Search Results (793)

We apply the recently proposed analytic extension of formal indicial umbral calculus to the evaluation and structural interpretation of Bessel moments, replacing formal symbolic constructions with Mellin–Barnes analytic transmutations. The classical umbral representation of $J_0$ converts products of Bessel functions into Gaussian integrals involving sums of independent symbolic operators. This formal mechanism may reproduce correct identities in suitable convergence chambers, but it may also lead to non-admissible hypergeometric expansions at the physically relevant parameter values. The cubic moment already exhibits this difficulty: the formal Appell $F_4$ expansion associated with the equilateral case lies outside its domain of convergence. We address this obstruction by replacing the formal expansion with Mellin–Barnes representations of the corresponding umbral pairings. In this formulation, Ramanujan’s Master Theorem selects the analytic ground state associated with a Bessel product. The factorisation $J_0^3=J_0{J}_0^2$ fuses the elementary Bessel state with the square state and gives the cubic moment as a one-dimensional Meijer–Barnes function. The same mechanism yields a scaled cubic formula and a fourth-moment Meijer–Barnes representation whose residues give a convergent harmonic-number expansion. The fifth moment marks the first higher-rank case: the natural grouping $J_0^5=J_0^2{J}_0^2{J}_0$ leads to a bivariate Barnes transmutation rather than to an ordinary Meijer G-function. Finally, real powers $J_0^{\alpha }$, $\alpha >2$, are interpreted through Mellin-selected ground states, which need not reduce to finite Gamma products. Thus, Bessel moments provide a concrete hierarchy of analytic umbral representations, from rank-one Meijer–Barnes functions to higher-rank Barnes structures, and distinguish the global analytic meaning of an umbral construction from the local convergence of its residue expansions. Full article

This paper studies symmetrized neural network (SNN) operators generated by an adjustable half-hyperbolic tangent activation function. The construction is based on the paired density kernels ${\aleph }_t$ and ${\aleph }_{1/t}$, whose average defines the symmetric kernel $\mathcal{F}.$ This kernel is positive, even, normalized, and preserves the partition of unity. Using $\mathcal{F}$, we define finite-interval and whole-line SNN operators in the Banach space-valued setting. Pointwise and uniform convergence estimates are obtained through the first modulus of continuity. Higher-order and fractional approximation estimates are also derived, the latter using Caputo–Bochner fractional derivatives. The numerical part compares the nonsymmetrized operator ${\mathcal{L}}_n$ and the symmetrized operator ${\mathcal{L}}_n^s$. For $n=80$, the uniform error decreases from $0.010463$ to $0.003479$, the root mean square error (RMSE) decreases from $0.006530$ to $0.000826$, and the coefficient of determination ($R^2$) improves from $0.999675$ to $0.999995$. This improvement is accompanied by an increase in central processing unit (CPU) time from $0.014161$ s to $0.027088$ s. The parameter tests further show that the performance depends on the joint choice of n, t, and $\xi$. Overall, the results indicate that symmetrization improves approximation accuracy, while parameter tuning remains necessary. Full article

Accurate measurement of three-dimensional flame temperature distribution is crucial for combustion diagnosis. Traditional optical methods rely on observation windows or multi-camera arrays, which can be difficult to deploy in environments with restricted optical access, such as aviation engine burners. This paper proposes a passive radiation temperature measurement method based on ellipsoidal reflector (ER). By using the confocal characteristics of the ER, the radiation inside the flame is collected through a single aperture at one focus and guided to the Charge-Coupled Device (CCD) at another focus. A complete measurement model has been developed, combining the ray tracing of each detector element through the ER with the discretized Radiative Transfer Equation (RTE) under the pure absorption approximation. Temperature reconstruction is performed using the Least Squares QR (LSQR) algorithm. The method is validated numerically on a cylindrical flame under three configurations with identical grid and detection settings, differing only in the temperature field and absorption coefficient: symmetric with uniform absorption, asymmetric with uniform absorption, and asymmetric with non-uniform absorption. Gaussian noise (0–5%) is added to the simulated measurements. Noise-free reconstruction converges to near machine precision. Under 5% noise, the mean relative errors are 3.1%, 8.7%, and 6.1% for the three cases, with errors concentrated at the flame periphery while the core remains accurately reconstructed. The proposed method provides a practical solution for temperature monitoring where optical access is severely limited. Full article

Addressing the critical challenge of signal degradation in biosensor cardiac monitoring, this paper introduces an efficient hybrid dilated–long short-term memory (LSTM) with residual learning (HDLR), which is a novel architecture engineered for a high-fidelity electrocardiogram (ECG) denoising signal. The proposed HDLR model synergistically integrates with dilated convolutions to expand the receptive field for multi-scale feature extraction. This is an LSTM-based backbone used to resolve long term temporal dependencies with residual learning paths to stabilize gradient flow and accelerate convergence. The proposed HDLR architecture integrates three core functional components with dilated convolutional layers utilized for local temporal feature extraction, where varying dilation rates expand the receptive field to capture both local waveform patterns and broader morphological structures without increasing computational complexity. Experimental results demonstrate a significant leap in performance, with the HDLR model achieving a mean squared error (MSE) of 0.002176, a signal-to-noise ratio (SNR) of 14.4420 dB, and a Matthews correlation coefficient (MCC) of 0.9822. Beyond quantitative metrics, the proposed HDLR architecture exhibits exceptional robustness in preserving cardiac morphology, specifically the P-wave and QRS complex of the ECG signal under stochastic noise conditions. These findings underscore the HDLR model’s potential as a backbone for next generation, real time diagnostic systems in intelligent healthcare. Full article

Accurate and fast fault detection is essential to ensure the stability and reliability of High Voltage AC (HVAC) transmission systems. Conventional protection methods, including impedance-based and traveling wave techniques, may exhibit reduced performance under noisy operating conditions, system uncertainties, and complex fault scenarios while often requiring separate approaches for fault classification, location detection, and stability assessment. This paper proposes a unified Artificial Neural Network (ANN) based framework for simultaneous fault classification, location detection, and stability assessment using Critical Clearing Time (CCT) within a single HVAC transmission line model. A detailed MATLAB Simulink model is developed to generate a structured dataset comprising twelve fault scenarios, including single-line, double-line, three-phase, and ground faults at different locations along the transmission line. Three-phase voltages and currents, along with zero-sequence components, are used as input features. The ANN model is trained using the Levenberg–Marquardt (LM) optimization algorithm, which was comparatively evaluated against Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG) and demonstrated faster convergence, lower prediction error, and higher regression accuracy. To further evaluate the robustness of the proposed framework under high-impedance fault conditions, supplementary simulations were performed using fault resistance values of 10 Ω and 50 Ω in addition to the baseline 0.01 Ω case. The resulting datasets were combined to form an expanded training and evaluation dataset, enabling comprehensive validation of the proposed LM-trained ANN under varying fault resistance conditions. Using the baseline dataset, the proposed framework achieved a high regression coefficient (R = 0.9882) and low mean squared error (MSE = 0.1386), demonstrating accurate fault classification and precise per-kilometer fault location estimation. Furthermore, the integration of fault inception time and duration enables direct computation of CCT, allowing the model to distinguish between stability-critical and non-critical fault conditions. The results confirm that the proposed framework provides a comprehensive and efficient solution for real-time fault analysis by combining classification, localization, temporal analysis, and stability-aware decision support within a single model. Full article

Upstream–downstream nutrient connectivity strongly regulates water-quality risk in reservoir cascades, yet its quantification remains difficult where discharge, reservoir release, and hydraulic residence-time records are unavailable. This study developed a causal–explainable framework to diagnose total nitrogen (TN) connectivity between the upstream Shimantan Reservoir and downstream Banqiao Reservoir in the Huai River Basin, China. Long-term water-quality records, meteorological variables, land-cover indicators, seasonal descriptors, and lagged upstream predictors were integrated within a leakage-safe analytical workflow combining nonlinear causal inference, time–frequency coupling diagnostics, predictive modeling, SHAP-based attribution, and counterfactual analysis. Convergent Cross Mapping identified statistically significant asymmetric bidirectional nonlinear coupling, with a CCM skill of ρ = 0.746 for Shimantan TN → Banqiao TN and p = 0.730 for the reverse direction (p = 0.002 for both directions). Wavelet coherence showed that upstream–downstream TN coupling was concentrated mainly at short temporal scales, with a cone-of-influence-restricted mean squared coherence of 0.7114 in the 2–6-month intra-seasonal band. The validation-selected Gradient Boosting model provided interpretable test-period predictive skill, on independent source-derived observations from 2021–2023, achieving R² = 0.567, RMSE = 0.391 mg/L, and MAE = 0.312 mg/L. The GAN-generated 2024–2025 segment was excluded from empirical model evaluation and retained only for exploratory future-scenario assessment. SHAP decomposition indicated that upstream-related predictors accounted for 77.04% of the total absolute model attribution during high-TN events, while seasonal conditioned counterfactual upstream neutralization produced mean model-predicted changes of 0.162 mg/L across all test observations and 0.807 mg/L during high-TN events. Together, these results demonstrate that hidden upstream-downstream TN connectivity can be diagnosed through convergent causal, temporal, predictive, and model-attribution evidence in data-limited reservoir cascades. The findings support asymmetric coupled dynamics and downstream inheritance of upstream information but should not be interpreted as proof of exclusively one-way physical nutrient transport. The proposed framework offers a diagnostic decision-support approach for reservoir systems with sufficiently long monitoring records where direct hydraulic observations are unavailable. Full article

Inverse kinematics (IK) is fundamental to robot motion planning. Classical analytical solvers require complete Denavit–Hartenberg (DH) parameters that are often proprietary or degraded by mechanical wear, and numerical solvers based on damped least squares (DLS) are sensitive to initialization, particularly near singularities. We propose XGNN, an explainable graph neural network positioned as a model-free, interpretable warm-start initializer for downstream numerical IK refinement rather than as a standalone replacement for analytical solvers. Each IK query is encoded as a 12-node graph in which six pose nodes and six joint nodes are connected through bipartite pose-to-joint attention edges and chain edges along the kinematic structure. GATv2 message passing aggregates information at each joint node; two ablation-validated design contributions (a learnable node-type embedding and an angle-aware composite loss) enable training to convergence. Evaluated on 300,000 trajectory-style samples generated from the ABB IRB 2400 kinematic model, XGNN achieves ${3.66}^{\circ }$ joint mean absolute error (MAE), comparable to a multilayer perceptron baseline (${3.09}^{\circ }$) and a bidirectional LSTM (${3.14}^{\circ }$) under identical training. The standalone joint accuracy of all learned models is too coarse for direct industrial use, but XGNN provides the strongest warm start for DLS refinement: the convergence rate improves from $98.4\%$ to $100\%$, mean iterations drop from 14.6 to 3.2, and wall-clock time per pose drops $5.0\times$ on the IRB 2400. The benefit transfers cross-platform to the Universal Robots UR5 collaborative manipulator (convergence rate $82.2\%$ to $100\%$, $10.0\times$ speedup) and survives DH parameter perturbation of up to $\pm 10\%$, simulating calibration drift or mechanical wear. The GATv2 attention coefficients additionally provide an interpretability signal at zero inference cost. XGNN therefore complements analytical and numerical IK methods as an interpretable, calibration-robust warm start when DH parameters are unavailable, proprietary, or degraded. Full article

To address the difficulty of accurately capturing the dynamic patterns of carbon emission time series—characterized by nonlinearity, non-stationarity, and complex fluctuations—this paper proposes a carbon emission prediction model based on an elite-guided collaborative social spider learning optimization algorithm (EGC-SSLO) integrated with a Long short-term memory (LSTM) network. First, considering the limitations of the standard stochastic social learning optimization (SSLO) algorithm in complex high-dimensional optimization problems, such as insufficient elite information guidance, weak local exploitation in the later stages, and a tendency to become trapped in local optima, three complementary improvement strategies are introduced. The adaptive elite mean-guided search strategy enhances the search directionality by incorporating the cooperative information of the best individual and the elite mean. The worst-individual hybrid Cauchy–Lévy search mechanism achieves a dynamic balance between early-stage global exploration and late-stage local exploitation through long-range Lévy flights and fine-grained Cauchy perturbations. The quadratic directional exploitation strategy further refines the search trajectory of candidate solutions, thereby improving convergence accuracy. These three strategies significantly enhance the optimization performance without increasing the time complexity order of the algorithm. Experimental results on the CEC2017 (30-dimensional), CEC2020 (20-dimensional), and CEC2022 (20-dimensional) benchmark suites demonstrate that EGC-SSLO consistently outperforms classical algorithms such as PSO, GWO, and HHO, as well as their improved variants, in terms of convergence accuracy, convergence speed, and robustness. Furthermore, the Wilcoxon rank-sum test and Friedman test confirm that the observed improvements are statistically significant. Finally, an EGC-SSLO-LSTM carbon emission prediction model is constructed and applied to daily carbon emission data in China from 2019 to 2025 for empirical analysis. The experimental findings show that the EGC-SSLO-LSTM model markedly outperforms both the standard LSTM and SSLO-LSTM approaches across key evaluation metrics, including mean absolute error (MAE), root mean square error (RMSE), and the coefficient of determination (R²). In particular, the MAE is decreased by 39.9% and 4.64% compared with the two benchmark models, respectively, which highlights the strong effectiveness and practical potential of the proposed method in real-world carbon emission forecasting applications. Full article

This work is devoted to the analysis of the limit behavior of the solution to a class of fractional stochastic differential equations with Markovian switching and multiplicative fractional Brownian motion. With the aid of fractional calculus, generalized Riemann-Stieltjes integrals, stopping time techniques and inequality techniques, an averaging principle is established within the framework of Hölder continuous spaces. We prove that the solution of the original fractional Markovian jump system converges in the mean-square sense to that of the averaged equation, thereby justifying the averaging method as an effective technique for reducing the system’s complexity. Finally, concrete examples are presented to demonstrate our theoretical findings. Full article

Eco-anxiety has emerged as an important construct in environmental psychology. The Hogg Eco-Anxiety Scale (HEAS-13), which consists of 13 items, is a multidimensional instrument designed to assess affective symptoms, rumination, behavioral responses, and anxiety related to environmental issues. This study examined the psychometric properties of the HEAS-13 in a general population sample from Czechia. The study assessed the scale’s validity in relation to generalized anxiety and self-reported housing damage associated with adverse weather-related events. Data were collected by conducting face-to-face interviews with a population-based sample in Czechia (n = 1027), with respondents selected using address-based sampling. The psychometric evaluation included descriptive statistics, an internal consistency analysis, inter-item correlations, an exploratory factor analysis (EFA) based on principal axis factoring with oblimin rotation, a confirmatory factor analysis (CFA) using a Weighted Least Squares Mean and Variance (WLSMV) estimator appropriate for ordinal indicators, and convergent, discriminant, and known-groups validity testing. The HEAS-13 demonstrated high internal consistency (Cronbach’s alpha = 0.962; McDonald’s omega = 0.958 for the total scale). EFA supported the original four-factor structure and CFA showed a good fit of the original model. Score distributions were positively skewed, and substantial floor effects indicated generally low levels of eco-anxiety symptom endorsement in the general population. The HEAS-13 total score was strongly correlated with the GAD-7 (rho = 0.839) supporting convergence with generalized anxiety, but also indicating possible construct overlap. Known-groups validity was supported by higher HEAS-13 scores among respondents reporting hazard-related home damage. Measurement invariance was examined across sex and age groups. The HEAS-13 appears to be a reliable and structurally well-fitted instrument for assessing multidimensional eco-anxiety in population-based research. The results provide evidence that the construct is meaningfully associated with generalized anxiety and experience of environmentally disruptive events. The HEAS-13 may serve as a useful tool for future research on environmental distress and climate- and environment-related mental health. It may also be useful for studies examining risk perception as an explanatory, associated, or contextual variable. Full article

This paper focuses on a heteroscedastic partially linear regression model in which the errors are asymptotically almost negatively associated (AANA) random variables with a stochastically dominated and zero mean. Under some suitable conditions, the $p$-th $\left(p>0\right)$ mean consistency of least squares estimators and weighted least squares estimators for the unknown parameter is established, and the $p$-th $\left(p>0\right)$ mean consistency of the estimators for non-parametric components is also obtained. In addition, the moment convergence rate of the estimators is also investigated. Some results derived in this paper extend and improve the corresponding ones of negatively associated (NA) random errors and independent random errors. Finally, a simulation is carried out to study the numerical performance of the results that we have established. Full article

Forecasting fine particulate matter with a diameter of 2.5 μm (PM_2.5) is critically important due to its adverse effects on human health and environmental sustainability. Although ground-based monitoring stations provide accurate measurements, their limited spatial coverage restricts large-scale PM_2.5 assessment, especially in complex urban regions. Consequently, aerosol optical depth (AOD) derived from satellite imagery, combined with advanced deep learning (DL) techniques, has emerged as an effective alternative by offering wide spatial coverage and rich spatio-temporal information. This paper proposed an optimization-driven fuzzy transformer–deep belief network (ODFT-DBN) for accurate PM_2.5 air pollution prediction. The proposed framework integrates a fuzzy inference module to model uncertainty and nonlinear environmental relationships, a transformer encoder to capture long-range spatio-temporal dependencies, and a DBN to extract hierarchical features and improve prediction robustness. In addition, a novel multi-objective gray wolf optimizer (NMOGWO) is employed to jointly optimize the model hyper-parameters and fuzzy membership functions. The proposed approach is implemented for the city of Tehran, Iran, using meteorological variables, topographical features, ground-based PM_2.5 measurements, and satellite-derived AOD data. The ODFT-DBN model is compared with several benchmark methods, including bidirectional encoder representations from transformers (BERT), transformer, long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network (CNN), DBN, and extreme gradient boosting (XGBoost). Experimental results demonstrate that the proposed framework achieves superior predictive performance, attaining an R² value of 0.94 and root mean square error (RMSE) of 0.8 μg/m³. Scatter plot analyses indicate a strong agreement between predicted and observed PM_2.5 values, while the proposed model exhibits low variance, stable convergence behavior, and acceptable computational time. Overall, the results confirm the effectiveness, robustness, and practical applicability of the proposed ODFT-DBN framework for spatio-temporal PM_2.5 forecasting. Full article

Floating offshore platforms are subjected to significant impact loads from ocean currents, which pose considerable challenges to the safety of floating offshore wind turbines. To address this issue, this study develops a novel infill criterion framework based on the parallel Efficient Global Optimization (EGO) algorithm. Compared with the traditional EGO algorithm, the proposed framework enables the simultaneous addition of multiple infill samples in each iteration, resulting in substantially improved optimization efficiency. The proposed method is applied to the optimization of floating offshore platforms, where drag minimization is considered the primary design objective. The results demonstrate that incorporating the mean squared error (MSE) criterion into the conventional EGO algorithm, while constraining the search space of the MSE criterion, effectively accelerates the convergence of the Expected Improvement (EI) criterion. Furthermore, an optimization method for floating platforms is established, leading to a reduction in drag of approximately 1.69% after optimization. The proposed optimization framework improves the drag performance of floating offshore platforms and provides a new approach for structural optimization in offshore engineering. Full article

Conventional I/O Buffer Information Specification (IBIS) models often suffer from reduced fidelity in high-speed signaling because their static table-lookup mechanism cannot accurately reproduce complex transient I/O-buffer dynamics. To address this limitation, this study proposes a Verilog-AMS-based dynamic parameter compensation method. First, the conventional IBIS model is reformulated into a three-layer architecture comprising a data interface layer, an intermediate variable computation layer, and a port response synthesis layer. Then, based on Kirchhoff’s current law (KCL), the monotonic dependence of the output voltage on the pull-up and pull-down driving factors, k_pu and k_pd, is analytically derived to provide a directional criterion for parameter correction. Building on this criterion, a pulse-width-driven compensation algorithm is developed by constructing a pulse-width-indexed dual-factor empirical adjustment matrix and detecting the pulse width of the input bitstream in real time during transient simulation. The detected pulse width is then used to dynamically update k_pu and k_pd, enabling the IBIS response to converge toward the transistor-level SPICE reference waveform. Three representative device models were evaluated at 666 Mbps and 1.302 Gbps using pseudo-random binary sequence excitation, and the model fidelity was quantified using the normalized mean square error (NMSE). The proposed method reduced the NMSE from −6.73 to −1.03 dB before compensation to −54.79 to −44.19 dB after compensation, demonstrating a substantial improvement in high-frequency IBIS modeling fidelity and confirming the robustness and adaptability of the pulse-width-aware dynamic compensation strategy under random high-speed excitation. Full article

Introduction: Day-to-day fluctuations in heart rate variability (HRV) are widely used to infer autonomic recovery in endurance athletes. However, the extent to which HRV can be forecast one day ahead from readily available external and internal training-load metrics remains unclear. In this study, we evaluated whether machine learning models can predict next-day HRV in competitive cyclists using the two load descriptors most commonly collected in practice: external load quantified as total mechanical work in kilojoules (kJ) and internal load quantified as session rating of perceived exertion (RPE). Methods: Seven male competitive endurance cyclists were monitored daily for sixteen weeks, yielding 590 athlete-days of longitudinal data (seven independent time series). Two machine learning approaches—support vector regression (SVR) and extreme gradient boosting (XGBoost)—were compared with a conventional autoregressive model with exogenous inputs (ARX) as a traditional time-series benchmark. Each model was trained individually per athlete under two predictor scenarios (using past HRV-only or past HRV plus kJ and RPE) and across multiple lag orders (1, 4, 7, 10 and 14 days), with forecasting accuracy expressed as root mean squared error (RMSE). Results: Across all athletes, adding kJ and RPE to the past HRV produced only modest reductions in RMSE relative to HRV-only models. XGBoost achieved the lowest one-step-ahead RMSE at short lag, while all models converged at longer lag orders. Predictive accuracy differed markedly between athletes, reflecting the well-known individual nature of autonomic responses. Conclusions: These findings suggest that the two routinely collected load descriptors examined here—total work (kJ) and RPE—add limited information beyond recent HRV history for forecasting next-day HRV, and that broader contextual variables are likely required to meaningfully improve athlete monitoring. Full article