. The potential of the principal directions and confidence domain methods for analyzing noise-induced excitation is demonstrated. The phenomena of coherence resonance and the global transition from order to chaos are explored. Full article

The paper explores the use of artificial neural networks for surface roughness parameter Ra prediction when milling the finishing of flat surfaces with toroidal milling on C45 steel. The experiments were conducted on a 5-axis CNC center, varying three main parameters: cutting speed, feed per tooth, and tool axis tilt angle. In total, 70 surfaces were processed, with multiple measurements of Ra roughness. The data were preprocessed in MATLAB (noise reduction by Z-score and augmentation to 630 values) and used to train an artificial feedforward neural network with Bayesian regularization. The resulting model showed good performance on the dataset and was experimentally validated on three new parameter combinations, processed and measured independently with a 3D scanner. The results confirm the network’s ability to estimate Ra roughness based on varying process parameters. The paper proposes the model as a useful tool for assessing surface quality in finishing milling and recommends extending the experimental base as the main direction of continuation. Full article

This paper develops a rigorous inferential framework for a class of Gaussian stochastic processes driven by white noise with constant drift, whose temporal evolution is governed by a Caputo fractional derivative of order ${\displaystyle \alpha \in (1/2,1)}$. The model belongs to the family of fractional Volterra processes, where memory is generated by the dynamics themselves rather than by correlated noise. We derive explicit analytical expressions for the mean, variance, and covariance structure of the solution, thereby characterizing in a precise manner how the fractional order ${\displaystyle \alpha }$ governs both variance growth and the strength of temporal dependence. In particular, the process exhibits correlated increments and a power-law variance scaling of order ${\displaystyle t^{2\alpha -1}}$, highlighting the dual role of ${\displaystyle \alpha }$ as a regularity and memory parameter. Building on this structural analysis, we address the statistical problem of estimating the parameter vector ${\displaystyle (\mu ,\sigma ,\alpha )}$ from discrete-time observations. Two complementary procedures are proposed for the estimation of the fractional order: a variance-growth method based on log–log regression of empirical variances, and a wavelet-based estimator exploiting multi-scale scaling properties of the process. For the drift and diffusion parameters ${\displaystyle (\mu ,\sigma )}$, we construct explicit Gaussian pseudo-maximum likelihood estimators derived from the Volterra covariance structure of the increment process. We establish unbiasedness, ${\displaystyle L^2}$-convergence, strong consistency, and asymptotic normality for all estimators. Furthermore, we derive Berry–Esseen type bounds that quantify the rate of convergence toward the Gaussian law, providing sharp distributional approximations in a genuinely fractional and non-Markovian setting. A Monte Carlo study is carried out, using high-resolution Volterra discretizations, large-scale simulation budgets, covariance-structured linear algebra, and multi-scale diagnostic tools. The numerical experiments confirm the theoretical convergence rates, demonstrate the finite-sample reliability of the estimators, and illustrate the sensitivity of the process dynamics to the fractional order ${\displaystyle \alpha }$: smaller values of ${\displaystyle \alpha }$ produce stronger memory effects and higher variability, while values closer to one lead to smoother and more stable trajectories. The proposed methodology unifies statistical inference for long-memory Gaussian processes with fractional differential stochastic dynamics, offering a coherent analytical and computational framework applicable in areas such as quantitative finance, anomalous diffusion in physics, hydrology, and engineering systems with hereditary effects. Full article

In recent years, multi-view learning has received extensive research interest. Most existing multi-view learning methods often rely on well-annotated data to improve decision accuracy. However, noisy labels are ubiquitous in multi-view data due to imperfect annotations. Although some methods have achieved promising performance using robust-loss designs and implicit regularization, they fail to explicitly model the reliability of the supervision signal and fail to dynamically correct noisy labels during training. Clearly, this largely constrains their performance ceiling. To deal with this problem, we propose an Error-Entropy-Guided Distillation network (EGD) for noisy multi-view classification. In this framework, we first design an Error-Entropy (EE) metric to explicitly evaluate the reliability of sample-wise supervision, which serves as the basis for identifying and filtering noisy labels. On this basis, we adopt the distillation paradigm based on Error-Entropy (EE). The teacher model provides the student with soft label distributions that are less affected by noisy labels in the early training stage. To further mitigate noise memorization and accumulated confirmation bias, we propose a periodic memory-clearing strategy and supervision signal update strategy to prevent the teacher from error memorization and accumulating confirmation bias. Meanwhile, the student model learns from the soft supervision of the teacher to capture structured inter-class relationships. Additionally, a consistency module is employed to enhance the consistency of the student across multiple views. Extensive experiments on five benchmark datasets demonstrate that EGD consistently outperforms state-of-the-art multi-view learning methods under various noise levels. Full article

Stock price sequences are characterized by pronounced nonlinearity, non-stationarity, and multi-scale volatility. They are further influenced by complex, multi-source factors, such as macroeconomic conditions and market behavior, making high-precision forecasting highly challenging. Existing approaches are limited by noise and multi-dimensional market features, as well as difficulties in balancing prediction accuracy with model complexity. To address these challenges, we propose Wavelet Entropy and Cross-Attention Network (WECA-Net), which combines wavelet decomposition with a multimodal cross-attention mechanism. From an information-theoretic perspective, stock price dynamics reflect the time-varying uncertainty and informational complexity of the market. We employ wavelet entropy to quantify the dispersion and uncertainty of energy distribution across frequency bands, and multiscale entropy to measure the scale-dependent complexity and regularity of the time series. These entropy-derived descriptors provide an interpretable prior of “information content” for cross-modal attention fusion, thereby improving robustness and generalization under non-stationary market conditions. Experiments on Chinese stock indices, A-Share, and CSI 300 component stock datasets demonstrate that WECA-Net consistently outperforms mainstream models in Mean Absolute Error (MAE) and R² across all datasets. Notably, on the CSI 300 dataset, WECA-Net achieves an R² of 0.9895, underscoring its strong predictive accuracy and practical applicability. This framework is also well aligned with sensor data fusion and intelligent perception paradigms, offering a robust solution for financial signal processing and real-time market state awareness. Full article

Feature weighting plays a central role in medical classification by enhancing predictive accuracy, interpretability, and clinical trust through the explicit quantification of variable relevance. Despite their widespread use, existing filter-, wrapper-, and embedded-based feature weighting methods are predominantly deterministic and exhibit pronounced sensitivity to label noise and outliers, which are pervasive in real-world medical data. This often results in unstable importance estimates and unreliable clinical interpretations. In this work, we introduce a novel Bayesian feature weighting model that fundamentally departs from existing approaches by jointly integrating simplex-constrained Dirichlet priors for global feature weights, hierarchical shrinkage priors for coefficient regularization, and contamination-aware priors for explicit modeling of label noise within a single coherent probabilistic framework. Unlike conventional Bayesian feature selection or robust classification models, the proposed formulation yields globally interpretable feature weights defined on the probability simplex, while simultaneously providing full posterior uncertainty quantification and robustness to both mislabeled observations and aberrant feature values through principled influence control. Comprehensive simulation studies across diverse contamination scenarios, together with applications to multiple real-world medical datasets, demonstrate that the proposed model consistently outperforms classical and state-of-the-art baselines in terms of discrimination, probabilistic calibration, and stability of feature-importance estimates. These results highlight the practical and methodological significance of the proposed framework as a robust, uncertainty-aware, and interpretable solution for medical decision making under noisy data conditions. Full article

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including seismicity and climatic processes. The study of these complex systems is commonly based on the analysis of the signals they generate, using mathematical tools to extract relevant information. A broad spectrum of mathematical disciplines converges in this context, including stochastic, probability and statistical theory, entropic and informational measures, fractal and multifractal analysis, natural time analysis, modeling of non-linearity and recurrence methods, generalized entropies, non-extensive systems, machine learning, and high-dimensional and multivariate complexity. Research in this area is largely focused on the characterization of complex systems, providing indicators of determinism or stochasticity, distinguishing between regularity, chaos, and noise, and identifying topological as well as disorder-regularity features. In addition, short- and long-term forecasting, together with the identification of short- and long-range correlations, play a central role in such characterization. To address these objectives, numerous mathematical tools have been developed for the analysis of time series and point processes, each designed to capture specific signal properties. In this work, many of the most important tools used in time series analysis are compiled and reviewed, highlighting their main characteristics and the different types of complex systems to which they have been applied. Full article

Flood susceptibility mapping in high-altitude ungauged basins faces a structural dichotomy: physically based models often suffer from systematic biases due to uncertain satellite precipitation, whereas data-driven models are prone to overfitting and lack physical consistency in data-scarce regions. To resolve this, this study proposes a Physically constrained Particle Swarm Optimization–Random Forest (P-PDRF) framework, validated in the Lhasa River Basin. The core innovation lies in coupling a hydrological model with statistical learning by utilizing the maximum daily runoff depth as a “Relative Hydraulic Intensity Index.” This approach leverages the topological correctness of physical simulations to circumvent absolute forcing errors. Furthermore, a Physiographically Constrained Negative Sampling (PCNS) strategy and a PSO-optimized “Shallow Tree” configuration are introduced to enforce structural regularization against stochastic noise. Empirical results demonstrate that P-PDRF achieves superior generalization (AUC = 0.942), significantly outperforming standard Random Forest, Support Vector Machine, and Analytic Hierarchy Process models. Ablation studies confirm that the dynamic index outweighs the static Topographic Wetness Index in feature importance, effectively correcting topographic artifacts where static models misclassify arid depressions as high-risk zones. This study offers a scalable Physics-Informed Machine Learning solution for the global “Prediction in Ungauged Basins” initiative. Full article

Deep learning systems deployed in regulated settings require explanations that are accurate and stable under nuisance transformations, yet classical post hoc transition matrices rely on fidelity-only fitting that fails to guarantee consistent explanations under spatial rotations or other group actions. In this work, we propose Equivariant Transition Matrices, a post hoc approach that augments transition matrices with Lie-group-aware structural constraints to bridge this research gap. Our method estimates infinitesimal generators in the formal and mental feature spaces, enforces an approximate intertwining relation at the Lie algebra level, and solves the resulting convex Least-Squares problem via singular value decomposition for small networks or implicit operators for large systems. We introduce diagnostics for symmetry validation and an unsupervised strategy for regularization weight selection. On a controlled synthetic benchmark, our approach reduces the symmetry defect from 13,100 to 0.0425 while increasing the mean squared error marginally from 0.00367 to 0.00524. On the MNIST dataset, the symmetry defect decreases by 72.6 percent (141.19 to 38.65) with changes in structural similarity and peak signal-to-noise ratio below 0.03 percent and 0.06 percent, respectively. These results demonstrate that explanation-level equivariance can be reliably imposed post-training, providing geometrically consistent interpretations for fixed deep models. Full article

Cooperative multi-UAV pursuit–evasion under occlusions and sensor noise is challenged by intermittent observability of the evader, varying observation-window lengths, and non-stationary evader tactics, all of which destabilize prediction and undermine safety-constrained cooperation. To address these challenges, we propose a safe decision-making framework that uses behavior mode and subgoal inference as intermediate representations for interpretable, uncertainty-aware cooperation. Specifically, an observation-driven generative intent–subgoal model infers the evader’s behavior mode and subgoal from short observation windows. Building on this model, a length-agnostic trajectory predictor is trained via multi-window knowledge distillation and consistency regularization to produce future trajectory predictions with calibrated uncertainty for arbitrary observation-window lengths, thereby reducing cross-window inference inconsistency and lowering online computational cost. Based on these predictions, we derive belief and risk features and develop a belief–risk-gated hierarchical multi-agent policy based on soft actor-critic with a safety projection layer, enabling adaptive strategy switching and a controllable trade-off between efficiency and safety. Experiments in obstacle-rich pursuit–evasion environments with randomized layouts and diverse obstacle configurations demonstrate more stable cooperative capture, safer maneuvering, and lower decision variance than representative baselines, indicating strong robustness and real-time feasibility. Specifically, across different observation-window settings, the proposed method improves the normalized expected return by approximately 5–7% over the strongest baseline and reduces pursuer losses by roughly 22–25%. Moreover, its end-to-end decision latency consistently remains within the 50 ms control cycle. Full article

Standard Retinex-based algorithms typically rely on gradient constraints to decompose an image, assuming that illumination is spatially smooth while reflectance contains sharp details. However, strictly gradient-based priors frequently produce halo artifacts or over-smoothing because they are unable to differentiate between intrinsic structural edges and high-frequency noise. In this paper, we propose a novel Similarity Image-Guided Retinex (SIMRET) model that fundamentally diverges from traditional derivative-based regularization. We present a color-based pixel-level similarity analysis to build a global guidance matrix rather than merely depending on local gradients. This Similarity Image functions as a reliable weight map during the decomposition process by mathematically encoding the chromatic relationships and spatial coherence between pixels. The model strictly maintains consistency across structural boundaries to avoid halo effects while adaptively enforcing smoothness in homogeneous regions to suppress noise by incorporating this similarity guidance into the optimization objective. We solve the proposed SIMRET model using an alternating optimization framework, where the similarity constraints effectively regularize the ill-posed decomposition problem. Extensive tests on various low-light datasets show that the suggested model successfully overcomes the trade-off between noise reduction and detail preservation, achieving better visual naturalness and signal fidelity than state-of-the-art techniques. Full article

Few-shot open-set object detection (FS-OSOD) remains challenging in real-world scenarios, where detectors must accurately recognize known objects from few examples while reliably rejecting vast unknown categories. Under this setting, decision boundaries between known and unknown classes are easily distorted by data scarcity and background clutter, leading to severe overfitting on base classes and overconfident misclassification of unknowns. Recent research attempts to alleviate these issues by regularizing detection heads to suppress base-class bias, or by leveraging vision–language priors through open-vocabulary alignment and prompt tuning to enhance semantic transferability. However, these solutions often overlook explicit modeling of truly out-of-set unknowns and the instability of prompt adaptation in low-data regimes, which can cause boundary drifts and make unknown proposals be absorbed by similar seen classes or even suppressed as background. To alleviate these issues, a guided prompt–monument network (GPMN) that is proposed, which jointly enhances prompt learning and feature representation learning for FS-OSOD. First, the contrastive distilled prompts (CDP) module employs a teacher–student prompt framework to decouple optimization across base, novel, and unknown classes. This strategy preserves transferability between zero-shot and few-shot settings while enhancing discrimination on base categories. Second, a synthesized monument module (SMM) maintains class-centered memory with momentum-updated prototypes and a non-parametric classifier, which compresses the overlap between seen and unseen distributions and provides a stable rejection margin for unknowns with strong co-occurrence and background noise. Compared with existing head-regularization and open-vocabulary prompt-tuning pipelines, GPMN explicitly targets both base-class bias and seen–unseen overlap at the region level. Extensive experiments on VOC10-5-5 and VOC-COCO benchmarks demonstrate that GPMN consistently improves unknown recall and few-shot mAP over representative FS-OSOD baselines. These results suggest that prompt-level decoupling mitigates base-class bias, whereas memory-anchored regularization enlarges the seen–unseen margin, jointly supporting reliable unknown rejection in scarce-supervision regimes. Full article

Traditional social recommendation methods often focus on static representations of users and items, neglecting dynamic changes in user interests and item attractiveness over time, which makes it challenging to adapt to temporal variations in user interests. Additionally, the propagation of information along explicit social relationships tends to over-smooth features and weaken individual preferences, while static implicit relationships may increase short-term noise. Thus, a Dual-channel Controllable Diffusion Network based on Hybrid Representations (HR-DCDN) is proposed for social recommendation. The HR-DCDN first incorporates temporal factors by combining dynamic and static representations to capture changes in user interests and item attractiveness. Then, our method proposes a dual-channel aggregation mechanism to obtain higher-order representations of users and items. Explicit social relationships serve as the social-influence channel, while implicit social relationships discovered via dynamic implicit relationship mining constitute the preference-homophily channel. In addition, a learnable polynomial spectral filter incorporates residual connections and dual-channel fusion information at each propagation step, stabilizing deep propagation and alleviating representation homogenization to a limited extent while preserving high-frequency preference information. Finally, we jointly optimize a cross-layer InfoNCE objective on the perturbed interaction branch with the supervised rating loss, which provides an additional empirical regularization effect, improves robustness, and helps preserve representation diversity without altering the graph structure. Experimental results demonstrate that our model outperforms baseline methods on two real-life social datasets. Full article