We consider the weak Galerkin finite element approximation of the singularly perturbed biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution exhibits boundary layers near the domain boundary. Error estimates in the equivalent norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings.
{"title":"Anisotropic error analysis of weak Galerkin finite element method for singularly perturbed biharmonic problems","authors":"Aayushman Raina , Srinivasan Natesan , Şuayip Toprakseven","doi":"10.1016/j.matcom.2024.09.017","DOIUrl":"10.1016/j.matcom.2024.09.017","url":null,"abstract":"<div><div>We consider the weak Galerkin finite element approximation of the singularly perturbed biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution exhibits boundary layers near the domain boundary. Error estimates in the equivalent <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo></mrow></math></span> norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 203-221"},"PeriodicalIF":4.4,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-05DOI: 10.1016/j.matcom.2024.10.001
Rakesh Kumar , Sudarshan Dhua
This article establishes an efficient solution scheme for a mathematical model of Hashimoto’s Thyroiditis (HT) employing artificial neural networks. HT is an auto-immune disorder hostile to the thyroid follicle cells, effectuating hypothyroid or hyperthyroidism. Under this condition, the thyroid-stimulating hormone (TSH) alters incomparably to the free thyroxine (FT4) interrupts the functioning of the hypothalamus-pituitary-thyroid (HPT) axis, implicating the thyroid follicle cells getting destroyed. We primarily focus on utilizing artificial neural network (ANN) to perform numerical simulations for the system of ordinary differential equations describing the dynamics of an existing 4D model of HT. The presented model comprises four time-dependent variables: TSH, FT4, anti-thyroid antibodies (Ab), and size of the thyroid gland (T). We utilize ND-Solver and ANN scheme in the Mathematica software to acquire the computational data and illustrate thus retrieved results with essential performance plots. Further, mean square error has been considered in validating the proposed ANN-based approach accurately. The plot for training and validation loss exhibits the effectiveness of the proposed methodology, and substantiate that the suggested ANN approach is a good fit for the solving the mathematical model of HT.
本文利用人工神经网络建立了桥本氏甲状腺炎（HT）数学模型的高效求解方案。桥本氏甲状腺炎是一种敌视甲状腺滤泡细胞的自身免疫性疾病，可导致甲状腺功能减退或亢进。在这种情况下，促甲状腺激素（TSH）与游离甲状腺素（FT4）会发生巨大变化，从而干扰下丘脑-垂体-甲状腺轴（HPT）的功能，导致甲状腺滤泡细胞遭到破坏。我们主要侧重于利用人工神经网络（ANN）对描述现有 HT 四维模型动态的常微分方程系统进行数值模拟。该模型由四个随时间变化的变量组成：TSH、FT4、抗甲状腺抗体（Ab）和甲状腺大小（T）。我们利用 Mathematica 软件中的 ND-Solver 和 ANN 方案获取计算数据，并用基本性能图说明检索结果。此外，我们还考虑了均方误差，以准确验证所提出的基于 ANN 的方法。训练和验证损失图显示了所建议方法的有效性，并证明所建议的方差网络方法非常适合 HT 数学模型的求解。
{"title":"Dynamic analysis of Hashimoto’s Thyroiditis bio-mathematical model using artificial neural network","authors":"Rakesh Kumar , Sudarshan Dhua","doi":"10.1016/j.matcom.2024.10.001","DOIUrl":"10.1016/j.matcom.2024.10.001","url":null,"abstract":"<div><div>This article establishes an efficient solution scheme for a mathematical model of Hashimoto’s Thyroiditis (HT) employing artificial neural networks. HT is an auto-immune disorder hostile to the thyroid follicle cells, effectuating hypothyroid or hyperthyroidism. Under this condition, the thyroid-stimulating hormone (TSH) alters incomparably to the free thyroxine (FT4) interrupts the functioning of the hypothalamus-pituitary-thyroid (HPT) axis, implicating the thyroid follicle cells getting destroyed. We primarily focus on utilizing artificial neural network (ANN) to perform numerical simulations for the system of ordinary differential equations describing the dynamics of an existing 4D model of HT. The presented model comprises four time-dependent variables: TSH, FT4, anti-thyroid antibodies (Ab), and size of the thyroid gland (T). We utilize ND-Solver and ANN scheme in the Mathematica software to acquire the computational data and illustrate thus retrieved results with essential performance plots. Further, mean square error has been considered in validating the proposed ANN-based approach accurately. The plot for training and validation loss exhibits the effectiveness of the proposed methodology, and substantiate that the suggested ANN approach is a good fit for the solving the mathematical model of HT.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 235-245"},"PeriodicalIF":4.4,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-04DOI: 10.1016/j.matcom.2024.09.027
A. Settati , T. Caraballo , A. Lahrouz , I. Bouzalmat , A. Assadouq
This study introduces a stochastic SIR (Susceptible–Infectious–Recovered) model on complex networks, utilizing a scale-free network to represent inter-human contacts. The model incorporates a threshold parameter, denoted as , which plays a decisive role in determining whether the disease will persist or become extinct. When , the disease exhibits exponential decay and eventually disappear. Conversely, when , the disease persists. The critical case of is also examined. Furthermore, we establish a unique stationary distribution for . Our findings highlight the significance of network topology in modeling disease spread, emphasizing the role of social networks in epidemiology. Additionally, we present computational simulations that consider the scale-free network’s topology, offering comprehensive insights into the behavior of the stochastic SIR model on complex networks. These results have substantial implications for public health policy, disease control strategies, and epidemic modeling in diverse contexts.
{"title":"Stochastic SIR epidemic model dynamics on scale-free networks","authors":"A. Settati , T. Caraballo , A. Lahrouz , I. Bouzalmat , A. Assadouq","doi":"10.1016/j.matcom.2024.09.027","DOIUrl":"10.1016/j.matcom.2024.09.027","url":null,"abstract":"<div><div>This study introduces a stochastic SIR (Susceptible–Infectious–Recovered) model on complex networks, utilizing a scale-free network to represent inter-human contacts. The model incorporates a threshold parameter, denoted as <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>σ</mi></mrow></msub></math></span>, which plays a decisive role in determining whether the disease will persist or become extinct. When <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>σ</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span>, the disease exhibits exponential decay and eventually disappear. Conversely, when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>σ</mi></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>, the disease persists. The critical case of <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>σ</mi></mrow></msub><mo>=</mo><mn>1</mn></mrow></math></span> is also examined. Furthermore, we establish a unique stationary distribution for <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>σ</mi></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. Our findings highlight the significance of network topology in modeling disease spread, emphasizing the role of social networks in epidemiology. Additionally, we present computational simulations that consider the scale-free network’s topology, offering comprehensive insights into the behavior of the stochastic SIR model on complex networks. These results have substantial implications for public health policy, disease control strategies, and epidemic modeling in diverse contexts.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 246-259"},"PeriodicalIF":4.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a novel analytical approach for the computation of the th conditional moments of an -state regime-switching extended Cox–Ingersoll–Ross process driven by a continuous-time finite-state irreducible Markov chain. This approach is applicable for all integers and , thereby ensuring wide-ranging utility. The key of our investigation is a complex hybrid system of inter-connected PDEs, derived through a utilization of the Feynman–Kac formula for regime-switching diffusion processes. Our exploration into the solutions of this hybrid PDE system culminates in the derivation of exact closed-form formulas for the conditional moments for diverse values of and . Additionally, we study the asymptotic characteristics of the first conditional moments for the 2-state regime-switching Cox–Ingersoll–Ross process, particularly focusing on the effects of the symmetry inherent in the Markov chain’s intensity matrix and the implications of various parameter configurations. Highlighting the practicality of our methodology, we conduct Monte Carlo simulations to not only corroborate the accuracy and computational efficacy of our proposed approach but also to demonstrate its applicability to real-world applications in financial markets. A principal application highlighted in our study is the valuation of VIX futures and VIX options within a dynamic, mean-reverting, hybrid regime-switching framework. This exemplifies the potential of our analytical method to significantly impact contemporary financial modeling and derivative pricing.
本文介绍了一种新颖的分析方法，用于计算由连续时间有限状态不可还原马尔可夫链驱动的 m 状态制度切换扩展 Cox-Ingersoll-Ross 过程的 n 次条件矩。这种方法适用于所有 n≥1 和 m≥1 的整数，从而确保了广泛的实用性。我们研究的关键是一个由相互连接的 PDEs 组成的复杂混合系统，该系统是通过利用制度切换扩散过程的费曼-卡克公式推导出来的。此外，我们还研究了双态制度切换 Cox-Ingersoll-Ross 过程的第一个条件矩的渐近特性，尤其关注马尔可夫链强度矩阵固有对称性的影响以及各种参数配置的影响。为了突出我们方法的实用性，我们进行了蒙特卡罗模拟，不仅证实了我们提出的方法的准确性和计算效率，还展示了它在金融市场实际应用中的适用性。我们研究中强调的一个主要应用是在动态、均值回复、混合制度切换框架内对 VIX 期货和 VIX 期权进行估值。这体现了我们的分析方法对当代金融建模和衍生品定价产生重大影响的潜力。
{"title":"Analytical computation of conditional moments in the extended Cox–Ingersoll–Ross process with regime switching: Hybrid PDE system solutions with financial applications","authors":"Sanae Rujivan , Nopporn Thamrongrat , Parun Juntanon , Boualem Djehiche","doi":"10.1016/j.matcom.2024.09.032","DOIUrl":"10.1016/j.matcom.2024.09.032","url":null,"abstract":"<div><div>In this paper, we introduce a novel analytical approach for the computation of the <span><math><mi>n</mi></math></span>th conditional moments of an <span><math><mi>m</mi></math></span>-state regime-switching extended Cox–Ingersoll–Ross process driven by a continuous-time finite-state irreducible Markov chain. This approach is applicable for all integers <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>m</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, thereby ensuring wide-ranging utility. The key of our investigation is a complex hybrid system of inter-connected PDEs, derived through a utilization of the Feynman–Kac formula for regime-switching diffusion processes. Our exploration into the solutions of this hybrid PDE system culminates in the derivation of exact closed-form formulas for the conditional moments for diverse values of <span><math><mi>n</mi></math></span> and <span><math><mi>m</mi></math></span>. Additionally, we study the asymptotic characteristics of the first conditional moments for the 2-state regime-switching Cox–Ingersoll–Ross process, particularly focusing on the effects of the symmetry inherent in the Markov chain’s intensity matrix and the implications of various parameter configurations. Highlighting the practicality of our methodology, we conduct Monte Carlo simulations to not only corroborate the accuracy and computational efficacy of our proposed approach but also to demonstrate its applicability to real-world applications in financial markets. A principal application highlighted in our study is the valuation of VIX futures and VIX options within a dynamic, mean-reverting, hybrid regime-switching framework. This exemplifies the potential of our analytical method to significantly impact contemporary financial modeling and derivative pricing.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 176-202"},"PeriodicalIF":4.4,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.matcom.2024.09.033
Jingjing Wang , Yunfeng Jia , Majun Shi
In this paper, we consider a pest-natural enemy model with additional food, pest-taxis and degeneracy. Firstly, in view of the regularity theory of elliptic equations and maximum principle, the asymptotic behaviors of positive solutions are investigated. We verify that when the maximum number of natural enemies that a unit volume can accommodate (caused by pest-taxis) is sufficiently large, or the quality or quantity of additional food is very poor or large, respectively, the model admits pest-free solution. Then, based on the bifurcation theory and stability theory, the existence and stability of bifurcation solutions are discussed. We obtain that the combination of additional food, pest-taxis and degeneracy can induce model to produce new positive solutions. Finally, we depict the control regions of pests by the bifurcation results. From a biological point of view, these results show that the combined introduction of additional food, pest-taxis and degeneracy not only induces model to generate new dynamics, but also has significant implications in controlling and eliminating pests.
{"title":"Analysis and simulation on dynamics of a pest-natural enemy model with additional food, pest-taxis and degeneracy","authors":"Jingjing Wang , Yunfeng Jia , Majun Shi","doi":"10.1016/j.matcom.2024.09.033","DOIUrl":"10.1016/j.matcom.2024.09.033","url":null,"abstract":"<div><div>In this paper, we consider a pest-natural enemy model with additional food, pest-taxis and degeneracy. Firstly, in view of the regularity theory of elliptic equations and maximum principle, the asymptotic behaviors of positive solutions are investigated. We verify that when the maximum number of natural enemies that a unit volume can accommodate (caused by pest-taxis) is sufficiently large, or the quality or quantity of additional food is very poor or large, respectively, the model admits pest-free solution. Then, based on the bifurcation theory and stability theory, the existence and stability of bifurcation solutions are discussed. We obtain that the combination of additional food, pest-taxis and degeneracy can induce model to produce new positive solutions. Finally, we depict the control regions of pests by the bifurcation results. From a biological point of view, these results show that the combined introduction of additional food, pest-taxis and degeneracy not only induces model to generate new dynamics, but also has significant implications in controlling and eliminating pests.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 319-339"},"PeriodicalIF":4.4,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-30DOI: 10.1016/j.matcom.2024.09.031
Jiang Li , Xianning Liu , Yangjiang Wei
Prudent predators may evolve a strategy of prudent feed at a suitable rate, which is detrimental to their survival, but would not overexploit the prey thus is beneficial to the sustainability of resources. In this paper, by introducing a prey-dependent predation rate function, a two prey and one predator system with prudent predation is established, and the dynamics of the system as well as its subsystems are investigated. The existence and stability of the equilibrium are analyzed and the occurrence of Hopf bifurcation is studied. Numerical simulations are carried out to verify the analytical results and expand the theoretical analyses: (i) In the subsystems, it is possible to have multiple Hopf bifurcation points and prudence acts as a stabilizing factor; (ii) Suitable level of prudence will benefit the predator while sustaining the prey; (iii) Prudent predation can stabilize the system from chaos, which means chaotic dynamics can be controlled by the prudent predation. These results may reveal the important role of predator initiative in predator–prey interactions and enrich the dynamics of predator–prey system.
{"title":"Modelling the prudent predation in predator–prey interactions","authors":"Jiang Li , Xianning Liu , Yangjiang Wei","doi":"10.1016/j.matcom.2024.09.031","DOIUrl":"10.1016/j.matcom.2024.09.031","url":null,"abstract":"<div><div>Prudent predators may evolve a strategy of prudent feed at a suitable rate, which is detrimental to their survival, but would not overexploit the prey thus is beneficial to the sustainability of resources. In this paper, by introducing a prey-dependent predation rate function, a two prey and one predator system with prudent predation is established, and the dynamics of the system as well as its subsystems are investigated. The existence and stability of the equilibrium are analyzed and the occurrence of Hopf bifurcation is studied. Numerical simulations are carried out to verify the analytical results and expand the theoretical analyses: (i) In the subsystems, it is possible to have multiple Hopf bifurcation points and prudence acts as a stabilizing factor; (ii) Suitable level of prudence will benefit the predator while sustaining the prey; (iii) Prudent predation can stabilize the system from chaos, which means chaotic dynamics can be controlled by the prudent predation. These results may reveal the important role of predator initiative in predator–prey interactions and enrich the dynamics of predator–prey system.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 129-150"},"PeriodicalIF":4.4,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-30DOI: 10.1016/j.matcom.2024.09.029
Guillaume Dujardin , Ingrid Lacroix-Violet , Anthony Nahas
This article implements a numerical method for the minimization under constraints of a discrete energy modelling multicomponents rotating Bose–Einstein condensates in the regime of strong confinement and with rotation. Moreover, this method allows to consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). The goal of this paper is to study numerically the structures of the minimizers. In order to do so, we introduce a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.
{"title":"A numerical study of vortex nucleation in 2D rotating Bose–Einstein condensates","authors":"Guillaume Dujardin , Ingrid Lacroix-Violet , Anthony Nahas","doi":"10.1016/j.matcom.2024.09.029","DOIUrl":"10.1016/j.matcom.2024.09.029","url":null,"abstract":"<div><div>This article implements a numerical method for the minimization under constraints of a discrete energy modelling multicomponents rotating Bose–Einstein condensates in the regime of strong confinement and with rotation. Moreover, this method allows to consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). The goal of this paper is to study numerically the structures of the minimizers. In order to do so, we introduce a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 409-434"},"PeriodicalIF":4.4,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a novel Hermite spline model for data regression, integrating both function values and derivatives along with a penalty term to control smoothness. A comparative analysis is conducted with conventional penalized models, specifically with P-spline models. The primary objective of this study is to empirically demonstrate the superior performance of the proposed model in reconstructing data, even in the absence of a penalty term (pure regression).
{"title":"A Hermite spline model for data regression","authors":"Rosanna Campagna , Mariantonia Cotronei , Domenico Fazzino","doi":"10.1016/j.matcom.2024.09.011","DOIUrl":"10.1016/j.matcom.2024.09.011","url":null,"abstract":"<div><div>This paper introduces a novel Hermite spline model for data regression, integrating both function values and derivatives along with a penalty term to control smoothness. A comparative analysis is conducted with conventional penalized models, specifically with P-spline models. The primary objective of this study is to empirically demonstrate the superior performance of the proposed model in reconstructing data, even in the absence of a penalty term (pure regression).</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 222-234"},"PeriodicalIF":4.4,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-28DOI: 10.1016/j.matcom.2024.09.024
Md Aktar Ul Karim , Ruqaiya Altaf Shaikh , Amiya Ranjan Bhowmick
Biological growth curves are pivotal in predicting natural growth across disciplines, typically analyzed using nonlinear least squares or maximum likelihood methods. Bhowmick et al. (2014) introduced the interval-specific rate of parameters (ISRP) for growth equations, improving the estimation of relative growth rate (RGR) and model selection accuracy. Despite its effectiveness, computing these model-specific RGR estimates involves complex calculations and lacks explicit expressions for many nonlinear models. Also, for highly nonlinear models and non-monotonic data where the parameters are non-linearly related, the computation of interval estimates is almost impossible and may suffer from significant approximation errors. So, the need for a more efficient computation method for ISRP remains a significant challenge in growth studies. In this article, we propose a computational approach to obtain interval estimates of parameters based on the maximum likelihood estimation method. The likelihood function is maximized using the data on smaller intervals. Our study underscores the importance of an efficient ISRP computation technique, providing a more stable, unbiased, and normally distributed estimator. The most important advantage is that it can be implemented using existing optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. Both simulation studies and real data analysis have been carried out to validate the proposed estimation process. Additionally, its applicability to non-monotonic growth profiles and its robustness in handling highly non-linear growth equations highlight its versatility. We also developed a web application GpEM-R which is freely available for researchers and practitioners to analyze growth data.
{"title":"Efficient approximation of global population dynamic models through statistical inference using local data","authors":"Md Aktar Ul Karim , Ruqaiya Altaf Shaikh , Amiya Ranjan Bhowmick","doi":"10.1016/j.matcom.2024.09.024","DOIUrl":"10.1016/j.matcom.2024.09.024","url":null,"abstract":"<div><div>Biological growth curves are pivotal in predicting natural growth across disciplines, typically analyzed using nonlinear least squares or maximum likelihood methods. Bhowmick et al. (2014) introduced the interval-specific rate of parameters (ISRP) for growth equations, improving the estimation of relative growth rate (RGR) and model selection accuracy. Despite its effectiveness, computing these model-specific RGR estimates involves complex calculations and lacks explicit expressions for many nonlinear models. Also, for highly nonlinear models and non-monotonic data where the parameters are non-linearly related, the computation of interval estimates is almost impossible and may suffer from significant approximation errors. So, the need for a more efficient computation method for ISRP remains a significant challenge in growth studies. In this article, we propose a computational approach to obtain interval estimates of parameters based on the maximum likelihood estimation method. The likelihood function is maximized using the data on smaller intervals. Our study underscores the importance of an efficient ISRP computation technique, providing a more stable, unbiased, and normally distributed estimator. The most important advantage is that it can be implemented using existing optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. Both simulation studies and real data analysis have been carried out to validate the proposed estimation process. Additionally, its applicability to non-monotonic growth profiles and its robustness in handling highly non-linear growth equations highlight its versatility. We also developed a web application GpEM-R which is freely available for researchers and practitioners to analyze growth data.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 96-128"},"PeriodicalIF":4.4,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-28DOI: 10.1016/j.matcom.2024.09.025
Minggang Liu , Ning Xu , Ben Niu , Naif D. Alotaibi
In this paper, the issue of sliding-mode surface (SMS)-based fixed-time adaptive tracking control under the framework of critic network is considered for the zero-sum game of switched nonlinear systems. Firstly, the tracking error and reference trajectory are combined to construct an augmented system, which transforms the optimal tracking control issue into a basic optimal regulation issue. Meanwhile, sliding mode control technology is introduced to improve the robustness and response speed of the system. Subsequently, a special cost function associated with SMS is developed to find a series of optimal control strategies. Besides, the numerical solution of a Hamilton-Jacobi-Isaacs equation is acquired based on a single-critic network architecture. Then, convergence of the tracking error in fixed time and boundedness of the closed-loop signals are strictly proved via the fixed-time stability theory. Finally, the feasibility and optimality of the developed control scheme are verified by two simulation examples.
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