Pub Date : 2023-08-03DOI: 10.3389/fams.2023.1260383
V. Breña-medina, Pablo Aguirre
{"title":"Editorial: Recent advances in bifurcation analysis: theory, methods, applications and beyond - volume II","authors":"V. Breña-medina, Pablo Aguirre","doi":"10.3389/fams.2023.1260383","DOIUrl":"https://doi.org/10.3389/fams.2023.1260383","url":null,"abstract":"","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45381284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-28DOI: 10.3389/fams.2023.1254646
A. Hutt
{"title":"Editorial: Insights in Dynamical Systems 2022","authors":"A. Hutt","doi":"10.3389/fams.2023.1254646","DOIUrl":"https://doi.org/10.3389/fams.2023.1254646","url":null,"abstract":"","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43809073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-11DOI: 10.3389/fams.2023.1214022
G. Tinoco-Guerrero, F. Domínguez-Mota, J. A. Guzmán-Torres, Ricardo Román-Gutiérrez, J. Tinoco-Ruiz
When designing and implementing numerical schemes, it is imperative to consider the stability of the applied methods. Prior research has presented different results for the stability of generalized finite-difference methods applied to advection and diffusion equations. In recent years, research has explored a generalized finite-difference approach to the advection-diffusion equation solved on non-rectangular and highly irregular regions using convex, logically rectangular grids. This paper presents a study on the stability of generalized finite difference schemes applied to the numerical solution of the wave equation, solved on clouds of points for highly irregular domains. The stability analysis presented in this work provides significant insights into the proper discretizations needed to obtain stable and satisfactory results. The proposed explicit scheme is conditionally stable, while the implicit scheme is unconditionally stable. Notably, the stability analyses presented in this paper apply to any scheme which is at least second order in space, not just the proposed approach. The proposed scheme offers effective means of numerically solving the wave equation, particularly for highly irregular domains. By demonstrating the stability of the scheme, this study provides a foundation for further research in this area.
{"title":"Study of the stability of a meshless generalized finite difference scheme applied to the wave equation","authors":"G. Tinoco-Guerrero, F. Domínguez-Mota, J. A. Guzmán-Torres, Ricardo Román-Gutiérrez, J. Tinoco-Ruiz","doi":"10.3389/fams.2023.1214022","DOIUrl":"https://doi.org/10.3389/fams.2023.1214022","url":null,"abstract":"When designing and implementing numerical schemes, it is imperative to consider the stability of the applied methods. Prior research has presented different results for the stability of generalized finite-difference methods applied to advection and diffusion equations. In recent years, research has explored a generalized finite-difference approach to the advection-diffusion equation solved on non-rectangular and highly irregular regions using convex, logically rectangular grids. This paper presents a study on the stability of generalized finite difference schemes applied to the numerical solution of the wave equation, solved on clouds of points for highly irregular domains. The stability analysis presented in this work provides significant insights into the proper discretizations needed to obtain stable and satisfactory results. The proposed explicit scheme is conditionally stable, while the implicit scheme is unconditionally stable. Notably, the stability analyses presented in this paper apply to any scheme which is at least second order in space, not just the proposed approach. The proposed scheme offers effective means of numerically solving the wave equation, particularly for highly irregular domains. By demonstrating the stability of the scheme, this study provides a foundation for further research in this area.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43976961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-10DOI: 10.3389/fams.2023.1233135
F. Yanuar, H. Yozza, A. Zetra
{"title":"Corrigendum: Modified quantile regression for modeling the low birth weight","authors":"F. Yanuar, H. Yozza, A. Zetra","doi":"10.3389/fams.2023.1233135","DOIUrl":"https://doi.org/10.3389/fams.2023.1233135","url":null,"abstract":"","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46428984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-05DOI: 10.3389/fams.2023.1152476
M. Taroni, I. Spassiani, N. Laskin, S. Barani
In this note, we study the distribution of earthquake numbers in both worldwide and regional catalogs: in the Global Centroid Moment Tensor catalog, from 1980 to 2019 for magnitudes Mw 5. 5+ and 6.5+ in the first case, and in the Italian instrumental catalog from 1960 to 2021 for magnitudes Mw 4.0+ and 5.5+ in the second case. A subset of the global catalog is also used to study the Japanese region. We will focus our attention on short-term time windows of 1, 7, and 30 days, which have been poorly explored in previous studies. We model the earthquake numbers using two discrete probability distributions, i.e., Poisson and Negative Binomial. Using the classical chi-squared statistical test, we found that the Poisson distribution, widely used in seismological studies, is always rejected when tested against observations, while the Negative Binomial distribution cannot be disproved for magnitudes Mw 6.5+ in all time windows of the global catalog. However, if we consider the Japanese or the Italian regions, it cannot be proven that the Negative Binomial distribution performs better than the Poisson distribution using the chi-squared test. When instead we compared the performances of the two distributions using the Akaike Information Criterion, we found that the Negative Binomial distribution always performs better than the Poisson one. The results of this study suggest that the Negative Binomial distribution, largely ignored in seismological studies, should replace the Poisson distribution in modeling the number of earthquakes.
{"title":"How many strong earthquakes will there be tomorrow?","authors":"M. Taroni, I. Spassiani, N. Laskin, S. Barani","doi":"10.3389/fams.2023.1152476","DOIUrl":"https://doi.org/10.3389/fams.2023.1152476","url":null,"abstract":"In this note, we study the distribution of earthquake numbers in both worldwide and regional catalogs: in the Global Centroid Moment Tensor catalog, from 1980 to 2019 for magnitudes Mw 5. 5+ and 6.5+ in the first case, and in the Italian instrumental catalog from 1960 to 2021 for magnitudes Mw 4.0+ and 5.5+ in the second case. A subset of the global catalog is also used to study the Japanese region. We will focus our attention on short-term time windows of 1, 7, and 30 days, which have been poorly explored in previous studies. We model the earthquake numbers using two discrete probability distributions, i.e., Poisson and Negative Binomial. Using the classical chi-squared statistical test, we found that the Poisson distribution, widely used in seismological studies, is always rejected when tested against observations, while the Negative Binomial distribution cannot be disproved for magnitudes Mw 6.5+ in all time windows of the global catalog. However, if we consider the Japanese or the Italian regions, it cannot be proven that the Negative Binomial distribution performs better than the Poisson distribution using the chi-squared test. When instead we compared the performances of the two distributions using the Akaike Information Criterion, we found that the Negative Binomial distribution always performs better than the Poisson one. The results of this study suggest that the Negative Binomial distribution, largely ignored in seismological studies, should replace the Poisson distribution in modeling the number of earthquakes.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42862857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.3389/fams.2023.1207643
Marina Mancuso, Kaitlyn Martinez, C. Manore, F. Milner, Martha Barnard, H. Godinez
Climate change is arguably one of the most pressing issues affecting the world today and requires the fusion of disparate data streams to accurately model its impacts. Mosquito populations respond to temperature and precipitation in a nonlinear way, making predicting climate impacts on mosquito-borne diseases an ongoing challenge. Data-driven approaches for accurately modeling mosquito populations are needed for predicting mosquito-borne disease risk under climate change scenarios. Many current models for disease transmission are continuous and autonomous, while mosquito data is discrete and varies both within and between seasons. This study uses an optimization framework to fit a non-autonomous logistic model with periodic net growth rate and carrying capacity parameters for 15 years of daily mosquito time-series data from the Greater Toronto Area of Canada. The resulting parameters accurately capture the inter-annual and intra-seasonal variability of mosquito populations within a single geographic region, and a variance-based sensitivity analysis highlights the influence each parameter has on the peak magnitude and timing of the mosquito season. This method can easily extend to other geographic regions and be integrated into a larger disease transmission model. This method addresses the ongoing challenges of data and model fusion by serving as a link between discrete time-series data and continuous differential equations for mosquito-borne epidemiology models.
{"title":"Fusing time-varying mosquito data and continuous mosquito population dynamics models","authors":"Marina Mancuso, Kaitlyn Martinez, C. Manore, F. Milner, Martha Barnard, H. Godinez","doi":"10.3389/fams.2023.1207643","DOIUrl":"https://doi.org/10.3389/fams.2023.1207643","url":null,"abstract":"Climate change is arguably one of the most pressing issues affecting the world today and requires the fusion of disparate data streams to accurately model its impacts. Mosquito populations respond to temperature and precipitation in a nonlinear way, making predicting climate impacts on mosquito-borne diseases an ongoing challenge. Data-driven approaches for accurately modeling mosquito populations are needed for predicting mosquito-borne disease risk under climate change scenarios. Many current models for disease transmission are continuous and autonomous, while mosquito data is discrete and varies both within and between seasons. This study uses an optimization framework to fit a non-autonomous logistic model with periodic net growth rate and carrying capacity parameters for 15 years of daily mosquito time-series data from the Greater Toronto Area of Canada. The resulting parameters accurately capture the inter-annual and intra-seasonal variability of mosquito populations within a single geographic region, and a variance-based sensitivity analysis highlights the influence each parameter has on the peak magnitude and timing of the mosquito season. This method can easily extend to other geographic regions and be integrated into a larger disease transmission model. This method addresses the ongoing challenges of data and model fusion by serving as a link between discrete time-series data and continuous differential equations for mosquito-borne epidemiology models.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48101139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-28DOI: 10.3389/fams.2023.1112937
M. Bonamente
This study presents the application of a new semi-analytical method of linear regression for Poisson count data to COVID-19 events. The regression is based on the maximum-likelihood solution for the best-fit parameters presented in an earlier publication, and this study introduces a simple analytical solution for the covariance matrix that completes the problem of linear regression with Poisson data for one independent variable. The analytical nature of both parameter estimates and their covariance matrix is made possible by a convenient factorization of the linear model proposed by J. Scargle. The method makes use of the asymptotic properties of the Fisher information matrix, whose inverse provides the covariance matrix. The combination of simple analytical methods to obtain both the maximum-likelihood estimates of the parameters and their covariance matrix constitutes a new and convenient method for the linear regression of Poisson-distributed count data, which are of common occurrence across a variety of fields. A comparison between this maximum-likelihood linear regression method for Poisson data and two alternative methods often used for the regression of count data—the ordinary least–square regression and the χ2 regression—is provided with the application of these methods to the analysis of recent COVID-19 count data. The study also discusses the relative advantages and disadvantages among these methods for the linear regression of Poisson count data.
{"title":"Linear regression for Poisson count data: a new semi-analytical method with applications to COVID-19 events","authors":"M. Bonamente","doi":"10.3389/fams.2023.1112937","DOIUrl":"https://doi.org/10.3389/fams.2023.1112937","url":null,"abstract":"This study presents the application of a new semi-analytical method of linear regression for Poisson count data to COVID-19 events. The regression is based on the maximum-likelihood solution for the best-fit parameters presented in an earlier publication, and this study introduces a simple analytical solution for the covariance matrix that completes the problem of linear regression with Poisson data for one independent variable. The analytical nature of both parameter estimates and their covariance matrix is made possible by a convenient factorization of the linear model proposed by J. Scargle. The method makes use of the asymptotic properties of the Fisher information matrix, whose inverse provides the covariance matrix. The combination of simple analytical methods to obtain both the maximum-likelihood estimates of the parameters and their covariance matrix constitutes a new and convenient method for the linear regression of Poisson-distributed count data, which are of common occurrence across a variety of fields. A comparison between this maximum-likelihood linear regression method for Poisson data and two alternative methods often used for the regression of count data—the ordinary least–square regression and the χ2 regression—is provided with the application of these methods to the analysis of recent COVID-19 count data. The study also discusses the relative advantages and disadvantages among these methods for the linear regression of Poisson count data.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48749583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-26DOI: 10.3389/fams.2023.1157992
I. Zahan, M. Kamrujjaman, M. Abdul Alim, Mohammad Shahidul Islam, T. Khan
Population diffusion in river-ocean ecologies and for wild animals, including birds, mainly depends on the availability of resources and habitats. This study explores the dynamics of the resource-based competition model for two interacting species in order to investigate the spatiotemporal effects in a spatially distributed heterogeneous environment with no-flux boundary conditions. The main focus of this study is on the diffusion strategy, under conditions where the carrying capacity for two competing species is considered to be unequal. The same growth function is associated with both species, but they have different migration coefficients. The stability of global coexistence and quasi-trivial equilibria are also studied under different conditions with respect to resource function and carrying capacity. Furthermore, we investigate the case of competitive exclusion for various linear combinations of resource function and carrying capacity. Additionally, we extend the study to the instance where a higher migration rate negatively impacts population growth in competition. The efficacy of the model in the cases of one- and two-dimensional space is also demonstrated through a numerical study. AMS subject classification 2010 92D25, 35K57, 35K50, 37N25, 53C35.
{"title":"The evolution of resource distribution, slow diffusion, and dispersal strategies in heterogeneous populations","authors":"I. Zahan, M. Kamrujjaman, M. Abdul Alim, Mohammad Shahidul Islam, T. Khan","doi":"10.3389/fams.2023.1157992","DOIUrl":"https://doi.org/10.3389/fams.2023.1157992","url":null,"abstract":"Population diffusion in river-ocean ecologies and for wild animals, including birds, mainly depends on the availability of resources and habitats. This study explores the dynamics of the resource-based competition model for two interacting species in order to investigate the spatiotemporal effects in a spatially distributed heterogeneous environment with no-flux boundary conditions. The main focus of this study is on the diffusion strategy, under conditions where the carrying capacity for two competing species is considered to be unequal. The same growth function is associated with both species, but they have different migration coefficients. The stability of global coexistence and quasi-trivial equilibria are also studied under different conditions with respect to resource function and carrying capacity. Furthermore, we investigate the case of competitive exclusion for various linear combinations of resource function and carrying capacity. Additionally, we extend the study to the instance where a higher migration rate negatively impacts population growth in competition. The efficacy of the model in the cases of one- and two-dimensional space is also demonstrated through a numerical study. AMS subject classification 2010 92D25, 35K57, 35K50, 37N25, 53C35.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47328598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-23DOI: 10.3389/fams.2023.1199011
S. Berres, Pablo Castañeda
This research focuses on a hyperbolic system that describes bidisperse suspensions, consisting of two types of small particles dispersed in a viscous fluid. The dependence of solutions on the relative position of contact manifolds in the phase space is examined. The wave curve method serves as the basis for the first and second analyses. The former involves the classification of elementary waves that emerge from the origin of the phase space. Analytical solutions to prototypical Riemann problems connecting the origin with any point in the state space are provided. The latter focuses on semi-analytical solutions for Riemann problems connecting any state in the phase space with the maximum packing concentration line, as observed in standard batch sedimentation tests. When the initial condition crosses the first contact manifold, a bifurcation occurs. As the initial condition approaches the second manifold, another structure appears to undergo bifurcation, although it does not represent an actual bifurcation according to the triple shock rule. The study reveals important insights into the behavior of solutions in relation to these contact manifolds. This research sheds light on the existence of emerging quasi-umbilic points within the system, which can potentially lead to new types of bifurcations as crucial elements of the elliptic/hyperbolic boundary in the system of partial differential equations. The implications of these findings and their significance are discussed.
{"title":"Bifurcation of solutions through a contact manifold in bidisperse models","authors":"S. Berres, Pablo Castañeda","doi":"10.3389/fams.2023.1199011","DOIUrl":"https://doi.org/10.3389/fams.2023.1199011","url":null,"abstract":"This research focuses on a hyperbolic system that describes bidisperse suspensions, consisting of two types of small particles dispersed in a viscous fluid. The dependence of solutions on the relative position of contact manifolds in the phase space is examined. The wave curve method serves as the basis for the first and second analyses. The former involves the classification of elementary waves that emerge from the origin of the phase space. Analytical solutions to prototypical Riemann problems connecting the origin with any point in the state space are provided. The latter focuses on semi-analytical solutions for Riemann problems connecting any state in the phase space with the maximum packing concentration line, as observed in standard batch sedimentation tests. When the initial condition crosses the first contact manifold, a bifurcation occurs. As the initial condition approaches the second manifold, another structure appears to undergo bifurcation, although it does not represent an actual bifurcation according to the triple shock rule. The study reveals important insights into the behavior of solutions in relation to these contact manifolds. This research sheds light on the existence of emerging quasi-umbilic points within the system, which can potentially lead to new types of bifurcations as crucial elements of the elliptic/hyperbolic boundary in the system of partial differential equations. The implications of these findings and their significance are discussed.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43682608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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