Search Results (132)

Accurate prediction, forecasting and interpretability of air pollutant concentrations are important for sustainable environmental management and protecting public health. An integrated artificial intelligence (AI) framework is proposed to predict, forecast and analyse six major air pollutants, such as particulate matter concentrations (PM_2.5 and PM₁₀), ground-level ozone (O₃), carbon monoxide (CO), nitrogen dioxide (NO₂), and sulphur dioxide (SO₂), using a combination of ensemble and deep learning models. Five years of hourly air quality and meteorological data are analysed through correlation and Granger causality tests to uncover pollutant interdependencies and driving factors. The results of the Pearson correlation analysis reveal strong positive associations among primary pollutants (PM_2.5–PM₁₀, CO–nitrogen oxides NO_x and VOCs) and inverse correlations between O₃ and NO_x (NO and NO₂), confirming typical photochemical behaviour. Granger causality analysis further identified NO₂ and NO as key causal drivers influencing other pollutants, particularly O₃ formation. Among the 23 tested AI models for prediction, XGBoost, Random Forest, and Convolutional Neural Networks (CNNs) achieve the best performance for different pollutants. NO₂ prediction using CNNs displays the highest accuracy in testing (R² = 0.999, RMSE = 0.66 µg/m³), followed by PM_2.5 and PM₁₀ with XGBoost (R² = 0.90 and 0.79 during testing, respectively). The Air Quality Index (AQI) analysis shows that SO₂ and PM₁₀ are the dominant contributors to poor air quality episodes, while ozone peaks occur during warm, high-radiation periods. The interpretability analysis based on Shapley Additive exPlanations (SHAP) highlights the key influence of relative humidity, temperature, solar brightness, and NO_x species on pollutant concentrations, confirming their meteorological and chemical relevance. Finally, a deep-NARMAX model was applied to forecast the next horizons for the six air pollutants studied. Six formulas were elaborated using input data at times (t, t − 1, t − 2, …, t − n) to forecast a horizon of (t + 1) hours for single-step forecasting. For multi-step forecasting, the forecast is extended iteratively to (t + 2) hours and beyond. A recursive strategy is adopted for this purpose, whereby the forecast at (t + 1) is fed back as an input to generate the forecasts at (t + 2), and so forth. Overall, this integrated framework combines predictive accuracy with physical interpretability, offering a powerful data-driven tool for air quality assessment and policy support. This approach can be extended to real-time applications for sustainable environmental monitoring and decision-making systems. Full article

To address the limitations of fixed-order update mechanisms in convolutional neural network parameter training, an adaptive parameter training method based on the Hausdorff difference is proposed in this paper. By deriving a Hausdorff difference formula that is suitable for discrete training processes and embedding it into the adaptive moment estimation framework, a generalized Hausdorff difference-based Adam algorithm (HAdam) is constructed. This algorithm introduces an order parameter to achieve joint dynamic control of the momentum intensity and the effective learning rate. Through theoretical analysis and numerical simulations, the influence of the order parameter and its value range on algorithm stability, parameter evolution trajectories, and convergence speed is investigated, and two adaptive order adjustment strategies based on iteration cycles and gradient feedback are designed. The experimental results on the Fashion-MNIST and CIFAR-10 benchmark datasets show that, compared with the standard Adam algorithm, the HAdam algorithm exhibits clear advantages in both convergence efficiency and recognition accuracy. Full article

Quantitative precipitation estimation (QPE) from radar reflectivity is fundamental for weather nowcasting and water resource management. Conventional Z-R relationship formulas, derived from Rayleigh scattering theory, rely heavily on empirical parameter fitting, which limits the estimation accuracy and generalization across different precipitation regimes. Recent deep learning (DL)-based QPE methods can capture the complex nonlinear relationships between radar reflectivity and rainfall. However, most of them overlook fundamental physical constraints, resulting in reduced robustness and interpretability. To address these issues, this paper proposes FusionQPE, a novel Physics-Constrained DL framework that integrates an adaptive Z-R formula. Specifically, FusionQPE employs a Dense convolutional neural network (DenseNet) backbone to extract multi-scale spatial features from radar echoes, while a modified squeeze-and-excitation (SE) network adaptively learns the parameters of the Z-R relationship. The final rainfall estimate is obtained through a linear combination of outputs from both the DenseNet backbone and the adaptive Z-R branch, where the trained linear weight and Z-R parameters provide interpretable insights into the model’s physical reasoning. Moreover, a physical-based constraint derived from the Z-R branch output is incorporated into the loss function to further strengthen physical consistency. Comprehensive experiments on real radar and rain gauge observations from Guangzhou, China, demonstrate that FusionQPE consistently outperforms both traditional and state-of-the-art DL-based QPE models across multiple evaluation metrics. The ablation and interpretability analysis further confirms that the adaptive Z-R branch improves both the physical consistency and credibility of the model’s precipitation estimation. Full article

Automatic Target Recognition (ATR) in single-view sonar imagery is severely hampered by geometric distortions, acoustic shadows, and incomplete target information due to occlusions and the slant-range imaging geometry, which frequently give rise to misclassification and hinder practical underwater detection applications. To address these critical limitations, this paper proposes a Multi-View Deep Convolutional Neural Network (MVDCNN) based on feature-level fusion for robust sonar image target recognition. The MVDCNN adopts a highly modular and extensible architecture consisting of four interconnected modules: an input reshaping module that adapts multi-view images to match the input format of pre-trained backbone networks via dimension merging and channel replication; a shared-weight feature extraction module that leverages Convolutional Neural Network (CNN) or Transformer backbones (e.g., ResNet, Swin Transformer, Vision Transformer) to extract discriminative features from each view, ensuring parameter efficiency and cross-view feature consistency; a feature fusion module that aggregates complementary features (e.g., target texture and shape) across views using max-pooling to retain the most salient characteristics and suppress noisy or occluded view interference; and a lightweight classification module that maps the fused feature representations to target categories. Additionally, to mitigate the data scarcity bottleneck in sonar ATR, we design a multi-view sample augmentation method based on sonar imaging geometric principles: this method systematically combines single-view samples of the same target via the combination formula and screens valid samples within a predefined azimuth range, constructing high-quality multi-view training datasets without relying on complex generative models or massive initial labeled data. Comprehensive evaluations on the Custom Side-Scan Sonar Image Dataset (CSSID) and Nankai Sonar Image Dataset (NKSID) demonstrate the superiority of our framework over single-view baselines. Specifically, the two-view MVDCNN achieves average classification accuracies of 94.72% (CSSID) and 97.24% (NKSID), with relative improvements of 7.93% and 5.05%, respectively; the three-view MVDCNN further boosts the average accuracies to 96.60% and 98.28%. Moreover, MVDCNN substantially elevates the precision and recall of small-sample categories (e.g., Fishing net and Small propeller in NKSID), effectively alleviating the class imbalance challenge. Mechanism validation via t-Distributed Stochastic Neighbor Embedding (t-SNE) feature visualization and prediction confidence distribution analysis confirms that MVDCNN yields more separable feature representations and more confident category predictions, with stronger intra-class compactness and inter-class discrimination in the feature space. The proposed MVDCNN framework provides a robust and interpretable solution for advancing sonar ATR and offers a technical paradigm for multi-view acoustic image understanding in complex underwater environments. Full article

The Horadam sequence $H_n(a,b;p,q)$ unifies a number of well-known sequences, such as Fibonacci and Lucas sequences. We use the context-free grammars as a new tool to study Horadam sequences. By introducing a set of auxiliary basis polynomials ($v_1,v_2,v_3$) and using the formal derivative associated with the Horadam grammar, we solve the convolution coefficients and provide a unified method to discover convolution formulas associated with binomial coefficients. These results are extended to subsequences with indices $kn$ through a parameterized grammar $G_k$. Using the modified grammar $\widetilde{G_k}$, we derive convolution formulas involving the weighting term ${(-q)}^{n-i}$. Furthermore, applying the proposed framework to $(p,q)$-Fibonacci and $(p,q)$-Lucas sequences, we derive explicit convolution formulas with parameters $(p,q)$. The framework is also applied to derive specific identities for Pell and Pell–Lucas numbers, as well as for Fermat and Fermat–Lucas numbers. Full article

Background/Objectives: Accurate patient weight estimation is critical for safe and effective drug dosing in emergency and critical care settings. Inaccurate estimates exceeding a 10% deviation from true weight can result in significant dosing errors in time-sensitive treatments such as thrombolysis for stroke or urgent sedation. In situations where direct weight measurement is impractical, reliable alternative estimation methods are essential. Methods: We propose a three-dimensional (3D) depth-camera system that employs a convolutional neural network (CNN) pipeline to automatically estimate total body weight (TBW), ideal body weight (IBW), and lean body weight (LBW) from volumetric features derived from a single supine patient image. Our approach was evaluated in a prospective pilot study to assess feasibility and accuracy. CNNs were selected because of their ability to extract spatial features from complex image data, outperforming regression and tree-based models in preliminary comparisons. Results: The results demonstrated that our 3D camera system was more accurate than conventional techniques, including clinician visual estimation (Mean Absolute Percentage Error [MAPE]: 12%), tape-based methods (±8.5%), and anthropometric formulas (±9.2%), achieving a mean error of ±5.4%. Conclusions: Future work will extend this technology to pediatric populations, support integration with automated dosing systems, and explore prehospital applications to further reduce medication errors and enhance patient safety. Full article

This paper develops a generalized Laplace transform theory within weighted function spaces tailored for the analysis of fractional differential equations involving the $\psi$-Hilfer derivative. We redefine the transform in a weighted setting, establish its fundamental properties—including linearity, convolution theorems, and action on ${\delta }_{\psi }$ derivatives—and derive explicit formulas for the transforms of $\psi$-Riemann–Liouville, $\psi$-Caputo, and $\psi$-Hilfer fractional operators. The results provide a rigorous analytical foundation for solving hybrid fractional Cauchy problems that combine classical and fractional derivatives. As an application, we solve a hybrid model incorporating both ${\delta }_{\psi }$ derivatives and $\psi$-Hilfer fractional derivatives, obtaining explicit solutions in terms of multivariate Mittag-Leffler functions. The effectiveness of the method is illustrated through a capacitor charging model and a hydraulic door closer system based on a mass-damper model, demonstrating how fractional-order terms capture memory effects and non-ideal behaviors not described by classical integer-order models. Full article

Let $q_1+\cdots +q_n+m$ objects be arranged in n rows with $q_1,\dots ,q_n$ objects and one last row with m objects. The Janjić–Petković counting function denotes the number of $(n+k)$-insets, defined as subsets containing $n+k$ objects such that at least one object is chosen from each of the first n rows, generalizing the binomial coefficient that is recovered for $q_1$ = … = $q_n$ = 1, as then only the last row matters. Here, we discuss two explicit forms, combinatorial interpretations, recursion relations, an integral representation, generating functions, convolutions, special cases, and inverse pairs of summation formulas. Based on one of the generating functions, we show that the Janjić–Petković counting function, like the binomial coefficients that it generalizes, may be regarded as a Riordan array, leading to additional identities. As an application to a physical system, we calculate the heat capacity of a many-body system for which the configurations are constrained as described by the Janjić–Petković counting function, resulting in a modified Schottky anomaly. Full article

Driven by the increasing global population and rapid urbanization, aircraft noise pollution has emerged as a significant environmental challenge, impeding the sustainable development of the aviation industry. Traditional noise prediction methods are limited by incomplete datasets, insufficient spatiotemporal consistency, and poor adaptability to complex meteorological conditions, making it difficult to achieve precise noise management. To address these limitations, this study proposes a novel noise prediction framework based on a hybrid Convolutional Neural Network–Bidirectional Long Short-Term Memory–Attention (CNN–BiLSTM–Attention) model. By integrating multi-source data, including meteorological parameters (e.g., temperature, humidity, wind speed) and aircraft trajectory data (e.g., altitude, longitude, latitude), the framework achieves high-precision prediction of aircraft noise. The Haversine formula and inverse distance weighting (IDW) interpolation are employed to effectively supplement missing data, while spatiotemporal alignment techniques ensure data consistency. The CNN–BiLSTM–Attention model leverages the spatial feature extraction capabilities of CNNs, the bidirectional temporal sequence processing capabilities of BiLSTMs, and the context-enhancing properties of the attention mechanism to capture the spatiotemporal characteristics of noise. The experimental results indicate that the model’s predicted mean value of 68.66 closely approximates the actual value of 68.16, with a minimal difference of 0.5 and a mean absolute error of 0.89%. Notably, the error remained below 2% in 91.4% of the prediction rounds. Furthermore, ablation studies revealed that the complete CNN–BiLSTM–AM model significantly outperformed single-structure models. The incorporation of the attention mechanism was found to markedly enhance both the accuracy and generalization capability of the model. These findings highlight the model’s robust performance and reliability in predicting aviation noise. This study provides a scientific basis for effective aviation noise management and offers an innovative solution for addressing noise prediction problems under data-scarce conditions. Full article

In landslide susceptibility evaluation, scientific sampling minimizes potential societal losses and enhances the efficiency of disaster prevention and mitigation. However, traditional sampling methods, such as selecting landslide and non-landslide samples based on equal proportions or area proportions, overlook the different societal losses resulting from landslide omission and misreporting, and the potential societal losses faced by their evaluation results are often not minimized. Therefore, this study proposes a sampling method that takes potential societal losses into account and uses the Landslide Misjudgment Potential Societal Loss Evaluation Index (LMPSLEI) to quantify the total potential social losses in the area due to landslide omission and misreporting. The LMPSLEI is minimized by optimizing the sample ratio, thus minimizing the potential societal losses faced by the evaluation results and enhancing the scientific basis of disaster prevention and mitigation efforts. This study takes the Wenchuan earthquake area as the research region, selects 13 conditional factors and employs two models—Random Forest (RF) and Convolutional Neural Network (CNN)—to conduct case studies. We derive the recommended sample ratio based on the formula, hypothesizing that the LMPSLEI will be minimized under this ratio. The results show that the sample ratio for LMPSLEI minimization in the RF model is similar to the recommended sample ratio, while the sample ratio for LMPSLEI minimization in the CNN model is slightly higher than the recommended sample ratio. The recommended sample ratio can achieve the minimum of LMPSLEI or reach a lower value under different societal losses weights of landslide omission/misreporting, and thus it can be used as a preliminary choice of sampling for landslide susceptibility evaluation considering the potential societal losses. Full article

The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article

This article is devoted to the derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag–Leffler-type, Wright, and Le Roy-type functions. These formulas show the interconnection of these functions and lead to a better understanding of their behavior on the real line. These formulas are represented in a convoluted form and reconstructed in a more suitable form by using the Efros theorem. Full article

In this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties. First, we show that this master equation can be embedded into the framework of continuous time random walks, and we derive an explicit formula for the waiting time probability density function of the continuous time random walk model in form of a convolution series generated by the Sonin kernel associated with the kernel of the regularized general fractional derivative. Next, we derive a fractional diffusion equation involving regularized general fractional derivatives with Sonin kernels from the continuous time random walk model in the asymptotical sense of long times and large distances. Another important result presented in this paper is a concise formula for the mean squared displacement of the particles governed by this fractional diffusion equation. Finally, we discuss several mathematical aspects of the fractional diffusion equation involving regularized general fractional derivatives with Sonin kernels, including the non-negativity of its fundamental solution and the validity of an appropriately formulated maximum principle for its solutions on the bounded domains. Full article

Using the generalized $\mathfrak{q}$-Sălăgean operator, we introduce a new class of meromorphic functions in a punctured unit disk ${\mathcal{U}}^{\ast }$ and investigate a majorization problem associated with this class. The principal tool employed in this analysis is the recently established $\mathfrak{q}$-Schwarz–Pick lemma. We investigate a majorization problem for meromorphic functions when the functions of the right hand side of the majorization belongs to this class. The main tool for this investigation is the generalization of Nehari’s lemma for the Jackson’s $\mathfrak{q}$-difference operator ${\partial }_{\mathfrak{q}}$ given recently by Adegani et al. Full article

Six well-known sequences (Fibonacci and Lucas numbers, Pell and Pell–Lucas polynomials, and Chebyshev polynomials) are characterized by quadratic linear recurrence relations. They are unified and reviewed under a common framework. Several useful properties (such as Binet-form expressions, Cassini identities, and Catalan formulae) and remarkable results concerning power sums, ordinary convolutions, and binomial convolutions are presented by employing the symmetric feature, series rearrangements, and the generating function approach. Most of the classical results concerning these six number/polynomial sequences are recorded as consequences. Full article