Quadratic Model Research Articles (Page 1)

Long-term prediction of radiation-induced optic neuropathy: A mixed-effects analysis of visual field kinetics following proton therapy.

Re-investigation of the relevant factors affecting quantitative precipitation of wine polysaccharides: A GC-MS and HRSEC-RI characterization study using central composite design and response surface methodology.

A graph-theoretical approach to characterizing anaesthetic agents using topological indices and QSPR models.

Guaranteed stable quadratic models and their applications in SINDy and operator inference

U-shaped association between post-stroke cognitive impairment and high-density lipoprotein cholesterol at the acute period of stroke.

Infectious diseases caused by pathogenic microorganisms are a significant global threat, affecting millions of people. The aim of this study was optimizing the eco-friendly synthesis of silver nanoparticles (AgNPs) using Discopodium Penninervium Hochst leaf extract via a response surface methodology approach. The ANOVA results revealed that the quadratic model (p < 0.0001) was sufficient to achieve the most precise prediction of particle size (R2 = 0.995). A minimum AgNPs size of 21.65nm, was achieved under optimal conditions. The ultraviolet-visible (UV-vis) UV-vs spectroscopy of the synthesized AgNPs revealed a strong absorption peak at 402nm. The X-ray diffraction (XRD) analysis confirmed a face-centered cubic crystal structure with average crystallite size of 17.60nm. Dynamic light scattering (DLS) value (38.62nm) displays AgNPs was in the nanoscale whereas the zeta potential value (-14.20 mV) indicates its stability. The scanning electron microscopy (SEM) image showed spherical in shape and exhibited an average particle size of 2μm with some agglomeration. Fourier transform infrared spectroscopy (FTIR) spectra depicted the presence of functional groups from plant extract, which used as a capping agent and bioreduction process. thermogravimetric analysis (TGA) measurement suggested that AgNPs exhibit good thermal stability. The AgNPs exhibited good antimicrobial activities against Gram-negative (Escherichia coli) and Gram-positive (Staphylococcus aureus) bacteria, as well as fungus (Candida albicans) with corresponding inhibition zones of 25mm (mm), 21mm, and 20mm, respectively. The phytochemical screening revealed the presence of bioactive components such as phenols, alkaloids, flavonoids, tannins, steroids, and terpenoids. This study presented rapid, simple, and eco-friendly methods for synthesizing AgNPs with potential antimicrobial applications.

Abstract Road safety is strongly influenced by pavement friction, which governs tire traction and braking efficiency, especially in wet conditions. Conventional friction evaluation methods, while widely used, are time-consuming, costly, and often lack generalizability. This study investigates advanced machine learning (ML) techniques for predicting the friction number of continuously reinforced concrete pavement (CRCP) using data from the Long-Term Pavement Performance (LTPP) database. The dataset comprised 170 observations from 33 CRCP sections, representing different climatic and structural conditions. A 5-fold cross-validation approach was employed within MATLAB’s Regression Learner App to ensure robust and unbiased model evaluation. Six ML models were examined, including regression trees, support vector machines (SVM), ensemble methods, Gaussian Process Regression (GPR), artificial neural networks (ANN), and kernel-based approaches. Results show that the Rational Quadratic GPR model achieved the highest predictive accuracy (R² = 0.70, RMSE = 5.29, MAE = 3.90), outperforming other conventional machine learning algorithms used for comparison. Feature importance and sensitivity analyses revealed that pavement age, traffic loads, thickness, temperature, and humidity are the most influential factors affecting surface friction. The findings provide practical insights for data-driven pavement management, offering transportation agencies reliable tools to enhance safety, optimize maintenance strategies, and extend pavement service life. Although the dataset size is moderate, the consistent cross-validation results indicate strong model reliability; future studies using larger and more diverse datasets are recommended to further validate the model’s generalizability.

To evaluate a deep learning (DL)-based approach for predicting air-bone gap (ABG) from tympanic membrane (TM) perforation images using automated segmentation and feature extraction, addressing the limitations of audiometry availability in certain populations or settings. Prospective, cross-sectional diagnostic study. Tertiary academic medical center. A total of 1239 otoscopic images were collected between January 2019 and May 2023. Of these, 1014 intact TM images and 150 perforated TM images were used for model development and validation, and 75 intraoperative perforated images were reserved for independent testing. A Mask region-based convolutional neural network (Mask R-CNN) model was trained to segment TM and perforation areas. Segmentation performance was evaluated using class pixel accuracy (CPA), intersection over union (IoU), and Dice coefficient. Quantitative features-including perforation ratio and spatial metrics-were extracted to predict ABG using theoretical and quadratic regression models. Model performance was assessed using R², root mean square error (RMSE), and the proportion of predictions within 10 dB of measured ABG. TM segmentation achieved CPA, IoU, and Dice scores of 0.794, 0.702, and 0.875; perforation segmentation yielded scores of 0.824, 0.729, and 0.894. ABG prediction showed R² values of 0.433 (theoretical) and 0.516 (quadratic), with RMSEs of 6.15 and 5.68 dB. Deep learning (DL)-assisted models achieved accuracy of 83% and 86%, comparable to manual annotation. DL-based analysis of TM images enables accurate ABG prediction and may provide a scalable tool to support assessment of conductive hearing loss in environments without access to audiometry.

This study presents a multi-temporal analysis of displacement data from Sentinel-1 Synthetic Aperture Radar data at Hurst Castle with datasets sourced from the European Ground Motion Service, and temperature records from Ventnor Park and Otterbourne, with datasets sourced from the CEDA archive. To reduce speckle noise inherent in Synthetic Aperture Radar time series, three speckle filtering techniques, Boxcar, Lee, and Frost, were applied. The filtered displacement and temperature data were modelled using a range of mathematical functions, linear, quadratic, sinusoidal, step function, phenomenological, exponential, Lagrangian, and higher-order polynomial models. Model performance was evaluated using a comprehensive set of error metrics, including Root Mean Squared Error, Least Mean Squares, Sum of Squared Errors, Akaike Information Criterion, and Bayesian Information Criterion. Further regression analysis involved Median Absolute Error, Mean Absolute Percentage Error, Symmetric Mean Absolute Percentage Error, coefficient of determination, adjusted coefficient of determination, and the Durbin–Watson statistic to assess autocorrelation in residuals. The best fitting models were determined based on the coefficient of determination and Durbin– Watson values to evaluate the robustness of model selection across different filters and data sources. The study underscores the importance of integrating displacement and temperature time series modelling for environmental monitoring and structural risk assessment at heritage sites.

This paper introduces a singular distance function rs in terms of a symmetric non-negative metric tensor S. If S satisfies a quadratic matrix equation involving a parameter β, then for the Laplace equation rsβ is a non-singular generalized radial basis function solution if 2 &gt; β &gt; 0, and a weaker singularity fundamental solution if −1 &lt; β &lt; 0. With a unit vector as a medium to express S, we can derive the metric tensor in closed form and prove that S is a singular projection operator. For the anisotropic Laplace equation, the corresponding closed-form representation of S is also derived. The concept of non-singular generalized radial basis function solution for the Laplace-type equations is novel and useful, which has not yet appeared in the literature. In addition, a logarithmic type method of fundamental solutions is developed for the anisotropic Laplace equation. Owing to non-singularity and weaker singularity of the bases of solutions, numerical experiments verify the accuracy and efficiency of the proposed methods.

A study of the linear quadratic (LQ) control problem on a finite-time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop representation of the unique optimal control, along with the derivation of a related coupled system of three quadratic (operator) equations which was shown to be well posed. Notably, in the absence of memory, the above elements – namely, formula and system – reduce to the known feedback formula and single differential Riccati equation, respectively. In this work, we take the next natural step and prove the said results for a class of evolutions where the control operator is no longer bounded. These findings appear to be the first ones of their kind; furthermore, they extend the classical theory of the LQ problem and Riccati equations for parabolic partial differential equations.

This paper introduces a modified version of the cyclic subgradient projection (CSP) method using blocks. Within each block, the CSP method is applied. Subsequently, an operator based on the subgradients derived from the CSP step is introduced. Optimal weights for this operator are determined by solving a small quadratic equation. These weights facilitate the acceleration of the process. Following this, the introduced operators for each block are utilized to address convex feasibility problems. We provide a comprehensive convergence analysis. We showcase the effectiveness of our approach through examples drawn from classical scenarios and tomographic imaging applications and conduct comparative evaluations with other pertinent methods.

In the present study, an intergeneric cross was conducted between Opsariichthys bidens (♀) and Zacco acanthogenys (♂);the morphological characteristics of the hybrid offspring generation (F1) were observed and recorded at various periods of the development of the embryos and young larvae; and comparative analyses of the external morphological data of the adult fish and the parameters of their external shape framework were carried out. Results demonstrated that hybrid fertilized eggs maintained at (25 ± 1)°C water temperature completed hatching within 42 h 47 min post-fertilization, requiring an accumulated temperature of 1026.72°C·h. Embryonic development consisted of 7 distinct phases subdivided into 28 developmental stages. Newly hatched larvae exhibited a mean total length (TL) of 5.23 ± 0.06 mm, with complete yolk-sac absorption occurring by 7 days post-hatching (dph). Early developmental growth patterns (0-30 dph) conformed to the quadratic equation: y = 0.02096x2 + 0.23443x + 5.6249 (R2 = 0.9559), where y represents TL (mm) and x denotes days post-hatching. Morphological analysis revealed that meristic traits of hybrid progeny predominantly aligned with the maternal lineage, whereas morphometric ratios exhibited intermediate values between parental species. Principal component analysis and cluster analysis of morphometric proportions and framework parameters demonstrated closer similarity to maternal characteristics. Linear discriminant analysis confirmed distinct phenotypic differentiation among the three groups (parental species and hybrids).

This work introduces and examines a new probability distribution from the G-rank-mapped transmuted Fréchet-Weibull (G-RTFW) family, using both quadratic and cubic models. The Quadratic Rank Transmuted Fréchet-Weibull (QRTFW) and Cubic Rank Transmuted Fréchet-Weibull (CRTFW) distributions are specifically investigated, with the current study focused solely on the CRTFW model. We calculated and investigated a wide range of statistical and mathematical aspects of the CRTFW distribution, including its moments, moment generating function, characteristic function, quantile function, mode, random variate generation, hazard rate function, entropy, and order statistics. The suggested model is highly adaptable, capable of simulating both unimodal and bimodal behaviors, as well as tolerating symmetric and asymmetric data structures with variable degrees of kurtosis. The maximum likelihood method was used for parameter estimation, and a full Monte Carlo simulation study was carried out to assess the estimators' performance and efficiency under various circumstances. The simulation results showed that the estimators performed effectively, with bias and mean square error reducing as the sample size increased. To demonstrate the CRTFW distribution's practical application, two real-world sustainability-related datasets were examined. The CRTFW model outperformed numerous well-known lifetime and reliability distributions in terms of flexibility and goodness-of-fit, emphasizing its use for both theoretical and applied data modeling.

This study implements Bayesian along with non-Bayesian approaches to estimate the parameters of the three-parameter quadratic hazard rate distribution using hybrid Type-II censoring. The model expands upon linear hazard rate, exponential, and Rayleigh distributions. In the non-Bayesian framework, point estimates and survival and hazard functions are calculated using maximum likelihood estimation (MLE). Asymptotic confidence intervals are derived, with a focus on the delta method. By applying independent normal and gamma priors, Bayesian inference produces point estimates and credible intervals using different symmetric and asymmetric loss functions. The analytical intractability of posterior distributions makes Markov chain Monte Carlo (MCMC) methods necessary for sampling purposes. The evaluation of point and interval estimates depends on root mean squared error (RMSE) in combination with mean relative absolute bias (MRAB), average confidence interval length (AL), and coverage probability (CP). The performance evaluation through different sample sizes and censoring schemes is conducted by simulation studies, while real-world data from COVID-19 mortality demonstrates the practical implementation of methods. Graphical and numerical analyses confirm the existence and uniqueness of the estimates. Results indicate that Bayesian methods deliver superior accuracy and more robust estimates than their non-Bayesian counterparts for survival analysis purposes in clinical and medical research.

Polyphenols have gained significant attention in recent decades due to their protective role against cancer, diabetes, obesity, osteoporosis, neurodegenerative, and cardiovascular diseases. This study explored the influence of radiation time, microwave power, and sample-to-solvent ratio on the microwave-assisted extraction of polyphenols from Pithecellobium dulce fruit peels. Extraction efficiency, antioxidant activity, and anti-cholesterol activity were optimised using both response surface methodology (RSM) and artificial neural networks combined with a genetic algorithm (ANN-GA). The ANN-GA model exhibited higher predictive accuracy (R2 = 0.9805–0.9813) and lower statistical error compared to quadratic RSM models (R2 = 0.9566–0.9767). Under optimised conditions, ANN-GA yielded 244.35 mg/g total polyphenols, 92.51% antioxidant activity, and 73.96% anti-cholesterol activity, outperforming RSM (242.35 mg/g, 92.18%, and 73.26%, respectively). These findings demonstrate the scientific novelty of ANN-GA as a more robust and reliable tool than RSM for process optimisation. Moreover, the study highlights the practical application of utilizing P. dulce fruit peels as a low-cost, natural source of health-promoting bioactives. Importantly, this work presents a broader impact by providing a sustainable strategy for waste valorisation into nutraceutical and pharmaceutical products.

This study delves into the concept of primitive Eisenstein triples, defined as positive integer solutions $(a, b, c)$ to the quadratic equation $a^2 - ab + b^2 = c^2$, subject to the condition $a&lt;c&lt;b$ and $\gcd(a, b, c) = 1$. We classify these triples according to the prime factorization of the integer $c$, elucidating how their existence is intricately linked to specific congruence conditions imposed on the prime {divisors} of $c$. Furthermore, we establish a bijective correspondence between these triples and a certain subset of the unit circle. This correspondence enables a comprehensive enumeration of the triples and precisely characterizes the conditions under which such solutions exist.

One well-known process detection tool that is sensitive to even little shift changes in the process is the Double Exponentially Weighted Moving Average (DEWMA) control chart. The present study aims to provide exact average run length (ARL) on the DEWMA chart under the data that is underlying the quadratic trend autoregressive (AR) model. At that point, the computed ARL via the numerical integral equation (NIE) technique was compared in terms of accuracy to the exact one that was developed by using the percentage accuracy (%Acc). And then, the computational times of both were also compared. The results revealed that the ARL results of exact ARL and ARL via the NIE method show hardly any difference in terms of accuracy, but exact ARL outperformed in terms of computational times that were computed instantly, whereas the other way spent approximately 2-3 seconds computing. Thereafter, the proposed ARL operating on the DEWMA chart was compared to the CUSUM and EEWMA charts. It was found to be more effective in terms of detection performance. Especially when there are little shift changes in the process. The run length formulas, which are the standard deviation run length (SDRL) and the median run length (MRL), were measures of sensitivity evaluation and were used to verify their capability. The sensitivity of detecting changes of exact ARL running on the DEWMA chart was illustrated by the real data utilized in fields of economics about natural gas importing in Thailand (Unit: 100 MMSCFD at heat value of natural gas 1,000 BTU/SCF). Apparently, the exact ARL of the DEWMA chart is an excellent choice to detect small shift changes under this scenario, which represents properties as a quadratic trend AR model.

In the present study, we examine the relationship among sovereign yields, temperature and precipitation using a large monthly panel data set, which consists of 20 eurozone members, over the period 1980M1–2023M4. To account for possible asymmetries along the distribution of the climate variables, we assume a quadratic modelling specification and apply various mean panel estimation techniques of heterogeneous coefficients. In the next step, to consider possible non-linearities in the distribution of the dependent variables (sovereign yields), we apply the quantile via moments methodology of Machado and Santos Silva, which accounts for possible cross-sectional dependence and slope heterogeneity. We contribute to the existing literature in two main ways. First, we apply a quantile methodology that provides a more in-depth analysis of the climate effects along the distribution of the sovereign yields, especially in the presence of non-normally distributed data. Second, we find that climate change, as proxied by higher temperatures or lower precipitation (drought), will increase the sovereign risk of all countries, but the magnitude of the impact will be higher for countries that are already characterised by higher sovereign risk levels and/or face extreme weather conditions (hotter countries and/or countries with low levels of precipitation). JEL Codes: C23, G15, H63, Q51, Q54

Latent growth curve (LGC) models, implemented through structural equation modeling, are widely used to analyze developmental and learning trajectories. Model selection in LGC often relies on goodness-of-fit indices (e.g., χ², Akaike information criterion, and root-mean-square error of approximation), but these metrics fail to assess the temporal constancy, or stability of parameters, an important aspect when forecasting longitudinal data. Addressing this gap, we propose a novel parameter constancy test (PCT) tailored for LGC models. This test evaluates internal constancy, identifies potential breakpoints, helps determine the minimal number of measurement waves needed for reliable modeling, and is also useful for comparing different explanatory models of the analyzed data. To validate this approach, we applied PCT to real-world data, comparing the widely used quadratic function model with the negative exponential model and other nonlinear functions. The results reveal that the negative exponential model, unlike the quadratic function, consistently exhibits parameter constancy even with fewer sampling waves, making it particularly suitable for longitudinal analysis. Additionally, PCT highlights how inappropriate model selection or instability may lead to misinterpretations, particularly in evaluating interventions or extrapolating beyond observed time frames. Our findings emphasize the dual importance of statistical fit and parameter constancy in selecting LGC models. By integrating PCT into standard practice, researchers can better ensure model consistency, optimize resource allocation, and avoid erroneous conclusions in developmental and learning studies. (PsycInfo Database Record (c) 2025 APA, all rights reserved).