This paper presents a comprehensive investigation into an inverse problem associated with a time-fractional diffusion process described by the Erdelyi–Kober operator. The objective is to determine both the diffusion concentration and a spatially dependent source term by means of additional data prescribed at a specific time T. Unlike classical diffusion models, the use of a fractional-order derivative—with order ranging between 0 and 1—allows the system to capture memory effects and anomalous transport phenomena observed in heterogeneous media. Such models are especially relevant in physics, engineering, and biological systems, where diffusion is influenced by long-range interactions or non-local processes. To solve the inverse problem, the analytical method based on eigenfunction expansion is employed. This approach decomposes the solution space into orthogonal modes, each satisfying the required boundary conditions, and enables the reconstruction of unknown quantities from the over specified condition. This methodology not only facilitates explicit representation of the diffusion concentration and source term but also provides deeper insight into their structural behaviour. The study further establishes the existence and uniqueness of the solution, demonstrating that the mathematical formulation is well-posed and yields physically meaningful results. These findings offer theoretical support for the application of Erdelyi–Kober diffusion models in practical scenarios, where accurate reconstruction of system parameters is critical for prediction, control, and interpretation of complex diffusion processes.

Objective: Research on variable selection within clinical data analysis has predominantly emphasized algorithmic methods, while the potential contribution of domain experts has received limited attention. This study aimed to compare the performance of domain experts with filter-based algorithms for selecting variables used in predicting clinical outcomes. Materials and Methods: Five clinical datasets—related to bacterial survival, birthweight, breast cancer, diabetes, and myocardial infarction—were analyzed. Fifteen domain specialists were asked to rank predictor variables using a five-point Likert scale. The same variables were also ranked using four filter algorithms: chi-squared, Fisher score, Pearson’s correlation, and the varImp function. Variable subsets obtained through expert judgment and those generated by the algorithms were independently used to train and evaluate classification models for each dataset. Results: Classification accuracies were assessed and compared. Non-parametric statistical tests revealed no significant differences in the predictive performance of models based on variables selected by experts compared to those chosen by the algorithms. Conclusions: Variable selection performed by domain experts was comparable to that achieved through algorithmic techniques. The findings affirm the importance of human expertise and experiential knowledge in clinical predictive modelling, underscoring that such contributions should not be overlooked in favour of automated methods. Future research should explore the development of supportive, automated systems that incorporate clinical knowledge and experience to enable efficient and reliable variable selection.

De-noising serves as a crucial technique for removing visual aberrations in images and has been widely adopted in numerous scientific and industrial applications. The present study introduces a novel deep learning–driven Profound Memory Affiliated Neural Network (PMANN) designed specifically for de-noising aerial images used in disaster management. To enhance precision in noise suppression, the architecture is integrated with an Adaptive Dual Threshold Wavelet Transform (ADTWT), which optimizes the filtering mechanism for aerial photography. This framework demonstrates superior performance when compared with established noise removal approaches, including Convolutional Neural Networks (CNN), hybrid CNN combined with Long Short-Term Memory (CNN-LSTM), Weighted Nuclear Norm Minimization (WNNM), and De-noising CNN (DNCNN). Quantitative analysis reveals that the proposed PMANN achieves an improvement in Peak Signal-to-Noise Ratio (PSNR) of 0.24%, 0.086%, 0.643%, and 0.720%, respectively. Similarly, the Structural Similarity Index Measure (SSIM) increases by 0.59%, 0.382%, 0.037%, and 0.465% over the same benchmark methods. Furthermore, the Mean Squared Error (MSE) is reduced by 8.93%, 2.1457%, 0.316%, and 0.582% relative to CNN, CNN-LSTM, WNNM, and DNCNN techniques. Overall, the proposed PMANN architecture offers enhanced accuracy, improved perceptual quality, and more efficient noise suppression, making it a promising tool for reliable image enhancement in disaster management systems.

Although digital content marketing (DCM) has rapidly developed as a contemporary marketing tool, research on this subject remains limited. This study investigates how the influence of DCM, together with Social Impact Theory (SIT), can stimulate electronic word of mouth (e-WOM) and consumer engagement (CEng) within the food industry. A quantitative, applied research approach was adopted, and a structured questionnaire was used to collect data to describe the research variables and examine the relationships between them. The sample consisted of followers of three well-known food and confectionery brands that actively promote their products through Instagram. Data analysis was conducted using structural equation modelling (SEM) through LISREL software. The findings demonstrate that DCM has a significant positive effect on consumer responses, and that SIT mediates the relationship between DCM and both e-WOM and consumer engagement. The study further offers theoretical discussion and managerial implications for organizations seeking to optimize the strategic use of content marketing.

Background: Disruptions in physical appearance and increasing vulnerability to lifestyle-related diseases among children have become critical global health concerns. Childhood obesity contributes to long-term health complications and significantly increases susceptibility to serious metabolic and cardiovascular disorders, ultimately compromising overall well-being at an early age. Conclusion: An increase in Body Mass Index (BMI), driven by excessive body fat accumulation, is strongly associated with early age obesity (EAO). Both parental and child-related risk factors play a vital role in influencing early-onset obesity. Integrating technical data analysis with medical information provides potential avenues for future research, enabling early diagnosis and improved therapeutic strategies for managing childhood obesity. Method: A systematic online review was conducted to identify primary determinants contributing to EAO among children aged 0–5 years. The collected data were examined and compared using health-related data analytic approaches to understand patterns associated with obesity in early childhood. Result: Existing literature emphasizes a dominant association between early childhood obesity and parental factors. Among children aged 0–2 years, excess weight gain is significantly influenced by parental BMI, sedentary household lifestyle, and gestational weight gain (GWG). For children aged 3–5 years, both parental factors and child-specific behaviours demonstrate strong associations with obesity risk.

This study introduces a Huntsberger-type shrinkage estimator for the entropy function of the normal distribution. The proposed estimator is constructed using a test statistic that removes the arbitrariness typically associated with selecting a shrinkage factor. Risk expressions for the estimator are derived under the Linear Exponential (LINEX) loss function. The performance of the proposed estimator is then compared with the best existing estimator across varying degrees of asymmetry and different significance levels. Based on the relative risk criteria, the results demonstrate that the proposed estimator performs more efficiently than the existing estimator in estimating the entropy function.