Search Results (1,398)

Shear-wave velocity (Vs) estimation from the Standard Penetration Test (SPT) can support preliminary site characterization when direct geophysical data are limited, but empirical correlations require validation schemes that reflect transferability between sites. This study evaluates Vs prediction using an interval-paired dataset derived from geotechnical investigations of school foundations in Piura, Peru. Its novelty lies in comparing the raw SPT blow count (NSPT) and the overburden- and energy-corrected SPT blow count ((N1)60) on the same strict common sample, using grouped cross-validation by school, thereby emphasizing transferability across sites rather than only internal fit. Five predictive scenarios were tested, from penetration-only formulations to geotechnically enriched specifications. The lowest grouped out-of-fold error among the evaluated models was obtained by a generalized power baseline using (N1)60 and the integral geotechnical predictor set, yielding root mean square error (RMSE) = 80.48 m/s, mean absolute error (MAE) = 60.15 m/s, and coefficient of determination (R2) = 0.338. This moderate R2 indicates limited standalone predictive capacity under transfer to unseen schools; therefore, the model is interpreted as a preliminary transfer-oriented correlation rather than as a substitute for direct Vs measurements or as an independent design equation. In the complementary full-data analysis, the strongest descriptive fit was obtained with Hist Gradient Boosting, whereas the strongest explicit equation corresponded to the log-semi baseline. Overall, the findings show that externally validated transferability, descriptive full-data fit, and equation-based interpretability represent different analytical roles in Vs-SPT modeling. Full article

This study develops and analyzes a four-state nonlinear policy–feedback dynamical system that couples a system stressor, an accumulated burden, a signed mitigation–response variable, and a signed policy-pressure variable. The proposed model represents governance response through a smooth threshold-centered feedback mechanism, in which the policy-pressure dynamics depend continuously on the deviation of the stressor from a prescribed reference threshold. Unlike reduced-order formulations with purely exogenous interventions, the present framework generates endogenous interactions among stress accumulation, burden evolution, mitigation response, and policy adjustment. The qualitative analysis establishes local well-posedness in the admissible phase domain, conditional nonnegativity of the accumulated burden, and boundedness of trajectories on admissible intervals. An autonomous effective system is then derived to characterize quasi-stationary mean behavior of the periodically forced dynamics. For this effective system, local stability is investigated using Gershgorin estimates and Routh–Hurwitz criteria, leading to explicit analytical conditions for local asymptotic stability and a critical policy-responsiveness threshold associated with possible Hopf-type oscillatory transitions. The analysis highlights the stabilizing role of mitigation damping and cubic saturation in regulating the feedback loop. To approximate the nonlinear system, a Physics-Informed Neural Network (PINN) surrogate is constructed by embedding the governing equations into a differentiable residual loss while enforcing the initial conditions analytically. The accumulated burden is represented through an admissible neural-network ansatz to preserve the well-definedness of the logarithmic coupling term, while the mitigation–response and policy-pressure variables remain signed in accordance with the model formulation. Numerical validation against reference ode45 solutions across two governance regimes shows maximum absolute errors of order ${10}^{-3}$, indicating that the PINN provides a reliable differentiable surrogate for the coupled policy–feedback dynamics. The resulting framework offers a foundation for future inverse modeling, parameter estimation, and data-assimilation studies involving policy responsiveness, intervention thresholds, and burden- suppression effects. Full article

Post-fire rehabilitation structures are widely used in Mediterranean burned landscapes to reduce runoff and sediment transfer, yet their ecological associations with early vegetation recovery remain insufficiently documented. This observational study assessed vascular plant composition, species richness, vegetation cover, plant density, aboveground biomass, and soil properties across log barriers, wattles, and log dams in the burned landscape of Ancient Olympia, western Greece. The study area belongs to the humid climatic class of the United Nations Environment Programme (UNEP) aridity framework based on the Thornthwaite aridity index, providing a comparatively wetter Mediterranean post-fire context. Paired depositional and eroded microsites in operationally restored post-fire areas were monitored in 2022 and 2023. The sampling design comprised nine plots and 18 microsites (n = 9 plots, 18 microsites). Generalized estimating equations (GEE), change-score models, principal component analysis (PCA) and permutational multivariate analysis of variance (PERMANOVA) were performed to examine associations of monitoring year, microsite condition and rehabilitation structure type with soil and vegetation patterns. A total of 27 vascular plant species belonging to 16 families were recorded. The average vegetation cover increased from 39.17 ± 21.44% in 2022 to 75.11 ± 12.90% in 2023. Model-based marginal estimates with 95% confidence intervals indicated a large positive increase in vegetation cover over this period. Further, rapid early recovery was indicated by large increases in species richness, plant density and biomass. Depositional microsites were associated with stronger recovery signals than eroded ones, characterized by a larger increase in vegetation cover, density, biomass and species richness. Among rehabilitation structures, log dams showed the highest cumulative floristic richness and a broader observed floristic spectrum, although the species-level contingency analysis provided only marginal evidence for structure-associated differences in floristic composition. Changes in selected soil properties including total nitrogen (total N), ammonium nitrogen (NH4-N), nitrate nitrogen (NO3-N), pH, electrical conductivity (EC), and exchangeable calcium (Ca), magnesium (Mg), and potassium (K), were detected between 2022 and 2023; the multivariate soil pattern was driven primarily by mineral nitrogen, pH, and EC. These findings suggest that, under operational post-fire restoration conditions, rehabilitation structures are associated not only with erosion-control functions but also with microsite differentiation that may shape early plant establishment and biodiversity recovery in Mediterranean burned landscapes. Full article

Individual tree modeling (ITM) is an effective system for thinned stands, especially in teak (Tectona grandis Linn F.) plantations, allowing the estimation of individual-tree-specific variables. Heartwood diameter and volume have high added value and can be estimated in living trees. Therefore, we developed an ITM system for clonal teak stands capable of projecting technical intervention ages and quantifying heartwood production throughout the rotation in the Eastern Brazilian Amazon. The system included equations for total tree height, site index, and taper of both stem and heartwood, with volumes obtained by integrating the respective taper equations. Future diameters and heights were projected using models based on the algebraic difference approach (ADA) and the generalized algebraic difference approach (GADA). Ages of technical intervention were defined by the maximum mean annual increment in volume with bark. The Lundqvist-Korf-ADA base model was the most accurate in estimating future trees’ diameters and heights. The inclusion of the number of trees as a covariate to represent thinning had a significant and positive impact on variable projections. Optimal technical rotations ranged from 17.1 to 21.3 years, considering volume with bark. An increase in the proportion of heartwood was observed, reaching 78% of the diameter and 53% of the volume at rotation ages. The modeling system developed in the present study enables the estimation of technical rotation ages and the quantification of heartwood production throughout the rotation, which provides reliable information for silvicultural planning and decision-making in the management of clonal teak stands. Full article

Background: Pancreatic cancer is characterized by increasing incidence and high mortality in Poland and worldwide. The aim of this study was to assess the relationship between selected risk factors and the age-standardized incidence rate of pancreatic cancer at the voivodeship level in Poland, and to evaluate the accuracy of a prediction model. Methods: Age-standardized incidence rate data for 16 Polish voivodeships in 2011–2023 were obtained from the Polish National Cancer Registry. The risk factor burden for 2011–2019, expressed as disability-adjusted life years (DALYs) per 100,000 population, was obtained from the System Analysis and Implementation Database of the Polish Ministry of Health. A generalized estimating equation model was constructed to predict the age-standardized incidence rate, with multicollinearity addressed using variance inflation factor analysis. Predictions for 2020–2023 were validated against observed data, and forecasts for 2024–2030 were subsequently calculated. Results: The number of new pancreatic cancer cases in Poland increased in eight out of 16 voivodeships. The highest burden was recorded in the Masovian, Subcarpathian, Świętokrzyskie and Greater Poland voivodeships. Air pollution was positively associated with pancreatic cancer incidence. Predictions for 2020–2023 showed satisfactory agreement with observed data, with the largest discrepancy being equal to 4.1 in terms of the age-standardized incidence rate. Based on the models, the incidence of pancreatic cancer was projected for all of 16 voivodeships through to 2030. Conclusions: Air pollution is associated with the regional burden of pancreatic cancer in Poland. The generalized estimating equation prediction approach demonstrated acceptable accuracy and can support monitoring and public health planning at the voivodeship level. Full article

Prediction-powered inference (PPI) studies statistical inference when a small set of gold-standard labels is combined with a much larger pool of machine-generated predictions. The central difficulty is that predictions can substantially reduce variance, yet naive substitution of predictions for outcomes generally changes the estimand and invalidates uncertainty quantification. The basic remedy in the literature is rectification: predictions are used to construct a low-variance plug-in term, while labeled observations are used to estimate and correct the inferential distortion induced by prediction substitution. We review PPI as a family of rectified plug-in procedures for hybrid measurement regimes. The survey develops a common statistical template based on mean estimation, estimating equations, and loss-based formulations, and then uses that template to compare modern variants according to the component they modify: the rectification engine, the label-acquisition design, predictor dependence, or the validity target. We also position PPI relative to model-assisted survey sampling, post-prediction correction, surrogate-outcome methods, classical measurement-error models, and semiparametric augmentation. Throughout, we distinguish questions of validity from questions of efficiency, robustness, and computation, and we emphasize that valid use of prediction assistance does not require a correct predictive model but does depend on how rectification, dependence, and sampling design are handled. The survey closes with recurrent failure modes, practical reporting recommendations, and open problems in finite-sample theory, heterogeneous proxy quality, and protocol-aware deployment. Full article

Background/Objectives: Melanoma is a major and growing public health concern in Poland, with a five-year survival around 60–70%. While UV radiation and genetic susceptibility are well-known risk factors, lifestyle and environmental exposures may also contribute. This study examined how selected risk factors relate to one-year melanoma prevalence across Poland’s 16 voivodeships and assessed whether these factors can support short-term prediction. Methods: Annual melanoma prevalence for 2011–2021 was obtained from the Polish National Cancer Registry, and voivodeship-level estimates of metabolic risk factors, physical inactivity, alcohol consumption, smoking, high BMI, air pollution, water pollution and limited data on UV exposure were used to build a general estimating equations model. Model predictions for 2020–2021 were compared with observed data, and forecasts were generated through 2030. Results: Melanoma cases increased in every voivodeship between 2011 and 2021. Metabolic risk factors, high BMI, low physical activity and smoking were associated with higher melanoma prevalence. When other factors were considered, air pollution showed an inverse association, suggesting complex relationships that warrant further analysis. Forecasts indicated increasing prevalence in all of 16 voivodeships through 2030, although three regions showed large prediction errors for 2020–2021. A key limitation was the lack of sufficient UV exposure data. Conclusions: The findings support further evaluation of public health actions targeting the reduction of unhealthy lifestyle regarding diet, low physical activity, and smoking to help slow the projected rise in melanoma. Full article

Neural ordinary differential equations (NODEs) have emerged as an effective methodology in artificial neural networks (ANNs) and deep learning for capturing unknown or unmodeled dynamics in compartmental and dynamical mathematical models arising from real-life applications, particularly under limited-data conditions, through learned data-driven corrections. Nevertheless, accurate one-step prediction errors do not necessarily guarantee reliable long-horizon rollouts. In this work, we study residual Neural ODE models of the form $\widehat{f}=f+h_{\theta }$ and derive a priori rollout-error estimates showing that long-time prediction behavior is generated by the incremental stability structure of the learned dynamics. Contracting regimes produce uniformly controlled rollout errors, whereas weakly contractive or expansive regimes can amplify persistent approximation errors over long time horizons. The analysis is illustrated on a flow-reactor chemical reaction network (CRN), where the washout parameter controls rollout reliability on the data-supported region. Numerical experiments further demonstrate that models with comparable empirical one-step prediction losses may exhibit substantially different multi-step behaviors. Rollout-error analysis and projected-gradient-descent (PGD) sensitivity directions additionally reveal that locally expansive regions align with worst-case perturbation amplification. Full article

The rapid growth of the sharing economy has improved resource utilization in car-sharing, yet it has also sharpened market competition and diversified user demand. A persistent obstacle is the low coordination efficiency between asset-heavy operating companies and traffic-driven platforms, whose misaligned objectives waste social resources. This paper uses differential game theory to analyze their dynamic coordination strategies and benefit allocation mechanisms. The Nerlove–Arrow model captures the evolution of brand goodwill, while the company’s decisions on station layout, vehicle dispatch, and pricing, together with the platform’s advertising investment, form the core decision variables in a two-party game framework linking the asset side and the traffic side. Compared with the non-cooperative Nash equilibrium, the cooperative mode removes the double marginalization effect, strengthens the investment incentives of both parties, and raises the system’s steady-state goodwill and total profit, achieving a Pareto improvement. To ground the cooperative framework in rigorous theory, we supply a verification theorem confirming that the linear candidate value functions satisfy the Hamilton–Jacobi–Bellman equations over the entire admissible state space. A formal proof of instantaneous rationality ensures that neither party falls into a cooperation trap on the horizon $[0,T]$, and the asymptotic stability of the steady-state goodwill trajectory is established. We further endogenize the revenue-sharing coefficient through a generalized Nash bargaining model that admits asymmetric bargaining structures, and introduce a Stackelberg leadership benchmark as a third comparative regime. Sensitivity analyses with respect to the discount rate and user heterogeneity confirm the robustness of the findings. A dedicated discussion section bridges the gap between idealized parameterization and data-driven calibration, describing practical pathways via A/B testing, user churn metrics, and econometric estimation of demand parameters. The results offer a scientific decision-making reference for strategic cooperation in the car-sharing industry. Full article

Background/Objectives: Delayed bone healing remains a relevant complication after polytrauma, where fracture repair occurs in the setting of systemic inflammation and repeated physiologic stress. This study evaluated whether serial changes in interleukin-6 (IL-6), C-reactive protein (CRP), and fibrinogen are associated with delayed union in polytrauma patients with long-bone fractures. Methods: We performed an exploratory retrospective cohort study including 115 adult polytrauma patients with long-bone fractures treated at a single tertiary trauma center between 2 January 2022 and 14 December 2024. Serum IL-6, CRP, and fibrinogen were recorded at 24 h, 72 h, 1 week, 2 weeks, and 4 weeks after injury. IL-6 was measured in the institutional clinical laboratory using routine immunoassay methods, whereas CRP and fibrinogen were measured using standard hospital analytical methods, including an immunoturbidimetric assay for CRP and the Clauss clotting method for fibrinogen. Radiographic healing was assessed at 6, 12, and 24 weeks using an mRUST-based healing score. The primary endpoint was clinician-assigned delayed union at 24 weeks; nonunion at 9 months was assessed secondarily. Complete-case multivariable logistic regression was performed in 86 patients, and exploratory longitudinal biomarker analyses used generalized estimating equations. Results: Delayed union at 24 weeks occurred in 39/115 patients (33.9%), while nonunion at 9 months occurred in 7/115 patients (6.1%). Patients with delayed union had longer time to definitive fixation (35.3 ± 10.2 h vs. 29.0 ± 14.0 h; p = 0.003) and more frequent shock on admission (43.6% vs. 23.7%; p = 0.047). IL-6 was higher in the delayed-union group at 1 week (57.3 ± 30.3 vs. 46.5 ± 29.2 pg/mL; p = 0.043) and 4 weeks (21.2 ± 11.6 vs. 17.1 ± 10.3 pg/mL; p = 0.022), whereas CRP was markedly higher at 4 weeks (29.4 ± 14.2 vs. 16.3 ± 10.6 mg/L; p < 0.001). After false-discovery-rate correction, only CRP at 4 weeks remained significant among serial biomarker comparisons. In multivariable analysis of 86 complete cases, CRP at 4 weeks remained independently associated with delayed union (adjusted OR 2.16 per 10 mg/L, 95% CI 1.36–3.43; p = 0.001). The model showed apparent discrimination with an AUC of 0.80 and acceptable calibration (Hosmer–Lemeshow p = 0.41). In sensitivity analysis excluding deep surgical-site infection cases, the association between CRP and delayed union persisted (adjusted OR 2.02 per 10 mg/L, 95% CI 1.26–3.26; p = 0.004). Conclusions: In this exploratory retrospective cohort of polytrauma patients with long-bone fractures, persistent post-traumatic CRP elevation at 4 weeks was associated with clinician-assigned delayed union, whereas IL-6 findings were weaker and exploratory. Because CRP is a nonspecific inflammatory marker, the observed association may reflect delayed healing, infection, reoperation, and/or persistent postoperative inflammatory burden. These data support association rather than validated prediction and require prospective validation with standardized outcome adjudication. Full article

This paper studies multiplication operators and their associated strongly continuous semigroups acting on variable exponent Lebesgue spaces. We study the abstract Cauchy problem $\dot{u}\left(t\right)=Au\left(t\right)$, $u\left(0\right)=u_0$, in the space $L^{p\left(x\right)}(0,\mathsf{\ell })$ with $\mathsf{\ell }>0$, where the generator A is given by the multiplication operator $A=M_q$. Using the modular ${\rho }_{p(·)}\left(u\right)={\int }_0^{\mathsf{\ell }}{\left|u\left(x\right)\right|}^{p\left(x\right)}dx$, we establish the fundamental properties of $M_q$, including ${\rho }_{p(·)}$-closedness, density of its domain, and boundedness criteria in terms of the essential range of q. We show that $M_q$ generates a strongly continuous semigroup ${\left(S\left(t\right)\right)}_{t\ge 0}$ given explicitly by $S\left(t\right)=e^{tA}=M_{e^{tq}}$, and we derive modular growth estimates for the semigroup. We also obtain a complete characterization of the spectrum and resolvent of A, showing that $\sigma \left(A\right)=q_{\mathrm{ess}}(0,\mathsf{\ell })$ and $R(\lambda ,A)={(\lambda I-A)}^{-1}=M_{1/(\lambda -q)}$ for $\lambda \notin \sigma \left(A\right)$. The spectral mapping behavior of the associated semigroup is also analyzed, highlighting the validity of the weak spectral mapping theorem and the possible failure of the full spectral identity. As an application, we present a concrete example on $(0,4)$ involving a singular initial datum that does not belong to $L^2(0,4)$ but lies in $L^{p\left(x\right)}(0,4)$ due to a suitable spatial variation of the exponent. The corresponding evolution is explicitly given by $u(t,x)=e^{tq\left(x\right)}f\left(x\right)$ and remains well posed in $L^{p\left(x\right)}(0,4)$ for all $t\ge 0$. This shows that the variable exponent framework can accommodate singular behavior while preserving semigroup dynamics. These results show that multiplication operators provide an explicit model for semigroup theory in variable exponent spaces, connecting modular analysis with pointwise evolution equations. Full article

Background and Objectives: Anastomotic leakage (AL) remains one of the most feared complications following colorectal resection, yet the relationship between cumulative surgeon experience and AL risk remains inconclusive in the literature. Most available evidence originates from high-volume or specialized centers, with limited data from mid-volume Central and Eastern European settings. This study aimed to evaluate the association between cumulative surgeon experience, operative time, and AL risk in a selected sample of colorectal resections with primary anastomosis for both benign and malignant indications, excluding right colectomies, abdominoperineal resections, TaTME, Hartmann’s procedures, and stoma-protected anastomoses, within a single-center multi-surgeon setting over a seven-year period. Materials and Methods: This retrospective observational study included 315 consecutive adult patients who underwent left-sided or segmental colorectal resection with primary anastomosis for both benign and malignant indications (excluding right colectomy, abdominoperineal resection, TaTME, Hartmann’s procedure, and stoma-protected cases) at Békés County Central Hospital, Gyula, Hungary, between January 2018 and December 2024. AL was defined according to ISREC criteria, with only clinically relevant grade B or C leaks recorded as events. The main exposure was cumulative surgeon experience (log2-transformed). The primary analysis used a multivariable generalized estimating equation (GEE) model clustered by surgeon, adjusted for operative time, surgical approach, conversion, wound infection, and resected segment. Eight surgeons participated, with cumulative experience ranging from 50 to 600 cases. Results: Among the 315 patients included, the median age was 68 years, with a male predominance (61.0%); most cases involved malignant pathology (82.9%) and at least one comorbidity (73.3%). The rectosigmoid was the most frequently resected segment (49.8%), and an open approach was used in 58.7% of cases. The overall AL incidence was 7.94% (25/315), with a median onset at postoperative day 5. In the multivariable GEE model, cumulative surgeon experience was not significantly associated with AL risk (OR per doubling 1.12; 95% CI 0.73–1.72; p = 0.597), nor was operative time (OR per 10 min 1.03; p = 0.294). Wound infection was the only variable significantly associated with AL (OR 3.48; 95% CI 1.06–11.44; p = 0.042), although its temporal relationship with AL could not be established from the available data. AL rates by experience category were 8.9%, 7.5%, and 7.9% for surgeons with <100, 100–199, and ≥200 cases, respectively (p = 0.913). AL was associated with a significantly prolonged hospital stay (median 17 vs. 7 days, p < 0.001) regardless of surgical approach. Conclusions: Cumulative surgeon experience was not independently associated with AL risk in the selected sample of colorectal resections with primary anastomosis in this single-center, mid-volume setting. Wound infection emerged as the only variable significantly associated with AL, although its temporal relationship with AL could not be determined and several established confounders, including anastomotic height, BMI, ASA class, and emergency status, were unavailable for adjustment. Considerable inter-surgeon variability was observed irrespective of case volume. These findings highlight the complexity of AL risk and the need for prospective multicenter studies with comprehensive risk adjustment. Full article

The ski-jump spillway is an energy-dissipating structure that discharges extra water beyond the dam’s capacity. The scour process occurs below spillways due to the collision of the water jet with high energy. It is critical to acquire information on scour holes to improve the dam’s safety and related components. Machine learning (ML) techniques have successfully demonstrated their effectiveness for modeling scour in hydraulic engineering. The present research considers novel approaches of ML models for estimating the scour hole geometries below ski-jump bucket spillways. This study investigates the capability of two novel feature-engineering approaches, namely Stronger Variable Creator Machine (SVCM) and High Correlated Variables Creator Machine (HCVCM), along with Gene Expression Programming (GEP) and their hybrid forms (SVCM+GEP and HCVCM+GEP), which were employed to predict normalized scour depth, scour length, and scour width below ski-jump spillways. Statistical metrics, graphical analyses, the Rank Mean (RM) method, the cross-validation approach, and $U_{95}$ index were used for the evaluation and reliability assessment of the proposed ML models. The results showed that hybrid ML models consistently outperformed individual algorithms. The results indicated that the SVCM+GEP method with $\mathrm{R}\mathrm{M}=1.83$ and $1.50$ had the highest performance compared to other methods for the prediction of ${\displaystyle \frac{Ds}{Dw}}$ and ${\displaystyle \frac{L_s}{D_w}}$, respectively. In addition, the HCVCM+GEP method with $\mathrm{R}\mathrm{M}=1.33$ was the best model for the prediction of ${\displaystyle \frac{Ws}{Dw}}$. In comparison with the conventional regression-based equations and previously reported ML methods, the proposed hybrid approaches improved the prediction results. In addition, the cross-validation method confirmed the robustness and generalization capability of the suggested hybrid ML models. The superior performance of the hybrid models is attributed to their ability to capture complex nonlinear interactions among hydraulic and geometric variables. The developed SVCM/HCVCM+GEP models provide accurate approaches for predicting scour parameters in hydraulic structures. Full article

In our research, we developed a Distributed Relaxation Spectrum Delay Differential Equation (DRSDDE) model to simulate viscoelastic responses exhibited by materials with multiple-scale relaxation mechanisms and finite delay times. Our model expanded upon traditional integer-order viscoelastic models to include a continuum relaxation process using a log-time-space Gaussian distribution representing a continuum of relaxation processes, including a direct representation of the effect of delayed feedback via an explicit time delay term. Consequently, the resultant model can be viewed as a generalized Maxwell-type formulation where the viscoelastic behavior exhibits distributed relaxation dynamics and has finite signal propagation characteristics. We then used experimental data obtained from three representative materials: PDMS Sylgard 184, bovine brain white matter, and polyurethane foam to calibrate the model. Calibration was achieved by estimating model parameters through the use of Gauss-Legendre quadrature combined with non-linear optimization of the relaxation spectrum. The results indicate that the coefficients of determination for each of the materials exceeded $R^2>0.83$. Therefore, the proposed DRSDDE model outperformed the classical Zener model when simulating materials that exhibit a wide relaxation spectrum. The parameter values estimated for each of the examined materials provided additional insight into their physical behaviors. Specifically, the characteristic relaxation times for the studied materials were determined based upon ${\tau }_c= {10}^{\mu }$ ranging from about 63 s to 158 s. These results illustrate different dominant relaxation regimes for the investigated materials. Additionally, both characteristic equations and frequency domain analyses were utilized to study the stability and bifurcation properties of the DRSDDE model. A significant finding resulted from identifying a delay-insensitive stability regime for materials with $\tilde{K}< 1$ (as illustrated by bovine brain white matter). For materials with $\tilde{K} > 1$, the analysis revealed Hopf bifurcation results illustrating critical delay thresholds and frequencies for the onset of oscillations. Further, it was established that all calibrated delay values were significantly less than these threshold values. This indicates that all identified models functioned well below the oscillation thresholds at realistic delay times. Ultimately, the proposed DRSDDE model represents a physically intuitive, robust, and flexible method for modeling complex viscoelastic systems. Future research will involve investigating temperature-dependent effects, nonlinear bifurcations, and experimental validations of predicted oscillatory dynamics. 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