Computational and Mathematical Methods最新文献

{"title":"Quantum approximate optimization of the coset leader problem for binary linear codes","authors":"Markel Epelde,&nbsp;Elías F. Combarro,&nbsp;Ignacio F. Rúa","doi":"10.1002/cmm4.1196","DOIUrl":"10.1002/cmm4.1196","url":null,"abstract":"<p>The security of a broad family of coding-based cryptographic techniques relies on the hardness of the Syndrome Decoding Problem (SDP). In this problem, the aim is to find a word with a given syndrome and of Hamming weight smaller than a prefixed bound. If this last condition is replaced by “of minimum weight,” then we have the Coset Leader Problem (CLP), being Finding Low Weight Codewords (FLWC) a particular case (when the zero syndrome is considered). An algorithm that has been proposed in order to obtain approximate solutions of problems of these kind (NP-complete) is the Quantum Approximate Optimization Algorithm (QAOA), a variational hybrid quantum-classical algorithm. In this paper, we apply the QAOA to the CLP for binary linear codes. We model the problem, make the theoretical analysis the case of the first level, and introduce some experiments to test its performance. The experiments have been carried out on quantum computer simulators with codes of different lengths and QAOA of different depth.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1196","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83121329","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 qualitative analysis of a Mycoplasma genitalium epidemiological\u0000 model","authors":"Ricardo Almeida,&nbsp;M. Teresa T. Monteiro,&nbsp;Ezio Venturino,&nbsp;Luís Machado","doi":"10.1002/cmm4.1199","DOIUrl":"10.1002/cmm4.1199","url":null,"abstract":"<p>The objective of the article is to present a qualitative analysis of a mathematical model for the spread of a sexually transmitted infection caused by <i>Mycoplasma genitalium</i>. Recent investigations revealed that this pathogen is becoming resistant to the use of macrolides and can turn into a superbug in the next few years. We present an epidemiological model to describe the spread of the disease. The equilibrium points are computed, and their local and global stability are studied. In order to make the mathematical problem more realistic, we propose two different optimal control problems that establish a balance between the number of infected individuals and the use of macrolides. Several numerical illustrations regarding the solutions of the proposed problems will be provided.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1199","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79841094","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":"Qualitative behavior of a two-dimensional discrete-time prey–predator model","authors":"Messaoud Berkal,&nbsp;Juan F. Navarro","doi":"10.1002/cmm4.1193","DOIUrl":"10.1002/cmm4.1193","url":null,"abstract":"<p>In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey–predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey–predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark–Sacker bifurcation.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1193","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74346265","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":"Computation of the reverse generalized Bessel polynomials and their zeros","authors":"T. Mark Dunster,&nbsp;Amparo Gil,&nbsp;Diego Ruiz-Antolín,&nbsp;Javier Segura","doi":"10.1002/cmm4.1198","DOIUrl":"10.1002/cmm4.1198","url":null,"abstract":"<p>It is well known that one of the most relevant applications of the reverse Bessel polynomials <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow></math> is filter design. In particular, the poles of the transfer function of a Bessel filter are basically the zeros of <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>. In this article we discuss an algorithm to compute the zeros of reverse generalized Bessel polynomials <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>;</mo>\u0000 <mi>a</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>. A key ingredient in the algorithm will be a method to compute the polynomials. For this purpose, we analyze the use of recurrence relations and asymptotic expansions in terms of elementary functions to obtain accurate approximations to the polynomials. The performance of all the numerical approximations will be illustrated with examples.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1198","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80662524","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":"Controlling crop pest with a farming awareness based integrated approach and optimal control","authors":"Teklebirhan Abraha,&nbsp;Fahad Al Basir,&nbsp;Legesse Lemecha Obsu,&nbsp;Delfim F. M. Torres","doi":"10.1002/cmm4.1194","DOIUrl":"10.1002/cmm4.1194","url":null,"abstract":"<p>We investigate a mathematical model in crop pest controlling, considering plant biomass, pest, and the effect of farming awareness. The pest population is divided into two compartments: susceptible pests and infected pests. We assume that the growth rate of self-aware people is proportional to the density of susceptible pests existing in the crop arena. Impacts of awareness are modeled through the usual mass action term and a saturated term. It is further assumed that self-aware people will adopt chemical and biological control methods, namely, integrated pest management. Bio-pesticides are costly and require a long-term process, expensive to impose. However, if chemical pesticides are introduced in the farming system along with bio-pesticides, the process will be faster as well as cost-effective. Also, farming knowledge is equally important. In this article, a mathematical model is derived for controlling crop pests through an awareness-based integrated approach. In order to reduce the negative effects of pesticides, we apply optimal control theory.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1194","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90225059","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":"Invariant measure for continuous open chain of contours with discrete time","authors":"Marina V. Yashina,&nbsp;Alexander G. Tatashev","doi":"10.1002/cmm4.1197","DOIUrl":"10.1002/cmm4.1197","url":null,"abstract":"<p>A dynamical system is studied. This system belongs to the class of contour networks introduced by A.P. Buslaev. The system is a version of the system called an open chain of contours. Continuous and discrete versions of the system were considered earlier. The system contains <i>N</i> contours. There is one adjacent contour for the utmost left and the utmost right contour, and there are two adjacent contours for any other contour. There is a common point of any two adjacent contours. This point is called a node. There is a cluster in each contour. For the continuous version, the cluster is a segment, moving with constant velocity if there is no delay. For the discrete version, the cluster is a group of adjacent particles. Delays are due to that two clusters may not move through the same node simultaneously. The main system characteristic, studied earlier, is the average velocity of clusters. In this paper, the continious and discrete version of the open chain of contours are considered. The following version of the system is also considered. Each cluster is a segment, and the cluster is shifted onto the distance <i>α</i> at any discrete moment if no delay occurs. We have obtained the limit distribution of the system states. We have also obtained the limit state distribution (invariant measure) for the open chain of contours with continuous state space and continuos time and for the open chain of contours with discrete state space and discrete time.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1197","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89964564","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":"Numerical approximations for a class of nonlinear higher order singular boundary value problem by using homotopy perturbation and variational iteration method","authors":"Biswajit Pandit,&nbsp;Amit Kumar Verma,&nbsp;Ravi P. Agarwal","doi":"10.1002/cmm4.1195","DOIUrl":"10.1002/cmm4.1195","url":null,"abstract":"<p>In this work, we focus on the non-linear fourth order class of singular boundary value problem which contains the parameter <math>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow></math>. We convert this non-linear differential equation into third order non-linear differential equation. The third order problem is singular, non self adjoint, and nonlinear. Moreover, depending upon <math>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow></math>, it admits multiple solutions. Hence, it is too difficult to capture these solutions by any discrete method such as finite difference and so forth. Here we develop an iterative technique with the help of homotopy perturbation method and variational iteration method in a suitable way. Convergence of this series solution is studied in a novel way. We compute these solutions numerically. For small positive values of <math>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow></math>, singular BVP has two solutions while solutions can not be found for large positive values of <math>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow></math>. Furthermore, we also find dual solutions for <math>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>0</mn>\u0000 </mrow></math>.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1195","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83353944","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":"An efficient family of Steffensen-type methods with memory for solving systems of nonlinear equations","authors":"Mona Narang,&nbsp;Saurabh Bhatia,&nbsp;Vinay Kanwar","doi":"10.1002/cmm4.1192","DOIUrl":"10.1002/cmm4.1192","url":null,"abstract":"<p>The article discusses derivative-free algorithms with and without memory for solving numerically nonlinear systems. We proposed a family of fifth- and sixth-order schemes and extended them to algorithms with memory. We further discuss the convergence and computational efficiency of these algorithms. Numerical examples of mixed Hammerstein integral equation, discrete nonlinear ordinary differential equation, and Fisher's partial differential equation with Neumann's boundary conditions are discussed to demonstrate the convergence and efficiency of these schemes. Finally, some numerical results are included to examine the performance of the developed methods.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1192","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80255999","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":"Data curation in the Internet of Things: A decision model approach","authors":"Francisco José de Haro-Olmo,&nbsp;Álvaro Valencia-Parra,&nbsp;Ángel Jesús Varela-Vaca,&nbsp;José Antonio Álvarez-Bermejo","doi":"10.1002/cmm4.1191","DOIUrl":"10.1002/cmm4.1191","url":null,"abstract":"<p>Current Internet of Things (IoT) scenarios have to deal with many challenges especially when a large amount of heterogeneous data sources are integrated, that is, data curation. In this respect, the use of poor-quality data (i.e., data with problems) can produce terrible consequence from incorrect decision-making to damaging the performance in the operations. Therefore, using data with an acceptable level of usability has become essential to achieve success. In this article, we propose an IoT-big data pipeline architecture that enables data acquisition and data curation in any IoT context. We have customized the pipeline by including the DMN4DQ approach to enable us the measuring and evaluating data quality in the data produced by IoT sensors. Further, we have chosen a real dataset from sensors in an agricultural IoT context and we have defined a decision model to enable us the automatic measuring and assessing of the data quality with regard to the usability of the data in the context.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1191","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74430662","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":"Convergence of collocation methods for solving periodic boundary value problems for renewal equations defined through finite-dimensional boundary conditions","authors":"Alessia Andò","doi":"10.1002/cmm4.1190","DOIUrl":"10.1002/cmm4.1190","url":null,"abstract":"<p>The problem of computing periodic solutions can be expressed as a boundary value problem and solved numerically via piecewise collocation. Here, we extend to renewal equations the corresponding method for retarded functional differential equations in (K. Engelborghs et al., <i>SIAM J Sci Comput</i>., 22 (2001), pp. 1593–1609). The theoretical proof of the convergence of the method has been recently provided in (A. Andò and D. Breda, <i>SIAM J Numer Anal</i>., 58 (2020), pp. 3010–3039) for retarded functional differential equations and in (A. Andò and D. Breda, submitted in 2021) for renewal equations and consists in both cases in applying the abstract framework in (S. Maset, <i>Numer Math</i>., 133 (2016), pp. 525–555) to a reformulation of the boundary value problem featuring an infinite-dimensional boundary condition. We show that, in the renewal case, the proof can also be carried out and even simplified when considering the standard formulation, defined by boundary conditions of finite dimension.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/cmm4.1190","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88490896","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}