Computational and Mathematical Methods最新文献

{"title":"Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution","authors":"Ayana Mateus,&nbsp;Frederico Caeiro","doi":"10.1155/2022/8400130","DOIUrl":"10.1155/2022/8400130","url":null,"abstract":"<div>\u0000 <p>The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah and Alzaatreh studied the best linear unbiased estimators for the location and the scale parameters of the three-parameter log-logistic model. The same authors also propose a shift-invariant Hill estimator for the unknown shape parameter. In this work, we propose a new estimation method for the shape parameter. We derive its nondegenerate asymptotic behaviour and analyse its finite sample performance through a Monte Carlo simulation study. To have precise estimates, we present a method for selecting the threshold. To illustrate the improvement achieved, efficiency comparisons are also provided.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8400130","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81981386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deterministic and Stochastic Dynamics of COVID-19: The Case Study of Italy and Spain","authors":"Akhil Kumar Srivastav,&nbsp;Nico Stollenwerk,&nbsp;Maíra Aguiar","doi":"10.1155/2022/5780719","DOIUrl":"10.1155/2022/5780719","url":null,"abstract":"<div>\u0000 <p>In December 2019, a severe respiratory syndrome (COVID-19) caused by a new coronavirus (SARS-CoV-2) was identified in China and spread rapidly around the globe. COVID-19 was declared a pandemic by the World Health Organization (WHO) in March 2020. With eventually substantial global underestimation, more than 225 million cases were confirmed by the end of August 2021, counting more than 4.5 million deaths. COVID-19 symptoms range from mild (or no symptoms) to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and preexisting health conditions enhancing the risks of disease severity manifestation. In this paper, a mathematical model for COVID-19 transmission is proposed and analyzed. The model stratifies the studied population into two groups, older and younger. Applied to the COVID-19 outbreaks in Spain and in Italy, we find the disease-free equilibrium and the basic reproduction number for each case study. A sensitivity analysis to identify the key parameters which influence the basic reproduction number, and hence regulate the transmission dynamics of COVID-19, is also performed. Finally, the model is extended to its stochastic counterpart to encapsulate the variation or uncertainty found in the transmissibility of the disease. We observe the variability of the infectious population finding its distribution at a given time, demonstrating that for small populations, stochasticity will play an important role.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/5780719","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81061582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of a Set of Symmetric Temporal Transformations for the Study of the Orbital Motion","authors":"José Antonio López Ortí,&nbsp;Vicente Agost Gómez,&nbsp;Miguel Barreda Rochera","doi":"10.1155/2022/9037530","DOIUrl":"10.1155/2022/9037530","url":null,"abstract":"<div>\u0000 <p>The main goal of this paper is to define a new one-parametric family of symmetric temporal transformations with respect to the ellipse. This new family contains as a particular case the eccentric anomaly, the regularized length of arc, and the elliptic anomaly. This family is a particular case of the biparametric family of anomalies introduced by the authors in 2016. The biparametric family comprises the most common anomalies used in the study of the two-body problem. Two approaches of this work have been taken. The first one involves the study of the analytical properties of the symmetric family of anomalies. The second approach explores the improvement of the numerical integration methods when the natural time is replaced by an anomaly of this family.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/9037530","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74594850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Probability Model Based on a Coherent System with Applications","authors":"Christophe Chesneau,&nbsp;Hassan S. Bakouch,&nbsp;Bilal A. Para,&nbsp;Mohammad H. Poursaeed","doi":"10.1155/2022/8564465","DOIUrl":"10.1155/2022/8564465","url":null,"abstract":"<div>\u0000 <p>The notion of a coherent system allows us to formalize how the random lifetime of the system is connected to the random lifetimes of its components. These connections are also generators of new pliant distributions, being those of various mixes of minimum and maximum of random variables. In this paper, a new four-parameter lifetime probability distribution is introduced by using the notion of a coherent system. Its structural properties are assessed and evaluated, including the analytical study of its main functions, stochastic dominance results, moments, and moment generating function. The proposed distribution, in particular, is proving to be efficient at fitting data with slight negative skewness and platykurtic as well as leptokurtic nature. This is illustrated by the analysis of three relevant real-life data sets, two in reliability and another in production, exhibiting the significance of the introduced model in comparison to various well-known models in statistical literature.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8564465","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84702125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Numerical Approach for Singularly Perturbed Nonlinear Delay Differential Equations Using a Trigonometric Spline","authors":"M. Lalu,&nbsp;K. Phaneendra","doi":"10.1155/2022/8338661","DOIUrl":"10.1155/2022/8338661","url":null,"abstract":"<div>\u0000 <p>In this paper, a computational procedure for solving singularly perturbed nonlinear delay differentiation equations (SPNDDEs) is proposed. Initially, the SPNDDE is reduced into a series of singularly perturbed linear delay differential equations (SPLDDEs) using the quasilinearization technique. A trigonometric spline approach is suggested to solve the sequence of SPLDDEs. Convergence of the method is addressed. The efficiency and applicability of the proposed method are demonstrated by the numerical examples.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8338661","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82701588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep Brain Stimulation with a Computational Model for the Cortex-Thalamus-Basal-Ganglia System and Network Dynamics of Neurological Disorders","authors":"Hina Shaheen,&nbsp;Roderick Melnik","doi":"10.1155/2022/8998150","DOIUrl":"10.1155/2022/8998150","url":null,"abstract":"<div>\u0000 <p>Deep brain stimulation (DBS) can alleviate the movement disorders like Parkinson’s disease (PD). Indeed, it is known that aberrant beta (13-30 Hz) oscillations and the loss of dopaminergic neurons in the basal ganglia-thalamus (BGTH) and cortex characterize the akinesia symptoms of PD. However, the relevant biophysical mechanism behind this process still remains unclear. Based on the prior striatal inhibitory model, we propose an extended BGTH model incorporating medium spine neurons (MSNs) and fast-spiking interneurons (FSIs) along with the effect of DBS. We are focusing in this paper on an open-loop DBS mode, where the stimulation parameters stay constant independent of variations in the disease state, and modifications of parameters rely mainly on trial and error of medical experts. Additionally, we propose a novel combined model of the cerebellar-basal-ganglia thalamocortical network, MSNs, and FSIs and show new results that indicate that Parkinsonian oscillations in the beta-band frequency range emerge from the dynamics of such a network. Our model predicts that DBS can be used to suppress beta oscillations in globus pallidus pars interna (GPi) neurons. This research will help our better understanding of the changes in the brain activity caused by DBS, providing new insight for studying PD in the future.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8998150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82439332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel two-parameter class of optimized hybrid block methods for integrating differential systems numerically","authors":"Gurjinder Singh,&nbsp;Arvind Garg,&nbsp;Rajat Singla,&nbsp;Vinay Kanwar","doi":"10.1002/cmm4.1214","DOIUrl":"10.1002/cmm4.1214","url":null,"abstract":"<p>In this article, a two-parameter class of hybrid block methods for integrating first-order initial value ordinary differential systems is proposed. The methods exhibit hybrid nature which helps in bypassing the first Dahlquist barrier existing for linear multistep methods. The approach used in the development of a class of methods is purely interpolation and collocation technique. The class of methods is based on four intra-step points from which two intra-step points have been optimized by using an optimization strategy. In this optimization strategy, the values of two intra-step points are obtained by minimizing the local truncation errors of the formulas at the points <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> and <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>.The order of accuracy of the proposed methods is six. A method as a special case of this class of methods is considered and developed into a block form which produces approximate numerical solutions at several points simultaneously. Further, the method is formulated into an adaptive step-size algorithm using an embedded type procedure. This method which is a special case of this class of methods has been tested on six well-known first-order differential systems.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1214","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91332636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A collection of efficient tools to work with almost strictly sign regular matrices","authors":"Pedro Alonso Velázquez,&nbsp;Jorge Jiménez Meana,&nbsp;Juan Manuel Peña Ferrández,&nbsp;María Luisa Serrano Ortega","doi":"10.1002/cmm4.1212","DOIUrl":"10.1002/cmm4.1212","url":null,"abstract":"<p>In this work, several algorithms have been implemented with Matlab to obtain an algorithmic characterizations of almost strictly sign regular matrices using Neville elimination.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90819506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The change of the Weierstrass structure under one row perturbation","authors":"Itziar Baragaña,&nbsp;Alicia Roca","doi":"10.1002/cmm4.1211","DOIUrl":"10.1002/cmm4.1211","url":null,"abstract":"<p>In this work we study the change of the structure of a regular pencil when we perform small perturbations over some of its rows and the other rows remain unaltered. We provide necessary conditions when several rows are perturbed, and prove them to be sufficient to prescribe the homogenous invariant factors or the Weyr characteristic of the resulting pencil when one row is perturbed.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1211","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87421869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid method for two parameter singularly perturbed elliptic boundary value problems","authors":"Anuradha Jha,&nbsp;Mohan Krishen Kadalbajoo","doi":"10.1002/cmm4.1210","DOIUrl":"10.1002/cmm4.1210","url":null,"abstract":"<p>In this article, a hybrid scheme for a two-parameter elliptic problem with regular exponential and boundary layers on Shishkin mesh is analyzed. The hybrid scheme comprises the central difference method in the layer region and the upwind method in the regular part. The use of the central difference in layer region results in a more accurate resolution of layers. The method is shown to have first-order parameter uniform convergence. The numerical results corroborate the error estimates presented here.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1210","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86916121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}