This study forecasts cumulative log returns at horizons of one to twenty trading days and reconstructs future adjusted prices by exponentiating those return forecasts; it does not optimize a price-level loss. This task is difficult because financial returns are nonstationary, heavy-tailed, horizon-dependent, and subject to rapidly changing volatility. We propose FreqCast, which combines a market-conditioned spectral decomposition, a structured state-space branch for the component designated low-frequency, causal multiscale encoders for the components designated intermediate- and high-frequency, and a horizon-conditioned reliability gate. The gate uses expert representations, predictive scale, and cross-expert disagreement to fuse four cumulative-return estimates. The joint objective covers point loss, an auxiliary directional score, Laplace likelihood, ordered quantile loss, decomposition regularization, and horizon coherence. Experiments use eight large U.S. stocks and a single 2021–2024 test interval. Within that restricted benchmark, the reported point estimates favor FreqCast over the included baselines and show horizon- and volatility-dependent expert allocation. Our main contribution is the coordinated frequency-dependent assignment and reliability fusion of heterogeneous forecasting mechanisms, while broad market robustness and statistical superiority remain to be established.
The U-shaped Disassembly Line Balancing Problem (UDLBP) is a challenging combinatorial optimization problem for which efficient solution approaches remain limited. This study proposes an efficient branch-bound-and-remember (BBR) algorithm that integrates a memory-based mechanism and U-shaped dominance rules to effectively reduce the search space. Specifically, a new branching method, an additional lower bounding method, and new dominance rules are developed to suit the UDLBP, and different search strategies are developed and explored. Extensive computational experiments are conducted on a comprehensive set of benchmark instances to evaluate the performance of the proposed approach. The results demonstrate that the proposed BBR algorithm can consistently identify the best-known solutions for the evaluated benchmark instances. Compared with constraint programming, mixed-integer linear programming, and several state-of-the-art metaheuristic algorithms, the proposed approach achieves competitive solution quality and computational efficiency, consistently matching the best-known solutions with an average recorded CPU time of 0.0199 s under the 500 s computational setting. These findings indicate that the proposed algorithm provides an efficient optimization framework for solving UDLBP, achieving high-quality solutions with substantially low computational cost.
The Newton Downhill Optimizer (NDO) provides a compact derivative-free search framework, but its random dimension mask, uniform treatment of individuals, and limited use of supplementary global-best candidates may restrict performance on high-dimensional problems. This study proposes an Enhanced Newton Downhill Optimizer (ENDO) that incorporates three mechanisms: an adaptive dimension mask, a DE/rand/2-based greedy mutation for inferior individuals, and dynamic-boundary opposition-based best guidance. ENDO was evaluated on the CEC2017 benchmark at 10, 30, 50, and 100 dimensions. The primary comparison involved nine representative optimizers, and an additional 100-dimensional comparison was conducted with six advanced optimizers. In the primary 100-dimensional tests, ENDO ranked first on 18 of 29 functions, remained among the top three on 26 functions, and achieved an average rank of 1.79. In the additional comparison, ENDO ranked third with an average rank of 3.52. Across the four dimensions, its average ranks were 1.79, 1.66, 1.38, and 1.79, indicating stable performance under changes in problem scale. ENDO was further applied to a 168-dimensional thermal–pumped-storage economic dispatch problem, where it achieved the lowest mean operating cost, the best average rank of 1.87, and a feasibility rate of 100% over 30 independent runs. Statistical analyses further supported the competitiveness of ENDO across the benchmark and engineering evaluations. These results show that ENDO improves the sustained search capability of NDO and provides competitive performance for complex high-dimensional and constrained optimization problems.
Alcohol Use Disorder (AUD) is associated with widespread neurophysiological dysregulation, yet accessible and objective biomarkers for early risk identification remain limited. This preliminary study investigates electroencephalographic (EEG) frequency-domain and event-related potential features as candidate group-associated markers in AUD, with a focus on band power reduction and P300 event-related potential attenuation. Using the Begleiter EEG Database (UCI Machine Learning Repository, 1995), comprising 77 individuals with AUD and 45 healthy controls and recorded from 64 channels, we performed power spectral density estimation via Welch’s method and extracted band power across five frequency bands: delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz), and gamma (30–50 Hz). Band power was computed at the trial level and averaged across trials at the subject level. Statistical comparisons using the Mann–Whitney U test with Benjamini–Hochberg FDR correction revealed significant band power reductions in the AUD group across frontal, central, and parietal channels, with the largest effects observed in parietal delta (P3: Hedges’ g=−0.97, q<0.0001; P4: g=−0.95, q<0.0001) and central theta (C4: g=−0.97, q<0.0001). P300 amplitude was significantly attenuated at parietal sites in S2 match (target) trials (Pz: g=−0.75, p=0.0002), consistent with hypothesised dopaminergic dysregulation of attentional processing networks. A Gaussian Naive Bayes classifier using the eight analysis channels selected for classification achieved a cross-validated ROC AUC = 0.713±0.088 [95% CI: 0.526, 0.833] under repeated stratified cross-validation, confirmed above chance by a permutation test (p=0.001). The complete analytical pipeline was executed on consumer-grade hardware without GPU acceleration, in line with Green AI principles. Topographic analysis indicated a spatially consistent parietal-dominant pattern of band power reduction. These findings suggest that task-evoked EEG frequency-domain and P300 features are systematically associated with AUD group membership and may warrant further investigation as candidate markers. The cross-sectional design of this study precludes conclusions regarding early risk identification, screening utility, or causal dopaminergic mechanisms; longitudinal validation in larger cohorts is required.
This paper describes an intelligent, CAD-based decision support and optimization framework for predicting fabric waste directly from geometry attributes of apparel pattern segments. It is applicable during the early design stage, providing a pre-screening alternative prior to the use of time-consuming nesting software. A synthetic database of 1000 apparel layouts was generated through a specifically developed Python algorithm, which creates realistic geometries of apparel pattern segments based on skirts, bodices and sleeves for a stipulated fabric width. Eight geometry attributes, with the ability to represent pattern fragmentation, pattern size, shape attributes, boundary complexity, and overall pattern variation were derived, and a random forest (RF) regressor was formulated to predict the essential nesting efficiency (NE) parameter. It was tested utilizing 500 decision trees, with 75% available features allocated for each split. Model performance was tested with 5-fold cross-validation (CV) which led to a coefficient of determination of 0.922, with an average prediction error of −0.0002. Validation of the method with layouts created with the Deepnest software demonstrated promising agreement between software-predicted and model-predicted values of fabric NE. The key influential features were revealed as total perimeter, convexity, number of pattern pieces and compactness, accounting for 90% of model information.
Granite residual and slope-wash soils are important disaster-prone geological bodies in the hilly and mountainous areas of Hunan Province, China. Their engineering classification has long relied on manual visual inspection and laboratory testing, which is inefficient and subjective. In this study, an automatic classification method based on deep learning image recognition is proposed for granite residual and slope-wash soils in the mountainous areas of Hunan Province. First, a three-class primary classification scheme was established, comprising residual clay (RNC), residual sandy clay (RNSC), and residual gravelly clay (RNGC), based primarily on the gravel content of particles larger than 2 mm (RNC < 5%, RNSC 5–20%, RNGC > 20%). Second, 7678 geotechnical test records from 21 counties in Hunan Province were collected, and classification labels were assigned through a strategy combining manual verification and automatic inference using Random Forest (5-fold cross-validation macro F1 = 0.913). From approximately 10,096 original field images, 3380 pure soil image patches were retained after segmentation and screening. A dataset of 43,940 samples was then generated through two-stage preprocessing (including denoising and illumination correction) and 13-fold data augmentation. A CNN image classification model was constructed based on a ResNet18 backbone network pre-trained on ImageNet. On the independent test set (6591 images), the primary classification accuracy reached 91.46%, with a macro F1-score of 0.9128; the per-class F1-scores for RNC, RNSC, and RNGC were 0.921, 0.885, and 0.933, respectively. Grad-CAM visualization analysis demonstrated that the model’s attention was primarily focused on soil particle distribution regions rather than non-soil background areas, confirming the effective learning of mixed-grain features. The study shows that the combined application of transfer learning and 13-fold data augmentation can significantly improve classification performance under limited sample size conditions (an improvement of 15.33 percentage points compared to the baseline of 76.13%), demonstrating promising potential for engineering applications.
Deep learning has shown promise for vibration-based damage detection, yet its practical deployment is hindered by data scarcity, environmental sensitivity, and limited interpretability. To address these issues, we propose a dual-stream framework that explicitly embeds fractional-order and multifractal physical priors. The Grünwald–Letnikov fractional derivative (ν = 1.3) sharpens damage-related singularities, while multifractal detrended fluctuation analysis (MF-DFA) produces spatial maps of multiscale complexity across the sensor array. A temporal stream (1D-CNN + BiLSTM) processes the fractional-order enhanced signals, and a spatial stream (2D-CNN) processes MF-DFA maps derived from the same enhanced signals. Under the evaluation protocol adopted in this study, the framework achieves 97.3% accuracy on Z24 and 94.8% in the independent within-dataset KW51 experiment. In a separate cross-bridge experiment, the Z24-pretrained model obtains 86.7% accuracy on KW51 without target-domain updating and 94.6% after fine-tuning on 10% of the target data.
(1) Background: Phishing remains a pervasive and economically damaging cyberthreat. The dominant detection paradigm has moved toward deep neural and transformer-based classifiers, a literature that reports high accuracy and that does not, in general, expose a per-decision justification, whereas interpretability and auditability are increasingly required in regulated environments; no comparison against transformer-scale detectors is made in this paper. This work asks how far a fully interpretable detector can close the accuracy gap to an opaque text classifier while preserving per-decision explanations, and what such a detector returns that accuracy alone does not measure. (2) Methods: HIEF, an interpretable evidence-fusion framework, is presented. Each email is represented by eighteen human-readable signals: fourteen structural and linguistic cues and four lexical aggregates derived from a published sparse log-odds lexicon. The signals are fused by three transparent layers, namely an L1-regularized logistic model, a shallow interaction-rule tree, and a calibrated Dempster–Shafer stage that reports belief, disbelief and ignorance masses together with an order-invariant global conflict coefficient derived in closed form. A logistic meta-learner fitted on out-of-fold component scores integrates the three layers. The evidential layer uses a type-aware calibration in which discrete signals are calibrated on their attainable values and continuous signals by isotonic regression. Evaluation uses 38,908 public emails, 38,512 of them after exact-duplicate removal, with near-duplicate control, group-aware partitioning, ten repeated splits, a source-held-out protocol, a two-class cross-source test set, a component ablation and a human audit of 100 messages annotated independently by two evaluators. (3) Results: Under group-aware partitioning, HIEF attains an F1 of 0.855 and the strongest term frequency–inverse document frequency (TF–IDF) baseline 0.954; a compact character n-gram neural reference model, evaluated over the same ten partitions, attains 0.973. The linear layer alone attains 0.872, so the two fusion layers do not improve accuracy over it, and the paired difference of 0.017 excludes zero. Type-aware calibration raises the evidential layer from 0.771 to 0.780 and more than halves its partition-to-partition standard deviation, but does not make it competitive; the weakness, therefore, lies in the fusion formulation rather than in the binning. What the evidential layer does supply is a decomposable account of decision uncertainty: the ignorance mass separates errors from correct decisions, 0.265 against 0.175. The human audit reaches an inter-annotator Cohen’s kappa of 0.950 over the five categories before adjudication, and shows that the permissive corpus label agrees with human phishing judgment at a Cohen’s kappa between 0.18 and 0.21, against 0.70 to 0.77 for the automatic strict rule; the audited block is annotated by two of the authors and its human positives are confined to the advance-fee family, so the audit is a bounded comparison of label assignments and not an independent annotation study. (4) Conclusions: HIEF is positioned as an uncertainty and explanation framework rather than as an accuracy-improving fusion method, since the measured accuracy cost of the fusion layers is not compensated by an accuracy gain. Quantifying how much of the performance reported on these widely used corpora is attributable to template leakage and to label permissiveness is a contribution independent of the detector itself. Cross-source operation has not been demonstrated: specificity falls to 0.041 on an unseen collection, so all evaluation reported here is proof-of-concept and no operational deployment claim is made. The Spanish-language evaluation rests on a small and entirely positive subset and is reported as preliminary.
To address slow convergence, local optimum stagnation, and multi-objective imbalance problems for unmanned aerial vehicle (UAV) three-dimensional (3D) path planning in complex obstacle environments, an improved adaptive two-stage pigeon swarm optimization (IPIO) algorithm is proposed. Firstly, a hybrid initialization strategy integrating Latin hypercube sampling and obstacle avoidance constraints is adopted to improve initial population diversity and the quality of feasible solutions. Secondly, in the map compass stage, a linearly decreasing adaptive map factor and population diversity-based dynamic perturbation strategy are introduced to balance global exploration and local exploitation while preventing premature convergence. In the landmark stage, an inverse fitness weighting elite center updating mechanism and linearly decreasing elite quantity strategy are designed to enhance the guidance of high-quality individuals and accelerate convergence. A multi-objective fitness function integrating path length, obstacle avoidance safety, and flight smoothness is constructed, whose weight coefficients (ωL=0.3, ωC=0.5, ωS=0.2) are calibrated through parameter-sensitivity analysis and Pareto frontier comparison across six representative weight combinations. Combining ablation validation for each improved module, single-UAV multi-scenario tests, and preliminary multi-UAV trials, these coordinated improvements realize targeted optimization for UAV 3D flight characteristics. Specifically, the preliminary multi-UAV trials involve three UAVs performing independent trajectory planning in shared obstacle environments without explicit inter-UAV collision avoidance constraints, and the reported improvements are based on single-UAV experiments. Finally, comparative experiments are conducted with a standard 100 × 100 × 50 m space, and varying obstacle densities are demonstrated in six diverse 3D test scenarios, where the proposed IPIO achieves an average path length reduction of 12.8% and 15.3% compared to the standard PIO and PSO, respectively. The average fitness improvement is 14.2% over PIO, 16.8% over PSO, 19.5% over GWO, 24.1% over CO, and 38.7% over CS. Key path-quality metrics include a minimum obstacle clearance of 2.37 m, average smoothness cost of 0.34, average convergence time of 0.60 s, and computational cost of O(N*D*MaxIter). Statistical tests confirm that these improvements are significant (p < 0.05) in all tested scenarios. This study presents an efficient and robust algorithm for autonomous three-dimensional path planning of UAVs in complex obstacle environments.
Multimodal affective analysis benefits from combining textual, acoustic, and visual cues, yet many methods implicitly mix modality-invariant information with modality-specific factors, which can reduce robustness when modalities vary in reliability. We propose DiMoE, a representation-first framework that integrates feature disentanglement with sparse Mixture of Experts (MoE) fusion. DiMoE first decomposes each modality into shared (modality-invariant) and private (modality-specific) representations. It then fuses these factors using top-k sparse MoE routing, enabling input-adaptive expert selection. We study two routing strategies with a shared expert pool, a joint router that operates on combined shared and private factors, and separate routers that process shared and private factors independently. We evaluate DiMoE on five widely used benchmarks spanning sentiment intensity prediction and emotion classification, covering both trimodal and bimodal settings. Across benchmarks, DiMoE consistently achieves strong performance against recent competitive baselines, indicating that explicit modality disentanglement combined with Mixture of Experts fusion yields effective multimodal affective representations.
The capacitated vehicle routing problem (CVRP) is a representative NP-hard combinatorial optimization problem with broad applications in logistics and transportation. This paper proposes a hybrid metaheuristic, termed SPSOM-CVRP, which integrates an improved set-based particle swarm optimization (SPSO) with a self-organizing map (SOM). In SPSOM-CVRP, the improved SPSO is responsible for constructing feasible CVRP solutions, whereas the SOM performs route-level refinement to improve solution quality. To strengthen exploration, when the personal best of a particle remains unchanged for a predefined number of generations, two new learning exemplars are randomly reassigned to the particle. To enhance exploitation while avoiding excessive computational cost, SOM-based route optimization is activated only when the global best solution stagnates and is applied to selected elite solutions. In this manner, particle-level and population-level stagnation information is jointly employed to coordinate exploration and exploitation. Experimental studies on three benchmark datasets demonstrate that SPSOM-CVRP achieves competitive solution quality with relatively low computational cost. In addition, the proposed method obtains several promising route configurations, including solutions with shorter travel distances than previously reported results under modified route numbers. It should be noted that the proposed algorithmic configuration is empirically motivated; its effectiveness is demonstrated on the selected CVRP benchmark suites and the specific route-number settings under test, rather than being claimed as a universally optimal solution for all possible CVRP instances or all combinatorial optimization problems.
The transition toward renewable energy in agricultural pumping requires robust decision-making tools capable of addressing multiple, often conflicting criteria. This study investigates the respective contributions of fuzzy weighting and fuzzy ranking within AHP–TOPSIS frameworks for photovoltaic (PV) self-consumption planning in agricultural pumping applications. Unlike conventional MCDM applications that focus on identifying a preferred alternative using a single classical or fuzzy formulation, this study systematically isolates the effects of fuzziness at the weighting and ranking stages. Four methodological configurations are comparatively analyzed: classical AHP–TOPSIS, fuzzy AHP–TOPSIS with fuzzy weighting, AHP–TOPSIS with fuzzy ranking, and a fully fuzzy AHP–TOPSIS approach incorporating both fuzzy weighting and fuzzy ranking. Triangular fuzzy numbers are employed to represent the vagueness and subjectivity inherent in expert judgments, which are commonly expressed using quantitative scales despite their imprecise nature. A real-world case study involving the planning of a self-consumption PV installation for an agricultural pumping system in southeastern Spain is used to assess and compare the four approaches. The results distinguish the effects of fuzzy weighting and fuzzy ranking on both criteria weights and alternative rankings, showing whether the differences between classical and fuzzy formulations arise primarily from the weighting stage, the ranking stage, or their combined application. Rather than assuming that fuzzy formulations provide universally superior results, the analysis identifies the specific circumstances and stages in which fuzzy modelling produces meaningful changes in the decision outcome. The findings contribute to sustainable energy planning by providing a systematic framework for PV self-consumption planning in agricultural pumping under uncertain and subjective decision environments.
Stabilized proposal pricing may reduce exact subproblem work, but it cannot by itself certify branch-and-price node termination. A conditional, tolerance-adjusted node-pricing bound is developed for deterministic unit commitment. At the unstabilized restricted-master dual, CSDW-S applies a Phase-II cascade comprising a period-separable operational-envelope bound (Tier E), a chronology-preserving ramp-relaxed dynamic-programming bound (Tier D), and exact mixed-integer-programming pricing fallback. Relaxed optimizers are proof objects rather than master columns; CSDW-X prices every Phase-II unit exactly. The mechanism was evaluated in a prespecified 79-task study with a 600 s scientific deadline per task. In the primary 24-pair, 24 h horizon set, accepted root endpoints were returned by CSDW-S and CSDW-X in 15 and 24 conditions, respectively. Across the 15 jointly accepted pairs, the maximum absolute bound difference was 2.24×10−8. Exact true-dual unit solves were reduced by CSDW-S in all 15 pairs (median paired difference, −29,228), although CSDW-S was slower in 14 pairs (median paired difference, +20.7 s). The previously submitted 10-cell assessment did not conform to the primary acceptance criteria. It is therefore retained separately as historical evidence, with completion flags of 0/10 for CSDW-S and 9/10 for CSDW-X, and is not pooled with the new study. Mechanism, tolerance, horizon stress, and two small full tree contrasts support a qualified interpretation. Exact pricing workload can be reduced by the selective cascade when an endpoint is completed.
High penetration of distributed energy resources (DERs) creates opportunities for planned island formation and operation in distribution networks, which can help mitigate voltage fluctuations, reduce reverse power flow, and improve renewable energy utilization. This paper proposes a rapid planned island formation method based on a graph attention network (GAT) and a multi-layer perceptron (MLP). First, considering the technical operation requirements of distribution networks, the factors affecting island formation, including topological connectivity, power balance, and DERs, are analyzed. Based on graph theory, the topology connections and node information of the distribution network are represented by an adjacency matrix, a node feature matrix, and an edge physical feature matrix, respectively, to construct the distribution network graph model. Second, the GAT is employed to learn the correlations among distribution network nodes and obtain a node feature matrix incorporating relational information. The obtained representations are fed into the MLP to learn the mapping between node representations and branch connectivity states, and an island partitioning scheme is generated based on the output probabilities. Finally, considering the power balance constraints of the distribution network, the boundary nodes of the islands are adjusted to obtain the final feasible island partitioning scheme. Simulation results on a modified IEEE 33-bus distribution system show that the proposed method achieves an F1 of 92.37%. Furthermore, the model maintains an average F1 of 91.32% in generalization tests, demonstrating its effectiveness and robustness for rapid planned island formation in distribution networks with high penetration of DERs.
This study introduces a novel clustering approach, namely Teacher–Student-based Deep Clustering (TSDC), that relies on intra- and inter-distillation-based feature representations. In fact, TSDC distils knowledge from (i) high- to low-response channels, forcing the latter to mimic the former, and (ii) deeper to shallower layers, prompting the transfer of semantic information to enhance representational consistency. Unlike CNN-based deep clustering that relies on pseudo-labels to improve representations, TSDC introduces a newly formulated objective function to simultaneously minimize losses from clustering and intra- and inter-distillation. The proposed approach was rigorously investigated using benchmark datasets and relevant performance measures. In particular, a linear top classifier protocol was adopted to assess TSDC performance. Notably, TSDC outperformed existing deep clustering frameworks, yielding improved classification accuracy. The empirical findings highlight the efficacy of combining intra- and inter-distillation to enrich feature representations. Notably, the most prominent improvement was observed on CIFAR-100, where classification accuracy rose from 54.77 ± 0.07 to 57.58 ± 1.85.
This paper develops a coupled behavioral–epidemiological framework for infectious-disease dynamics by integrating an SIQRS compartmental model with an evolutionary game-theoretic representation of quarantine behavior. Unlike conventional epidemic models with exogenously specified behavioral rates, the proposed framework allows transmission and quarantine uptake to respond endogenously to payoff differences between behavioral strategies. This creates a feedback mechanism in which epidemic conditions influence individual incentives, while behavioral adaptation subsequently modifies disease transmission. The mathematical analysis establishes well-posedness and positive invariance of the coupled system, characterizes the disease-free equilibrium and the associated reproduction threshold, and investigates local stability. Sufficient small-gain conditions are also derived to characterize stability of the coupled behavioral–epidemiological dynamics. A discrete-time formulation based on the forward-Euler method is developed together with positivity and consistency conditions. Numerical experiments compare easy, moderate, and strict behavioral-response regimes under a common epidemiological and payoff parameterization. The results show that stronger behavioral responsiveness reduces the principal infectious peak and delays its occurrence. However, behavioral mitigation does not necessarily imply disease eradication, as waning immunity can replenish the susceptible population and generate recurrent epidemic activity over longer horizons. The discrete-time simulations closely reproduce the continuous-time trajectories for a sufficiently small time step, supporting the consistency of the numerical formulation. Overall, the proposed framework provides a mathematically tractable approach for studying the coevolution of strategic behavior and epidemic transmission and for evaluating how behavioral incentives can modify the magnitude, timing, and recurrence of epidemic outbreaks.
Infrared and visible image fusion combines the thermal cues captured by infrared sensors with the rich structural and texture information provided by visible images. This technique is particularly valuable for security surveillance, nighttime scene perception, and target recognition under challenging environmental conditions. Existing methods generally adopt fixed fusion strategies and neglect dynamic dual-modality changes under low illumination, overexposure and strong light interference, failing to preserve both thermal target saliency and visible structural details in fused images. To address this problem, this paper proposes a Lighting-Aware Spatial–Frequency Fusion Network (LASFNet) for security surveillance. It first estimates modality reliability across low-light, overexposed and infrared-salient regions, incorporating it into the fusion of frequency-domain amplitude and phase. Spatial infrared, visible and frequency-domain compensation features are then jointly fused to generate the output. Experiments on M3FD, MSRS and RoadScene datasets show that LASFNet achieves competitive fusion performance with strong cross-dataset generalization. On M3FD, YOLOv8s with LASFNet-fused inputs achieves 84.825% mAP@0.5 and 57.319% mAP@0.5:0.95, outperforming visible, infrared and YDTR-fused inputs. The proposed method balances target saliency and scene structure, providing more effective visual input for object detection under complex illumination.
We construct and analyze optimal quadrature formulas for the right-sided Riemann–Liouville fractional integral in the Sobolev space L2(m)(t,1), using φ,φ′,…,φ(m−1) at N+1 equally spaced nodes. The analysis is carried out through the Peano kernel of the error functional, for which we give an exact closed form; this yields the norm of the error functional, existence and uniqueness of the optimal coefficients by an orthogonal-projection argument, and computable error bounds. Our main result is structural: the functions attached to the coefficients form a basis of the space of discontinuous piecewise polynomials of degree m−1 on the mesh, so that the optimality problem is an L2 projection that decouples panel by panel. Consequently, the globally optimal (Sard) coefficients—not only the sequentially optimal ones—are available in closed form for every m, at a cost of O(m3N) operations with no global linear system and with a condition number independent of N, h, α and t. The globally optimal rule is exact on polynomials of degree 2m−1 and converges as O(h2m) for smooth integrands, whereas the sequential rule is exact on degree m; we quantify the gap between them. We also prove sharp asymptotics for the error norm, ∥R∥2∼κm(1−t)2α−1(2α−1)−1h2m for α>12 with κm=(−1)m−1B2m/(2m)!, with a ln(1/h) factor exactly at α=12 and a loss of half an order for α<12. An extensive numerical study over five fractional orders, three evaluation points and eight integrands of prescribed Sobolev regularity confirms every theoretical statement, and the formulas are compared with product, spline and Gauss–Jacobi quadratures and applied to an Abel integral equation.
Decision tables are widely used for representing and executing decision logic in business rules systems, regulatory compliance, and automated workflows. However, real-world decision tables often contain incomplete condition values. Existing rough set approaches typically treat missing values uniformly and cannot distinguish between occurrences of the same unknown value and occurrences of different unknown values. This paper introduces Labeled Null Decision Tables (LN-DTs), a framework that extends decision table semantics with labeled nulls from incomplete database theory. Missing values are represented by labeled nulls, where identical labels denote the same unknown value and distinct labels may denote different values. We define a possible-world semantics in which each possible world corresponds to a complete valuation of nulls. Based on this semantics, we define certain, possible, and conditional decisions. We develop symbolic algorithms that avoid explicit enumeration of possible worlds, analyze their computational complexity, and establish precise relationships with rough set approximations. We show that LN-DT possible decisions are always contained in the rough upper approximation, that the rough lower approximation is sound for LN-DT certain decisions under completeness and well-formedness, and that labeled null identities and constraints can yield strict precision gains by eliminating tolerant rules that cannot match in any admissible possible world. To provide evidence beyond small illustrative examples, we also include a medium-scale synthetic benchmark suite containing 105 instances with up to 500 rules and 32 labeled nulls. The benchmarks vary the number of rules, the number of labeled nulls, and the constraint type, and report runtime, precision, and verification metrics. Across all benchmark instances, the symbolic evaluator produces known results with no solver timeouts, the LN-DT possible decision set is contained in the rough upper approximation in 100% of cases, and the hybrid evaluator agrees with exact symbolic evaluation in 100% of cases. The average rough upper decision set size is 1.905, while the average LN-DT possible decision set size is 1.019, corresponding to an average upper-bound reduction of approximately 46.5%. These results provide medium-scale evidence that LN-DT is practically feasible and that labeled-null constraints can yield measurable precision gains over tolerance-based rough set approximation.
This paper presents an optimized control strategy that enables a grid-connected photovoltaic (PV) system to operate as a static synchronous compensator (PV-STATCOM) to damp power oscillations in the transmission system, using an arithmetic optimization algorithm (AOA). The key contribution of this work is a synchronized, AOA-optimized multi-mode switching approach that includes standard PV operation, Full STATCOM, and Partial STATCOM with ramp-rate recovery, rather than relying solely on PI-gain adjustment. This is accomplished across the complete pre-fault, fault, and post-fault cycle. Under the proposed strategy, the PV system temporarily curtails its real power output when power oscillations arise following a system disturbance, thereby releasing the full inverter capacity for STATCOM operation and, hence, for oscillation damping. Once the oscillations are damped, the PV system ramps its real power back to the pre-disturbance level; at night, the inverter’s full capacity remains available for damping oscillations. The control scheme is implemented with a set of proportional–integral (PI) controllers whose parameters are tuned with the AOA, and its performance is benchmarked against tuning with the cuckoo search (CS) algorithm. Simulation results demonstrate that the AOA-tuned PV-STATCOM significantly improves damping, reduces oscillation amplitudes, maintains the point-of-common-coupling voltage within the low-voltage ride-through envelope, and keeps the system frequency within grid-code limits, thereby ensuring stable grid operation. Compared to a CS-tuned benchmark, the AOA-tuned design keeps the frequency continuously within the grid code band, settles at nominal 50 Hz, and reduces the maximum voltage overshoot from 20% to 15%.
