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25 pages, 13524 KB  
Article
Remote Sensing Image Dehazing via RGB-Space Physical Constraints
by Minxian Shen, Xucong Jiang, Chenyang Shao, Houzheng Zhang and Mingye Ju
Sensors 2026, 26(13), 4026; https://doi.org/10.3390/s26134026 (registering DOI) - 25 Jun 2026
Abstract
Haze commonly degrades visible-spectrum remote sensing (RS) images by reducing contrast and distorting colors. Existing RS dehazing methods still face two limitations. Prior-driven methods rely on handcrafted assumptions that may become unreliable in complex wide-area scenes without explicit sky regions. Learning-based methods require [...] Read more.
Haze commonly degrades visible-spectrum remote sensing (RS) images by reducing contrast and distorting colors. Existing RS dehazing methods still face two limitations. Prior-driven methods rely on handcrafted assumptions that may become unreliable in complex wide-area scenes without explicit sky regions. Learning-based methods require paired training data, yet real aligned hazy/haze-free RS image pairs are difficult to collect, which limits their real-world generalization. To address these limitations, we propose a method called Remote Sensing Image Dehazing via RGB-Space Physical Constraints (RDPC). The new method revisits the atmospheric scattering model (ASM) from the perspective of RS imaging and builds the restoration process on several physical properties of hazy image formation. For atmospheric light estimation, the RGB-space line-convergence behavior of local regions with similar reflectance and slight depth variations is exploited, allowing atmospheric light to be estimated without explicit sky areas. For transmission estimation, the geometric relation between observed pixels and atmospheric light is used in RGB space, where local perpendicularity provides physically plausible haze-removal guidance and global compensation helps avoid excessive darkening and color degradation. The estimated transmission and albedo guidance are further refined by enforcing ASM consistency and variation sparsity through joint optimization. Experiments on synthetic and real-world RS image dehazing benchmarks demonstrate that RDPC achieves competitive performance against representative prior-based and learning-based methods, including Image Dehazing and Exposure (IDE), Iterative Predictor-Critic (IPC), Curvature-to-Plane Prior (C2P), Adaptive Structure-Texture Awareness (ASTA), Asymmetric U-Net (AU-Net), Efficient Multi-scale Prior Fusion (EMPF), and Lightweight Feature Dehazing (LFD), in terms of peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), learned perceptual image patch similarity (LPIPS), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE), neural image assessment (NIMA), and processing time. Full article
(This article belongs to the Special Issue AI-Driven Video and Image Processing for Multi-Sensor Data Fusion)
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23 pages, 4539 KB  
Article
Improved Land Surface Phenology Detection in China’s Drylands and Associated Spatiotemporal Trends
by Yongjian Mai, Jie Peng, Jianming Deng, Dong Tang, Zifan Li and Yaning Kuang
Remote Sens. 2026, 18(13), 2073; https://doi.org/10.3390/rs18132073 (registering DOI) - 24 Jun 2026
Abstract
Vegetation phenology is a sensitive indicator of climate change in China’s drylands (aridity index, AI < 0.65). However, accurate phenological monitoring remains challenging due to low signal-to-noise ratios, persistent soil background interference, and the scarcity of ground phenological sites. Existing global phenology products [...] Read more.
Vegetation phenology is a sensitive indicator of climate change in China’s drylands (aridity index, AI < 0.65). However, accurate phenological monitoring remains challenging due to low signal-to-noise ratios, persistent soil background interference, and the scarcity of ground phenological sites. Existing global phenology products also perform poorly in hyper-arid and arid regions. This study developed an optimal phenology detection framework for China’s drylands by systematically evaluating various vegetation indices, noise-reduction techniques, fitting functions, and dynamic thresholds against ground observations, generating a dataset at 500-m resolution spanning 2001–2024. Specifically, we determined vegetation index thresholds to distinguish vegetated from non-vegetated pixels based on 453 field survey sites. Our results indicate that the Normalized Difference Phenology Index (NDPI) coupled with a 10% threshold and polynomial fitting provided the highest accuracy for Start of Season (SOS) (RMSE = 12.02 days). For End of Season (EOS), EVI2 combined with a 70% threshold and self-weighted double-logistic fitting yielded superior performance (RMSE = 19.89 days). Compared to the MODIS global phenology product (MCD12Q2), our dataset demonstrates significantly higher accuracy (higher R and lower RMSE) and broader spatial coverage, particularly in hyper-arid and arid regions. Spatiotemporal analysis reveals that SOS was earlier while EOS was later in more arid areas, potentially reflecting the opportunistic life strategies of ephemeral plants. Notably, a trend of delayed SOS was observed in these regions, which we potentially linked to the shifts in precipitation regimes under global change. This optimized framework and the resulting Chinese dryland phenology dataset provide a robust foundation for assessing ecosystem resilience and carbon cycle dynamics in water-limited environments. Full article
42 pages, 1584 KB  
Article
Hierarchical Indexing with Controlled Expansion for Efficient Semantic Search over Encrypted Cloud Data
by Yu Zhang, Rui Zhu and Yin Li
Entropy 2026, 28(7), 721; https://doi.org/10.3390/e28070721 (registering DOI) - 24 Jun 2026
Abstract
The proliferation of cloud-based data outsourcing has intensified the need for efficient semantic retrieval over encrypted data. Existing searchable encryption schemes often face a coupled bottleneck: (i) semantic index can be unstable or overly coarse, yielding loose pruning bounds and high query cost, [...] Read more.
The proliferation of cloud-based data outsourcing has intensified the need for efficient semantic retrieval over encrypted data. Existing searchable encryption schemes often face a coupled bottleneck: (i) semantic index can be unstable or overly coarse, yielding loose pruning bounds and high query cost, and (ii) semantic query expansion can easily introduce noise, forcing an unfavorable accuracy–efficiency trade-off. To address these issues, we propose SES-HI, a Semantically Enhanced Searchable Encryption scheme with a stability-oriented hierarchical index for efficient ranked semantic search over encrypted cloud data. SES-HI contains three core innovations. First, it constructs a balanced ω-ary hierarchical index using a two-stage clustering pipeline (Ward → k-means) to produce semantically compact groups and more representative node vectors, enabling tighter pruning bounds. Second, it performs topic-guided query expansion using LDA and applies Word2Vec-based similarity filtering to enrich semantic coverage while suppressing expansion noise. Third, it introduces a dual-pruning strategy that couples a global threshold with top-k competitive pruning to reduce traversal and ranking overhead without sacrificing recall. We formally prove that SES-HI is secure against adaptive chosen-keyword attacks under an explicit leakage profile. Extensive experiments on the TREC dataset demonstrate that SES-HI consistently improves the accuracy–latency trade-off compared with state-of-the-art baselines, supporting practical semantic search for privacy-sensitive cloud applications. Full article
36 pages, 9888 KB  
Article
Experimental Investigation of the Acoustic Performance of a Louvered Hemp Fiber Noise Barrier
by Edgaras Strazdas and Tomas Januševičius
Buildings 2026, 16(13), 2482; https://doi.org/10.3390/buildings16132482 (registering DOI) - 23 Jun 2026
Abstract
Considering the issue of noise generated by equipment that requires high air permeability for operation, a louvered noise barrier was designed. In accordance with sustainability principles, hemp fiber was used in the louvers. The aim of this experimental research was to investigate the [...] Read more.
Considering the issue of noise generated by equipment that requires high air permeability for operation, a louvered noise barrier was designed. In accordance with sustainability principles, hemp fiber was used in the louvers. The aim of this experimental research was to investigate the effectiveness of the louvered noise barrier in a semi-anechoic chamber and to evaluate the influence of the number of louvers, the angle of inclination of the louvers, and the hemp fiber density on the performance of the barrier. An investigation of the barrier in a semi-anechoic chamber was carried out, using the rotating microphone method. The louvers in the barrier were tilted at angles of 0, 15, 30, or 45 degrees, and the density of fiber used in the different structures was 50, 100, 150, or 200 kg/m3. The highest insertion loss (IL) of the barrier reached 18.13 dB, and the sound reduction index (R′) reached up to 23.0 dB. The highest determined weighted sound reduction index (R′w) was 14.1 dB, and the equivalent sound level loss (LAeq) reached 9.9 dB (A). Full article
(This article belongs to the Section Building Energy, Physics, Environment, and Systems)
36 pages, 35201 KB  
Article
Fuzzy Logic-Based Network Quality Evaluation for Standalone Non-Public Networks
by Sinta Novanana, Ajib Setyo Arifin, Adrian Kliks and Gunawan Wibisono
Appl. Sci. 2026, 16(13), 6314; https://doi.org/10.3390/app16136314 (registering DOI) - 23 Jun 2026
Abstract
Private Networks or Standalone Non-Public Networks (SNPNs) are essential for Industry 4.0 and enterprise connectivity. However, most existing studies rely on simulations, evaluate only a single radio access technology, or report raw key performance indicators (KPIs) without an interpretable quality assessment framework. In [...] Read more.
Private Networks or Standalone Non-Public Networks (SNPNs) are essential for Industry 4.0 and enterprise connectivity. However, most existing studies rely on simulations, evaluate only a single radio access technology, or report raw key performance indicators (KPIs) without an interpretable quality assessment framework. In practical deployment, operators require measurement-driven evidence to assess the performance and feasibility of 4G LTE and 5G SNPN solutions. This study presents a controlled experimental comparison of software-defined radio (SDR)-based 4G LTE and 5G SNPNs using the same Universal Software Radio Peripheral (USRP) platform, Open5GS, srsRAN, and commercial off-the-shelf user equipment (COTS-UE). The evaluation was conducted in an indoor environment under line-of-sight (LOS) and non-line-of-sight (NLOS) conditions. Experimental iPerf3 results show that the SDR-based 5G SNPN achieves higher downlink and uplink throughput than the SDR-based 4G LTE SNPN across all tested scenarios. The 5G deployment reaches up to 55 Mbps downlink and 40.5 Mbps uplink under LOS conditions, while maintaining 42 Mbps downlink and 28 Mbps uplink under NLOS conditions. Furthermore, 5G achieves lower latency than 4G LTE, with average values ranging from 21 ms to 31 ms. To provide interpretable network quality assessment, a Mamdani fuzzy logic-based Network Quality Index (NQI) with 81 inference rules is proposed to map signal-to-interference-plus-noise ratio (SINR), throughput, latency, and jitter into linguistic quality levels. The proposed approach enables nonlinear integration of heterogeneous KPIs and provides a technology-agnostic framework for practical SNPN deployment. Full article
(This article belongs to the Special Issue 5G/6G Mechanisms, Services, and Applications: 2nd Edition)
35 pages, 3804 KB  
Article
A Confound-Aware Framework for Multi-Class EEG Classification and Explainable Model Evaluation
by Ahmed Alqurashi and Abdullah Alharthi
Mathematics 2026, 14(13), 2239; https://doi.org/10.3390/math14132239 (registering DOI) - 23 Jun 2026
Abstract
Objective diagnosis in psychiatry remains challenging due to the lack of reliable biological markers and the presence of confounding variables in observational data. While EEG-based machine learning models have shown promising classification performance, their validity remains unclear when confounding factors such as age [...] Read more.
Objective diagnosis in psychiatry remains challenging due to the lack of reliable biological markers and the presence of confounding variables in observational data. While EEG-based machine learning models have shown promising classification performance, their validity remains unclear when confounding factors such as age are not explicitly controlled. In this work, we propose a confound-aware mathematical framework for supervised learning, where classification is formulated as a mapping f:RE×C×TY under the presence of a confounding variable A. Within this formulation, model performance is interpreted as a function of both predictive structure and confound dependence. The proposed framework integrates classification, regression, and feature selection into a unified evaluation pipeline. A central contribution is the Cross-Task Explanation Concordance (CTEC) index, a rank-based metric that quantifies the stability of feature importance across models and predictive tasks. Experimental results on a large-scale EEG dataset (N = 670) demonstrate that deep learning models outperform handcrafted approaches under standard evaluation. However, under confound-controlled settings, handcrafted models show a dual response to confound control: age residualization improves classification by removing feature-level noise (+20.3%), while age-matching collapses performance to chance (balanced accuracy, BA = 0.238) by eliminating demographic separability. Deep learning models retain partial robustness under both conditions. These findings highlight that conventional performance metrics may overestimate model validity in the presence of structured bias. The proposed framework provides a general mathematical approach for evaluating supervised learning models under confounding effects and is applicable to a wide range of data-driven systems beyond EEG. Full article
(This article belongs to the Special Issue Artificial Intelligence and Data Science, 2nd Edition)
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30 pages, 3047 KB  
Article
Air Pollution Prediction Based on Stacked Deep Autoencoder Network Model
by Dhuha Saad Ismael, Nurulkamal Masseran and Sakhinah Abu Bakar
Electronics 2026, 15(13), 2756; https://doi.org/10.3390/electronics15132756 (registering DOI) - 23 Jun 2026
Abstract
Urban air pollution, especially the problem of PM2.5, is one of the major health challenges facing the planet today. To provide accurate PM2.5 predictions despite data noise and missing data, the authors proposed a deep learning model. We constructed a [...] Read more.
Urban air pollution, especially the problem of PM2.5, is one of the major health challenges facing the planet today. To provide accurate PM2.5 predictions despite data noise and missing data, the authors proposed a deep learning model. We constructed a Stacked Autoencoder–Convolutional Neural Network–Bidirectional Long Short-Term Memory–Long Short-Term Memory (SAE-CNN-BiLSTM-LSTM) model that (1) utilises convolutional layers to extract spatial features from the input data, (2) employs bidirectional LSTM layers to capture long-term temporal dependencies, and (3) utilises an autoencoder to learn latent representations of the data to mitigate the effects of missing data. The model was trained on a large dataset of hourly measurements of air quality and meteorological parameters collected between 2018 and 2020 in Klang, Malaysia. The performance of the model on data that were not used during training was evaluated using a range of metrics. The SAE-CNN-BiLSTM-LSTM model achieved a test RMSE of approximately 11.97 µg/m3 and an R2 statistic of approximately 0.85 for PM2.5 concentrations, outperforming the other models tested on the same datasets. The additional metrics of MAE, MAPE, Mean Bias Error, and Index of Agreement confirmed the model’s accuracy and low bias in the prediction of air pollution levels. Statistical tests, such as the Diebold–Mariano test, confirmed the significance of the model’s accuracy over the CNN-LSTM models. These findings indicate that the proposed model effectively captures the dynamics of the air pollution data. The proposed model structure efficiently achieved an accurate and lightweight model for urban air pollution forecasting. Full article
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35 pages, 7584 KB  
Article
A Comparative Study of Time Series Clustering Performance with Classification as a Benchmark
by Maria Sadowska and Krzysztof Gajowniczek
Big Data Cogn. Comput. 2026, 10(7), 201; https://doi.org/10.3390/bdcc10070201 (registering DOI) - 23 Jun 2026
Abstract
This paper extends a previous classification study by examining clustering methods on the same synthetic datasets and comparing their behavior with the previously obtained classification results. This study investigates the performance of selected time series clustering methods under controlled changes in noise level [...] Read more.
This paper extends a previous classification study by examining clustering methods on the same synthetic datasets and comparing their behavior with the previously obtained classification results. This study investigates the performance of selected time series clustering methods under controlled changes in noise level and class complexity. Six clustering methods representing distance-based, feature-based, and deep learning approaches were evaluated on 82 balanced synthetic datasets. The datasets contained from two to six classes, different levels of additive Gaussian noise, 200 time series per dataset, and 1000 observations per time series. The analysis focused on clustering quality, comparative behavior with classification models, and computational cost in terms of training time and peak memory usage. Clustering quality was assessed mainly using Adjusted Rand Index and V-measure, while accuracy after Hungarian label matching was used as an auxiliary measure for comparison with classification models. The results show that distance-based methods, and particularly TimeSeriesKMedoids, achieved the most robust and consistent clustering performance across the considered settings. Clustering quality decreased with both the number of classes and the noise level, but the effect of noise was clearly stronger. Feature-based and deep learning-based clustering methods were generally more sensitive to noise, while deep models were also associated with substantially higher computational cost. In terms of memory usage, classical clustering methods remained below 50 MiB, whereas deep learning-based clustering methods required substantially more memory. This study further shows that accuracy computed after Hungarian label matching may provide an overly optimistic view of clustering quality. Accuracy after Hungarian label matching is reported only as an auxiliary metric, while the main interpretation of clustering quality is based on structure-sensitive measures such as Adjusted Rand Index and V-measure. Overall, the findings highlight the importance of robust distance-based approaches and of using structure-sensitive evaluation measures when analyzing time series clustering. Full article
(This article belongs to the Section Data Mining and Machine Learning)
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25 pages, 4206 KB  
Article
Intensified and Extended Growing Seasons in Abies marocana Forests (2000–2024): A Robust Seasonal Trend Analysis Using 16-Day MODIS EVI Time Series
by Oliver Gutiérrez-Hernández and Luis V. García
Remote Sens. 2026, 18(12), 2052; https://doi.org/10.3390/rs18122052 (registering DOI) - 22 Jun 2026
Viewed by 229
Abstract
We modelled, for the first time, the seasonal dynamics and long-term trends of Abies marocana forests (Rif Mountains, northern Morocco) using remote-sensing-derived vegetation indices. Using the MODIS Terra Vegetation Indices product MOD13Q1 (enhanced vegetation index, EVI; 16-day frequency; 250 m spatial resolution) from [...] Read more.
We modelled, for the first time, the seasonal dynamics and long-term trends of Abies marocana forests (Rif Mountains, northern Morocco) using remote-sensing-derived vegetation indices. Using the MODIS Terra Vegetation Indices product MOD13Q1 (enhanced vegetation index, EVI; 16-day frequency; 250 m spatial resolution) from 2000 to 2024 (575 images over 25 years), we applied a robust seasonal trend analysis (RSTA) workflow, representing an inferential extension of classical seasonal trend analysis (STA) through the explicit control of Type I error under serial and spatial correlation. This approach combined: (i) harmonic regression to capture the annual and semi-annual cycles of A. marocana forests, estimating seasonal amplitudes and phases while filtering out low-frequency noise; (ii) an iterative trend-free prewhitening (TFPW) procedure following Wang and Swail, applied only to time series with significant serial autocorrelation according to the Durbin–Watson test; (iii) the Theil–Sen slope (TS) estimator, a robust non-parametric method, to quantify the magnitude and direction of seasonality trends; (iv) the contextual Mann–Kendall (CMK) test to assess the statistical significance of seasonality trends, while correcting for spatial autocorrelation and accounting for cross-correlation among neighbouring pixels; (v) the Benjamini–Hochberg (BH) procedure to control the false discovery rate (FDR), ensuring that only statistically robust seasonality trends were retained; and (vi) reconstruction of seasonal curves representing the beginning and end of the study period and derivation of phenological metrics from the statistically significant seasonal trends retained after inferential filtering. After applying the complete analytical workflow, statistically significant trends were detected in 79.2% of pixels within A. marocana forests, compared with 86.4% when prewhitening and false discovery rate control were not applied. All Theil–Sen slopes retained by the RSTA workflow were positive, with a mean slope of approximately 0.00175 EVI year−1, corresponding to an average annual increase of roughly 0.7% and an overall increase of approximately 15% over the 2000–2024 study period relative to the initial mean EVI conditions. Browning trends identified by classical STA were not supported after inferential filtering and FDR control, indicating that all these patterns were spurious or only marginal, and confined to limited areas and edge zones. The reconstructed seasonal trend curves were consistent with a longer growing season, although this inference is based on land-surface vegetation dynamics rather than direct phenological observations. The long-term ecological consequences of these changes in seasonal vegetation activity will hinge on the interactions among warming, rising water demand, and potential disturbance regimes under future climatic conditions. Full article
(This article belongs to the Section Forest Remote Sensing)
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23 pages, 24608 KB  
Article
Harmonic and Phase-Modulated Activation Functions for Implicit Neural Representations: A Comprehensive Benchmark Study
by Ahmad S. Tarawneh, Omar Lasassmeh, Anas A. Alkasasbeh, Abdulkareem Alzahrani, Khalid Almohammadi, Maha Alamri and Ahmad B. Hassanat
Mach. Learn. Knowl. Extr. 2026, 8(6), 170; https://doi.org/10.3390/make8060170 (registering DOI) - 21 Jun 2026
Viewed by 125
Abstract
It is well-known that activation functions are crucial in determining spectral expressiveness, training dynamics, and reconstruction accuracy in implicit neural representations (INRs), which employ coordinate-based multilayer perceptrons to represent continuous signals. Despite showing excellent performance, sinusoidal activations, for example SIREN, are limited in [...] Read more.
It is well-known that activation functions are crucial in determining spectral expressiveness, training dynamics, and reconstruction accuracy in implicit neural representations (INRs), which employ coordinate-based multilayer perceptrons to represent continuous signals. Despite showing excellent performance, sinusoidal activations, for example SIREN, are limited in their adaptability to diverse signal types due to their fixed harmonic structure. In this paper, we propose two novel periodic activation functions for INRs. (1) Harmonic generalizes sinusoidal activations by combining the fundamental frequency with learned second and third harmonics through per-neuron trainable amplitude coefficients, resulting in a richer spectral basis within the SIREN initialization framework. (2) PM-FINER (Phase-Modulated FINER) extends the variable-periodic FINER activation by embedding frequency modulation synthesis directly into the instantaneous phase, enabling data-driven phase distortion via a learnable modulation index and carrier ratio. We conducted comprehensive experiments spanning nine architectural configurations (including SIREN, WIRE, FINER, Gaussian, Harmonic, PM-FINER, and an additional direct comparison against the Subtractive Modulative Network (SMN)), using six natural images, three learning rate schedulers, and three random seeds, totaling 486 main training runs (534 runs total including an ω0 sensitivity sweep). Our evaluation combined peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and rigorous statistical analysis, such as paired t-tests, Wilcoxon signed-rank tests, Cohen’s d effect sizes, and Friedman rank tests. Under cosine annealing, Harmonic achieves a mean PSNR gain of 6.08 dB over SIREN and 2.57 dB over FINER (both p<0.001, Cohen’s d>3.7), while PM-FINER ranks statistically on par with Harmonic (mean difference 0.17 dB, p=0.36), outperforming all of the other baselines. Compared with SMN, Harmonic outperforms it by +7.94 dB under cosine annealing (Bonferroni-adjusted p<105, Cohen’s d=12.3), winning on all six images. Additionally, the Friedman ranking across the six images confirmed Harmonic (with mean rank =1.33) and PM-FINER (with mean rank =1.67), being the top two methods under cosine annealing. Our results establish interpretable multi-harmonic and phase-modulated activations as real alternatives to the existing INR activation functions. Full article
(This article belongs to the Section Learning)
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38 pages, 2692 KB  
Article
Observability- and Identifiability-Guided Sensor-Set Design for Digital-Twin-Assisted Consolidated Bioprocessing
by Mark Korang Yeboah, Nana Yaw Asiedu and Ahmad Addo
Sensors 2026, 26(12), 3948; https://doi.org/10.3390/s26123948 (registering DOI) - 21 Jun 2026
Viewed by 341
Abstract
Consolidated bioprocessing (CBP) is difficult to monitor because enzyme production, lignocellulose degradation, sugar release, and fermentation occur simultaneously under sparse measurement, feedstock variability, and plant–model mismatch conditions. This study proposes a computational sensor-set design framework for digital-twin-assisted CBP monitoring. A five-state virtual plant, [...] Read more.
Consolidated bioprocessing (CBP) is difficult to monitor because enzyme production, lignocellulose degradation, sugar release, and fermentation occur simultaneously under sparse measurement, feedstock variability, and plant–model mismatch conditions. This study proposes a computational sensor-set design framework for digital-twin-assisted CBP monitoring. A five-state virtual plant, consisting of active biomass, cellulolytic enzyme activity, residual insoluble substrate, soluble sugar, and ethanol, was used to evaluate all 16 ethanol-mandatory measurement packages formed from ethanol, sugar, biomass, enzyme, and residual-substrate proxy channels. Candidate sensor sets were assessed using finite-difference output sensitivities, Fisher-information-based state-observability and parameter-identifiability analyses, eigenvalue and parameter-correlation diagnostics, and paired Monte Carlo unscented Kalman filter soft-sensing reconstruction. Within the tested five-state virtual-plant benchmark and with the specified excitation schedule, noise assumptions, burden indices, and scoring objective, ethanol-only sensing provided the weakest support for state-aware CBP digital-twin reconstruction. At a 6h sampling interval, the state-observability log-pseudodeterminant increased from 4.18 with ethanol-only sensing to 8.56 after adding soluble sugar and to 16.42 with full-proxy monitoring. The ethanol–sugar–biomass–substrate package also gave strong reduced state-observability performance, with log-pseudodeterminants of 15.12, 13.76, and 12.51 at 6, 12, and 24h, respectively. Biomass and enzyme proxies contributed strongly to parameter learning, and the ethanol–sugar–biomass–enzyme package gave the strongest active parameter-identifiability performance, with log-pseudodeterminants of 10.82, 9.06, and 6.67 at 6, 12, and 24h, respectively. In the paired soft-sensing analysis, full-proxy monitoring reduced the mean latent-state RMSE from 1.1899 to 0.3756, followed by ethanol–biomass–enzyme–substrate with 0.3843 and ethanol–sugar–biomass–substrate with 0.4121. The primary aggregate ranking identified ethanol–sugar–biomass–substrate as the best overall package, with a sensor-value score of 0.8432 and a burden index of 7.0, followed by full-proxy monitoring with a score of 0.8173 and a burden index of 10.0. Robustness tests showed that ethanol–sugar–biomass–substrate remained top-ranked under uniform noise scaling, full UKF missingness, delay and bias stress test conditions, most scoring-weight scenarios, and all tested sensor-specific burden workflows. Full-proxy monitoring remained a close competitor under independent sensor-specific noise variation conditions and became top-ranked for some alternative operating trajectories. The proposed framework provides a simulation-based method for prioritizing informative measurement packages before implementing CBP digital twins in laboratory and pilot-plant settings. Full article
(This article belongs to the Special Issue Soft Sensors and Sensing Techniques (2nd Edition))
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42 pages, 15288 KB  
Article
A Hybrid Model for Stock Index Forecasting Integrating Adaptive Frequency-Domain Decomposition and Enhanced Transformer Encoder
by Hairong Zheng, Xiaozheng Zeng, Guoyu Hu and Tingting Zhang
Mathematics 2026, 14(12), 2202; https://doi.org/10.3390/math14122202 - 18 Jun 2026
Viewed by 214
Abstract
Stock index price series are composed of superimposed multi-frequency components, including long-term trends, cyclical fluctuations, and stochastic noise. Effectively decoupling these heterogeneous components and modeling them separately is key to improving forecasting accuracy. Existing methods under the “decomposition–prediction” paradigm mostly employ fixed-scale decomposition, [...] Read more.
Stock index price series are composed of superimposed multi-frequency components, including long-term trends, cyclical fluctuations, and stochastic noise. Effectively decoupling these heterogeneous components and modeling them separately is key to improving forecasting accuracy. Existing methods under the “decomposition–prediction” paradigm mostly employ fixed-scale decomposition, and the forecasting models are not specifically adapted to the non-stationary and high-noise characteristics of financial data, resulting in limitations in adaptivity and local dynamic capture. This paper proposes a frequency-aware adaptive multi-scale decomposition Transformer hybrid model (FAMS-Transformer). At the decomposition level, the fast Fourier transform is used to dynamically identify dominant cycles, thereby adaptively decoupling trends and fluctuations, overcoming the limitations of fixed-scale decomposition. At the forecasting level, a lightweight depthwise separable convolution is embedded between the self-attention and feedforward network of the Transformer encoder, enhancing the model’s ability to capture local temporal dynamics and achieving collaborative modeling of global dependencies and local information. Comparative experiments with 15 baseline models including LSTM, Transformer, TimesNet, and FreTS on three representative Chinese market indices—Shanghai Composite Index, Shenzhen Component Index, and Small and Medium Enterprises 100 Index—across four prediction horizons from one step to 15 steps demonstrate that FAMS-Transformer achieves the best forecasting accuracy in all scenarios. The coefficient of determination for 15-step prediction remains stably between 0.730 and 0.928. Moreover, the model still performs well on the S & P 500 dataset. Ablation studies and significance tests further validate the effectiveness of each core module and the statistical significance of the performance improvements. Full article
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23 pages, 2184 KB  
Article
A Hybrid Topological–Metric Clustering Framework Based on Persistent Homology: TCSI, HTCI, and NHTSI
by Nurhan Halisdemir, Yunus Güral and Mehmet Gürcan
Axioms 2026, 15(6), 457; https://doi.org/10.3390/axioms15060457 (registering DOI) - 18 Jun 2026
Viewed by 106
Abstract
While classical clustering methods, particularly k-means, produce powerful and practical solutions based on metric distances between data points, they can be limited in complex, nonlinear, and structurally disordered datasets. This study proposes a hybrid topological–metric clustering framework, referred to as Hybrid-NHTSI, that integrates [...] Read more.
While classical clustering methods, particularly k-means, produce powerful and practical solutions based on metric distances between data points, they can be limited in complex, nonlinear, and structurally disordered datasets. This study proposes a hybrid topological–metric clustering framework, referred to as Hybrid-NHTSI, that integrates persistent homology-based structural information into the clustering update process. The method is based on the Topological Cluster Separation Index (TCSI), a persistent homology (PH)-based metric for topological separation. In addition to TCSI, the proposed framework uses the Normalized Topological Cluster Separation Index (NTCSI), the Hybrid Topological Clustering Index (HTCI), and the Normalized Hybrid Topological Separation Index (NHTSI) to evaluate clustering performance from both geometric and topological perspectives. In the proposed approach, while the topological separation between clusters is increased, intra-cluster geometric scattering is controlled by a regularization term. This formulation enables the extraction of clusters that are consistent not only topologically but also geometrically. The performance of the method was evaluated on synthetic circles-and-moons benchmark datasets under different noise and overlap levels, and on the UCI Human Activity Recognition real sensor dataset. The experimental results showed that DBSCAN achieved the strongest overall performance on the density-favorable synthetic benchmark, which is consistent with the nonconvex and density-separable structure of the data. However, Hybrid-NHTSI produced higher NTCSI, HTCI, and NHTSI values than classical metric/geometric baselines such as k-means, Spectral Clustering, and Agglomerative Clustering. Pairwise statistical comparisons based on NHTSI confirmed that these improvements were significant against several competing methods. In the real-data experiment, although Spectral Clustering achieved the highest ARI value, Hybrid-NHTSI obtained the highest NTCSI, HTCI, and NHTSI values and significantly outperformed all competing methods in terms of NHTSI. The findings demonstrate that considering both metric and topological information together, rather than relying solely on metric or topological information, provides a more structurally informed evaluation and optimization mechanism for complex clustering problems. Accordingly, the proposed method should not be interpreted as a universally superior clustering algorithm across all metrics, but rather as a topology-aware hybrid refinement framework that enriches metric-based clustering with persistent homology. Full article
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15 pages, 695 KB  
Review
Deep Learning for Brain MRI Artifact Correction: Current Challenges and Future Directions
by Jiangfan Yu, Sibusiso Mdletshe, Hamid Abbasi, Eryn Kwon, Samantha Holdsworth and Alan Wang
Bioengineering 2026, 13(6), 699; https://doi.org/10.3390/bioengineering13060699 - 18 Jun 2026
Viewed by 335
Abstract
Structural magnetic resonance imaging (sMRI) is progressively used to diagnose brain diseases; however, brain sMRI scans can be easily corrupted by artifacts, e.g., motion artifacts. To remove artifacts, deep learning (DL) algorithms have been extensively studied recently. However, their performance and the challenges [...] Read more.
Structural magnetic resonance imaging (sMRI) is progressively used to diagnose brain diseases; however, brain sMRI scans can be easily corrupted by artifacts, e.g., motion artifacts. To remove artifacts, deep learning (DL) algorithms have been extensively studied recently. However, their performance and the challenges currently faced in clinical practice (e.g., real-world robustness, hallucination and over-smoothing) have not been adequately studied in a quantitative manner. In this structured literature review, we quantitatively examined DL-based artifact correction studies (N = 30), retrieved from the major databases (i.e., Google Scholar, PubMed, Web of Science, and Scopus), which particularly focused on clinical-field-strength (defined as 1.5 Tesla (T) and above) sMRI in a non-pediatric setting. Our review suggests that current DL-based approaches exhibit promising fidelity measured by structural similarity (SSIM, 0.92 ± 0.05) index and peak signal-to-noise ratio (PSNR, 32.85 ± 4.53 dB). In addition, We identified the factors underlying hallucination or over-smoothing, which are associated with neural network (NN) architecture and the training process. This study also reveals the potential advantages, brought about by frequency-aware NN. Finally, we outline several future directions, including an emerging paradigm in DL, namely physics-informed NN (PINN). Full article
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32 pages, 9223 KB  
Article
Evaluation of Supervised Machine Learning Algorithms for Mapping Hydrothermal Alteration Zones Associated with Porphyry Copper Mineralization Using ASTER Satellite Imagery
by Mahin Rostami and Amin Beiranvand Pour
Mining 2026, 6(2), 42; https://doi.org/10.3390/mining6020042 - 16 Jun 2026
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Abstract
Hydrothermal alteration mapping is a critical component of porphyry copper exploration because alteration assemblages provide important vectors toward mineralization. This study presents a systematic evaluation of supervised machine learning algorithms for delineating hydrothermal alteration zones using Advanced Spaceborne Thermal Emission and Reflection Radiometer [...] Read more.
Hydrothermal alteration mapping is a critical component of porphyry copper exploration because alteration assemblages provide important vectors toward mineralization. This study presents a systematic evaluation of supervised machine learning algorithms for delineating hydrothermal alteration zones using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) short-wave infrared (SWIR) surface reflectance data (AST_07XT). The investigation focuses on the Nain region within the central Urumieh–Dokhtar Magmatic Arc (UDMA), Iran, a major metallogenic belt hosting numerous porphyry copper systems. Representative spectral endmembers corresponding to Al–OH-bearing and Mg–OH-bearing hydrothermal alteration minerals were extracted using Minimum Noise Fraction (MNF), Pixel Purity Index (PPI), and n-dimensional visualization techniques. These endmembers were subsequently used to train and evaluate a comprehensive suite of supervised machine learning classifiers, including linear, kernel-based, tree-based, ensemble, probabilistic, boosting, and neural-network algorithms for pixel-wise hydrothermal alteration mapping. Model performance was evaluated using multiple statistical metrics, including overall accuracy (OA), average accuracy (AA), precision, recall, F1-score, Cohen’s kappa coefficient, area under the ROC curve (AUC), spatial cross-validation accuracy, uncertainty analysis, and spatial agreement analysis. Among the evaluated classifiers, SVM_Linear, SVM_RBF, LDA, and MLP achieved the highest classification performance, with overall accuracies exceeding 94% and strong spatial consistency between classified maps. The resulting alteration maps display spatially coherent distributions of Al–OH and Mg–OH minerals that are consistent with established hydrothermal alteration zoning models in porphyry–epithermal systems. The mapped hydrothermal alteration zones show strong spatial correspondence with known mineralized areas and alteration patterns within the Urumieh–Dokhtar Magmatic Arc, confirming the geological reliability of the classification results. Uncertainty analysis further indicates high model confidence across most alteration zones, with higher uncertainty values mainly restricted to transitional and spectrally heterogeneous regions. The results demonstrate that integrating ASTER SWIR imagery with supervised machine learning algorithms provides a robust, scalable, and transferable framework for regional-scale hydrothermal alteration mapping and mineral exploration in porphyry copper provinces. Full article
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