Search Results (2,128)

Accurate and wide-area estimation of seaweed biomass is essential for evaluating blue carbon. Conventional diver surveys and two-dimensional (2D) aerial imagery analysis face challenges such as intensive labor and biomass underestimation. While Unmanned Aerial Vehicle-based Light Detection and Ranging (UAV-LiDAR) provides dense 3D spatial data, classifying point clouds in extremely shallow coastal waters with dense kelp and artificial structures remains difficult. This study establishes a high-accuracy biomass estimation method using UAV-LiDAR and PointNet. A heuristic hybrid filtering approach combining physical constraints and local statistics was developed to automatically generate high-quality reference data. The trained PointNet successfully segmented complex point clouds into four classes with an overall accuracy of 94.2%. To calculate biomass, we introduced a volume correction model based on point cloud density (coverage) to mitigate overestimation caused by internal canopy gaps. This correction yielded estimated wet weights nearly identical to the in situ measurements (an approximate 3% difference), confirming highly accurate biomass reproduction. Furthermore, while the conventional 2D maximum likelihood method underestimated total biomass, our 3D point cloud analysis successfully quantified the dense, overlapping canopy. This framework significantly improves the efficiency and accuracy of blue carbon monitoring. Full article

Land Surface Temperature (LST) is essential for climate monitoring, drought assessment, and urban heat analysis. Despite its importance, the Landsat-8 Collection 2 Level-2 (C2L2) LST product has not been rigorously validated using ground measurements—a critical gap this study addresses. We present the first comprehensive accuracy assessment using 382 coincident satellite–ground observations collected from seven Surface Radiation Budget Network (SURFRAD) stations distributed across diverse climatic regions of the United States during the period 2023–2025. The validation results indicate strong overall agreement between satellite-derived and ground-measured temperatures, yielding an RMSE of 4.20 °C, a coefficient of determination (R²) of 0.91, and a Pearson correlation coefficient (r) of 0.98. These statistics demonstrate the high reliability of the C2L2 LST product across a wide range of environmental conditions. Nevertheless, a systematic warm bias of 1.75 °C was observed, indicating a tendency toward temperature overestimation. Model performance exhibited pronounced seasonal variability. The highest accuracy was achieved during winter conditions (RMSE = 2.17 °C; r = 0.99), whereas performance declined considerably during summer months (RMSE = 5.84 °C; r = 0.91). Analysis of atmospheric water vapor content revealed significant associations with retrieval errors at high-elevation and arid locations, particularly at FPK (r = 0.78) and DRA (r = 0.75), based on 106 matched observations. These relationships provide important insight into the atmospheric factors contributing to seasonal variations in retrieval accuracy. Temperature-dependent analyses further demonstrated that retrieval uncertainty increases with surface temperature. Performance progressively deteriorated from cooler to warmer thermal regimes, with RMSE values increasing from approximately 2.05 °C for temperatures below 20 °C to 5.71 °C for temperatures exceeding 40 °C. Spatial evaluation also revealed substantial differences among stations. Relatively homogeneous, low-elevation sites exhibited superior performance (GWN: RMSE = 2.60 °C; SXF: RMSE = 2.55 °C), whereas stations located in mountainous or topographically complex environments showed reduced accuracy (TBL: RMSE = 5.14 °C; FPK: RMSE = 5.62 °C). These outcomes emphasize the influence of terrain complexity and atmospheric heterogeneity on LST retrieval performance. Overall, this study establishes the first comprehensive benchmark for evaluating the reliability of Landsat-8 C2L2 LST products. The results provide valuable guidance for their application in climate research, precision agriculture, hydrological modeling, and environmental monitoring. Furthermore, the findings identify specific environmental conditions requiring enhanced validation efforts and suggest opportunities for future algorithm refinement through improved atmospheric correction procedures and more accurate surface emissivity characterization. Full article

Background: Chronic kidney disease presents a significant health challenge among the elderly, with recent data indicating a 13.9% prevalence for early stages (1–3) and a lower 0.6% prevalence for advanced stages. Notably, many geriatric patients die from cardiovascular complications before reaching end-stage kidney disease, highlighting the critical interplay between renal and cardiovascular health. Central to this connection is endothelial dysfunction, considered the initial trigger for cardiovascular mortality. We aimed to investigate the correlation between different measurement methods demonstrating endothelial dysfunction and sVE-cadherin levels. Another objective was to examine the relationship between decreased glomerular filtration rate (GFR) and sVE-cadherin levels. We hypothesized an inverse relationship between impaired renal function, endothelial dysfunction, and sVE-cadherin. Methods: The study included geriatric patients with CKD who were not receiving RRT. Non-geriatric patients, those with cardiovascular disease, atrial fibrillation, heart failure, active immunosuppressive use, active infection, history of active malignancy, Raynaud’s phenomenon, and renal transplantation patients were excluded. Demographic data of the patients, nailfold capillary measurements, carotid intima-media thickness, flow-mediated dilatation, sVE-cadherin, and serum fibroblast growth factor 23 (FGF23) levels were measured. Results: We analyzed 96 patients. Key findings revealed a significant inverse correlation between serum sVE-cadherin levels and glomerular filtration rate (GFR), suggesting that, as kidney function declines, endothelial integrity is compromised. Interestingly, patients treated with sodium–glucose co-transporter-2 inhibitors had notably lower sVE-cadherin levels, indicating the possible modulatory effect of these drugs on endothelial function. Additional correlations were observed: fibroblast growth factor 23 levels were positively related to capillary diameter, and carotid intima-media thickness was associated with mean platelet volume. Declining GFR corresponded to reductions in capillary count, while use of dipeptidyl peptidase-4 inhibitors was linked to higher capillary density. Over a 2.3-year follow-up, survivors had higher lymphocyte counts (p = 0.088, not statistically significant) and baseline sVE-cadherin levels tended to be higher in those who died, although this was not statistically significant. Conclusions: These findings suggest that uremic toxins may worsen endothelial injury by disrupting intercellular connections, highlighting the complex pathogenic environment in CKD. Given these insights, the need for standardized diagnostic thresholds for endothelial dysfunction in geriatric CKD patients is clear. Serum sVE-cadherin emerges as a promising novel biomarker for assessing endothelial health, offering potential for earlier intervention and improved cardiovascular outcomes. It may be a potent indicator of endothelial dysfunction and should be featured in future studies of elderly CKD patients. Full article

An increasing number of higher education institutions in the Republic of Serbia are experiencing a decline in first-year enrollment, posing a significant challenge to their sustainability and effective resource planning. Timely identification of factors influencing candidates’ enrollment decisions, as well as those at risk of not enrolling, is crucial for implementing appropriate institutional measures. This study aims to build and evaluate a machine learning model to predict candidates’ decisions to enroll in a higher education institution based on relevant educational, administrative, demographic, social, and geographic characteristics. Various classification models, including ensemble approaches, were applied and compared in this study. Experimental results indicate that the Stacking Ensemble model achieved slightly higher values of the evaluated imbalance-sensitive metrics compared to the other evaluated models, with an Area Under the ROC Curve (AUC) of 0.756 and a Matthews Correlation Coefficient (MCC) of 0.364, indicating moderately balanced predictive performance in the context of imbalanced data. However, the statistical analysis conducted between the Logistic Regression and Stacking Ensemble models did not indicate a statistically significant difference in performance. The results suggest that ensemble methods may provide certain advantages over individual models, particularly for complex classification problems involving imbalanced data. The application of the proposed model may contribute to improving the decision-making process at higher education institutions, enabling more efficient enrollment policy planning and more optimal resource management. Full article

Corporate balance sheets report aggregate equity and liability totals but conceal the internal allocation of financing sources across asset categories—an identification problem that conventional econometric methods cannot resolve without additional parametric assumptions. This paper develops a maximum entropy (ME) panel estimator to recover two latent scalar parameters: x ∈ (0,1), the share of equity capital directed toward long-term asset financing, and y ∈ (0,1), the corresponding debt allocation share. Grounded in maximum entropy principle, the estimator selects the unique parameter vector that satisfies the mean-level balance-sheet constraint while maximising joint Shannon entropy—the least-biassed solution consistent with observable data. The closed-form logistic representation yields a scalar Lagrange multiplier λ*, interpreted as a financing pressure index, recoverable via bisection in at most 21 iterations at tolerance ε = 10⁻⁵. Building on the ME estimates, we introduce a continuous matching alignment index M* = x* − y* that measures the degree of compliance with the financial matching principle along a continuous spectrum rather than as a binary categorisation. Applied to a ten-firm, cross-sectoral panel spanning Technology, Finance, Energy, and Automotive sectors over an observation window spanning 2001 to 2025 (with firm-specific subperiods reflecting differences in IPO dates and data availability), the framework reveals substantial heterogeneity in latent financing flows: equity allocation shares range from 30.1% (NVIDIA) to 75.1% (ExxonMobil), while debt allocation shares span 37.1% to 77.5%. Across the panel, only Meta exhibits substantial positive matching alignment, while Microsoft, ExxonMobil, Apple, and Tesla show only very slight differences that fall within the neutral band, and the remaining firms show varying degrees of structural departure from the matching benchmark; the thresholds used to summarise these descriptive labels are interpretive aids rather than re-imposed binary criteria, and the substantive ranking of firms along M* does not depend on the specific threshold values adopted. The ME solution’s entropy H(x*, y*) and the normalised diversification index D(x*, y*) describe allocation balance under the estimator’s information–theoretic criterion rather than independently observed firm complexity; in the present sample, the cross-firm ordering of these values is not recovered by firm size, leverage, or sector classification alone. These findings, based on a ten-firm case-study panel with time-invariant allocation parameters, should be interpreted as descriptive patterns of the present sample rather than statistically validated regularities. They provide a theoretically rigorous and computationally tractable identification of unobservable corporate financing flows, with potential implications for capital structure theory, financial risk assessment, and balance sheet analysis that would benefit from validation on larger and more representative samples in future work. Full article

E-commerce has reshaped short-term financial management by altering transaction speed, payment structures, and supply chain coordination. This study examines how large publicly listed e-commerce firms, viewed as complex digital business systems, adjusted their working capital policies during and after the COVID-19 shock. The sample is based on the 100 largest e-commerce companies worldwide by market capitalization, as reported by CompaniesMarketCap (February 2026), and is reduced to 76 firms from 23 countries due to data availability, yielding 802 firm-year observations. Firm-level data are obtained from LSEG Datastream, while macroeconomic variables are sourced from the World Bank. The analysis distinguishes between two dimensions of working capital: flow-based operational adjustment, measured by the cash conversion cycle (CCC), and stock-based balance-sheet adjustment, captured by net working capital relative to total assets (WC/TA). Fixed-effects models with firm-clustered standard errors are employed. The results indicate a substantial contraction of the CCC during the pandemic, followed by partial persistence of that contraction rather than a return to pre-pandemic norms. In contrast, WC/TA remains broadly stable during the crisis but declines in the post-pandemic period, suggesting a delayed balance-sheet adjustment. Business-model heterogeneity is not statistically significant, which may reflect a common system-level response across e-commerce firm types. Leverage and supply-chain pressures are associated with working capital intensity (WC/TA), while inflation shapes operate cycle duration (CCC). The findings are consistent with a two-stage adaptive response to systemic disruption. Full article

The Gompertz distribution is a well-known lifetime model in survival and reliability analysis, but its hazard rate is restricted to monotone increasing behavior, which limits its applicability to more complex data structures. In this study, we investigate the New Extended Gompertz (NEG) distribution, which is obtained by applying the existing NE-X generator framework to the classical Gompertz baseline distribution. Thus, the NEG model is a special case within an already established generator family rather than an entirely new family of distributions. The main contribution of this paper is not the introduction of a new generator, but rather a comprehensive and systematic investigation of this particular Gompertz-based extension, including its statistical properties, estimation procedures, and practical applications. The proposed model introduces an additional shape parameter that provides increased flexibility in modeling skewness, tail behavior, and hazard-rate structures, allowing for increasing, decreasing, bathtub-shaped, and unimodal hazard patterns under different parameter configurations. Several mathematical properties of the NEG distribution are derived, including explicit expressions for the density, distribution, survival, and hazard-rate functions, as well as moments, entropy measures, and series representations. Parameter estimation is performed using both maximum likelihood and Bayesian approaches, with numerical optimization and Metropolis–Hastings MCMC procedures employed due to the absence of closed-form estimators. The finite-sample behavior of the estimators is investigated through extensive Monte Carlo simulation studies under three different parameter settings. The practical usefulness of the NEG distribution is illustrated using two real datasets on carbon-fiber tensile strength. Comparative results with several competing Gompertz-type models indicate that the NEG distribution provides competitive performance. However, all comparisons should be interpreted within the context of the considered datasets and parameter settings, rather than as claims of universal superiority. The findings suggest that the NEG distribution offers a flexible and practical extension of the Gompertz model for lifetime data analysis. Full article

The fractal natural microstructure of shale reservoirs significantly influences hydraulic fracture propagation and reservoir stimulation. However, there is a lack of quantitative mathematical descriptions for the coupled regulation of micropores, natural fractures, and injection rates. This study develops a mathematical evaluation method for hydraulic fracture evolution in complex microstructured reservoirs using digital core technology, fractal geometry and a hydraulic–mechanical–damage coupling algorithm. High-resolution SEM images were used to reconstruct the microscopic fractal features. Integrated digital image processing and fractal analysis, along with geometric indices such as fractal dimension, fracture coverage, and stimulated area, and statistical measures including directional entropy, variance, and the Pearson correlation coefficient, were employed to systematically quantify fracture network evolution and complexity under different injection rates. Results show that fracture morphology, spatial complexity, and mineral damage mechanisms are jointly controlled by microstructure and injection rate. In particular, the directional distribution of pores and natural fractures is found to exert a dominant control on the propagation paths and branching behavior of hydraulic fractures, revealing a strong coupling between microstructural anisotropy and fracture directionality. Increased injection rates enhance fracture complexity and stimulation range, with varying effects from different microstructures. At low rates, fracture propagation is mainly determined by the initial microstructure, whereas at high rates, fractures tend to develop multiple pathways. Natural fracture structures contribute more to fracture complexity at high rates. The proposed comprehensive fracturability index (FI)-based fracturability evaluation model provides a systematic, quantitative approach to optimizing fracturing processes. Full article

Background: Distal radius fractures (DRFs) are the most common upper limb fractures worldwide. The main goal of DRF treatment is to achieve optimal functional outcomes with the lowest complication rate as rapidly as possible. Achieving full limb function may be delayed by emerging complications or, in some cases, may never occur. Preserving muscle strength and as full a range of motion (ROM) in the wrist as possible are key in DRF management since they enable patients to perform the activities of daily living. The purpose of this study was to assess the effect of ossein–hydroxyapatite complex (OHC), used as an adjunct in conservative DRF treatment, on muscle strength and ROM. Methods: This was a prospective randomized clinical study. We assessed 31 patients who underwent non-surgical DRF treatment at our center in the years 2024–2025 and were receiving OHC throughout their fracture treatment. K-Grip and K-Push dynamometers were used to measure the maximum and average muscle strength via tests of grip strength, palmar flexion, and dorsal flexion. Wrist ROM was also evaluated. The results were compared with those of the control group (31 patients receiving DRF treatment without OHC) and with the intact limb. Results: The medians of the maximum muscle strength in each test were comparable between the study groups. Both groups showed a higher median average strength in the intact limb than in the treated limb. We observed no intergroup differences in wrist ROM, with ROM parameters lower in the fractured limb than in the intact limb. Conclusions: The additional use of OHC was not associated with statistically significant improvements in functional outcomes. The patients from both groups achieved worse muscle strength and ROM outcomes in the fractured than in the intact limb. We recommend a longer and more intense rehabilitation of patients with DRFs. More studies on this topic are needed in order to unequivocally verify the effects of OHC on functional parameters in fracture patients. Full article

This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three major sources of complexity in modern functional data analysis: infinite-dimensional covariates, smoothly time-varying stochastic dynamics, and incomplete response observations. The methodology is based on a class of kernel-type estimators combining temporal localization, functional single-index smoothing, and inverse-propensity correction. Temporal localization captures the gradual evolution of the underlying regression structure, the single-index projection provides an effective dimension-reduction mechanism for functional covariates, and the propensity adjustment restores the target conditional functional under the MAR sampling scheme. The principal contribution of the paper is the establishment of weak convergence, in a suitable space of bounded functions, for the resulting propensity-adjusted conditional U-process indexed by a general class of measurable kernels. Under absolute regularity conditions, local stationarity assumptions, small-ball probability requirements, entropy restrictions of VC type, and uniform consistency of the propensity-score estimator, the normalized process is shown to converge weakly to a tight centered Gaussian process. The limiting covariance structure explicitly reflects the interaction between temporal smoothing, functional concentration, dependence, and the random loss of responses. In parallel, uniform convergence rates are derived for the associated conditional single-index U-statistic estimators, thereby quantifying the respective contributions of smoothing bias, stochastic fluctuation, local-stationarity approximation error, and missingness-induced variance inflation. A substantial part of the analysis is devoted to the technical difficulties created by the simultaneous presence of dependence, nonstationarity, functional covariates, and incomplete observations. The proofs combine Hoeffding-type decompositions adapted to weighted incomplete data, blocking and coupling arguments for absolutely regular triangular arrays, refined entropy bounds for kernel-indexed function classes, and small-ball probability techniques for functional covariates. The MAR mechanism is incorporated via inverse-propensity weighting, and its effects on the effective sample size, asymptotic variance, and bias structure are made explicit. The theory also provides a rigorous foundation for bandwidth selection through blocked, propensity-adjusted cross-validation and clarifies its relation to the corresponding oracle risk. The proposed framework encompasses a broad class of statistical learning and inference problems involving pairwise or higher-order functionals of functional time series. In particular, it applies to conditional Kendall-type functionals, discrimination problems, metric learning with incomplete labels, and conditional independence testing under local stationarity. A simulation study illustrates the finite-sample behavior of the proposed estimators and supports the theoretical findings across varying regimes of temporal nonstationarity, serial dependence, functional concentration, and response missingness. Overall, the results provide a mathematically rigorous and methodologically flexible foundation for inference from evolving functional data when dependence, infinite dimensionality, and incomplete observation are present simultaneously. Full article

Background: Rare diseases are associated with chronic progression, functional impairment, and complex care needs, requiring long-term and coordinated rehabilitation. Physical and Rehabilitation Medicine (PRM) plays a key role in maintaining functional capacity and improving quality of life; however, access to rehabilitation services remains uneven across regions. Aim: This study aims to assess the regional structural availability of PRM services across Bulgaria and to identify territorial differences in the organizational profile of rehabilitation services that may influence the potential availability of rehabilitation care for patients with rare diseases. Methods: A descriptive cross-sectional study was conducted using publicly available aggregated data from the NHIF and the National Statistical Institute as of 31 December 2024. Structural indicators included the number of outpatient and inpatient PRM healthcare facilities and PRM specialists, standardized per 100,000 population, as well as the outpatient-to-inpatient facility ratio (OFs/IFs). Hierarchical cluster analysis (Ward’s method, Euclidean distance) was applied as an exploratory tool to identify similarities in regional service availability profiles. Results: Substantial regional differences in the structural availability of PRM services were identified. Outpatient facilities ranged from 4.46 to 6.74 per 100,000 population, while inpatient facilities ranged from 2.30 to 3.42 per 100,000 population. The OFs/IFs ratio varied between 1.30 and 2.26, indicating different organizational profiles of PRM service provision. Exploratory hierarchical clustering suggested two broad regional service profiles: one characterized by a relatively balanced distribution of outpatient and inpatient structures and another characterized by a predominance of outpatient-oriented rehabilitation services. Conclusion: The findings reveal substantial regional differences in the organization of PRM services in Bulgaria. Regions with a predominance of outpatient structures may demonstrate different capacities for delivering comprehensive rehabilitation services, particularly for patients with complex long-term needs, including rare diseases. The results highlight the need for targeted regional planning, improved integration of rehabilitation services, and policy measures aimed at ensuring equitable access to care. Full article

In complex low-altitude environments, unmanned aerial vehicles (UAVs) require reliable positioning, yet Global Navigation Satellite System (GNSS) signals are vulnerable to occlusion and interference. Pseudolite-augmented cooperative localization, which combines ground base-station signals with inter-UAV relative observations, can complement GNSS in such environments. However, two practical issues remain in real-world deployment: UAV-to-base-station (U-B) and UAV-to-UAV (U-U) observations have markedly different error statistics that a unified noise adjustment cannot handle, and the conservative covariance estimates produced by Covariance Intersection (CI) fusion bias the innovation-based adaptive noise estimation in distributed architectures. To address these issues, this paper proposes a Distributed Group Covariance Compensation Adaptive Kalman Filter (DGCC-AKF) for collaborative enhancement of UAV regional localization. DGCC-AKF establishes a group adaptive mechanism that independently adjusts the noise covariance matrices of U-B and U-U observations, enabling observation-type-level adaptive weighting that suppresses anomalous U-B or U-U measurements at the group level. In addition, a bounded covariance compensation factor is incorporated to alleviate the CI-induced conservatism in the adaptive noise estimation. The proposed method is evaluated on a 2800 km² semi-physical testbed based on the Ground-based High-precision Local Positioning System (GH-LPS) pseudolite network using measured U-B observations and high-dynamic (>300 km/h) flight trajectories collected from a fixed-wing platform across three independent flight sessions. Results demonstrate that under observation fault periods, the proposed method improves 3D positioning accuracy by up to about 75% over single-UAV extended Kalman filter (EKF). Compared with two advanced algorithms in this field, variational Bayesian adaptive Kalman filter (VBAKF) and maximum correntropy criterion Kalman filter (MCC-EKF), it is the only scheme that remains accurate and stable across all UAVs and fault types. The framework provides a practical step toward field deployment for resilient multi-UAV cooperative navigation in pseudolite-augmented GNSS-denied regions. Full article

Radio occultation (RO) has become a key technique for monitoring the ionosphere by deriving electron density (Ne) profiles and total electron content (TEC) from GNSS signals. This study assesses the newly deployed PlanetiQ GNOMES constellation by validating its ionospheric Ne profiles and profile-based TEC against collocated measurements from ionosondes and the COSMIC-2 mission under both quiet and disturbed geomagnetic conditions. Data matching for the statistical validation uses conservative spatial thresholds of less than 1° in latitude and longitude and temporal limits of 30 min for ionosondes and 1 h for COSMIC-2, supported by a dedicated sensitivity analysis, whereas storm-time case studies apply tighter temporal collocation and explicit control of the ray path geometry. Quantitative agreement is evaluated using root mean square error (RMSE), mean and absolute mean differences, correlation coefficients, regression analysis, and normalized percentage differences for key F-layer parameters, including the maximum Ne of the F2 layer (NmF2), the peak height of the F2 layer (hmF2), and the critical frequency of the F2 layer (foF2), along with altitude-dependent Ne profiles. PlanetiQ shows strong consistency with ionosonde profiles, with RMSE ranging from 2.94 × 10⁴ to 2.76 × 10⁵ el/cm³, correlations typically exceeding 0.90, and normalized absolute mean differences often near or below about 10–20%, although lower correlations of about 0.31 and 0.69 are found at Poker Flat and Awase, respectively, reflecting complex local structures and regional variability. Comparisons with COSMIC-2 during quiet conditions yield RMSE values between 7.06 × 10⁴ and 2.16 × 10⁵ el/cm³, correlations from 0.94 to 0.99, and percentage differences that generally remain within a few tens of percent, while storm-time analyses show RMSE between 1.12 × 10⁵ and 3.70 × 10⁵ el/cm³ with correlations from 0.80 to 0.99, confirming robust agreement across a wide range of geophysical conditions. Regression results demonstrate slopes near 1.00 and correlation coefficients above 0.90 for NmF2 and foF2 between PlanetiQ and both ionosondes and COSMIC-2, whereas hmF2 exhibits larger scatter, particularly during geomagnetic disturbances; additional binning by spatial and temporal separation indicates that temporal mismatches generally have a stronger impact on discrepancies than horizontal distance. Overall, the results demonstrate that PlanetiQ ionospheric RO data provide accurate and consistent measurements of key ionospheric parameters, comparable to those from COSMIC-2 and ionosondes, and can reliably complement existing observing systems for monitoring ionospheric variability and space-weather impacts. Full article

Estimating dependency relationships between variables is an important issue in statistics. Mutual information (MI) is a measure of dependency which quantifies the amount of shared information between two variables. It is free of distribution assumption and captures both linear and non-linear dependencies. MI estimation methods were primarily developed for datasets with exclusively discrete variables, exclusively continuous variables, or a mixture of both. In practice, complex variables containing both discrete and continuous values (discrete-continuous variables), specifically continuous censored variables, are often present in real datasets (e.g., biological measures from analytical tools with lower detection limit). Methods have been developed to handle discrete-continuous data, but their effectiveness on the specific case of continuous censored data has not yet been evaluated. We propose a new estimation method based on the decomposition of the MI formula, with a first part handling the censoring status of the data, and a second part handling its continuous section. This estimation method works as a correction, as it takes in parameter one MI estimator for continuous data, and makes it able to handling censoring. We constructed different simulation scenarios of pairs of correlated censored log-normal variables, by varying the censoring rate, correlation, and sample size. We evaluated our correction on a few existing estimators previously developed for continuous, mixed or discrete-continuous data. We compared the selected estimators, with and without the correction, on these different scenarios. We found that the correction globally enables to reduce bias, and allows convergence towards the true MI value as the number of observations increases. Full article

Longitudinal data, characterized by repeated measurements on the same subjects over time, are ubiquitous in biomedical sciences, economics, social sciences, and engineering. Analyzing such data presents unique statistical and computational challenges, including within-subject correlation, time-varying covariates, irregular observation times, informative dropout, and high dimensionality. While traditional statistical methods, such as linear mixed-effects models and generalized estimating equations, remain foundational, they often struggle with complex nonlinear dynamics, ultra-high-dimensional feature spaces, and very large sample sizes. Over the past two decades, machine learning (ML) and artificial intelligence (AI) methods have emerged as powerful complementary approaches to address these limitations. This review provides a comprehensive survey of mathematical and computational methods for longitudinal data analysis. We cover classical statistical models, penalized regression techniques, tree-based ensemble methods, kernel machines, Bayesian hierarchical models, and modern deep learning architectures, including recurrent neural networks, temporal convolutional networks, attention-based Transformers, neural ordinary differential equations, and generative models. We propose a unified taxonomy that organizes existing methods along two primary axes: the underlying mathematical framework and the analytical objective. For each category, we present detailed mathematical formulations, discuss key theoretical properties, examine computational considerations, and summarize representative reported applications drawn from the published literature. To increase the practical value of this review, we provide a cross-cutting comparison of method families against five key challenges (within-subject correlation, irregular sampling, missing data, high dimensionality, and scalability) and offer concrete guidance on method selection according to sample size, dimensionality, and analytical objective. Finally, we critically evaluate the strengths and limitations of these approaches, with particular emphasis on interpretability, scalability, handling of missing data, robustness to covariance misspecification, and uncertainty quantification. Full article