Editorial Summary: Mathematical Models and Methods in Various Sciences

The Special Issue of Symmetry, “Mathematical Models and Methods in Various Sciences”, aimed to bring together innovative papers on the theory, methodology, and applications of symmetric/asymmetric mathematical models and methods in various areas of science.

The published papers covered a range of topics, including SIMEX estimation, scaled-invariant extended quasi-Lindley models, convective boundary conditions, investment and pricing strategies, dispersion monitoring structures, daily semiparametric GARCH models, survival analysis, gamma processes, queue-size distribution, synergies in depressive symptoms, bivariate proportional hazard models, single transferable vote, bounded rational decision-making models, and reliability analysis.

Paper [1] addresses the issue of mismeasured covariates in the context of a partially linear multiplicative regression model. The authors propose a statistical inference method for a partially linear multiplicative regression model, using relative errors as a criterion. They introduce SIMEX estimators based on the least product relative error criterion and B-spline approximation. Extensive simulation studies demonstrate the effectiveness of their method in eliminating bias caused by measurement errors. The asymptotic normality of their proposed estimator is established under certain conditions. A real example is provided to illustrate the practical use of their method.

The authors of [2] propose new empirical models to analyze data that do not fit traditional statistical models. They study an extension of the quasi-Lindley model that is asymmetrically distributed. Various algorithms are used to estimate the model’s parameters. The authors find that the expectation-maximization approach has the lowest error. They also demonstrate the usefulness of the proposed model by analyzing a reliability data set and showing its superiority over other models.

In [3], a computational approach for examining the convective heat transport and solutal profiles is presented in a two-phase nanofluid model, considering factors such as chemical reactions and the combined effects of Brownian and thermophoresis phenomena. A three-dimensional model is developed and solved using similarity variables and traditional numerical techniques, with careful selection of physical parameters for accuracy. The proposed model demonstrates the flow pattern of fluid particles in the domain, influenced by changes in kinematic viscosity, stream values, and enhanced Brownian motion.

In [4], the investment and pricing strategies of media platforms for two-sided value-added services are examined using game theory. Equilibrium investments, prices, and profits are determined for asymmetric (A) and symmetric (S) scenarios, and the impact of key parameters is analyzed. The results show that ad prices are higher in scenario A compared to scenario S, but the same is not always true for value-added service levels.

The utilization of memory-type control charts is suggested by the authors of [5] as a cost-effective and efficient method for monitoring manufacturing and service operations in the Industry 4.0 era. They demonstrate the superiority of memory-type control charts over memoryless control charts in detecting changes in location and dispersion parameters of symmetrically distributed processes.

In [6], the authors suggest enhancing the estimation of the volatility function in GARCH models by integrating high-frequency intraday data, as traditional GARCH models that rely on daily frequency data may not effectively utilize all available financial market information. To address this concern, they propose a semiparametric volatility proxy model that considers both symmetric and asymmetric cases and establish the asymptotic normality of estimators under mild conditions while analyzing the impact of various volatility proxies on estimation precision. The results of simulations and empirical analysis confirm that incorporating high-frequency data improves the estimation of the volatility function.

The authors of [7] introduce a novel weighted Nadarajah-Haghighi (WNH) distribution as a competitor to existing models. They employ maximum likelihood, Bayesian estimation, and bootstrapping techniques to estimate parameters and construct intervals and demonstrate the efficacy of the proposed WNH distribution through three real-world engineering applications.

The authors of [8] propose an approach to degradation modeling that considers both the internal structure of reliable products and the environmental conditions. The model incorporates three sources of variability and effectively captures and models the degradation of products through simulation and case studies.

In [9], the authors propose investigating a discrete-time queueing system with geometric interarrival times and generally distributed processing times, incorporating a power-saving mechanism in the form of random duration vacations. They suggest that implementing a single vacation policy can achieve cost symmetry in the system. Furthermore, they analyze the system using differential equations and linear algebraic approaches and validate their findings through numerical studies.

An expansion of Multiple Indicators Multiple Causes (MIMIC) models to identify impartial, asymmetrical, and bidirectional influences using indicators of the same items within subgroups defined by variables, emphasizing the need to differentiate between comorbidity patterns in research processes and providing recommendations for adaptive modeling, conceptualizing symptom clusters, metabolomics, and economic or social monitoring is proposed in [10].

The study in [11] proposes the examination of bivariate models that include proportional hazard components. The authors investigate models with proportional hazard marginals and proportional hazard conditional distributions and demonstrate the relationship between bivariate distributions with marginal proportional hazards and certain known bivariate exponential models.

The authors in [12] present two strategies for achieving proportional representation in elections: the single transferable vote (STV) and party-list-based methods. They propose the Weighted Inclusive Gregory method as a replacement for the largest remainder method and also develop a faster algorithm for using the STV with party-list preferences.

The authors of [13] argue that while classical decision theory assumes completeness in rational preference, they propose alternative preferences that do not require this assumption. They further examine the connections between expansion and contraction conditions, as well as the relationships between rationality conditions and bounded rational choice behavior, using interval ordinal numbers as an illustrative example. These findings provide valuable references for the investigation of boundedly rational decision making.

Finally, a method for modeling degradation and estimating reliability using a Wiener process with a transmuted–truncated normal distribution is presented in [14]. The authors demonstrate the effectiveness of this approach through numerical examples and a practical application with laser degradation data and compare it to existing models using deviance information criteria to show its superior reliability estimation results.

In conclusion, the papers demonstrated the adaptability and capabilities of mathematical modeling in resolving intricate issues and tackling practical obstacles, which underscores the increasing significance and applicability of mathematical models and techniques across diverse scientific fields; thus, I extend our heartfelt gratitude to all the authors who shared their work in this Special Issue, as well as to the reviewers for their invaluable input and the Symmetry editorial team for their continuous support during the publication journey.