Mahmoud M. Abdelwahab, M. R. Abonazel, Ali T. Hammad, Amera M. El-Masry
This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus leading to multicollinearity, the variance or standard error of the PMLE is inflated. To address this issue, several alternative estimators have been introduced, including the Poisson ridge regression estimator (PRRE), Liu estimator (PLE), and adjusted Liu estimator (PALE), each of them relying on a single shrinkage parameter. The PMTPLE uses two shrinkage parameters, which enhances its adaptability and robustness in the presence of multicollinearity between explanatory variables. To assess the performance of the PMTPLE compared to the four existing estimators (the PMLE, PRRE, PLE, and PALE), a simulation study is conducted that encompasses various scenarios and two empirical applications. The evaluation of the performance is based on the mean square error (MSE) criterion. The theoretical comparison, simulation results, and findings of the two applications consistently demonstrate the superiority of the PMTPLE over the other estimators, establishing it as a robust solution for count data analysis under multicollinearity conditions.
{"title":"Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model","authors":"Mahmoud M. Abdelwahab, M. R. Abonazel, Ali T. Hammad, Amera M. El-Masry","doi":"10.3390/axioms13010046","DOIUrl":"https://doi.org/10.3390/axioms13010046","url":null,"abstract":"This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus leading to multicollinearity, the variance or standard error of the PMLE is inflated. To address this issue, several alternative estimators have been introduced, including the Poisson ridge regression estimator (PRRE), Liu estimator (PLE), and adjusted Liu estimator (PALE), each of them relying on a single shrinkage parameter. The PMTPLE uses two shrinkage parameters, which enhances its adaptability and robustness in the presence of multicollinearity between explanatory variables. To assess the performance of the PMTPLE compared to the four existing estimators (the PMLE, PRRE, PLE, and PALE), a simulation study is conducted that encompasses various scenarios and two empirical applications. The evaluation of the performance is based on the mean square error (MSE) criterion. The theoretical comparison, simulation results, and findings of the two applications consistently demonstrate the superiority of the PMTPLE over the other estimators, establishing it as a robust solution for count data analysis under multicollinearity conditions.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"27 6","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions. Furthermore, we extend certain definitions, presenting novel and fascinating results. We also derive several interesting properties of the results of third-order strong differential subordinations for analytic functions associated with the Srivastava–Attiya operator.
{"title":"Results of Third-Order Strong Differential Subordinations","authors":"M. M. Soren, A. Wanas, Luminița-Ioana Cotîrlă","doi":"10.3390/axioms13010042","DOIUrl":"https://doi.org/10.3390/axioms13010042","url":null,"abstract":"In this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions. Furthermore, we extend certain definitions, presenting novel and fascinating results. We also derive several interesting properties of the results of third-order strong differential subordinations for analytic functions associated with the Srivastava–Attiya operator.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"6 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
(1) Background: A new probabilistic physico-chemical model of the drifting key parameter of measuring equipment is proposed. The model allows for the integrated consideration of degradation processes (electrolytic corrosion, oxidation, plastic accumulation of dislocations, etc.) in nodes and elements of measuring equipment. The novelty of this article lies in the analytical solutions that are a combination of the Fokker–Planck–Kolmogorov equation and the equation of chemical kinetics. The novelty also consists of the simultaneous simulation and analysis of probabilistic, physical and chemical processes in one model. (2) Research literature review: Research works related to the topic of the study were analyzed. The need for a probabilistic formulation of the problem is argued, since classical statistical methods are not applicable due to the lack of statistical data. (3) Statement of the research problem: A probabilistic formulation of the problem is given taking into account the physical and chemical laws of aging and degradation. (4) Methods: The author uses methods of probability theory and mathematical statistics, methods for solving the stochastic differential equations, the methods of mathematical modeling, the methods of chemical kinetics and the methods for solving a partial differential equations. (5) Results: A mathematical model of a drifting key parameter of measuring equipment is developed. The conditional transition density of the probability distribution of the key parameter of measuring equipment is constructed using a solution to the Fokker–Planck–Kolmogorov equation. The results of the study on the developed model and the results of solving the applied problem of constructing the function of the failure rate of measuring equipment are presented. (6) Discussion: The results of comparison between the model developed in this paper and the known two-parameter models of diffusion monotonic distribution and diffusion non-monotonic distribution are discussed. The results of comparison between the model and the three-parameter diffusion probabilistic physical model developed by the author earlier are also discussed. (7) Conclusions: The developed model facilitates the construction and analysis of a wide range of metrological characteristics such as measurement errors and measurement ranges and acquisition of their statistical estimates. The developed model is used to forecast and simulate the reliability of measuring equipment in general, as well as soldered joints of integrated circuits in special equipment and machinery, which is also operated in harsh conditions and corrosive environments.
{"title":"A Probabilistic Physico-Chemical Diffusion Model of the Key Drifting Parameter of Measuring Equipment","authors":"Rustam Khayrullin","doi":"10.3390/axioms13010041","DOIUrl":"https://doi.org/10.3390/axioms13010041","url":null,"abstract":"(1) Background: A new probabilistic physico-chemical model of the drifting key parameter of measuring equipment is proposed. The model allows for the integrated consideration of degradation processes (electrolytic corrosion, oxidation, plastic accumulation of dislocations, etc.) in nodes and elements of measuring equipment. The novelty of this article lies in the analytical solutions that are a combination of the Fokker–Planck–Kolmogorov equation and the equation of chemical kinetics. The novelty also consists of the simultaneous simulation and analysis of probabilistic, physical and chemical processes in one model. (2) Research literature review: Research works related to the topic of the study were analyzed. The need for a probabilistic formulation of the problem is argued, since classical statistical methods are not applicable due to the lack of statistical data. (3) Statement of the research problem: A probabilistic formulation of the problem is given taking into account the physical and chemical laws of aging and degradation. (4) Methods: The author uses methods of probability theory and mathematical statistics, methods for solving the stochastic differential equations, the methods of mathematical modeling, the methods of chemical kinetics and the methods for solving a partial differential equations. (5) Results: A mathematical model of a drifting key parameter of measuring equipment is developed. The conditional transition density of the probability distribution of the key parameter of measuring equipment is constructed using a solution to the Fokker–Planck–Kolmogorov equation. The results of the study on the developed model and the results of solving the applied problem of constructing the function of the failure rate of measuring equipment are presented. (6) Discussion: The results of comparison between the model developed in this paper and the known two-parameter models of diffusion monotonic distribution and diffusion non-monotonic distribution are discussed. The results of comparison between the model and the three-parameter diffusion probabilistic physical model developed by the author earlier are also discussed. (7) Conclusions: The developed model facilitates the construction and analysis of a wide range of metrological characteristics such as measurement errors and measurement ranges and acquisition of their statistical estimates. The developed model is used to forecast and simulate the reliability of measuring equipment in general, as well as soldered joints of integrated circuits in special equipment and machinery, which is also operated in harsh conditions and corrosive environments.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"52 14","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139442186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article investigates finite-time passivity for fuzzy inertial complex-valued neural networks (FICVNNs) with time-varying delays. First, by using the existing passivity theory, several related definitions of finite-time passivity are illustrated. Consequently, by adopting a reduced-order method and dividing complex-valued parameters into real and imaginary parts, the proposed FICVNNs are turned into first-order real-valued neural network systems. Moreover, appropriate controllers and the Lyapunov functional method are established to obtain the finite-time passivity of FICVNNs with time delays. Furthermore, some essential conditions are established to ensure finite-time synchronization for finite-time passive FICVNNs. In the end, corresponding simulations certify the feasibility of the proposed theoretical outcomes.
{"title":"Finite-Time Passivity and Synchronization for a Class of Fuzzy Inertial Complex-Valued Neural Networks with Time-Varying Delays","authors":"Jing Han","doi":"10.3390/axioms13010039","DOIUrl":"https://doi.org/10.3390/axioms13010039","url":null,"abstract":"This article investigates finite-time passivity for fuzzy inertial complex-valued neural networks (FICVNNs) with time-varying delays. First, by using the existing passivity theory, several related definitions of finite-time passivity are illustrated. Consequently, by adopting a reduced-order method and dividing complex-valued parameters into real and imaginary parts, the proposed FICVNNs are turned into first-order real-valued neural network systems. Moreover, appropriate controllers and the Lyapunov functional method are established to obtain the finite-time passivity of FICVNNs with time delays. Furthermore, some essential conditions are established to ensure finite-time synchronization for finite-time passive FICVNNs. In the end, corresponding simulations certify the feasibility of the proposed theoretical outcomes.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"19 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139448504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vladica S. Stojanović, Hassan S. Bakouch, Zorica Gajtanović, Fatimah E. Almuhayfith, Kristijan Kuk
This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and correlation structure. In addition, the marginal distribution, over-dispersion and zero-inflation properties of the INSB(1) process are also examined. To estimate the unknown parameters of the INSB(1) process, an estimation procedure based on probability generating functions (PGFs) is proposed. For the obtained estimators, their asymptotic properties, as well as the appropriate simulation study, are examined. Finally, the INSB(1) process is applied in the dynamic analysis of some real-world series, namely, the numbers of serious traffic accidents in Serbia and forest fires in Greece.
{"title":"Integer-Valued Split-BREAK Process with a General Family of Innovations and Application to Accident Count Data Modeling","authors":"Vladica S. Stojanović, Hassan S. Bakouch, Zorica Gajtanović, Fatimah E. Almuhayfith, Kristijan Kuk","doi":"10.3390/axioms13010040","DOIUrl":"https://doi.org/10.3390/axioms13010040","url":null,"abstract":"This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and correlation structure. In addition, the marginal distribution, over-dispersion and zero-inflation properties of the INSB(1) process are also examined. To estimate the unknown parameters of the INSB(1) process, an estimation procedure based on probability generating functions (PGFs) is proposed. For the obtained estimators, their asymptotic properties, as well as the appropriate simulation study, are examined. Finally, the INSB(1) process is applied in the dynamic analysis of some real-world series, namely, the numbers of serious traffic accidents in Serbia and forest fires in Greece.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"32 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139448523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dynamic scheduling represents an important class of combinatorial optimisation problems that are usually solved with simple heuristics, the so-called dispatching rules (DRs). Designing efficient DRs is a tedious task, which is why it has been automated through the application of genetic programming (GP). Various approaches have been used to improve the results of automatically generated DRs, with ensemble learning being one of the best-known. The goal of ensemble learning is to create sets of automatically designed DRs that perform better together. One of the main problems in ensemble learning is the selection of DRs to form the ensemble. To this end, various ensemble construction methods have been proposed over the years. However, these methods are quite computationally intensive and require a lot of computation time to obtain good ensembles. Therefore, in this study, we propose several simple heuristic ensemble construction methods that can be used to construct ensembles quite efficiently and without the need to evaluate their performance. The proposed methods construct the ensembles solely based on certain properties of the individual DRs used for their construction. The experimental study shows that some of the proposed heuristic construction methods perform better than more complex state-of-the-art approaches for constructing ensembles.
动态调度是一类重要的组合优化问题，通常采用简单的启发式方法，即所谓的调度规则（DR）来解决。设计高效的调度规则是一项繁琐的任务，这也是通过应用遗传编程（GP）实现自动化的原因。人们采用了各种方法来改进自动生成的 DR 的结果，其中最著名的是集合学习。集合学习的目标是创建一组自动设计的 DR，这些 DR 组合在一起会有更好的表现。集合学习的主要问题之一是如何选择 DR 来组成集合。为此，多年来人们提出了各种集合构建方法。然而，这些方法的计算量相当大，需要大量的计算时间才能获得良好的集合。因此，在本研究中，我们提出了几种简单的启发式集合构建方法，可用于相当高效地构建集合，且无需评估其性能。所提出的方法完全基于用于构建集合的单个 DR 的某些属性来构建集合。实验研究表明，所提出的一些启发式集合构建方法比最先进的复杂集合构建方法性能更好。
{"title":"Heuristic Ensemble Construction Methods of Automatically Designed Dispatching Rules for the Unrelated Machines Environment","authors":"Marko Đurasević, D. Jakobović","doi":"10.3390/axioms13010037","DOIUrl":"https://doi.org/10.3390/axioms13010037","url":null,"abstract":"Dynamic scheduling represents an important class of combinatorial optimisation problems that are usually solved with simple heuristics, the so-called dispatching rules (DRs). Designing efficient DRs is a tedious task, which is why it has been automated through the application of genetic programming (GP). Various approaches have been used to improve the results of automatically generated DRs, with ensemble learning being one of the best-known. The goal of ensemble learning is to create sets of automatically designed DRs that perform better together. One of the main problems in ensemble learning is the selection of DRs to form the ensemble. To this end, various ensemble construction methods have been proposed over the years. However, these methods are quite computationally intensive and require a lot of computation time to obtain good ensembles. Therefore, in this study, we propose several simple heuristic ensemble construction methods that can be used to construct ensembles quite efficiently and without the need to evaluate their performance. The proposed methods construct the ensembles solely based on certain properties of the individual DRs used for their construction. The experimental study shows that some of the proposed heuristic construction methods perform better than more complex state-of-the-art approaches for constructing ensembles.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"68 3","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139383465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad Waseem Asghar, Mujahid Abbas, Behzad Djafari Rouhani
The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained through the proposed method is proved under some mild assumptions. Consequently, approximations of the solution of the split feasibility problem, the relaxed split feasibility problem, the split common null point problem and the split minimization problem are given. The applicability of our proposed algorithm has been illustrated with the help of a numerical example. Our iterative method was then compared graphically with different comparable methods in the existing literature.
{"title":"The AA-Viscosity Algorithm for Fixed-Point, Generalized Equilibrium and Variational Inclusion Problems","authors":"Muhammad Waseem Asghar, Mujahid Abbas, Behzad Djafari Rouhani","doi":"10.3390/axioms13010038","DOIUrl":"https://doi.org/10.3390/axioms13010038","url":null,"abstract":"The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained through the proposed method is proved under some mild assumptions. Consequently, approximations of the solution of the split feasibility problem, the relaxed split feasibility problem, the split common null point problem and the split minimization problem are given. The applicability of our proposed algorithm has been illustrated with the help of a numerical example. Our iterative method was then compared graphically with different comparable methods in the existing literature.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"53 24","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139384310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Pérez-Ortega, Carlos Fernando Moreno-Calderón, Sandra Silvia Roblero-Aguilar, N. N. Almanza-Ortega, J. Frausto-Solís, Rodolfo Pazos-Rangel, J. M. Rodríguez-Lelis
One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for its initialization and convergence. In this research, a new convergence strategy is proposed, which is based on the difference of the objective function values, in two consecutive iterations, expressed as a percentage of its value in the next to the last one. Additionally, a new method is proposed to optimize the selection of values of the convergence or stop threshold of the algorithm, which is based on the Pareto principle. To validate our approach, a collection of real datasets was solved, and a significant reduction in the number of iterations was observed, without affecting significantly the solution quality. Based on the proposed method and the experiments carried out, we found it is convenient to use threshold values equal to 0.73 and 0.35 if a decrease in the number of iterations of approximately 75.2% and 64.56%, respectively, is wanted, at the expense of a reduction in solution quality of 2% and 1%, respectively. It is worth mentioning that, as the size of the datasets is increased, the proposed approach tends to obtain better results, and therefore, its use is suggested for datasets found in Big Data and Data Science.
{"title":"A New Criterion for Improving Convergence of Fuzzy C-Means Clustering","authors":"J. Pérez-Ortega, Carlos Fernando Moreno-Calderón, Sandra Silvia Roblero-Aguilar, N. N. Almanza-Ortega, J. Frausto-Solís, Rodolfo Pazos-Rangel, J. M. Rodríguez-Lelis","doi":"10.3390/axioms13010035","DOIUrl":"https://doi.org/10.3390/axioms13010035","url":null,"abstract":"One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for its initialization and convergence. In this research, a new convergence strategy is proposed, which is based on the difference of the objective function values, in two consecutive iterations, expressed as a percentage of its value in the next to the last one. Additionally, a new method is proposed to optimize the selection of values of the convergence or stop threshold of the algorithm, which is based on the Pareto principle. To validate our approach, a collection of real datasets was solved, and a significant reduction in the number of iterations was observed, without affecting significantly the solution quality. Based on the proposed method and the experiments carried out, we found it is convenient to use threshold values equal to 0.73 and 0.35 if a decrease in the number of iterations of approximately 75.2% and 64.56%, respectively, is wanted, at the expense of a reduction in solution quality of 2% and 1%, respectively. It is worth mentioning that, as the size of the datasets is increased, the proposed approach tends to obtain better results, and therefore, its use is suggested for datasets found in Big Data and Data Science.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"135 45","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139453038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Matter grows and self-assembles to produce complex structures such as virus capsids, carbon fullerenes, proteins, glasses, etc. Due to its complexity, performing pen-and-paper calculations to explain and describe such assemblies is cumbersome. Many years ago, Richard Kerner presented a pen-and-paper path integral approach to understanding self-organized matter. Although this approach successfully addressed many important problems, including the yield of fullerene formation, the glass transition temperature of doped chalcogenide glasses, the fraction of boroxol rings in B2O3 glasses, the first theoretical explanation for the empirical recipe of window and Pyrex glass and the understanding of virus capsid self-assembly, it still is not the primary choice when tackling similar problems. The reason lies in the fact that it diverges from mainstream approaches based on the energy landscape paradigm and non-equilibrium thermodynamics. In this context, a critical review is presented, demonstrating that the Richard Kerner method is, in fact, a clever way to identify relevant configurations. Its equations are simplified common physical sense versions of those found in the energy landscape kinetic equations. Subsequently, the utilization of equilibrium Boltzmann factors in the transition Markov chain probabilities is analyzed within the context of local two-level energy landscape models kinetics. This analysis demonstrates that their use remains valid when the local energy barrier between reaction coordinate states is small compared to the thermal energy. This finding places the Richard Kerner model on par with other more sophisticated methods and, hopefully, will promote its adoption as an initial and useful choice for describing the self-agglomeration of matter.
{"title":"Richard Kerner’s Path Integral Approach Aims to Understand the Self-Organized Matter Agglomeration and Its Translation into the Energy Landscape Kinetics Paradigm","authors":"Gerado G. Naumis","doi":"10.3390/axioms13010008","DOIUrl":"https://doi.org/10.3390/axioms13010008","url":null,"abstract":"Matter grows and self-assembles to produce complex structures such as virus capsids, carbon fullerenes, proteins, glasses, etc. Due to its complexity, performing pen-and-paper calculations to explain and describe such assemblies is cumbersome. Many years ago, Richard Kerner presented a pen-and-paper path integral approach to understanding self-organized matter. Although this approach successfully addressed many important problems, including the yield of fullerene formation, the glass transition temperature of doped chalcogenide glasses, the fraction of boroxol rings in B2O3 glasses, the first theoretical explanation for the empirical recipe of window and Pyrex glass and the understanding of virus capsid self-assembly, it still is not the primary choice when tackling similar problems. The reason lies in the fact that it diverges from mainstream approaches based on the energy landscape paradigm and non-equilibrium thermodynamics. In this context, a critical review is presented, demonstrating that the Richard Kerner method is, in fact, a clever way to identify relevant configurations. Its equations are simplified common physical sense versions of those found in the energy landscape kinetic equations. Subsequently, the utilization of equilibrium Boltzmann factors in the transition Markov chain probabilities is analyzed within the context of local two-level energy landscape models kinetics. This analysis demonstrates that their use remains valid when the local energy barrier between reaction coordinate states is small compared to the thermal energy. This finding places the Richard Kerner model on par with other more sophisticated methods and, hopefully, will promote its adoption as an initial and useful choice for describing the self-agglomeration of matter.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"42 7","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the exponential growth of high dimensional unlabeled data, unsupervised feature selection (UFS) has attracted considerable attention due to its excellent performance in machine learning. Existing UFS methods implicitly assigned the same attribute score to each sample, which disregarded the distinctiveness of features and weakened the clustering performance of UFS methods to some extent. To alleviate these issues, a novel UFS method is proposed, named unsupervised feature selection with latent relationship penalty term (LRPFS). Firstly, latent learning is innovatively designed by assigning explicitly an attribute score to each sample according to its unique importance in clustering results. With this strategy, the inevitable noise interference can be removed effectively while retaining the intrinsic structure of data samples. Secondly, an appropriate sparse model is incorporated into the penalty term to further optimize its roles as follows: (1) It imposes potential constraints on the feature matrix to guarantee the uniqueness of the solution. (2) The interconnection between data instances is established by a pairwise relationship situation. Extensive experiments on benchmark datasets demonstrate that the proposed method is superior to relevant state-of-the-art algorithms with an average improvement of 10.17% in terms of accuracy.
{"title":"Unsupervised Feature Selection with Latent Relationship Penalty Term","authors":"Ziping Ma, Yulei Huang, Huirong Li, Jingyu Wang","doi":"10.3390/axioms13010006","DOIUrl":"https://doi.org/10.3390/axioms13010006","url":null,"abstract":"With the exponential growth of high dimensional unlabeled data, unsupervised feature selection (UFS) has attracted considerable attention due to its excellent performance in machine learning. Existing UFS methods implicitly assigned the same attribute score to each sample, which disregarded the distinctiveness of features and weakened the clustering performance of UFS methods to some extent. To alleviate these issues, a novel UFS method is proposed, named unsupervised feature selection with latent relationship penalty term (LRPFS). Firstly, latent learning is innovatively designed by assigning explicitly an attribute score to each sample according to its unique importance in clustering results. With this strategy, the inevitable noise interference can be removed effectively while retaining the intrinsic structure of data samples. Secondly, an appropriate sparse model is incorporated into the penalty term to further optimize its roles as follows: (1) It imposes potential constraints on the feature matrix to guarantee the uniqueness of the solution. (2) The interconnection between data instances is established by a pairwise relationship situation. Extensive experiments on benchmark datasets demonstrate that the proposed method is superior to relevant state-of-the-art algorithms with an average improvement of 10.17% in terms of accuracy.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"68 22","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138950486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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