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Auxiliary information is an essential component in the field of survey sampling since it enables precise estimation of population parameters like mean, variance, distribution function, and so on, which in turn guarantees the best possible outcomes. In order to estimate the population mean of a study variable, this study makes use of auxiliary information in a two-fold approach. Through a stratified random sampling scheme, we introduce a novel class of estimators that utilize auxiliary information and their corresponding ranks. By conducting a thorough evaluation based on metrics such as mean square error and percentage relative efficiency, these proposed estimators have been shown to be effective in the estimation process. Empirical validation is conducted using a real dataset sourced from the domain of real estate. Exploring the relationship between Assessed Value (X) and Sale Amount (Y) during a five-year period extending from 2017 to 2021 is the primary emphasis of the empirical validation process, which is carried out with the assistance of a real dataset of real estate data. Furthermore, in order to demonstrate that our suggested estimator is superior to conventional unbiased estimators, as well as traditional regression estimators and other estimators that have been considered in the literature, a full simulation analysis is carried out. Our proposed estimator appears to be the most effective choice after being subjected to a comparison study against a variety of preexisting approaches. The findings of this study not only make a significant contribution to the development of the methodology of survey sampling but also offer vital insights for predictive modeling within the real estate sector. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical study applied to Hepatitis B disease utilizing fractional calculus and numerical methods. We begin by discussing mathematical fundamentals, focusing on fractional calculus concepts and relevant numerical aspects for disease modeling. We then formulate the problem, describing a nonlinear fractional differential system that models hepatitis B virus (HBV) infection and its response to drug therapy. A detailed theoretical analysis explores system properties and biological implications. We provide a qualitative analysis of the model, discussing important dynamic behaviors such as stability and parameter sensitivity. Subsequently, numerical analysis is performed to validate the model and estimate unknown parameters from patient data. Our findings include significant insights into biological parameters and their impact on therapeutic response. We conclude that the proposed fractional-order model is effective, offering optimal therapeutic strategies for hepatitis B. [ABSTRACT FROM AUTHOR]

This article presents the current state and development directions of the tire industry. One of the main requirements that a tire must meet before it can leave the factory is achieving values of quantities describing uniformity at a defined level. Of particular importance areconicity and the components of the tire with the greatest impact on its value. This research is based on the possibility of using an ANN to meet contemporary challenges faced by tire manufacturers. In order to achieve a satisfactory level of prediction, we compared the use of a multi-layer perceptron and decision trees XGBoost, LightGbmRegression, and FastTreeRegression. Based on data analysis and similar examples from the literature, metrics were selected to evaluate the models' ability to solve regression problems in relation to the described problem. We selected the best possible solution, standing at the top of the features covered by the criterion analysis. The proposed solutions can be the basis for acquiring new knowledge and contributions in the field of the computational analysis of industrial data in tire production. These solutions are characterized by the required accuracy and efficiency for online work, and they also contribute to the creation of the best fit elements of complex systems (including computational models). The results of this study will contribute to reducing the volume of waste in the tire industry by eliminating defective tire parts in the early stages of the production process. [ABSTRACT FROM AUTHOR]

Auxiliary information is an essential component in the field of survey sampling since it enables precise estimation of population parameters like mean, variance, distribution function, and so on, which in turn guarantees the best possible outcomes. In order to estimate the population mean of a study variable, this study makes use of auxiliary information in a two-fold approach. Through a stratified random sampling scheme, we introduce a novel class of estimators that utilize auxiliary information and their corresponding ranks. By conducting a thorough evaluation based on metrics such as mean square error and percentage relative efficiency, these proposed estimators have been shown to be effective in the estimation process. Empirical validation is conducted using a real dataset sourced from the domain of real estate. Exploring the relationship between Assessed Value (X) and Sale Amount (Y) during a five-year period extending from 2017 to 2021 is the primary emphasis of the empirical validation process, which is carried out with the assistance of a real dataset of real estate data. Furthermore, in order to demonstrate that our suggested estimator is superior to conventional unbiased estimators, as well as traditional regression estimators and other estimators that have been considered in the literature, a full simulation analysis is carried out. Our proposed estimator appears to be the most effective choice after being subjected to a comparison study against a variety of preexisting approaches. The findings of this study not only make a significant contribution to the development of the methodology of survey sampling but also offer vital insights for predictive modeling within the real estate sector.

In this paper, a new mathematical model of Hepatitis B is studied to investigate the transmission dynamics of the Hepatitis B virus (HBV). Many diseases can start from the womb and find us humans throughout our lives. These diseases are specific abnormal conditions that negatively affect the structure or function of all or part of an organism and do not suddenly occur in any region due to external injury. In this study, we focus on HBV, and we state the graphics, interpretations, and detailed information about the disease and the newly established mathematical model of the disease. A fractional order differential equation system with a memory effect is used to model anomalous processes and to understand the effect of past infection events on the future spread dynamics of the system. In the model, susceptible, latent, acute, carrier, and recovered populations are taken into account by considering vertical transmission, which provides information about the inter-generational course of the disease. However, the migration effect is also used in the model due to the risk of disease transmission and increased migration in recent years. The course of the disease is examined using real data from the USA. Moreover, the model's positivity and boundedness are studied, and the equilibrium points are calculated. Additionally, the stability conditions for the disease-free equilibrium (DFE) are stated. A parameter calibration technique is used to determine the most accurate parameter values in the model. Finally, we provide numerical results and their biological interpretations to estimate the future course of the disease. The paper addresses the current migration problem with the migration parameter in the model. These differences from the literature can be regarded as important novelties of the paper.

A mathematical model is designed to investigate Tuberculosis (TB) disease under the vaccination, treatment, and environmental impact with real cases. First, we introduce the model formulation in non-integer order derivative and then, extend the model into fractional order derivative. The fractional system's existence, uniqueness, and other relevant properties are shown. Then, we study the stability analysis of the equilibrium points. The disease-free equilibrium (DFE) 0 is locally asymptotically stable (LAS) when ℛ v < 1. Further, we show the global asymptotical stability (GAS) of the endemic equilibrium (EE) ∗ for ℛ v > 1 and 0 for ℛ v ≤ 1. The existence of bifurcation analysis in the model is investigated, and it is shown the system possesses the forward bifurcation phenomenon. Sensitivity analysis has been performed to determine the sensitive parameters that impact ℛ v. We consider the real TB statistics from Khyber Pakhtunkhwa in Pakistan and parameterized the model. The computed basic reproduction number obtained using the real cases is ℛ 0 ≈ 3.6615. Various numerical results regarding disease elimination of the sensitive parameters are shown graphically. [ABSTRACT FROM AUTHOR]

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This work examines a solar power plant connected to the Nouakchott electricity grid in Mauritania. Operating since 2013, the 15 MWp plant's reliability and energy yield have been evaluated using a performance index. The assessment involves three phases. First, the plant's meteorological environment and technical indicators are presented. In the second phase, mathematical performance models specified by the International Energy Agency (IEA) are applied to calculate performance indices using data from the data acquisition system (SCADA). The third phase compares actual production data for 2015, 2017, and 2020 with results simulated for PVsyst for the same years. The obtained results are thoroughly analyzed to highlight relevant physical phenomena. The analysis focuses on the plant's 7-year operating period and its impact on performance indicators for electricity production fed into the grid. This study provides insights into the solar power plant's reliability and energy yield, aiding future operational enhancements. It underscores the importance of performance monitoring and assessment in optimizing solar power generation systems. [ABSTRACT FROM AUTHOR]

Background In epidemiology, indicators such as the relative excess risk due to interaction (RERI), attributable proportion (AP), and synergy index (S) are commonly used to assess additive interactions between two variables. However, the results of these indicators are sometimes inconsistent in real world applications and it may be difficult to draw conclusions from them. Method Based on the relationship between the RERI, AP, and S, we propose a method with consistent results, which are achieved by constraining $e^{\theta_3}-e^{\theta_1}-e^{\theta_2}+1=0$eθ3−eθ1−eθ2+1=0 , and the interpretation of the results is simple and clear. We present two pathways to achieve this end: one is to complete the constraint by adding a regular penalty term to the model likelihood function; the other is to use model selection. Result Using simulated and real data, our proposed methods effectively identified additive interactions and proved to be applicable to real-world data. Simulations were used to evaluate the performance of the methods in scenarios with and without additive interactions. The penalty term converged to 0 with increasing λ, and the final models matched the expected interaction status, demonstrating that regularized estimation could effectively identify additive interactions. Model selection was compared with classical methods (delta and bootstrap) across various scenarios with different interaction strengths, and the additive interactions were closely observed and the results aligned closely with bootstrap results. The coefficients in the model without interaction adhered to a simplifying equation, reinforcing that there was no significant interaction between smoking and alcohol use on oral cancer risk. Conclusion In summary, the model selection method based on the Hannan-Quinn criterion (HQ) appears to be a competitive alternative to the bootstrap method for identifying additive interactions. Furthermore, when using RERI, AP, and S to assess the additive interaction, the results are more consistent and the results are simple and easy to understand.

This paper presents a novel two-parameter distribution derived from the Rayleigh distribution, thoroughly investigating its essential mathematical properties. We employ estimation techniques to determine the proposed distribution's estimated parameters. Through extensive simulation studies, we analyze and evaluate the asymptotic behavior of the model estimators. Furthermore, we calculate various actuarial measures to highlight the practical utility of the proposed distribution in actuarial science. To further substantiate the applicability of our distribution, we perform a comprehensive regression analysis. The practical relevance of the proposed distribution is demonstrated by modeling a lifetime dataset from the insurance field, where it exhibits a superior fit compared to existing distributions. The findings suggest that the new distribution significantly improves modeling capabilities, making it a valuable tool for theoretical research and practical applications in fields requiring accurate lifetime data modeling.

Objectives: This study aims to determine the effectiveness of the Mantel Haenszel Log Odds Ratio method in detecting Differential Item Functioning (DIF) across gender, while considering variations in sample size and test length. Utilizing real data, the study draws from a sample of tenth-grade students in Jordan who participated in the 2018 PISA International Mathematics Test. Methods: The study employs the experimental methodology, utilizing three levels of sample size and test length: (342, 200, and 100) and (30, 20, and 10), respectively. Nine iterations of the DDFS program were conducted to collect the results, representing nine scenarios resulting from the intersection of sample size and test length levels. Results: The study indicates that variations in sample size and test length significantly affect the Mantel-Hanzel (MH) method. Specifically, it observes an improvement in the MH method’s ability to detect DIF items with larger sample sizes, while maintaining a consistent test length. Conversely, the method’s efficacy declines with longer test lengths, despite maintaining a fixed sample size at a specific level. Conclusion: The study recommends using a large sample size and a short test length for effective detection of DIF items using the MH method.

In the initial construction of unit-level virtual models in the discrete production system, the understanding of physical entities and the actual operating environment is lacking, and the virtual models need to be iteratively updated to resemble the physical entities more closely. To solve the above problems, an updating method for knowledge in the virtual model driven by data is studied. Firstly, the behavior model in the virtual model can be divided into basic functional models such as forward kinematics, trajectory planning, and material generation, and the knowledge components to support functional model computation are constructed. Secondly, the evaluation indexes for the quality, maintainability, and reliability of the knowledge components are established, and appropriate knowledge component combinations can be selected from the knowledge component base. Then, based on the measurements, it is used to the triggering judgment, and a knowledge component combination with the smallest difference between the simulation output of the virtual model and the real data of physical entities is selected from multiple combinations to realize the iterative update of the model. Finally, the feasibility and effectiveness of the method are verified by examples. [ABSTRACT FROM AUTHOR]

The Surface Water and Ocean Topography (SWOT) mission, launched in December 2022, aims to address the crucial environmental goal of water monitoring to support preparedness for extreme events and facilitate adaptation to climate change on global and local scales. This mission will provide a comprehensive inventory of worldwide water resources, lakes, reservoir storage, and river dynamics. In this work, we carried out a preliminary assessment of SWOT's Lake product Level 2 version 1.1, also known as "L2_HR_LakeSP". The analysis was performed across six diverse lakes on three continents, revealing an average median bias of 0.08 m with respect to the considered reference, after suitable outlier removal. An overall precision of 0.22 m was found, combined with an average correlation of 68% between SWOT and reference time series. Moreover, the accuracy varied in the considered six lakes, since biases up to some decimeters were found for some of them; they could be due to residual inconsistencies between the vertical reference frame of SWOT and that of the considered reference. In summary, the first analysis of the "L2_HR_LakeSP" product, Version 1.1, demonstrated the promising potential of SWOT for monitoring seasonal variations in water levels. Nevertheless, notable anomalies were found in the water masks, particularly in higher latitudes, suggesting potential difficulties in accurately delineating water bodies in those regions. Additionally, a discernible reduction in accuracy was observed towards the end of the monitoring period. These preliminary findings indicate some issues that should be addressed in future investigations about the quality and potential of SWOT's lake products for advancing our understanding of global water dynamics. [ABSTRACT FROM AUTHOR]

A patient co-infected with COVID-19 and viral hepatitis B can be at more risk of severe complications than the one infected with a single infection. This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19. The model is fitted to real COVID-19 data from Pakistan. The proposed model incorporates logistic growth and saturated incidence functions. Rigorous analyses using the tools of stochastic calculus, are performed to study appropriate conditions for the existence of unique global solutions, stationary distribution in the sense of ergodicity and disease extinction. The stochastic threshold estimated from the data fitting is given by: ℛS0 = 3.0651. Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases. The effects of stochastic white noise intensities are also highlighted. [ABSTRACT FROM AUTHOR]

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution's uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders (γ) and fractal dimensions (θ), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models. [ABSTRACT FROM AUTHOR]

With the development of photovoltaic (PV) power generation systems in single houses, research has recently focused on the prediction of PV power generation to match PV power generation with building energy consumption characteristics. However, prediction models for PV power generation under different weather conditions based on the actual monitoring data of the PV power generation system in a single house are still lacking. The present study is based on the actual monitoring of PV power generation data of a single house with a PV system that was installed in Beijing 5 years ago. We analysed the main weather factors affecting PV power generation and power conversion efficiency (PCE). The results showed a positive correlation between power generation and solar radiation, with the ambient temperature (Ta) and total cloud cover (TCC) being the main weather factors affecting power generation and PCE. Based on the analysis results, a support vector regression (SVR) model was established to predict PV power generation. In addition, the mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of variation (R2) of the SVR model were 3.39, 34.7% and 0.86, respectively, which can accurately be used to predict PV power generation under different weather types. [ABSTRACT FROM AUTHOR]

The progression of the still ongoing COVID-19 epidemic must be studied in the world of differential operators other than those specified with integer-order temporal derivatives, according to ongoing scientific studies in the fields of fractional calculus, mathematical modeling, and epidemiology. Infectious diseases leave behind a historical footprint because of their long memory. With this in mind, the article below makes an effort to probe an epidemiological model using a Caputo differential operator with a singular kernel of power-law type. The ability of the Caputo operator to capture the evolution of complicated phenomena has been demonstrated in a number of studies, prompting us to conduct the analysis presented here. The analysis contains solid reasons while using the fractional operator for the COVID-19 epidemiological paradigm and presents the fixed point concept for the existence and uniqueness of its solutions. Hyers–Ulam–Rassias stability aids in finding model equilibrium, and the nonlinear least squares method yields the unknown parameters that also include the model’s fractional order. The actual cases of the infection support the superiority of the Caputo concept with evidence of smaller residuals. The numerical simulations are run to see how varying important parameters affect the disease’s spread.

Gathering useful and trustworthy wireless data using crowdsourcing to train/validate machine learning (ML) algorithms can be difficult due to two factors: 1) correctness and reliability of the gathered data from various independent wireless access points (APs) can be unknown, and 2) designing a metric that can capture the value of the collected data for the considered model can be a challenge. To address the challenge of reliable data collection, we propose a game-theoretic crowdsourcing-based wireless data collection mechanism that can be used to reliably collect the data. We also propose a metric that can capture the value of the collected data for the considered model. Our proposed method provides protection against selfish deviations and unlike other game-theoretic works does not make an assumption that the actions of the crowdsourcing agent APs are known to the crowdsourcing entity. We consider a technique that can be used to infer the actions of agent APs and propose that the participants utilize the n-round Win-stay lose shift (WSLS) strategy. In our work, we compare the performance of the proposed strategy against various other game-theoretic strategies, such as always high, always low, WSLS with probability p, and tit for tat. In our performance evaluation, we utilize both real and synthetic wireless channel utilization data. Our results show that the n-round WSLS strategy outperforms the other game-theoretic strategies.

In the context of this investigation, we introduce an innovative mathematical model designed to elucidate the intricate dynamics underlying the transmission of Anthroponotic Cutaneous Leishmania. This model offers a comprehensive exploration of the qualitative characteristics associated with the transmission process. Employing the next-generation method, we deduce the threshold value $ R_0 $ for this model. We rigorously explore both local and global stability conditions in the disease-free scenario, contingent upon $ R_0 $ being less than unity. Furthermore, we elucidate the global stability at the disease-free equilibrium point by leveraging the Castillo-Chavez method. In contrast, at the endemic equilibrium point, we establish conditions for local and global stability, when $ R_0 $ exceeds unity. To achieve global stability at the endemic equilibrium, we employ a geometric approach, a Lyapunov theory extension, incorporating a secondary additive compound matrix. Additionally, we conduct sensitivity analysis to assess the impact of various parameters on the threshold number. Employing center manifold theory, we delve into bifurcation analysis. Estimation of parameter values is carried out using least squares curve fitting techniques. Finally, we present a comprehensive discussion with graphical representation of key parameters in the concluding section of the paper.

This study addresses the difficulties associated with parameter estimation in the generalized power unit half-logistic geometric distribution by employing a progressive Type-Ⅱ censoring technique. The study uses a variety of methods, including maximum likelihood, maximum product of spacing, and Bayesian estimation. The work investigates Bayesian estimators taking into account a gamma prior and a symmetric loss function while working with observed data produced by likelihood and spacing functions. A full simulation experiment is carried out with varying sample sizes and censoring mechanisms in order to thoroughly evaluate the various estimation approaches. The highest posterior density approach is employed in the study to compute credible intervals for the parameters. Additionally, based on three optimal criteria, the study chooses the best progressive censoring scheme from a variety of rival methods. The study examines two real datasets in order to confirm the applicability of the generalized power unit half-logistic geometric distribution and the efficacy of the suggested estimators. The results show that in order to generate the necessary estimators, the maximum product of the spacing approach is better than the maximum likelihood method. Furthermore, as compared to traditional methods, the Bayesian strategy that makes use of probability and spacing functions produces estimates that are more satisfactory.

This study addresses the difficulties associated with parameter estimation in the generalized power unit half-logistic geometric distribution by employing a progressive Type-II censoring technique. The study uses a variety of methods, including maximum likelihood, maximum product of spacing, and Bayesian estimation. The work investigates Bayesian estimators taking into account a gamma prior and a symmetric loss function while working with observed data produced by likelihood and spacing functions. A full simulation experiment is carried out with varying sample sizes and censoring mechanisms in order to thoroughly evaluate the various estimation approaches. The highest posterior density approach is employed in the study to compute credible intervals for the parameters. Additionally, based on three optimal criteria, the study chooses the best progressive censoring scheme from a variety of rival methods. The study examines two real datasets in order to confirm the applicability of the generalized power unit half-logistic geometric distribution and the efficacy of the suggested estimators. The results show that in order to generate the necessary estimators, the maximum product of the spacing approach is better than the maximum likelihood method. Furthermore, as compared to traditional methods, the Bayesian strategy that makes use of probability and spacing functions produces estimates that are more satisfactory. [ABSTRACT FROM AUTHOR]

While there are references available in the literature regarding learning experiences with Dataset-Based Learning (DBL) approaches, there is a noticeable absence of a standardized model for designing DBL activities. This gap was identified in this work after performing a systematic literature review (SLR). In contrast to other active learning methodologies, the lack of a common framework for the DBL methodology makes it challenging to compare different DBL approaches. This paper highlights the knowledge gap in the methodology for designing DBL activities and aims to provide a common approach for sharing the view and details about what DBL entails in higher education and how to design a DBL activity. Additionally, we illustrate these concepts with three case studies in different engineering fields. Based on the SLR results and the review of additional literature, this work defines DBL as an active teaching methodology that focuses on using datasets to promote the learning and understanding of specific concepts and skills. These datasets should contain real data presented in different formats. As a common starting point, in a DBL lesson, the dataset not only provides information and context in the activity statement but also serves as the material to work with, and the solution to the activity is entirely extracted from the information contained in the dataset. [ABSTRACT FROM AUTHOR]

The World Health Organization (WHO) announced on March 11, 2020, that COVID-19 could be considered a pandemic. This epidemic has become a huge issue for academics, doctors, healthcare providers, epidemiologists, and decision-makers alike. Motivated by studying natural phenomena, we concentrated on making a statistical model capable of fitting natural pandemics into the whole world. In this manuscript, we introduced a new novel distribution called the Inverse Power Haq (IPH) distribution. We created this distribution due to its formidable merits. We introduced its statistical properties and plotted its probability density function (PDF), cumulative distribution function (CDF), and hazard rate function (HRF). We utilized classical estimation techniques to determine the parameters for the suggested distribution. In the paper's conclusion, we performed a data analysis, applying the distribution to COVID-19 infection in Kuwait for practical purposes. Our analysis demonstrated the superior performance of the proposed distribution compared to its competitors, establishing it as the most suitable choice for modeling COVID-19 data in patients of different ages. Lastly, the conclusion section includes a summary of our overall findings and conclusions.

This article presents the current state and development directions of the tire industry. One of the main requirements that a tire must meet before it can leave the factory is achieving values of quantities describing uniformity at a defined level. Of particular importance areconicity and the components of the tire with the greatest impact on its value. This research is based on the possibility of using an ANN to meet contemporary challenges faced by tire manufacturers. In order to achieve a satisfactory level of prediction, we compared the use of a multi-layer perceptron and decision trees XGBoost, LightGbmRegression, and FastTreeRegression. Based on data analysis and similar examples from the literature, metrics were selected to evaluate the models’ ability to solve regression problems in relation to the described problem. We selected the best possible solution, standing at the top of the features covered by the criterion analysis. The proposed solutions can be the basis for acquiring new knowledge and contributions in the field of the computational analysis of industrial data in tire production. These solutions are characterized by the required accuracy and efficiency for online work, and they also contribute to the creation of the best fit elements of complex systems (including computational models). The results of this study will contribute to reducing the volume of waste in the tire industry by eliminating defective tire parts in the early stages of the production process.

AbstractBeing a teacher or a student in a class with a large enrollment can be intimidating. Often, teachers view comforts that are common to small classes as unattainable in a larger class, including knowing students’ names, using active learning, employing group work, and creating group discussion. Students in large classes may find that the class size leads to isolation. At Utah State University, we offer introductory statistics classes for various audiences using a large lecture format. The authors have collectively led these large lectures dozens of times and found that, despite its shortcomings, the large lecture format can be an asset when teaching statistics. With an active learning approach such as recommended by the revised GAISE College report, large class sizes permit realistic sampling, facilitate student-driven simulation, and provide bountiful opportunities for experimentation. In this article, we discuss the benefits of large classes for statistics teaching and present examples of using large class sizes to create an engaging environment that where students are involved in active learning and collecting real data to foster statistical thinking.

The post-effects of COVID-19 have begun to emerge in the long term in society. Stroke has become one of the most common side effects in the post-COVID community. In this study, to examine the relationship between COVID-19 and stroke, a fractional-order mathematical model has been constructed by considering the fear effect of being infected. The model's positivity and boundedness have been proved, and stability has been examined for disease-free and co-existing equilibrium points to demonstrate the biological meaningfulness of the model. Subsequently, the basic reproduction number (the virus transmission potential ( R 0 )) has been calculated. Next, the sensitivity analysis of the parameters according to R 0 has been considered. Moreover, the values of the model parameters have been calculated using the parameter estimation method with real data originating from the United Kingdom. Furthermore, to underscore the benefits of fractional-order differential equations (FODEs), analyses demonstrating their relevance in memory trace and hereditary characteristics have been provided. Finally, numerical simulations have been highlighted to validate our theoretical findings and explore the system's dynamic behavior. From the findings, we have seen that if the screening rate in the population is increased, more cases can be detected, and stroke development can be prevented. We also have concluded that if the fear in the population is removed, the infection will spread further, and the number of people suffering from a stroke may increase. [ABSTRACT FROM AUTHOR]

In this article, we propose an estimator for a bivariate residual entropy function based on smoothed kernel procedure. Asymptotic properties of the proposed estimator are established under some regularity conditions. Simulation studies demonstrate that the estimator performs well even for increased sample sizes and different combinations of lifetimes. The performances of the proposed estimator are tabulated and illustrated through a data on recurrence of cancer. [ABSTRACT FROM AUTHOR]

The Surface Water and Ocean Topography (SWOT) mission, launched in December 2022, aims to address the crucial environmental goal of water monitoring to support preparedness for extreme events and facilitate adaptation to climate change on global and local scales. This mission will provide a comprehensive inventory of worldwide water resources, lakes, reservoir storage, and river dynamics. In this work, we carried out a preliminary assessment of SWOT’s Lake product Level 2 version 1.1, also known as “L2_HR_LakeSP”. The analysis was performed across six diverse lakes on three continents, revealing an average median bias of 0.08 m with respect to the considered reference, after suitable outlier removal. An overall precision of 0.22 m was found, combined with an average correlation of 68% between SWOT and reference time series. Moreover, the accuracy varied in the considered six lakes, since biases up to some decimeters were found for some of them; they could be due to residual inconsistencies between the vertical reference frame of SWOT and that of the considered reference. In summary, the first analysis of the “L2_HR_LakeSP” product, Version 1.1, demonstrated the promising potential of SWOT for monitoring seasonal variations in water levels. Nevertheless, notable anomalies were found in the water masks, particularly in higher latitudes, suggesting potential difficulties in accurately delineating water bodies in those regions. Additionally, a discernible reduction in accuracy was observed towards the end of the monitoring period. These preliminary findings indicate some issues that should be addressed in future investigations about the quality and potential of SWOT’s lake products for advancing our understanding of global water dynamics.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution’s uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders (γ) and fractal dimensions (θ), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models.

This research article investigates the application of Lévy noise to understand the dynamic aspects of measles epidemic modeling and seeks to explain the impact of vaccines on the spread of the disease. After model formulation, the study utilises uniqueness and existence techniques to derive a positive solution to the underlying stochastic model. The Lyapunov function is used to investigate the stability results associated with the proposed stochastic model. The model's dynamic characteristics are analyzed in the vicinity of the infection-free and endemic states of the associated ODEs model. The stochastic threshold R s that ensures disease's extinction whenever R s < 1 is calculated. We utilized data from Pakistan in 2019 to estimate the parameters of the model and conducted simulations to forecast the future behavior of the disease. The results were compared to actual data using standard curve fitting tools. [ABSTRACT FROM AUTHOR]

Being a teacher or a student in a class with a large enrollment can be intimidating. Often, teachers view comforts that are common to small classes as unattainable in a larger class, including knowing students' names, using active learning, employing group work, and creating group discussion. Students in large classes may find that the class size leads to isolation. At Utah State University, we offer introductory statistics classes for various audiences using a large lecture format. The authors have collectively led these large lectures dozens of times and found that, despite its shortcomings, the large lecture format can be an asset when teaching statistics. With an active learning approach such as recommended by the revised GAISE College report, large class sizes permit realistic sampling, facilitate student-driven simulation, and provide bountiful opportunities for experimentation. In this article, we discuss the benefits of large classes for statistics teaching and present examples of using large class sizes to create an engaging environment that where students are involved in active learning and collecting real data to foster statistical thinking. [ABSTRACT FROM AUTHOR]

This study aims to describe the design and development of a STEM problem-solving activity involving mathematics and physics content. It is an activity whose starting point is a question based on a real problem: to identify the areas of the classroom where the intensity of sound is higher. In this way, the problem involves the physics of sound. However, in addition, by trying to give an answer to the initial question, students have the opportunity to develop progressively more complex mathematical models from already known mathematical concepts and procedures. The analysis of the results of the implementation based on the identification of the learning opportunities and the catalyst elements that generate them, allows us to state that the activity encourages students to enrich their mathematical models by incorporating new mathematical concepts such as the function of two variables. We conclude that the design of the activity and the choice of data acquisition technology are key, but also the interaction between the students and the teacher. [ABSTRACT FROM AUTHOR]

A stochastic epidemic model with random noise transmission is taken into account, describing the dynamics of the measles viral infection. The basic reproductive number is calculated corresponding to the stochastic model. It is determined that, given initial positive data, the model has bounded, unique, and positive solution. Additionally, utilizing stochastic Lyapunov functional theory, we study the extinction of the disease. Stationary distribution and extinction of the infection are examined by providing sufficient conditions. We employed optimal control principles and examined stochastic control systems to regulate the transmission of the virus using environmental factors. Graphical representations have been offered for simplicity of comprehending in order to further verify the acquired analytical findings. [ABSTRACT FROM AUTHOR]

This paper presents a detailed investigation of a stochastic model that rules the spreading behavior of the measles virus while accounting for the white noises and the influence of immunizations. It is hypothesized that the perturbations of the model are nonlinear, and that a person may lose the resistance after vaccination, implying that vaccination might create temporary protection against the disease. Initially, the deterministic model is formulated, and then it has been expanded to a stochastic system, and it is well-founded that the stochastic model is both theoretically and practically viable by demonstrating that the model has a global solution, which is positive and stochastically confined. Next, we infer adequate criteria for the disease's elimination and permanence. Furthermore, the presence of a stationary distribution is examined by developing an appropriate Lyapunov function, wherein we noticed that the disease will persist for R 0 s > 1 and that the illness will vanish from the community when R 0 s < 1 . We tested the model against the accessible data of measles in Pakistan during the first ten months of 2019, using the conventional curve fitting methods and the values of the parameters were calculated accordingly. The values obtained were employed in running the model, and the conceptual findings of the research were evaluated by simulations and conclusions were made. Simulations imply that, in order to fully understand the dynamic behavior of measles epidemic, time-delay must be included in such analyses, and that advancements in every vaccine campaign are inevitable for the control of the disease. [ABSTRACT FROM AUTHOR]

Natural symmetries exist in several processes of chemistry, physics, and biology. Symmetries possess interesting dynamical characteristics that cannot be seen in non-symmetric systems. The present paper investigates the competition between two banking systems, rural and commercial, in Indonesia, in parameterized fractional order Caputo derivative. A novel numerical method is used to discretize the competition system using the real data of rural and commercial banks in Indonesia for the period 2004–2014. The new scheme is more suitable and reliable for data fitting results and has good accuracy. The integer model is formulated in Caputo derivative and their stability results are presented. With the available parameters, the data for the model is analyzed using various scenarios. We shall compare the result with the previous method used in the literature and show that the present method is better than the previous method in the literature. It is shown that fractional order α and the parameter ρ involved in the numerical scheme provide excellent fitting. [ABSTRACT FROM AUTHOR]

This dataset was collected for the purpose of applying fault detection and diagnosis (FDD) techniques to real data from an industrial facility. The data for an air handling unit (AHU) is extracted from a building management system (BMS) and aligned with the Project Haystack naming convention. This dataset differs from other publicly available datasets in three main ways. Firstly, the dataset does not contain fault detection ground truth. The lack of labelled datasets in the industrial setting is a significant limitation to the application of FDD techniques found in the literature. Secondly, unlike other publicly available datasets that typically record values every 1 min or 5 min, this dataset captures measurements at a lower frequency of every 15 min, which is due to data storage constraints. Thirdly, the dataset contains a myriad of data issues. For example, there are missing features, missing time intervals, and inaccurate data. Therefore, we hope this dataset will encourage the development of robust FDD techniques that are more suitable for real world applications.

The data article describes a real operational dataset for the Concrete Delivery Problem (CDP). The dataset consists of 263 instances corresponding to daily orders of concrete from construction sites in Quebec, Canada. A concrete producer, i.e., a concrete-producing company that delivers concrete, provided the raw data. We cleaned the data by removing entries corresponding to non-complete orders. We processed these raw data to form instances useful for benchmarking optimization algorithms developed to solve the CDP. We also anonymized the published dataset by removing any client information and addresses corresponding to production or construction sites. The dataset is useful for researchers and practitioners studying the CDP. It can be processed to create artificial data for variations of the CDP. In its current form, the data contain information about intra-day orders. Thus, selected instances from the dataset are useful for CDP's dynamic aspect considering real-time orders.

While there are references available in the literature regarding learning experiences with Dataset-Based Learning (DBL) approaches, there is a noticeable absence of a standardized model for designing DBL activities. This gap was identified in this work after performing a systematic literature review (SLR). In contrast to other active learning methodologies, the lack of a common framework for the DBL methodology makes it challenging to compare different DBL approaches. This paper highlights the knowledge gap in the methodology for designing DBL activities and aims to provide a common approach for sharing the view and details about what DBL entails in higher education and how to design a DBL activity. Additionally, we illustrate these concepts with three case studies in different engineering fields. Based on the SLR results and the review of additional literature, this work defines DBL as an active teaching methodology that focuses on using datasets to promote the learning and understanding of specific concepts and skills. These datasets should contain real data presented in different formats. As a common starting point, in a DBL lesson, the dataset not only provides information and context in the activity statement but also serves as the material to work with, and the solution to the activity is entirely extracted from the information contained in the dataset.

In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.

Asthma is a chronic respiratory disease affecting over 358 million people worldwide; for this reason analysing big data on asthma from different countries could give a more detailed picture of current disease burden. We aim to investigate the correlations between asthma and key socio-demographic parameters from different world databases. We found a direct correlation with the gross domestic product (GDP) per capita and its nominal counterpart, with wealthiest countries seen to have the highest prevalence of asthma, as also confirmed by a similar correlation with the human development index (HDI). A positive correlation was also seen between asthma prevalence and a number of socio-cultural data being representative of a good life quality index and prevalent in more developed and wealthier countries. Concerning medical data, an inverse relationship was seen between asthma prevalence and helminthiasis. Those data indicate a higher prevalence for asthma in more developed countries, where socio-economic status is higher and also the access to medical care is more ubiquitous. The approach used in our study highlighted the role of medical literacy and access to healthcare facilities in the correct diagnosis of asthma and vice versa. Our data appear to be suitable in terms of a health programming approach because of the high burden of disease worldwide.

As an important source of water for human beings, groundwater plays a significant role in human production and life. However, different sources of uncertainty may lead to unsatisfactory simulations of groundwater hydrodynamics with hydrological models. The goal of this study is to investigate the impact of assimilating groundwater data into the Terrestrial System Modeling Platform (TSMP) for improving hydrological modeling in a real-world case. Daily groundwater table depth (WTD) measurements from the year 2018 for the Rur catchment in Germany were assimilated by the Localized Ensemble Kalman Filter (LEnKF) into TSMP. The LEnKF is used with a localization radius so that the assimilated measurements only update model states in a limited radius around the measurements, in order to avoid unphysical updates related to spurious correlations. Due to the mismatch between groundwater measurements and the coarse model resolution (500 m), the measurements need careful screening before data assimilation (DA). Based on the spatial autocorrelation of the WTD deduced from the measurements, three different filter localization radii (2.5, 5, and 10 km) were evaluated for assimilation. The bias in the simulated water table and the root mean square error (RMSE) are reduced after DA, compared with runs without DA [i.e., open loop (OL) runs]. The best results at the assimilated locations are obtained for a localization radius of 10 km, with an 81% reduction of RMSE at the measurement locations, and slightly smaller RMSE reductions for the 5 and 2.5 km radius. The validation with independent WTD data showed the best results for a localization radius of 10 km, but groundwater table characterization could only be improved for sites

Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for R 0 ≤ 1 . We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is R 0 ≈ 1.1367 . We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically. [ABSTRACT FROM AUTHOR]