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19 pages, 823 KB  
Article
A Variational Bayesian Constrained EKF for Sonar-Based Underwater Target Tracking in Shallow Water
by Hongkun Zhou, Yunfei Ding, Hanlin Gao, Gang Wang, Tong Ge and Ying Zhang
Sensors 2026, 26(17), 5591; https://doi.org/10.3390/s26175591 - 3 Sep 2026
Viewed by 185
Abstract
Accurate localization of underwater targets in shallow water is challenging because nonlinear sonar geometry, range-amplified angular errors, uncertain measurement noise, and environmental constraints jointly degrade state estimation. This paper proposes a variational Bayesian constrained extended Kalman filter (VB-C-EKF) for active-sonar-based underwater target tracking. [...] Read more.
Accurate localization of underwater targets in shallow water is challenging because nonlinear sonar geometry, range-amplified angular errors, uncertain measurement noise, and environmental constraints jointly degrade state estimation. This paper proposes a variational Bayesian constrained extended Kalman filter (VB-C-EKF) for active-sonar-based underwater target tracking. A weak-maneuver motion model and an active-sonar range–bearing–elevation–Doppler measurement model are adopted, while bathymetric depth, speed, and reachable-region constraints are incorporated through sequential local Mahalanobis projection with a conservatively regularized covariance correction. To address unknown and time-varying measurement noise, the measurement-noise covariance is recursively estimated using a variational Bayesian scheme with an inverse-Wishart prior and a forgetting mechanism. In Monte Carlo experiments, the proposed method achieved an overall three-dimensional position RMSE of 7.57 m with a 95% confidence-interval half-width of 0.25 m, while maintaining zero depth/speed violations. Its mean normalized innovation squared and normalized estimation error squared were 4.04 and 6.79, respectively, and its average runtime was 0.225 ms per update. These results show that jointly adapting measurement uncertainty and enforcing physical constraints improves accuracy, feasibility, and covariance consistency under the simulated shallow-water conditions. Full article
(This article belongs to the Section Navigation and Positioning)
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23 pages, 3452 KB  
Article
A Portable Colorimetric Biosensor Platform for Urinary Colorectal Cancer Biomarker Testing in Low-Resource Settings
by Prashanthi Kovur, Scott MacKay, Songtian Bai, James Cook, Claudia Torres-Calzada, Dipanjan Bhattacharyya, Upasana Singh and David S. Wishart
Biosensors 2026, 16(9), 485; https://doi.org/10.3390/bios16090485 - 2 Sep 2026
Viewed by 281
Abstract
Early detection of colorectal cancer (CRC) is challenging in low-resource settings because access to colonoscopy and centralized laboratory testing is limited. Urine-based metabolite biomarkers offer a non-invasive alternative for CRC triage, but translating a laboratory assay into a point-of-care (PoC) system requires standardized [...] Read more.
Early detection of colorectal cancer (CRC) is challenging in low-resource settings because access to colonoscopy and centralized laboratory testing is limited. Urine-based metabolite biomarkers offer a non-invasive alternative for CRC triage, but translating a laboratory assay into a point-of-care (PoC) system requires standardized fluid handling, operator-independent timing, field-compatible reagents, and quantitative calibration. Here, we present a low-cost, semi-automated PoC platform integrating a validated, sequential, three-metabolite CRC-biomarker assay with robotic fluid handling, a motorized chromatographic module, an optical reader, Bluetooth electronics, and tablet-guided control. The platform measures urinary diacetylspermine and hippuric acid, with creatinine serving as a normalization reference, and reports absolute quantitative concentrations. Automated dilution, tube positioning, timed incubation, controlled column elution, and software-guided transfer reduce operator-dependent variation. Using pooled urine samples spiked at clinically relevant concentrations, the creatinine assay showed a strong quadratic response (0–50 mM, R2 = 0.998), as did the diacetylspermine assay (0–4 μM, R2 = 0.979), while the hippuric acid assay showed a linear response of R2 = 0.989. The RGB sensor tracked the concentration-dependent trend observed with a laboratory microplate reader (R2 = 0.968–0.999). Reagents reformulated as lyophilized or pre-weighed, vacuum-sealed kits withstood accelerated heat and humidity (45 °C/70% RH) testing and international shipping to the pilot site very well. At approximately USD 490 for the complete instrument (including tablet) and roughly USD 7.65 in consumables per screening test, the platform offers a practical, quantitative, and portable route for decentralized CRC screening. Full article
(This article belongs to the Special Issue Biosensors for Disease Analysis)
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30 pages, 818 KB  
Article
Bayesian Modeling and Forecasting of Double Seasonal Vector Autoregressive Processes
by Ayman A. Amin and Fatimah E. Almuhayfith
Mathematics 2026, 14(16), 2870; https://doi.org/10.3390/math14162870 - 7 Aug 2026
Viewed by 290
Abstract
A wide range of real-world multivariate time series encountered in practice exhibit two simultaneous and interacting seasonal cycles, for example hourly electricity demand, intraday financial prices, and sub-daily traffic volumes. Existing Bayesian frameworks for vector autoregressive (VAR) processes accommodate at most a single [...] Read more.
A wide range of real-world multivariate time series encountered in practice exhibit two simultaneous and interacting seasonal cycles, for example hourly electricity demand, intraday financial prices, and sub-daily traffic volumes. Existing Bayesian frameworks for vector autoregressive (VAR) processes accommodate at most a single seasonal periodicity, leaving no established methodology for the double seasonal case commonly observed in high-frequency multivariate data. This paper bridges that gap by introducing the double seasonal VAR (DSVAR) models, which extend the univariate double seasonal literature to a coherent multivariate setting. These models are defined through a multiplicative triple autoregressive operator that naturally accommodates the second seasonal cycle. Under a Gaussian error assumption, we derive a comprehensive and analytically convenient Bayesian framework for both modeling and forecasting of DSVAR processes. We consider two prior families: a conjugate matrix normal-Wishart prior which yields exact closed-form inference, and a Jeffreys’ non-informative prior. Under each prior, we derive the marginal posterior distribution of the coefficient matrix as a matrix-t distribution and the marginal posterior of the precision matrix as a Wishart distribution. Moreover, we derive the predictive distribution of future observations as a multivariate-t with an exact analytic form, together with its highest predictive density regions. The methodology is validated through a Monte Carlo simulation experiment and applied to hourly electricity loads in Czech Republic and Germany, two physically interconnected markets with pronounced intraday and intraweek seasonal cycles. Benchmark comparisons against standard VAR, single-seasonal VAR, and univariate seasonal AR models confirm the substantial forecasting gains delivered by the proposed DSVAR framework at both short and long horizons. Full article
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24 pages, 1739 KB  
Article
The Transcriptomic and Proteomic Molecular Signatures of Equine Multiple-System Neuropathy (Grass Sickness)
by Kim M. Summers, Anna E. Karagianni, Paula Ledesma Fernandez, Philippa M. Beard, R. Scott Pirie, John A. Keen, Thomas M. Wishart and Bruce C. McGorum
Cells 2026, 15(15), 1328; https://doi.org/10.3390/cells15151328 - 24 Jul 2026
Viewed by 508
Abstract
Equine grass sickness (EGS or equine dysautonomia) is a predominantly fatal multi-system neuropathy affecting grazing horses, likely caused by a neurotoxic phospholipase A2 (nPLA2) derived from a plant or microorganism. We studied neuronal tissue gene and protein expression patterns in EGS to elucidate [...] Read more.
Equine grass sickness (EGS or equine dysautonomia) is a predominantly fatal multi-system neuropathy affecting grazing horses, likely caused by a neurotoxic phospholipase A2 (nPLA2) derived from a plant or microorganism. We studied neuronal tissue gene and protein expression patterns in EGS to elucidate the possible mechanisms of neurotoxicity and neurodegeneration. Tissue from the cranial cervical ganglion of eight EGS horses and six controls was examined histologically and used for transcriptomic analysis. These transcriptomic data were compared with previously published EGS-related proteomic datasets from different horses. Results were visualized using the network analysis tool BioLayout and Ingenuity Pathway Analysis. The cranial cervical ganglia from all affected horses showed pathology typical of EGS. They also showed distinct gene and protein expression profiles that were different from the controls. The EGS signature consisted ofreduced expression of genes and proteins involved in neurological function (including ion-channel and synaptic-function genes and genes encoding mitochondrial proteins) and increased expression of genes and proteins indicative of cellular stress, cell death and inflammation. This signature likely reflects more generalized neurodegeneration. This study thus improves our understanding of the molecular changes likely to be associated with a neurotoxic neurodegenerative process. Full article
(This article belongs to the Section Cellular Neuroscience)
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21 pages, 1703 KB  
Article
Bayesian Identification of Double-Seasonal Vector Autoregressive Models
by Ayman A. Amin and Fatimah E. Almuhayfith
Mathematics 2026, 14(14), 2476; https://doi.org/10.3390/math14142476 - 9 Jul 2026
Viewed by 326
Abstract
Identifying the autoregressive (AR) orders of a multivariate time series is a foundational step whose accuracy governs every downstream modelling and forecasting task. When the series exhibits two simultaneously operating seasonal periodicities, as is routinely observed in hourly electricity loads and intraday financial [...] Read more.
Identifying the autoregressive (AR) orders of a multivariate time series is a foundational step whose accuracy governs every downstream modelling and forecasting task. When the series exhibits two simultaneously operating seasonal periodicities, as is routinely observed in hourly electricity loads and intraday financial prices, no principled Bayesian identification framework currently exists. This paper addresses this gap by introducing a complete Bayesian order identification procedure for double-seasonal vector autoregressive (DSVAR) models. These DSVAR models are multivariate processes governed by a multiplicative triple autoregressive operator that jointly captures regular, first-seasonal, and second-seasonal dynamics. We treat the three order indices as unknown discrete parameters and derive closed-form expressions for the joint posterior probability mass function of the order triple. Two complementary prior specifications are considered: a conjugate matrix normal-Wishart prior and Jeffreys’ non-informative prior. The analysis is carried out under the assumption of symmetric, normally distributed errors, which ensures analytical tractability and allows for the posterior probabilities to be evaluated exactly for every admissible combination of orders. Specifically, under each prior, the posterior mass function reduces to explicit determinantal expressions that can be evaluated by a straightforward three-dimensional grid search. Monte Carlo experiments on various DSVAR processes confirm that the proposed technique achieves high identification accuracy even at moderate sample sizes across a range of parameter configurations and prior choices. The proposed Bayesian procedure is benchmarked against the standard Bayesian information criterion (BIC), consistently achieving higher correct identification rates across all cases. Empirical applications to hourly electricity load data from the Czech Republic and Germany, as well as to hourly solar radiation in Najran, Saudi Arabia, demonstrate the practical applicability of the Bayesian identification method. Full article
(This article belongs to the Special Issue Advances in Statistical Methods for Time Series Analysis)
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28 pages, 2963 KB  
Article
Spawning Poisson Multi-Bernoulli Mixture Filter for Multi-Extended Object Tracking Using Dynamic Hybrid Detection
by Youpeng Sun, Peng Li, Wenhui Wang, Ye Xu, Wenqi Geng and Jiajun Ding
Algorithms 2026, 19(7), 538; https://doi.org/10.3390/a19070538 - 2 Jul 2026
Viewed by 323
Abstract
The Poisson multi-Bernoulli mixture (PMBM) filter is an effective approach for multi-object tracking in complex scenarios. However, its performance deteriorates when surviving objects spawn, as the PMBM filter only classifies detected objects as either new-born or surviving, thereby ignoring information from the surviving [...] Read more.
The Poisson multi-Bernoulli mixture (PMBM) filter is an effective approach for multi-object tracking in complex scenarios. However, its performance deteriorates when surviving objects spawn, as the PMBM filter only classifies detected objects as either new-born or surviving, thereby ignoring information from the surviving objects and preventing timely identification of spawning events. To address this limitation, this paper proposes the Dynamic Hybrid Detection-Gamma Gaussian inverse Wishart Spawning Poisson multi-Bernoulli mixture (DHD-GGIW-SPMBM) filter, which models spawning objects independently using a Bernoulli process to enhance tracking accuracy. The probability generating functional is employed to derive the recursive prediction and update equations of the proposed filter, and its conjugacy after prediction and update is formally proven. Additionally, a dynamic hybrid detection method is introduced to evaluate the consistency between measurements and theoretical samples, enabling the detection of spawning events. The detection results guide an evidential Gaussian mixture model (EGMM) for fuzzy partitioning of the spawning process, reducing errors under closely spaced and high-clutter conditions. Simulation results demonstrate that, compared with existing spawning-capable filters, the proposed DHD-GGIW-SPMBM filter achieves superior tracking performance, faster identification of spawned objects, and robust operation in complex scenarios. Full article
(This article belongs to the Section Randomized, Online, and Approximation Algorithms)
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19 pages, 9119 KB  
Article
Sampling Quantum States with Inequality Constraints
by Weijun Li, Rui Han, Jiangwei Shang, Hui Khoon Ng and Berthold-Georg Englert
Entropy 2026, 28(6), 614; https://doi.org/10.3390/e28060614 - 29 May 2026
Viewed by 364
Abstract
Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one already encounters when working with a few qubits, the quantum state space has a very [...] Read more.
Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one already encounters when working with a few qubits, the quantum state space has a very complicated boundary, and it is challenging to incorporate the specific properties into the sampling algorithm. In this paper, we present the Sequentially Constrained Monte Carlo (SCMC) algorithm as a practical and versatile method for sampling quantum states in accordance with properties that can be stated as inequalities. We apply the SCMC algorithm to the generation of samples of bound entangled states; for example, we obtain nearly ten thousand bound, entangled, two-qutrit states in a few minutes, compared with less than ten such states per day from independence sampling in our implementation. In the second application, we draw samples of high-dimensional quantum states from a narrowly peaked target distribution and observe, for the system sizes investigated, that SCMC sampling remains computationally manageable as the dimensions grow. In yet another application, the SCMC algorithm produces uniformly distributed quantum states in regions bounded by values of the problem-specific target distribution; such samples are needed when estimating parameters from the probabilistic data acquired in quantum experiments. Full article
(This article belongs to the Special Issue Quantum Measurements and Quantum Metrology)
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28 pages, 4324 KB  
Article
Multi-Platform Milk Metabolomics Identifies Distinctive Biomarker Signatures of Subclinical Ketosis in Dairy Cows
by Guanshi Zhang, David S. Wishart and Burim N. Ametaj
Dairy 2026, 7(3), 39; https://doi.org/10.3390/dairy7030039 - 28 May 2026
Viewed by 1327
Abstract
Ketosis is one of the most economically significant metabolic disorders affecting periparturient dairy cows, causing production losses and predisposing animals to secondary complications. Current blood-based diagnostics are invasive and provide limited insight into the underlying metabolic perturbations. This study employed an integrated three-platform [...] Read more.
Ketosis is one of the most economically significant metabolic disorders affecting periparturient dairy cows, causing production losses and predisposing animals to secondary complications. Current blood-based diagnostics are invasive and provide limited insight into the underlying metabolic perturbations. This study employed an integrated three-platform metabolomics approach to characterize milk metabolite alterations in ketotic Holstein dairy cows and to evaluate milk-based biomarker panels for early ketosis detection. Milk samples from 20 healthy control (CON) cows and 6 ketotic cows were collected at 2 weeks postpartum and analyzed by direct injection/liquid chromatography–tandem mass spectrometry (DI/LC-MS/MS), proton nuclear magnetic resonance (1H-NMR) spectroscopy, and inductively coupled plasma mass spectrometry (ICP-MS). Ketosis was confirmed by serum β-hydroxybutyrate concentrations ≥ 1400 μmol/L. Principal component analysis, partial least squares-discriminant analysis, and receiver operating characteristic (ROC) curve analyses were applied. All three platforms discriminated ketotic cows from healthy cows, with clear cluster separation validated by 2000 permutation tests (p < 0.05). DI/LC-MS/MS identified 16 significantly altered metabolites (p < 0.05), with butyrylcarnitine (C4), phosphatidylcholine 30:0 (PC 30:0), ether-linked phosphatidylcholine O-38:3 (PC O-38:3), and citrulline identified as the top discriminatory biomarkers (AUC = 0.920; 95% CI: 0.85–0.98; sensitivity = 91.7%; specificity = 93.3%). ICP-MS revealed significantly reduced selenium (Se, p = 0.017), manganese (Mn, p = 0.045), and chromium (Cr, p = 0.037), as well as elevated cobalt (Co, p = 0.014) in ketotic milk (AUC = 0.870). 1H-NMR detected no individually significant metabolites; however, multivariate analysis distinguished groups (AUC = 0.890), with succinate (numerical fold change: +5.77×; p = 0.059), methanol (−1.94×; not significant), and acetate (+2.88×; not significant) as top VIP contributors. The combined multi-platform biomarker panel (joint classification using top VIP features from all three platforms, without formal data fusion) achieved superior diagnostic performance (AUC = 0.970; 95% CI: 0.93–1.00; sensitivity = 95.0%; specificity = 96.7%). These findings identify coordinated perturbations in glycerophospholipid metabolism, acylcarnitine profiles, amino acid homeostasis, antioxidant mineral status, and energy metabolism during early ketosis, and suggest that milk metabolomics is a promising non-invasive approach for precision dairy health monitoring, pending validation in independent cohorts. We acknowledge the small ketotic group size (n = 6) as a limitation; therefore, these findings should be considered discovery cohort observations requiring prospective validation before clinical translation. Full article
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17 pages, 996 KB  
Article
Integration of Patient-Reported Outcome Measures in Clinical Practice for Head and Neck Cancer Patients: A Cross-Sectional Survey
by Tatiana Dragan, Niclas Hubel, Jens Lehmann, Katherine J. Taylor, Renée Bultijnck, Tihana Gašpert, Luigi Lorini, Vincent Bourbonne, Arnaud Beddok, Bartłomiej Tomasik, Daan Nevens, Stefano Cavalieri, Ruth Gabriela Herrera Gómez, Esmée Lauren Looman, Iyizoba-Ebozue Zsuzsanna, Fatjona Kraja, Emma Lidington, Csongor György Lengyel, Marc Oliva, Gerardo Petruzzi, Ana Varges Gomes, Maria Pilar Solis Hernandez, Sophie Veldhuijzen van Zanten, Jesus Brenes Castro, Francesca Caparrotti, Giuseppe Fanetti, Yannick G. Eller, Chiara Gottardi, Laurelie R. Wishart and Petr Szturzadd Show full author list remove Hide full author list
Curr. Oncol. 2026, 33(5), 275; https://doi.org/10.3390/curroncol33050275 - 8 May 2026
Viewed by 1842
Abstract
Background: Head and neck cancer (HNC) and its multimodal treatment substantially impair speech, swallowing, breathing, appearance, and psychosocial well-being. Patient-reported outcome measures (PROMs) improve symptom monitoring and quality of life in oncology, yet their integration into routine HNC care remains inconsistent. This study [...] Read more.
Background: Head and neck cancer (HNC) and its multimodal treatment substantially impair speech, swallowing, breathing, appearance, and psychosocial well-being. Patient-reported outcome measures (PROMs) improve symptom monitoring and quality of life in oncology, yet their integration into routine HNC care remains inconsistent. This study assessed patterns of PROM use, perceived value, and barriers to implementation among healthcare professionals (HCPs) involved in HNC care. Methods: A 30-item cross-sectional survey was distributed to HCPs treating HNC patients between June 2024 and April 2025. The questionnaire explored PROM use in clinical practice and trials, perceived relevance across care phases, and implementation barriers. Respondents were classified as non-users, occasional users, or regular users. Data were analyzed descriptively with comparisons between groups. Results: Among 133 respondents, 33.8% were non-users, 29.3% occasional users, and 36.8% regular users of PROMs. Users reported inviting half of patients to complete PROMs, predominantly via paper-based questionnaires (67.8%). PROMs were mainly applied during active treatment and early follow-up to monitor symptoms, overall health, and emotional well-being, and were less frequently used to guide treatment decisions. The EORTC QLQ-C30 and HNC-specific tools were most commonly reported. Compared with users, non-users more often cited lack of time, limited training in interpreting PROM data, insufficient institutional support, resource constraints, and lack of appropriate instruments (all p < 0.05). PROM use in clinical trials was associated with routine use (p < 0.001). Conclusions: Although PROMs are widely valued in HNC care, their integration into clinical decision-making remains limited. Addressing organizational, educational, and digital barriers is essential to support sustainable implementation. Full article
(This article belongs to the Section Head and Neck Oncology)
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22 pages, 8380 KB  
Article
An Improved Multiple-Component Decomposition Method of Polarimetric SAR Interferometry Using Refined Volume Scattering Models
by Yu Wang, Daqing Ge, Bin Liu, Weidong Yu and Chunle Wang
Remote Sens. 2026, 18(9), 1277; https://doi.org/10.3390/rs18091277 - 23 Apr 2026
Viewed by 380
Abstract
In this research paper, we introduce an improved multiple-component decomposition technique based on the refined volume scattering models (MCSMRV) for polarimetric interferometric synthetic aperture radar (PolInSAR) system. The primary objective of this methodology is to address the issue of overestimation in volume scattering [...] Read more.
In this research paper, we introduce an improved multiple-component decomposition technique based on the refined volume scattering models (MCSMRV) for polarimetric interferometric synthetic aperture radar (PolInSAR) system. The primary objective of this methodology is to address the issue of overestimation in volume scattering (OVS) and to clarify the mixed ambiguities associated with scattering mechanisms. Our approach incorporates an innovative inversion technique for rotation angles in urban areas, alongside the newly proposed volume scattering models. Furthermore, a refined Wishart mixture model (RWMM) is proposed for distinguishing building regions from non-building regions, which can effectively support the rational selection of volume scattering models. Additionally, the polarimetric interferometric similarity parameter (PISP) is employed to modify the volume scattering models for buildings with diverse orientation angles. To validate the effectiveness of MCSMRV, we utilize ESAR PolInSAR data and the PolInSAR data collected by the Aerospace Information Research Institute. Various mathematical methods are applied to assess the performance of MCSMRV. The experimental results clearly demonstrate that MCSMRV represents a robust method for characterizing the scattering mechanisms across different terrain types. Full article
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27 pages, 6233 KB  
Article
Effects of Dimethylamino Functional Group Substitution on the Physical, Structural and Radiolytic Properties of Pyridinium Ionic Liquids
by Matthew S. Emerson, Sharon I. Lall-Ramnarine, Jasmine L. Hatcher-Lamarre, Marie F. Thomas, Masao Gohdo, Boning Wu, Min Liang, Sharon Ramati, Fei Wu, Claudio J. Margulis, Edward W. Castner, Robert R. Engel and James F. Wishart
Processes 2026, 14(8), 1208; https://doi.org/10.3390/pr14081208 - 9 Apr 2026
Viewed by 867
Abstract
A diverse range of 4-dimethylaminopyridinium (DMAP) bis(trifluoromethylsulfonyl)-amide ionic liquids with specific functionalities (alkyl, alkoxy, hydroxyalkyl and benzyl) were designed, characterized and compared with their pyridinium analogs in terms of their physical and radiolytic properties. The influence of the dimethylamino group on ionic liquid [...] Read more.
A diverse range of 4-dimethylaminopyridinium (DMAP) bis(trifluoromethylsulfonyl)-amide ionic liquids with specific functionalities (alkyl, alkoxy, hydroxyalkyl and benzyl) were designed, characterized and compared with their pyridinium analogs in terms of their physical and radiolytic properties. The influence of the dimethylamino group on ionic liquid structure was investigated by X-ray diffraction and molecular dynamics simulations. The influence of the electron-donating ability of the dimethylamino-substituted cation is evident in the differences in the electronic density of states between the DMAP and pyridinium ILs. This leads to substantial changes in the radical transients observed in pulse radiolysis of the neat ILs. It was found that the DMAP salts were higher melting, more viscous and less conducting than their pyridinium analogs. However, the DMAP salts exhibited higher thermal stabilities and could therefore be useful for high-temperature applications. Full article
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18 pages, 331 KB  
Article
Some Distributional Properties of the Matrix-Variate Generalized Gamma Model
by Arak M. Mathai and Serge B. Provost
Axioms 2026, 15(3), 238; https://doi.org/10.3390/axioms15030238 - 23 Mar 2026
Viewed by 935
Abstract
This paper employs Jacobians of matrix transformations to derive the density function of a matrix-variate generalized gamma distribution, together with its normalizing constant. By applying the inverse Mellin transform, explicit expressions for the density functions of the determinant and the trace are obtained [...] Read more.
This paper employs Jacobians of matrix transformations to derive the density function of a matrix-variate generalized gamma distribution, together with its normalizing constant. By applying the inverse Mellin transform, explicit expressions for the density functions of the determinant and the trace are obtained in terms of generalized hypergeometric functions. The characteristic function and the first two moments follow from an associated density generator. Both the real and complex cases are treated, and several important special cases are identified. A simulation study reveals that the proposed model provides a more accurate fit than other distributions that are also defined on the cone of positive definite matrices. Moreover, it is shown to exhibit superior performance when applied to two empirical data sets. Applications involving the modeling of scatter matrices arising in financial studies, biostatistics, and reliability analysis are also discussed. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)
15 pages, 1214 KB  
Article
What Is the Long-Term Fate of Green Roofs?
by Taylor Wishart and Michael L. McKinney
Urban Sci. 2026, 10(3), 124; https://doi.org/10.3390/urbansci10030124 - 27 Feb 2026
Cited by 1 | Viewed by 980
Abstract
Despite the rapid expansion of green roof installations in the United States, little empirical evidence exists regarding their long-term persistence or post-installation management. This study evaluates post-installation outcomes for 46 green roofs across ten southeastern U.S. states using a structured survey and publicly [...] Read more.
Despite the rapid expansion of green roof installations in the United States, little empirical evidence exists regarding their long-term persistence or post-installation management. This study evaluates post-installation outcomes for 46 green roofs across ten southeastern U.S. states using a structured survey and publicly available records. Roofs were classified by status (managed, abandoned, removed, mid-refurbishment, or unknown) and management intensity. Associations with ownership change, building type, and Leadership in Energy and Environmental Design (LEED) certification status were examined using Fisher’s Exact Tests and logistic regression. Only 47.8% of roofs were actively managed at the time of data collection, while 45.7% had been abandoned or removed. Ownership change was significantly associated with roof failure (Fisher’s Exact Test, p = 0.001), with no managed roofs experiencing post-installation ownership turnover. In contrast, LEED certification status was not associated with either roof persistence or management intensity. These findings indicate that institutional continuity and sustained management play a critical role in determining long-term green roof outcomes and suggest that installation-based incentives may overestimate the number of functioning green roofs. By shifting evaluation beyond ecological performance metrics alone, this study highlights governance and institutional stability as central factors shaping roof longevity. Full article
(This article belongs to the Section Urban Environment and Sustainability)
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32 pages, 43285 KB  
Article
Polarimetric SAR Salt Crust Classification via Autoencoded and Attention-Enhanced Feature Representation
by Fabin Dong, Qiang Yin, Juan Zhang, Qunxiong Yan and Wen Hong
Remote Sens. 2026, 18(1), 164; https://doi.org/10.3390/rs18010164 - 4 Jan 2026
Cited by 1 | Viewed by 882
Abstract
Qarhan Salt Lake, located in the Qaidam Basin of northwestern China, is a highland lake characterized by diverse surface features, including salt lakes, salt crusts, and saline-alkali lands. Investigating the distribution and dynamic variations of salt crusts is essential for mineral resource development [...] Read more.
Qarhan Salt Lake, located in the Qaidam Basin of northwestern China, is a highland lake characterized by diverse surface features, including salt lakes, salt crusts, and saline-alkali lands. Investigating the distribution and dynamic variations of salt crusts is essential for mineral resource development and regional ecological monitoring. To this end, the surface of the study area was categorized into several types according to micro-geomorphological characteristics. Polarimetric synthetic aperture radar (PolSAR), which provides rich scattering information, is well suited for distinguishing these surface categories. To achieve more accurate classification of salt crust types, the scattering differences among various types were comparatively analyzed. Stable samples were further selected using unsupervised Wishart clustering with reference to field survey results. Besides, to address the weak inter-class separability among different salt crust types, this paper proposes a PolSAR classification method tailored for salt crust discrimination by integrating unsupervised feature learning, attention-based feature optimization, and global context modeling. In this method, convolutional autoencoder (CAE) is first employed to learn discriminative local scattering representations from original polarimetric features, enabling effective characterization of subtle scattering differences among salt crust types. Vision Transformer (ViT) is introduced to model global scattering relationships and spatial context at the image-patch level, thereby improving the overall consistency of classification results. Meanwhile, the attention mechanism is used to bridge local scattering representations and global contextual information, enabling joint optimization of key scattering features. Experiments on fully polarimetric Gaofen-3 and dual-polarimetric Sentinel-1 data show that the proposed method outperforms the best competing method by 2.34% and 1.17% in classification accuracy, respectively. In addition, using multi-temporal Sentinel-1 data, recent temporal changes in salt crust distribution are identified and analyzed. Full article
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22 pages, 10044 KB  
Article
Robust Extended Object Tracking Based on Variational Bayesian for Unmanned Aerial Vehicles Under Unknown Outliers
by Haibo Yang, Yu Zhu, Yanning Zhang and Xueling Chen
Drones 2026, 10(1), 4; https://doi.org/10.3390/drones10010004 - 23 Dec 2025
Cited by 1 | Viewed by 913
Abstract
The application of extended object tracking (EOT) in unmanned aerial vehicles (UAVs) has increasingly gained attention in recent years. However, EOT is often corrupted by heavy-tailed measurement noise due to outliers, which can be caused by factors such as UAV interference or partial [...] Read more.
The application of extended object tracking (EOT) in unmanned aerial vehicles (UAVs) has increasingly gained attention in recent years. However, EOT is often corrupted by heavy-tailed measurement noise due to outliers, which can be caused by factors such as UAV interference or partial object occlusion. Student’s t distribution (STD) is widely adopted for modeling this type of noise, and the estimation accuracy of EOT is highly dependent on prior knowledge of the noise. Although existing methods typically assume such prior knowledge is available, this assumption often fails in practice. Furthermore, the fact that the posterior of the measurement noise is estimated leads to coupling. This coupling, which cannot be adequately resolved by existing methods, prevents the direct derivation of variational Bayesian (VB) inference. We propose an adaptive EOT approach that employs a decoupling model to address unknown outliers in UAV tracking. Then, a novel dual-extended distortion model from sensor’s FoV is proposed to address the coupling. Subsequently, the measurement likelihood is formulated as a hierarchical structure, where the degrees of freedom (DoF) and measurement noise covariance matrix (MNCM) are modeled by Gamma and inverse Wishart (IW) distributions, respectively. The hierarchical structure allows the model to account for unknown noise characteristics. Based on these models, we derive an approach recursively for estimation. Finally, the performance of the proposed approach is validated with both simulated and real-world datasets. The results demonstrate the superior effectiveness and robustness of our approach. Full article
(This article belongs to the Special Issue Detection, Identification and Tracking of UAVs and Drones)
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