One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times by a few minutes will have a significant impact on the number of trips made by an aircraft, as well as enabling improvements in key measures such as the median and 75th and 95th percentiles. Looking at such measures other than the mean is critical as it is well known that the mean can under- or overestimate the performance of any model. While there is considerable literature on the study of strategies to decrease boarding times, the same cannot be said about the study of the boarding time given a particular strategy for boarding. Thus, the focus of this paper is to study analytically (using suitable stochastic models) and numerically the impact of reducing the average time on the key measures to help the system to plan accordingly. This is achieved using a well-known probability distribution, namely the phase type distribution, to model various events involved in the boarding process. Illustrative numerical results show a reduction in the percentile values when the average boarding times are decreased. Understanding the percentiles of the boarding times, as opposed to relying only on the average boarding times, will help management to adopt a better boarding strategy that in turn will lead to an increase in the number of trips that an aircraft can make.
{"title":"Quantitative and Qualitative Analysis of Aircraft Round-Trip Times Using Phase Type Distributions","authors":"Srinivas R. Chakravarthy","doi":"10.3390/math12172795","DOIUrl":"https://doi.org/10.3390/math12172795","url":null,"abstract":"One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times by a few minutes will have a significant impact on the number of trips made by an aircraft, as well as enabling improvements in key measures such as the median and 75th and 95th percentiles. Looking at such measures other than the mean is critical as it is well known that the mean can under- or overestimate the performance of any model. While there is considerable literature on the study of strategies to decrease boarding times, the same cannot be said about the study of the boarding time given a particular strategy for boarding. Thus, the focus of this paper is to study analytically (using suitable stochastic models) and numerically the impact of reducing the average time on the key measures to help the system to plan accordingly. This is achieved using a well-known probability distribution, namely the phase type distribution, to model various events involved in the boarding process. Illustrative numerical results show a reduction in the percentile values when the average boarding times are decreased. Understanding the percentiles of the boarding times, as opposed to relying only on the average boarding times, will help management to adopt a better boarding strategy that in turn will lead to an increase in the number of trips that an aircraft can make.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"12 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177119","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}
A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data are to the training set.
{"title":"Coarse-Gridded Simulation of the Nonlinear Schrödinger Equation with Machine Learning","authors":"Benjamin F. Akers, Kristina O. F. Williams","doi":"10.3390/math12172784","DOIUrl":"https://doi.org/10.3390/math12172784","url":null,"abstract":"A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data are to the training set.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"34 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177093","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}
We consider a two-group social conflict under the corporates’ research and development (R&D) business processes. Conflict participants are divided into two groups depending on their attitude to new ideas, technologies, and behavioral style for R&D creative problems—innovators and adapters. We reveal the contradiction that arises between the need to include both types of employees in one project team and their objectively antagonistic positions regarding the methods and approaches to R&D processes. The proposed research methodology is based on a modern post-non-classical paradigm formed on the principles of coherence, interdisciplinarity, openness, and nonlinearity, as well as a sociophysical approach to the social conflicts modeling. We use the general theories of magnetism, paramagnetism, and functions of P. Langevin and L. Brillouin to describe the dynamics of group participants’ preferences regarding the style of conflict behavior. The analogy of paramagnetism, consisting in the orienting effect of the magnetic field, is used to describe social groups interactions that have not only their own interests, but are also influenced by the opinions of opposite social groups. A two-dimensional, four-parameter map represents the dynamics of group conflict. Modeling results show that regardless of the initial states and with certain parameters of intra-group and intergroup interactions, the trajectories eventually converge to an attractor (limit cycle) in a two-dimensional space. No non-periodic or chaotic modes are identified in the two-group conflict, which determines the controllability of the described conflict. The results of the simulation experiments are used as decision support and contradictions resolution aimed at forming the required modes of the corporates’ research and development business processes and ensuring the group participants’ cohesion and depolarization. The results of testing the model at an industrial enterprise are presented.
我们考虑了企业研发（R&D）业务流程下的两组社会冲突。冲突参与者根据其对新想法、新技术的态度以及对研发创造性问题的行为方式被分为两组--创新者和适应者。我们揭示了将这两类员工纳入一个项目团队的必要性与他们在研发流程的方法和途径方面的客观对立立场之间的矛盾。我们提出的研究方法是基于一种现代的后非经典范式，这种范式是在一致性、跨学科性、开放性和非线性原则以及社会冲突建模的社会物理学方法的基础上形成的。我们使用 P. 朗热文和 L. 布里卢安的磁学、准磁学和函数的一般理论来描述群体参与者对冲突行为方式的偏好动态。准磁学的类比，包括磁场的定向效应，被用来描述社会群体的互动，这些群体不仅有自己的利益，而且还受到相反社会群体意见的影响。一个二维四参数图代表了群体冲突的动态。建模结果表明，无论初始状态如何，只要有一定的群体内和群体间互动参数，轨迹最终都会收敛到二维空间中的吸引子（极限循环）。在两组冲突中没有发现非周期性或混乱模式，这就决定了所述冲突的可控性。模拟实验的结果被用作决策支持和矛盾解决，旨在形成企业研发业务流程所需的模式，确保群体参与者的凝聚力和去极化。本文介绍了该模型在一家工业企业的测试结果。
{"title":"A Novel Brillouin and Langevin Functions Dynamic Model for Two Conflicting Social Groups: Study of R&D Processes","authors":"Ekaterina V. Orlova","doi":"10.3390/math12172788","DOIUrl":"https://doi.org/10.3390/math12172788","url":null,"abstract":"We consider a two-group social conflict under the corporates’ research and development (R&D) business processes. Conflict participants are divided into two groups depending on their attitude to new ideas, technologies, and behavioral style for R&D creative problems—innovators and adapters. We reveal the contradiction that arises between the need to include both types of employees in one project team and their objectively antagonistic positions regarding the methods and approaches to R&D processes. The proposed research methodology is based on a modern post-non-classical paradigm formed on the principles of coherence, interdisciplinarity, openness, and nonlinearity, as well as a sociophysical approach to the social conflicts modeling. We use the general theories of magnetism, paramagnetism, and functions of P. Langevin and L. Brillouin to describe the dynamics of group participants’ preferences regarding the style of conflict behavior. The analogy of paramagnetism, consisting in the orienting effect of the magnetic field, is used to describe social groups interactions that have not only their own interests, but are also influenced by the opinions of opposite social groups. A two-dimensional, four-parameter map represents the dynamics of group conflict. Modeling results show that regardless of the initial states and with certain parameters of intra-group and intergroup interactions, the trajectories eventually converge to an attractor (limit cycle) in a two-dimensional space. No non-periodic or chaotic modes are identified in the two-group conflict, which determines the controllability of the described conflict. The results of the simulation experiments are used as decision support and contradictions resolution aimed at forming the required modes of the corporates’ research and development business processes and ensuring the group participants’ cohesion and depolarization. The results of testing the model at an industrial enterprise are presented.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"7 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177094","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}
Guoquan Yuan, Xinjian Zhao, Liu Li, Song Zhang, Shanming Wei
Traditional machine learning-based entity extraction methods rely heavily on feature engineering by experts, and the generalization ability of the model is poor. Prototype networks, on the other hand, can effectively use a small amount of labeled data to train models while using category prototypes to enhance the generalization ability of the models. Therefore, this paper proposes a prototype network-based named entity recognition (NER) method, namely the FSPN-NER model, to solve the problem of difficult recognition of sensitive data in data-sparse text. The model utilizes the positional coding model (PCM) to pre-train the data and perform feature extraction, then computes the prototype vectors to achieve entity matching, and finally introduces a boundary detection module to enhance the performance of the prototype network in the named entity recognition task. The model in this paper is compared with LSTM, BiLSTM, CRF, Transformer and their combination models, and the experimental results on the test dataset show that the model outperforms the comparative models with an accuracy of 84.8%, a recall of 85.8% and an F1 value of 0.853.
{"title":"Few-Shot Learning Sensitive Recognition Method Based on Prototypical Network","authors":"Guoquan Yuan, Xinjian Zhao, Liu Li, Song Zhang, Shanming Wei","doi":"10.3390/math12172791","DOIUrl":"https://doi.org/10.3390/math12172791","url":null,"abstract":"Traditional machine learning-based entity extraction methods rely heavily on feature engineering by experts, and the generalization ability of the model is poor. Prototype networks, on the other hand, can effectively use a small amount of labeled data to train models while using category prototypes to enhance the generalization ability of the models. Therefore, this paper proposes a prototype network-based named entity recognition (NER) method, namely the FSPN-NER model, to solve the problem of difficult recognition of sensitive data in data-sparse text. The model utilizes the positional coding model (PCM) to pre-train the data and perform feature extraction, then computes the prototype vectors to achieve entity matching, and finally introduces a boundary detection module to enhance the performance of the prototype network in the named entity recognition task. The model in this paper is compared with LSTM, BiLSTM, CRF, Transformer and their combination models, and the experimental results on the test dataset show that the model outperforms the comparative models with an accuracy of 84.8%, a recall of 85.8% and an F1 value of 0.853.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177116","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}
Ramandeep Behl, Ioannis K. Argyros, Sattam Alharbi
This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results.
{"title":"Accelerating the Speed of Convergence for High-Order Methods to Solve Equations","authors":"Ramandeep Behl, Ioannis K. Argyros, Sattam Alharbi","doi":"10.3390/math12172785","DOIUrl":"https://doi.org/10.3390/math12172785","url":null,"abstract":"This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2016 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177090","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}
Omer Ajmal, Shahzad Mumtaz, Humaira Arshad, Abdullah Soomro, Tariq Hussain, Razaz Waheeb Attar, Ahmed Alhomoud
The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For instance, DENsity CLUstEring (DENCLUE)—a density-based clustering algorithm—requires a trial-and-error approach to find suitable parameters for optimal clusters. Earlier attempts to automate the parameter estimation of DENCLUE have been highly dependent either on the choice of prior data distribution (which could vary across datasets) or by fixing one parameter (which might not be optimal) and learning other parameters. This article addresses this challenge by learning the parameters of DENCLUE through the differential evolution optimisation technique without prior data distribution assumptions. Experimental evaluation of the proposed approach demonstrated consistent performance across datasets (synthetic and real datasets) containing clusters of arbitrary shapes. The clustering performance was evaluated using clustering validation metrics (e.g., Silhouette Score, Davies–Bouldin Index and Adjusted Rand Index) as well as qualitative visual analysis when compared with other density-based clustering algorithms, such as DPC, which is based on weighted local density sequences and nearest neighbour assignments (DPCSA) and Variable KDE-based DENCLUE (VDENCLUE).
利用样本的邻近性在数据集中寻找自然分组的任务被称为聚类，这是一种无监督学习方法。基于密度的聚类算法利用空间维度和邻域方面识别任意形状的聚类，对参数的选择非常敏感。例如，基于密度的聚类算法 DENsity CLUstEring（DENCLUE）需要通过反复试验才能找到合适的参数，从而获得最佳聚类。早期对 DENCLUE 参数估计自动化的尝试高度依赖于先验数据分布的选择（不同数据集的先验数据分布可能不同），或者通过固定一个参数（可能不是最佳参数）并学习其他参数。本文通过微分进化优化技术学习 DENCLUE 的参数，而无需先验数据分布假设，从而解决了这一难题。对所提出方法的实验评估表明，该方法在包含任意形状聚类的数据集（合成数据集和真实数据集）中具有一致的性能。在与其他基于密度的聚类算法（如基于加权局部密度序列和近邻分配的 DPC（DPCSA）和基于 KDE 的可变 DENCLUE（VDENCLUE））进行比较时，使用聚类验证指标（如剪影得分、戴维斯-博尔丁指数和调整后兰德指数）以及定性视觉分析对聚类性能进行了评估。
{"title":"Enhanced Parameter Estimation of DENsity CLUstEring (DENCLUE) Using Differential Evolution","authors":"Omer Ajmal, Shahzad Mumtaz, Humaira Arshad, Abdullah Soomro, Tariq Hussain, Razaz Waheeb Attar, Ahmed Alhomoud","doi":"10.3390/math12172790","DOIUrl":"https://doi.org/10.3390/math12172790","url":null,"abstract":"The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For instance, DENsity CLUstEring (DENCLUE)—a density-based clustering algorithm—requires a trial-and-error approach to find suitable parameters for optimal clusters. Earlier attempts to automate the parameter estimation of DENCLUE have been highly dependent either on the choice of prior data distribution (which could vary across datasets) or by fixing one parameter (which might not be optimal) and learning other parameters. This article addresses this challenge by learning the parameters of DENCLUE through the differential evolution optimisation technique without prior data distribution assumptions. Experimental evaluation of the proposed approach demonstrated consistent performance across datasets (synthetic and real datasets) containing clusters of arbitrary shapes. The clustering performance was evaluated using clustering validation metrics (e.g., Silhouette Score, Davies–Bouldin Index and Adjusted Rand Index) as well as qualitative visual analysis when compared with other density-based clustering algorithms, such as DPC, which is based on weighted local density sequences and nearest neighbour assignments (DPCSA) and Variable KDE-based DENCLUE (VDENCLUE).","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177096","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}
Manuel A. Duarte-Mermoud, Abdiel Ricaldi-Morales, Juan Carlos Travieso-Torres, Rafael Castro-Linares
This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for these controllers are optimized using the particle swarm optimization (PSO) algorithm with an objective function tailored to the control goals. This study employs models of both a bank series of five flotation cells and a flotation column. Their performance results are compared against traditional controllers, such as an integer-order PID and MRAC. The findings reveal that fractional-order controllers offer notable advantages over their integer-order counterparts, showing improved performance metrics with minimal changes to the existing control framework. This research highlights the effectiveness of fractional control in enhancing flotation processes and introduces a novel application of fractional control techniques in this area.
{"title":"Design and Comparison of Fractional-Order Controllers in Flotation Cell Banks and Flotation Columns Used in Copper Extraction Processes","authors":"Manuel A. Duarte-Mermoud, Abdiel Ricaldi-Morales, Juan Carlos Travieso-Torres, Rafael Castro-Linares","doi":"10.3390/math12172789","DOIUrl":"https://doi.org/10.3390/math12172789","url":null,"abstract":"This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for these controllers are optimized using the particle swarm optimization (PSO) algorithm with an objective function tailored to the control goals. This study employs models of both a bank series of five flotation cells and a flotation column. Their performance results are compared against traditional controllers, such as an integer-order PID and MRAC. The findings reveal that fractional-order controllers offer notable advantages over their integer-order counterparts, showing improved performance metrics with minimal changes to the existing control framework. This research highlights the effectiveness of fractional control in enhancing flotation processes and introduces a novel application of fractional control techniques in this area.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"4 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177097","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}
Chun-Ming Yang, Chang-Hsien Hsu, Tian Chen, Shiyao Li
Evaluating the performance of city construction not only helps optimize city functions and improve city quality, but it also contributes to the development of sustainable cities. However, most of the scoring rules for evaluating the performance of city construction are overly cumbersome and demand very high data integrity. Moreover, the properties, change scale, and scope of different evaluation indicators of city construction often lead to uncertain and ambiguous results. In this study, a hybrid fuzzy method is proposed to conduct the performance evaluation of city construction in two phases. Firstly, a city performance index (CPI) was developed by combining the means and standard deviations of indicators of city construction to address the volatility of historical statistical data as well as different types of data. Considering the sampling errors in data analysis, the parameter estimation method was used to derive the 100% × (1 − α) confidence interval of the CPI. Buckley’s fuzzy approach was then adopted to extend the statistical estimators from the CPI into fuzzy estimators, after which a fuzzy CPI was proposed. To identify the specific improvement directions for city construction, the fuzzy axiom design (fuzzy AD) method was applied to explore the relationship between the targets set by city managers and actual performance. Finally, an example of six cities in China is provided to illustrate the effectiveness and practicality of the proposed method. The results show that the performance of Chongqing on several evaluation indicators is lower than that of other cities. The proposed method takes into account the issues of uniformity and diversity in the performance evaluation of city construction. It can enable a quantitative assessment of the city construction level in all cities and provide theoretical support and a decision-making basis for relevant government departments to optimize city construction planning and scientifically formulate city construction policies.
{"title":"Hybrid Fuzzy Method for Performance Evaluation of City Construction","authors":"Chun-Ming Yang, Chang-Hsien Hsu, Tian Chen, Shiyao Li","doi":"10.3390/math12172792","DOIUrl":"https://doi.org/10.3390/math12172792","url":null,"abstract":"Evaluating the performance of city construction not only helps optimize city functions and improve city quality, but it also contributes to the development of sustainable cities. However, most of the scoring rules for evaluating the performance of city construction are overly cumbersome and demand very high data integrity. Moreover, the properties, change scale, and scope of different evaluation indicators of city construction often lead to uncertain and ambiguous results. In this study, a hybrid fuzzy method is proposed to conduct the performance evaluation of city construction in two phases. Firstly, a city performance index (CPI) was developed by combining the means and standard deviations of indicators of city construction to address the volatility of historical statistical data as well as different types of data. Considering the sampling errors in data analysis, the parameter estimation method was used to derive the 100% × (1 − α) confidence interval of the CPI. Buckley’s fuzzy approach was then adopted to extend the statistical estimators from the CPI into fuzzy estimators, after which a fuzzy CPI was proposed. To identify the specific improvement directions for city construction, the fuzzy axiom design (fuzzy AD) method was applied to explore the relationship between the targets set by city managers and actual performance. Finally, an example of six cities in China is provided to illustrate the effectiveness and practicality of the proposed method. The results show that the performance of Chongqing on several evaluation indicators is lower than that of other cities. The proposed method takes into account the issues of uniformity and diversity in the performance evaluation of city construction. It can enable a quantitative assessment of the city construction level in all cities and provide theoretical support and a decision-making basis for relevant government departments to optimize city construction planning and scientifically formulate city construction policies.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"151 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177117","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}
Oleg O. Khamisov, Oleg V. Khamisov, Todor D. Ganchev, Eugene S. Semenkin
We propose a novel distributed method for non-convex optimization problems with coupling equality and inequality constraints. This method transforms the optimization problem into a specific form to allow distributed implementation of modified gradient descent and Newton’s methods so that they operate as if they were distributed. We demonstrate that for the proposed distributed method: (i) communications are significantly less time-consuming than oracle calls, (ii) its convergence rate is equivalent to the convergence of Newton’s method concerning oracle calls, and (iii) for the cases when oracle calls are more expensive than communication between agents, the transition from a centralized to a distributed paradigm does not significantly affect computational time. The proposed method is applicable when the objective function is twice differentiable and constraints are differentiable, which holds for a wide range of machine learning methods and optimization setups.
{"title":"A Method for Transforming Non-Convex Optimization Problem to Distributed Form","authors":"Oleg O. Khamisov, Oleg V. Khamisov, Todor D. Ganchev, Eugene S. Semenkin","doi":"10.3390/math12172796","DOIUrl":"https://doi.org/10.3390/math12172796","url":null,"abstract":"We propose a novel distributed method for non-convex optimization problems with coupling equality and inequality constraints. This method transforms the optimization problem into a specific form to allow distributed implementation of modified gradient descent and Newton’s methods so that they operate as if they were distributed. We demonstrate that for the proposed distributed method: (i) communications are significantly less time-consuming than oracle calls, (ii) its convergence rate is equivalent to the convergence of Newton’s method concerning oracle calls, and (iii) for the cases when oracle calls are more expensive than communication between agents, the transition from a centralized to a distributed paradigm does not significantly affect computational time. The proposed method is applicable when the objective function is twice differentiable and constraints are differentiable, which holds for a wide range of machine learning methods and optimization setups.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177121","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}
Waleed B. Altukhaes, Mahdi Roozbeh, Nur A. Mohamed
Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear constraints are assumed to hold in the parameter space. The Liu estimator is used to address the multicollinearity, while robust methods are used to handle the outlier problem. In the literature on the Liu methodology, obtaining the best value for the biased parameter plays an important role in model prediction and is still an unsolved problem. In this regard, some robust estimators of the biased parameter are proposed based on the least trimmed squares (LTS) technique and its extensions using a semidefinite programming approach. Based on a set of observations with a sample size of n, and the integer trimming parameter h ≤ n, the LTS estimator computes the hyperplane that minimizes the sum of the lowest h squared residuals. Even though the LTS estimator is statistically more effective than the widely used least median squares (LMS) estimate, it is less complicated computationally than LMS. It is shown that the proposed robust extended Liu estimators perform better than classical estimators. As part of our proposal, using Monte Carlo simulation schemes and a real data example, the performance of robust Liu estimators is compared with that of classical ones in restricted partially linear models.
异常值与多重共线性是应用统计中的常见问题。本文在部分线性模型中引入了稳健的刘估计器，以应对误差项不独立且假定参数空间中存在某些线性约束时出现的多重共线性和异常值难题。刘估计器用于解决多重共线性问题，而稳健方法则用于处理离群值问题。在有关刘估计法的文献中，如何获得偏置参数的最佳值在模型预测中起着重要作用，这仍是一个尚未解决的问题。在这方面，基于最小修剪平方（LTS）技术及其使用半有限编程方法的扩展，提出了一些稳健的偏差参数估计器。基于一组样本量为 n 的观测数据，以及整数修剪参数 h ≤ n，LTS 估计器计算出使最低 h 平方残差之和最小化的超平面。尽管 LTS 估计器在统计上比广泛使用的最小中位数方差（LMS）估计器更有效，但在计算上却没有 LMS 那么复杂。结果表明，所提出的稳健扩展刘估计器的性能优于经典估计器。作为我们建议的一部分，我们使用蒙特卡罗模拟方案和一个真实数据示例，比较了鲁棒性刘估计器与经典估计器在受限部分线性模型中的性能。
{"title":"Robust Liu Estimator Used to Combat Some Challenges in Partially Linear Regression Model by Improving LTS Algorithm Using Semidefinite Programming","authors":"Waleed B. Altukhaes, Mahdi Roozbeh, Nur A. Mohamed","doi":"10.3390/math12172787","DOIUrl":"https://doi.org/10.3390/math12172787","url":null,"abstract":"Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear constraints are assumed to hold in the parameter space. The Liu estimator is used to address the multicollinearity, while robust methods are used to handle the outlier problem. In the literature on the Liu methodology, obtaining the best value for the biased parameter plays an important role in model prediction and is still an unsolved problem. In this regard, some robust estimators of the biased parameter are proposed based on the least trimmed squares (LTS) technique and its extensions using a semidefinite programming approach. Based on a set of observations with a sample size of n, and the integer trimming parameter h ≤ n, the LTS estimator computes the hyperplane that minimizes the sum of the lowest h squared residuals. Even though the LTS estimator is statistically more effective than the widely used least median squares (LMS) estimate, it is less complicated computationally than LMS. It is shown that the proposed robust extended Liu estimators perform better than classical estimators. As part of our proposal, using Monte Carlo simulation schemes and a real data example, the performance of robust Liu estimators is compared with that of classical ones in restricted partially linear models.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"28 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177091","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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