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14 pages, 6712 KB  
Article
An Adaptive Sticky Hidden Markov Model for Robust State Inference in Non-Stationary Physiological Time Series
by Qizheng Wang, Yuping Wang, Shuai Zhao, Yuhan Wu and Shengjie Li
Mathematics 2026, 14(7), 1107; https://doi.org/10.3390/math14071107 - 25 Mar 2026
Abstract
The accurate inference of hidden states from non-stationary physiological signals remains a significant challenge in stochastic process modeling. This paper proposes an Adaptive Sticky Hidden Markov Model (Sticky-HMM) framework designed to enhance the robustness of state decoding in noisy environments. To address the [...] Read more.
The accurate inference of hidden states from non-stationary physiological signals remains a significant challenge in stochastic process modeling. This paper proposes an Adaptive Sticky Hidden Markov Model (Sticky-HMM) framework designed to enhance the robustness of state decoding in noisy environments. To address the “state-flickering” issue inherent in traditional HMMs, we incorporate a “Sticky” parameter into the transition matrix, imposing a temporal penalty on spurious state switching to maintain continuity. Furthermore, we introduce a Dynamic Prior Strategy that adaptively calibrates self-transition probabilities by mapping frequency-domain features of the observed sequence to the model’s parameter space. The proposed decoding process employs a two-pass refinement strategy and the Viterbi algorithm in the logarithmic domain to ensure numerical stability. The model’s efficacy was validated using a high-fidelity dataset of simulated apnea events. This work provides a computationally efficient and mathematically rigorous approach that demonstrates strong potential for long-term respiratory health monitoring. Full article
(This article belongs to the Special Issue Machine Learning and Graph Neural Networks)
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22 pages, 7073 KB  
Article
Forecasting a Hailstorm in Western China Plateau by Assimilating XPAR Radar Network Data with WRF-FDDA-HLHN
by Jingyuan Peng, Bosen Jiang, Qiuji Ding, Lei Cao, Zhigang Chu, Yueqin Shi and Yubao Liu
Remote Sens. 2026, 18(7), 968; https://doi.org/10.3390/rs18070968 - 24 Mar 2026
Abstract
Hailstorms frequently develop in Yun-Gui Plateau, Western China, which bring about significant economic damage. Due to the high terrain, these storms are typically shallow, rapidly evolving, and challenging to forecast. An X-band phased-array radar (XPAR) network is set up at Weining in Yun-Gui [...] Read more.
Hailstorms frequently develop in Yun-Gui Plateau, Western China, which bring about significant economic damage. Due to the high terrain, these storms are typically shallow, rapidly evolving, and challenging to forecast. An X-band phased-array radar (XPAR) network is set up at Weining in Yun-Gui Plateau to study these storms. To explore these XPAR data for numerical prediction of hailstorms in this region, we implement the Weather Research and Forecast (WRF) model and Hydrometeor and Latent Heat Nudging (HLHN) method to assimilate the data and conduct prediction experiments. The XPAR data was evaluated along with the operational Severe Weather Automatic Nowcast (SWAN) system radar mosaic data. Furthermore, a humidity adjustment scheme is used to overcome inconsistency of the humidity field and related prediction errors. The model results show that in comparison to the SWAN data, assimilating XPAR data in 1-min intervals significantly reduces the model error, and improves the representation of rapid hail cloud evolution. Additionally, adjusting the model humidity based on vertically integrated liquid (VIL) derived from the radar data can effectively correct model analyses of humidity and temperatures, suppressing spurious convection, thus improving the hailstorm forecast. Overall, we recommend joint assimilation of the high spatiotemporal resolution XPAR data along with SWAN radar data with the improved WRF-HLHN for hailstorm prediction over the study region, and the algorithm can be promptly adapted to forecasting hailstorms in other regions. Full article
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13 pages, 1643 KB  
Article
Characterization and Comparative Analyses of Nuclear Mitochondrial DNAs in Genomes of the Leaf-Roller Moths (Lepidoptera: Tortricidae)
by Weifeng Peng, Jiayi Yu, Zhengbing Wang, Zhen Li, Xin Miao, Jin Liu, Jiahui Zhang, Liuyong Xie, Weili Ding, Keshi Ma and Mingsheng Yang
Biology 2026, 15(6), 517; https://doi.org/10.3390/biology15060517 - 23 Mar 2026
Viewed by 53
Abstract
During eukaryotes evolution, mitochondrial DNA (mtDNA) fragments integrate into nuclear genomes, forming nuclear mitochondrial DNA sequences (Numts). Tortricidae (Lepidoptera), a species-rich and economically critical family, lacks systematic characterization of Numts, which hinders reliable molecular research. Here, we systematically characterized Numts in 27 Tortricidae [...] Read more.
During eukaryotes evolution, mitochondrial DNA (mtDNA) fragments integrate into nuclear genomes, forming nuclear mitochondrial DNA sequences (Numts). Tortricidae (Lepidoptera), a species-rich and economically critical family, lacks systematic characterization of Numts, which hinders reliable molecular research. Here, we systematically characterized Numts in 27 Tortricidae species spanning two subfamilies via genome download, mitochondrial genome annotation, and Numt identification and characterization. With each species’ mtDNA as query, Numt identification was performed with an E-value threshold of 10−4 and a sequence similarity cut-off of >60%, with a minimum length of 50 bp to exclude spurious hits. Results showed that all species contained Numts, with copy numbers varying drastically (9–208). Numt numbers positively correlated with nuclear genome length, but not mitochondrial genome length. Numts insertion flanking regions had significantly higher AT content than nuclear genome, indicating the insertion preference for AT-rich regions. Numts were predominantly derived from the mitochondrial cox1 gene, highlighting the risk of co-amplification when cox1 is used as a DNA barcode for species identification or phylogenetic studies. This study represents a systematic charaterizition of copy number, length distribution, insertion sequence preferences, and mitochondrial gene origins of Numts in Tortricidae, offering valuable references for refining molecular systematics, comparative genomics, and pest management in Tortricidae and related lepidopteran groups. Full article
(This article belongs to the Section Genetics and Genomics)
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49 pages, 8802 KB  
Article
An Efficient Solver for Fractional Diffusion on Unbounded Combs with Exact Absorbing Boundary Conditions
by Jingyi Mo, Guitian He, Yan Tian and Hui Cheng
Fractal Fract. 2026, 10(3), 208; https://doi.org/10.3390/fractalfract10030208 - 23 Mar 2026
Viewed by 46
Abstract
Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly due to the nonlocal memory effect and slow spatial decay [...] Read more.
Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly due to the nonlocal memory effect and slow spatial decay of solutions. To the best of our knowledge, we address this long-standing gap by presenting a fully integrated framework that simultaneously resolves both challenges. We derive the governing equation from constitutive relations and establish exact absorbing boundary conditions (ABCs) for the multi-skeleton comb model, a result absent in prior work. A transparent Dirichlet-to-Neumann (DtN) map, constructed via Laplace analysis, rigorously handles skeletal Dirac delta singularities and eliminates spurious reflections without empirical parameters. Furthermore, we propose a novel structure-preserving finite difference scheme that applies the sum-of-exponentials (SOE) approximation not only to the interior Caputo derivative but also to the convolution kernels arising from the ABCs. This yields a dramatic reduction in computational complexity, from quadratic O(Nt2) to quasi-linear O(NtlogNt), while preserving the physics of anomalous transport. We prove the well-posedness, unconditional stability, and convergence of the method. Numerical results confirm theoretical error estimates and show excellent agreement between simulated particle distributions, mean square displacement profiles, and exact asymptotics, validating both accuracy and robustness. The speedup (CPU time ratio Direct/Fast) is about 1.00×1.23× for Nt=5000 in our tests. Our approach sets a new benchmark for simulating anomalous dynamics in fractal-inspired media. Full article
(This article belongs to the Section Numerical and Computational Methods)
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43 pages, 10109 KB  
Article
Stabilizer Variables for Measurement Invariance–Induced Heterogeneity: Identification Theory and Testing in Multi-Group Models
by Salim Yilmaz and Erhan Cene
Mathematics 2026, 14(6), 1064; https://doi.org/10.3390/math14061064 (registering DOI) - 21 Mar 2026
Viewed by 71
Abstract
When measurement invariance (MI) is violated in multi-group structural equation models, group-specific measurement artifacts inflate the between-group variance of structural parameters beyond their true values. Existing remedies—partial invariance, group-specific estimation, or moderation analysis—address the consequences of inflation but not its mechanism. This article [...] Read more.
When measurement invariance (MI) is violated in multi-group structural equation models, group-specific measurement artifacts inflate the between-group variance of structural parameters beyond their true values. Existing remedies—partial invariance, group-specific estimation, or moderation analysis—address the consequences of inflation but not its mechanism. This article introduces the stabilizer variable, a covariate that absorbs measurement-induced parameter heterogeneity while maintaining structural independence from the focal relationship. Two theoretical results are established: a variance decomposition theorem showing that MI violations inflate dispersion through an identifiable artifactual component, and a purification theorem proving that a stabilizer reduces this dispersion via Frisch–Waugh–Lovell projection. Two stabilization mechanisms are identified: variance purification (Type A) and directional alignment (Type B). We then develop the stabilizer variable test, a dual-criterion procedure combining nonparametric bootstrap testing for stabilization magnitude with binomial testing for directional consistency, incorporating adaptive MI severity scoring with calibrated fit-index weights. Simulations comprising 949,100 replications across varying group counts, sample sizes, and MI severity levels demonstrate 80–99% power with false-positive rates below 2%. Practical guidelines recommend K10 groups and n100 per group for conservative applications. The framework generalizes to any multi-group regression context where systematic measurement error induces spurious parameter heterogeneity. Full article
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15 pages, 3888 KB  
Article
Ultra-Miniaturized, High-Q Embedded Loaded Coaxial Substrate Integrated Waveguide Filter
by Nawaf R. Almuqati, Gokhan Ariturk and Hjalti H. Sigmarsson
Electronics 2026, 15(6), 1310; https://doi.org/10.3390/electronics15061310 - 20 Mar 2026
Viewed by 155
Abstract
This paper presents an ultra-miniaturized and high-quality factor embedded loaded coaxial substrate integrated waveguide (ELCSIW) filter. Integrating a substrate-integrated coaxial resonator with a capacitively loaded air cavity achieves a 99% reduction in size compared to a conventional SIW cavity. Incorporating an air gap [...] Read more.
This paper presents an ultra-miniaturized and high-quality factor embedded loaded coaxial substrate integrated waveguide (ELCSIW) filter. Integrating a substrate-integrated coaxial resonator with a capacitively loaded air cavity achieves a 99% reduction in size compared to a conventional SIW cavity. Incorporating an air gap in the capacitive loading structure significantly enhances the resonator’s quality factor. A comprehensive analysis of the miniaturization factor and quality factor in relation to cavity structure dimensions is performed. Guidelines for fabricating the highly loaded cavity are presented. To demonstrate the benefits of this technique, a two-pole band-pass filter with a 6.3% bandwidth at 1.1 GHz is designed, fabricated, and measured. The overall footprint of the filter is 10.5 mm × 20.5 mm, which is comparable to 0.07 λg× 0.14 λg. The measured insertion loss is 0.54 dB, and the upper band is spurious-free up to 7 times the resonant frequency. The exceptional performance and compactness of the loaded coaxial substrate integrated waveguide cavities highlight their immense potential for compact advanced wireless systems. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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23 pages, 4705 KB  
Article
CSFPR-RTDETR-CR: A Causal Intervention Enhanced Framework for Infrared UAV Small Target Detection with Feature Debiasing
by Honglong Wang and Lihui Sun
Sensors 2026, 26(6), 1941; https://doi.org/10.3390/s26061941 - 19 Mar 2026
Viewed by 145
Abstract
Infrared UAV small target detection is critical in areas such as military reconnaissance, disaster monitoring, and border patrol. However, it faces challenges due to the small size of targets, weak texture, and complex backgrounds in infrared images. Existing deep learning-based object detection models [...] Read more.
Infrared UAV small target detection is critical in areas such as military reconnaissance, disaster monitoring, and border patrol. However, it faces challenges due to the small size of targets, weak texture, and complex backgrounds in infrared images. Existing deep learning-based object detection models often learn spurious correlations between targets and their backgrounds. This leads to poor generalization and higher rates of false positives and missed detections in complex scenes. To overcome feature bias and improve performance, this paper proposes an enhanced detection framework based on causal reasoning. The framework builds on the advanced CSFPR-RTDETR detector. Guided by the principles of structural causal models, it explicitly separates causal and non-causal features in the feature space. Feature debiasing is achieved through a three-path approach. First, a causal data augmentation module is introduced. It applies frequency perturbations drawn from a Gaussian distribution to non-causal features. This strengthens the model’s robustness against mixed disturbances. Second, a counterfactual reasoning module is integrated into the backbone network. This module generates counterfactual samples to intervene in the feature distribution, helping the model identify and utilize causal features more effectively. Third, a causal attention mechanism module is added to the encoder. By distinguishing and weighting causal and non-causal features, it guides the model to focus on features that are essential for detecting targets. Experiments on the HIT-UAV public dataset show that the proposed framework improves mAP@50 by 5.6% and mAP@50:95 by 1.8%. Visualization analysis further confirms that the framework enhances feature discrimination and overall detection performance. Full article
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26 pages, 4173 KB  
Article
Physics-Guided Variational Causal Intervention Network for Few-Shot Radar Jamming Recognition
by Dong Xia, Liming Lv, Youjian Zhang, Yanxi Lu, Fang Li, Lin Liu, Xiang Liu, Yajun Zeng and Zhan Ge
Sensors 2026, 26(6), 1900; https://doi.org/10.3390/s26061900 - 18 Mar 2026
Viewed by 105
Abstract
Rapid and accurate recognition of radar active jamming is a prerequisite for cognitive electronic countermeasures. However, under complex electromagnetic environments with scarce training samples, existing deep learning models are prone to capturing spurious correlations induced by environmental confounders, resulting in notable performance degradation. [...] Read more.
Rapid and accurate recognition of radar active jamming is a prerequisite for cognitive electronic countermeasures. However, under complex electromagnetic environments with scarce training samples, existing deep learning models are prone to capturing spurious correlations induced by environmental confounders, resulting in notable performance degradation. To address this causal confounding issue, we propose a physics-guided variational causal intervention network (PG-VCIN). First, we reconstruct a structured causal model of jamming signal generation, decoupling observations into robust physical statistical features and sensitive time–frequency image representations. Physical priors are then leveraged to perform dynamic precision-weighted modulation of visual feature extraction, enforcing physical consistency at the representation learning stage. Second, we formulate deconfounding within an active inference framework and introduce a variational information bottleneck to optimize mutual information, thereby filtering out high-complexity redundant information attributable to confounders while preserving the essential causal semantics. Finally, we numerically approximate the causal effect by imposing dual intervention constraints in the latent space, including intra-class invariance and confounder invariance. Experiments on a semi-physical simulation dataset demonstrate that the proposed method achieves substantially higher recognition accuracy than several representative few-shot baselines in extremely low-sample regimes, validating the effectiveness of integrating physical mechanisms with causal inference. Full article
(This article belongs to the Section Radar Sensors)
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25 pages, 8047 KB  
Article
On the Numerical Reliability of Lyapunov-Based Chaos Analysis in Optically Injected Semiconductor Lasers: A Phasor-Quadrature Comparison
by Gerardo Antonio Castañón Ávila, Ana Maria Sarmiento-Moncada, Alejandro Aragón-Zavala and Ivan Aldaya Garde
Appl. Sci. 2026, 16(6), 2835; https://doi.org/10.3390/app16062835 - 16 Mar 2026
Viewed by 183
Abstract
Lyapunov-exponent-based diagnostics are widely used to quantify deterministic chaos in optically injected semiconductor lasers (OISLs). In most numerical implementations, the optical field is represented either in phasor coordinates (A,ψ,N) or in Cartesian quadrature coordinates [...] Read more.
Lyapunov-exponent-based diagnostics are widely used to quantify deterministic chaos in optically injected semiconductor lasers (OISLs). In most numerical implementations, the optical field is represented either in phasor coordinates (A,ψ,N) or in Cartesian quadrature coordinates (X,Y,N). Although these representations are mathematically related through a smooth coordinate transformation away from vanishing field amplitude, their numerical realizations can exhibit markedly different robustness in variational calculations, directly impacting the reliability of Lyapunov exponent estimation and chaoticity maps. In this work, we present a systematic assessment of the numerical reliability of Lyapunov-based chaos analysis in master-slave optically injected semiconductor lasers using both phasor and quadrature formulations. The full Lyapunov spectrum was computed via a noise-free variational method that integrates the nonlinear dynamics together with the corresponding Jacobian equations using a fourth-order Runge-Kutta scheme combined with periodic QR orthonormalization. High-resolution Lyapunov maps were constructed in the injection strength-frequency detuning parameter space, and the consistency between both formulations was quantitatively evaluated. While both approaches reproduce the overall structure of chaotic and non-chaotic regions, the phasor formulation may generate spurious positive Lyapunov exponents in regimes where the optical field amplitude approaches low values. These discrepancies originate from singular terms proportional to 1/A and 1/A2 in the variational Jacobian of the phasor model, which can lead to numerical amplification and artificial chaotic signatures. The quadrature formulation avoids these singularities and provides numerically stable and physically consistent Lyapunov spectra across the explored parameter space. The results establish practical guidelines for robust chaos quantification in optically injected semiconductor lasers and highlight the importance of representation choice in variational Lyapunov analysis of nonlinear photonic systems. Full article
(This article belongs to the Special Issue Advances in Optical Communication and Photonic Integrated Devices)
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21 pages, 11196 KB  
Article
CR-MAT: Causal Representation Learning for Few-Shot Non-Intrusive Load Monitoring
by Xianglong Li, Shengxin Kong, Jiani Zeng, Hanqi Dai, Lu Zhang, Weixian Wang, Zihan Zhang and Liwen Xu
Electronics 2026, 15(6), 1195; https://doi.org/10.3390/electronics15061195 - 13 Mar 2026
Viewed by 222
Abstract
Non-intrusive load monitoring (NILM) is a key enabler for smart-grid applications, yet practical deployment is often hindered by limited appliance-level labels and severe distribution shifts across households and operating conditions. As a result, many deep learning approaches become unreliable in small-sample and out-of-distribution [...] Read more.
Non-intrusive load monitoring (NILM) is a key enabler for smart-grid applications, yet practical deployment is often hindered by limited appliance-level labels and severe distribution shifts across households and operating conditions. As a result, many deep learning approaches become unreliable in small-sample and out-of-distribution (OOD) settings. In this paper, we propose CR-MAT, a causality-driven representation learning framework for few-shot NILM classification. Instead of relying on large-scale training or heavy data augmentation, CR-MAT injects causal representation learning into multi-appliance task modeling, encouraging the network to learn appliance-discriminative features that are stable across environments while suppressing spurious, domain-specific correlations. We conduct extensive experiments under multiple OOD scenarios and consistently observe improved classification robustness compared with deep NILM baselines. Further analysis indicates that causal representation learning enhances resilience to non-stationary consumption patterns and improves generalization under OOD scenarios. The proposed framework provides a practical route toward reliable NILM classification and supports downstream smart-grid applications such as flexible load control and demand response. Full article
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26 pages, 4782 KB  
Article
CausalTransPV: Causal Invariant Representation Learning for Cross-Site Photovoltaic Power Forecasting via Selective Domain Alignment
by Yantong Ge and Xunsheng Ji
Energies 2026, 19(6), 1410; https://doi.org/10.3390/en19061410 - 11 Mar 2026
Viewed by 233
Abstract
Cross-site transfer learning is a promising approach to address data scarcity at newly deployed photovoltaic (PV) stations by leveraging knowledge from data-rich source sites. However, existing domain adaptation methods align feature representations without distinguishing physically meaningful causal relationships from site-specific spurious correlations, leading [...] Read more.
Cross-site transfer learning is a promising approach to address data scarcity at newly deployed photovoltaic (PV) stations by leveraging knowledge from data-rich source sites. However, existing domain adaptation methods align feature representations without distinguishing physically meaningful causal relationships from site-specific spurious correlations, leading to negative transfer when local environmental conditions differ substantially between stations. This paper proposes CausalTransPV, a causal invariant representation learning framework that integrates explicit temporal causal discovery with selective domain alignment for cross-site PV power forecasting. The framework comprises three synergistic modules: (i) a multi-station temporal causal discovery module that jointly learns shared and station-specific causal graphs through differentiable acyclicity-constrained optimization with a cross-station invariance regularizer; (ii) a causal-guided disentangled encoder that decomposes representations into causal-invariant and site-specific subspaces using the discovered causal graph as a structural prior; and (iii) a causal-subspace transfer and prediction module that performs maximum mean discrepancy (MMD)-based domain alignment exclusively on the causal subspace. Experiments on the Desert Knowledge Australia Solar Centre (DKASC) multi-station dataset under varying target label ratios (0–50%) demonstrate that CausalTransPV achieves relative mean absolute error (MAE) reductions of 6.9–9.9% over the strongest baseline. Ablation studies, causal graph analysis, feature space visualization, and weather-conditioned case studies further validate the contribution of each component. These results suggest that causal-guided selective transfer offers an effective paradigm for reliable PV forecasting under data-scarce cross-site scenarios. Full article
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20 pages, 9183 KB  
Article
Simulation of Nitrogen Migration and Output Loads Under Field Scale in Small Watershed, China
by Yixiao Song, Ling Jiang and Ming Liang
Land 2026, 15(3), 442; https://doi.org/10.3390/land15030442 - 10 Mar 2026
Viewed by 255
Abstract
Field-scale nitrogen migration mechanisms in small watersheds remain poorly quantified due to insufficient representation of microtopographic heterogeneity. This study investigates nitrogen transport dynamics in a 1.27 km2 agricultural watershed in China’s Jianghuai region using unmanned aerial vehicle (UAV) -derived 0.1 m digital [...] Read more.
Field-scale nitrogen migration mechanisms in small watersheds remain poorly quantified due to insufficient representation of microtopographic heterogeneity. This study investigates nitrogen transport dynamics in a 1.27 km2 agricultural watershed in China’s Jianghuai region using unmanned aerial vehicle (UAV) -derived 0.1 m digital elevation models (DEMs) and coupled hydrological–erosion modeling. The Soil Conservation Service Curve Number (SCS-CN) and Modified Universal Soil Loss Equation (MUSLE) models quantified nitrogen output loads, while the multi-flow direction algorithm simulated migration trajectories for total nitrogen (TN), ammonium, and nitrate. Results revealed strong spatial heterogeneity in nitrogen exports (watershed mean: 29.66 kg TN/km2·a), with bare land and greenhouses exhibiting the highest outputs (448.54 and 363.41 kg/km2·a) and forested areas showing minimal export (<6.1 kg/km2·a). Nitrogen migration was predominantly controlled by topographic gradients, with microtopographic features—field ridges, ditches, and buildings—physically redirecting flows and creating critical export nodes at field boundaries. DEM resolution critically affected simulation accuracy: erosion intensity displayed a non-monotonic response with an inflection point near 1 m resolution, corresponding to the median elevation difference (1.2 m) of field ridges. Structural equation modeling confirmed that high-resolution DEMs (0.1–2 m) maintained topographic control over nitrogen migration (~80% contribution), whereas 30 m DEMs reduced this influence to 30%, inducing spurious meteorological dominance. This study demonstrates that decimeter-scale DEMs are essential for accurately capturing microtopographic regulation of nitrogen transport, providing a methodological basis for precision management of agricultural non-point source pollution. Full article
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21 pages, 554 KB  
Article
Spurious or Genuine? Evaluating Large Language Models in Validating Counterexamples for Loop Invariant Inference
by Guangsheng Fan, Dengping Wei and Banghu Yin
Electronics 2026, 15(6), 1148; https://doi.org/10.3390/electronics15061148 - 10 Mar 2026
Viewed by 233
Abstract
Whether a counterexample is genuine or spurious fundamentally influences the effectiveness and completeness of loop invariant inference, which is a core component of automated program verification. However, reliably determining the validity of a counterexample remains a challenging task. In this paper, we present [...] Read more.
Whether a counterexample is genuine or spurious fundamentally influences the effectiveness and completeness of loop invariant inference, which is a core component of automated program verification. However, reliably determining the validity of a counterexample remains a challenging task. In this paper, we present a systematic evaluation of large language models (LLMs) on this problem. We construct a benchmark of program states that serve as counterexamples, categorized into three representative types: (i) pre-states of inductive counterexamples derived from LLM-proposed invariants and (ii–iii) boundary states derived from correct inductive invariants, where the states themselves either violate (ii) or satisfy (iii) the program’s precondition. Ground-truth labels are established using a state-of-the-art program verifier. We evaluate multiple LLMs under diverse prompting strategies. Our results show that LLMs perform well on the first two types of counterexamples in the benchmark but poorly on the third. Moreover, LLMs are substantially more accurate in classifying spurious counterexamples than genuine ones. These findings offer valuable guidance for future research on LLM-assisted loop invariant inference. Full article
(This article belongs to the Section Computer Science & Engineering)
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16 pages, 19451 KB  
Article
A 200 MS/s 12-Bit Current-Steering DAC Using Split–Sort–Symmetric Grouping for Microdisplay Drivers
by Yichen Gao, Yingqi Feng, Yibo Su, Haoran Zeng and Zunkai Huang
Electronics 2026, 15(5), 1102; https://doi.org/10.3390/electronics15051102 - 6 Mar 2026
Viewed by 288
Abstract
High-resolution microdisplay driver applications impose stringent requirements on the static linearity and dynamic performance of digital-to-analog converters (DACs). To meet these requirements, this paper presents a 200 MS/s 12-bit current-steering DAC. To reduce mismatches among high-weight current sources, a split–sort–symmetric grouping calibration (SSSGC) [...] Read more.
High-resolution microdisplay driver applications impose stringent requirements on the static linearity and dynamic performance of digital-to-analog converters (DACs). To meet these requirements, this paper presents a 200 MS/s 12-bit current-steering DAC. To reduce mismatches among high-weight current sources, a split–sort–symmetric grouping calibration (SSSGC) scheme is introduced, in which each most-significant-bit (MSB) current source is split into sub-cells and reorganized through sorting and symmetric pairing. This approach improves static linearity without complex current measurement or compensation loops. Additionally, a group-domain dynamic element matching (DEM) technique is employed to randomize current-source selection and suppress harmonic distortion. Designed in a 0.18 μm BCD process, the proposed DAC achieves an integral nonlinearity (INL) of 0.79 LSB, a differential nonlinearity (DNL) of 0.42 LSB, and a spurious-free dynamic range (SFDR) of 74.9 dB at an output signal of 4.05 MHz. Full article
(This article belongs to the Special Issue Advances and Applications in Blockchain Technology)
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21 pages, 3308 KB  
Article
NILM-Based Feedback for Demand Response: A Reproducible Binary State-Detection Algorithm Using Active Power
by Yuriy Zhukovskiy, Pavel Suslikov and Daniil Rasputin
Electricity 2026, 7(1), 23; https://doi.org/10.3390/electricity7010023 - 5 Mar 2026
Viewed by 324
Abstract
Non-intrusive load monitoring (NILM) can provide actionable feedback for demand response (DR) when direct measurements of device states are unavailable. We propose a reproducible, engineering-oriented pipeline for detecting ON/OFF states of end-use load groups from an aggregated active power time series. The method [...] Read more.
Non-intrusive load monitoring (NILM) can provide actionable feedback for demand response (DR) when direct measurements of device states are unavailable. We propose a reproducible, engineering-oriented pipeline for detecting ON/OFF states of end-use load groups from an aggregated active power time series. The method uses robust hysteresis-based labeling with adaptive thresholds derived from the median and median absolute deviation, followed by compact feature engineering restricted to global active power (GAP). After removing collinear features (|r| > 0.98), permutation importance is used to retain informative predictors. Probabilistic binary classifiers (LGBM, Histogram-based Gradient Boosting, XGBoost, and CatBoost) are trained for each target load, and the decision threshold is optimized via Fβ to balance missed events and false alarms. A post-processing stage stabilizes predictions by smoothing probabilities and suppressing spurious triggers. Model quality is assessed with both sample-wise metrics and event-based metrics that credit the correct detection of switching intervals within a time tolerance. Experiments on the open “Individual Household Electric Power Consumption” dataset (1-min resolution, 2007–2010) demonstrate that lightweight gradient boosting models, particularly LGBM, deliver reliable and interpretable state estimates suitable for practical DR integration and edge deployment. Full article
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