Pub Date : 2023-04-27DOI: 10.3389/fams.2023.1156785
J. Hay, L. Schories, E. Bayerschen, P. Wimmer, Oliver Zehbe, S. Kirschbichler, J. Fehr
Surrogate models are a must-have in a scenario-based safety simulation framework to design optimally integrated safety systems for new mobility solutions. The objective of this study is the development of surrogate models for active human model responses under consideration of multiple sampling strategies. A Gaussian process regression is chosen for predicting injury values based on the collision scenario, the occupant's seating position after a pre-crash movement and selected restraint system parameters. The trained models are validated and assessed for each sampling method and the best-performing surrogate model is selected for restraint system parameter optimization.
{"title":"Application of data-driven surrogate models for active human model response prediction and restraint system optimization","authors":"J. Hay, L. Schories, E. Bayerschen, P. Wimmer, Oliver Zehbe, S. Kirschbichler, J. Fehr","doi":"10.3389/fams.2023.1156785","DOIUrl":"https://doi.org/10.3389/fams.2023.1156785","url":null,"abstract":"Surrogate models are a must-have in a scenario-based safety simulation framework to design optimally integrated safety systems for new mobility solutions. The objective of this study is the development of surrogate models for active human model responses under consideration of multiple sampling strategies. A Gaussian process regression is chosen for predicting injury values based on the collision scenario, the occupant's seating position after a pre-crash movement and selected restraint system parameters. The trained models are validated and assessed for each sampling method and the best-performing surrogate model is selected for restraint system parameter optimization.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48238662","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 : 2023-04-26DOI: 10.3389/fams.2023.1094971
D. Aldila, Chita Aulia Puspadani, Rahmi Rusin
This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.
{"title":"Mathematical analysis of the impact of community ignorance on the population dynamics of dengue","authors":"D. Aldila, Chita Aulia Puspadani, Rahmi Rusin","doi":"10.3389/fams.2023.1094971","DOIUrl":"https://doi.org/10.3389/fams.2023.1094971","url":null,"abstract":"This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42448151","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 : 2023-04-21DOI: 10.3389/fams.2023.1138663
Mauricio Contreras G., Roberto Ortiz H.
The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation with the same initial interest rate of r. The second theorem states that if AN ≠ 0, then the interacting solution can be expressed in terms of all higher derivatives of the solutions to the free Black–Scholes equation with an initial interest rate of r. The third theorem states that for a given arbitrage number, the interacting solution is a solution to the free Black–Scholes equation but with a variable interest rate of r(τ) = r + (1/τ)AN(τ), where τ = T − t.
{"title":"Three little arbitrage theorems","authors":"Mauricio Contreras G., Roberto Ortiz H.","doi":"10.3389/fams.2023.1138663","DOIUrl":"https://doi.org/10.3389/fams.2023.1138663","url":null,"abstract":"The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation with the same initial interest rate of r. The second theorem states that if AN ≠ 0, then the interacting solution can be expressed in terms of all higher derivatives of the solutions to the free Black–Scholes equation with an initial interest rate of r. The third theorem states that for a given arbitrage number, the interacting solution is a solution to the free Black–Scholes equation but with a variable interest rate of r(τ) = r + (1/τ)AN(τ), where τ = T − t.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46917930","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 : 2023-04-17DOI: 10.3389/fams.2023.1045218
D. Devianto, Mutia Yollanda, M. Maiyastri, F. Yanuar
Introduction Time series models on financial data often have problems with the stationary assumption of variance on the residuals. It is well known as the heteroscedasticity effect. The heteroscedasticity is represented by a nonconstant value that varies over time. Methods The heteroscedasticity effect contained in the basic classical time series model of Autoregressive Integrated Moving Average (ARIMA) can adjust its residuals as the variance model by using Generalized Autoregressive Conditional Heteroscedasticity (GARCH). In improving the model accuracy and overcoming the heteroscedasticity problems, it is proposed a combination model of ARIMA and Feed-Forward Neural Network (FFNN), namely ARIMA-FFNN. The model is built by applying the soft computing method of FFNN to replace the variance model. This soft computing approach is one of the numerical methods that can not be only applied in the theoretical subject but also in the data processing. Results In this research, the accuracy of the time series model using the case study of the exchange rate United States dollar-Indonesia rupiah with a monthly period from January 2001 to May 2021 shows that the best accuracy of the possible models is the model of ARIMA-FFNN, which applies soft computing to obtain the optimal fitted parameters precisely. Discussion This result indicates that the ARIMA-FFNN model is better used to approach this exchange rate than the rest model of ARIMA-GARCH and ARIMA-GARCH-FFNN.
{"title":"The soft computing FFNN method for adjusting heteroscedasticity on the time series model of currency exchange rate","authors":"D. Devianto, Mutia Yollanda, M. Maiyastri, F. Yanuar","doi":"10.3389/fams.2023.1045218","DOIUrl":"https://doi.org/10.3389/fams.2023.1045218","url":null,"abstract":"Introduction Time series models on financial data often have problems with the stationary assumption of variance on the residuals. It is well known as the heteroscedasticity effect. The heteroscedasticity is represented by a nonconstant value that varies over time. Methods The heteroscedasticity effect contained in the basic classical time series model of Autoregressive Integrated Moving Average (ARIMA) can adjust its residuals as the variance model by using Generalized Autoregressive Conditional Heteroscedasticity (GARCH). In improving the model accuracy and overcoming the heteroscedasticity problems, it is proposed a combination model of ARIMA and Feed-Forward Neural Network (FFNN), namely ARIMA-FFNN. The model is built by applying the soft computing method of FFNN to replace the variance model. This soft computing approach is one of the numerical methods that can not be only applied in the theoretical subject but also in the data processing. Results In this research, the accuracy of the time series model using the case study of the exchange rate United States dollar-Indonesia rupiah with a monthly period from January 2001 to May 2021 shows that the best accuracy of the possible models is the model of ARIMA-FFNN, which applies soft computing to obtain the optimal fitted parameters precisely. Discussion This result indicates that the ARIMA-FFNN model is better used to approach this exchange rate than the rest model of ARIMA-GARCH and ARIMA-GARCH-FFNN.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45379488","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 : 2023-04-17DOI: 10.3389/fams.2023.961158
Abdou Khadre Dit Jadir Fall
This article aimed to study the choice that people have to make between two health insurance systems in a monopolistic scheme. The first health insurance system proposes a uniform contribution level and the second one proposes a contribution level that is proportional to the probability of getting sick. The individuals differ (or are distinguished) by their number in a group, the net income, the contribution level, the probability of getting sick, and health cost. Two kinds of voting models using the welfare function are used; a direct vote that involves a size effect and a probabilistic vote that involves a bias in favor of one system. The results, according to theoretical models, indicate that a uniform contribution level is adopted by high-risk individuals and also if wealth and illness are strongly negatively correlated. However, when wealth and illness are not correlated or are poorly correlated, a contribution proportional to the probability of getting sick is adopted. These results were explained by the fact that the loss of wellbeing for low-income and sick people is more important.
{"title":"Modeling the political choice of public health insurance","authors":"Abdou Khadre Dit Jadir Fall","doi":"10.3389/fams.2023.961158","DOIUrl":"https://doi.org/10.3389/fams.2023.961158","url":null,"abstract":"This article aimed to study the choice that people have to make between two health insurance systems in a monopolistic scheme. The first health insurance system proposes a uniform contribution level and the second one proposes a contribution level that is proportional to the probability of getting sick. The individuals differ (or are distinguished) by their number in a group, the net income, the contribution level, the probability of getting sick, and health cost. Two kinds of voting models using the welfare function are used; a direct vote that involves a size effect and a probabilistic vote that involves a bias in favor of one system. The results, according to theoretical models, indicate that a uniform contribution level is adopted by high-risk individuals and also if wealth and illness are strongly negatively correlated. However, when wealth and illness are not correlated or are poorly correlated, a contribution proportional to the probability of getting sick is adopted. These results were explained by the fact that the loss of wellbeing for low-income and sick people is more important.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43415342","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 : 2023-04-11DOI: 10.3389/fams.2023.1206017
Alex Van'o-Vinuales
Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity (ℐ+). This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are extracted for gravitational wave modeling purposes. One promising method to include future null infinity in the numerical domain is the evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity. The main challenge in this approach is the treatment of the compactified asymptotic region at ℐ+. Evolution on a hyperboloidal slice of a spacetime including a black hole entails an extra layer of difficulty in part due to the finite coordinate distance between the black hole and future null infinity. Spherical symmetry is considered here as the simplest setup still encompassing the full complication of the treatment along the radial coordinate. First, the construction of constant-mean-curvature hyperboloidal trumpet slices for Schwarzschild and Reissner-Nordström black hole spacetimes is reviewed from the point of view of the puncture approach. Then, the framework is set for solving hyperboloidal-adapted hyperbolic gauge conditions for stationary trumpet initial data, providing solutions for two specific sets of parameters. Finally, results of testing these initial data in evolution are presented.
{"title":"Spherically symmetric black hole spacetimes on hyperboloidal slices","authors":"Alex Van'o-Vinuales","doi":"10.3389/fams.2023.1206017","DOIUrl":"https://doi.org/10.3389/fams.2023.1206017","url":null,"abstract":"Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity (ℐ+). This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are extracted for gravitational wave modeling purposes. One promising method to include future null infinity in the numerical domain is the evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity. The main challenge in this approach is the treatment of the compactified asymptotic region at ℐ+. Evolution on a hyperboloidal slice of a spacetime including a black hole entails an extra layer of difficulty in part due to the finite coordinate distance between the black hole and future null infinity. Spherical symmetry is considered here as the simplest setup still encompassing the full complication of the treatment along the radial coordinate. First, the construction of constant-mean-curvature hyperboloidal trumpet slices for Schwarzschild and Reissner-Nordström black hole spacetimes is reviewed from the point of view of the puncture approach. Then, the framework is set for solving hyperboloidal-adapted hyperbolic gauge conditions for stationary trumpet initial data, providing solutions for two specific sets of parameters. Finally, results of testing these initial data in evolution are presented.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42905789","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 : 2023-04-06DOI: 10.3389/fams.2023.1064130
M. Mulk, Kazi Nusrat Islam, M. H. A. Biswas
Tissue-mimicking materials [e.g., polyvinyl alcohol cryogel (PVA-C)] are extensively used in clinical applications such as tissue repair and tissue engineering. Various mechanical testing techniques have been used to assess the biomechanical compatibility of tissue-mimicking materials. This article presents the development of inverse finite element (FE) techniques that are solved using numerical optimization to characterize the mechanical properties of PVA-C specimens. In this study, a numerical analysis where the displacement influence factor was employed in conjunction with a linear elastic model of finite thickness was performed. In the analysis, the effects of Poisson's ratio, specimen aspect ratio, and relative indentation depth were investigated, and a novel mathematical term was introduced to Sneddon's equation. In addition, a robust optimization algorithm was developed in MATLAB that utilized FE modeling for parameter estimation before it was rigorously validated.
{"title":"Modeling and numerical analysis for mechanical characterization of soft tissue mechanism applying inverse finite element technique","authors":"M. Mulk, Kazi Nusrat Islam, M. H. A. Biswas","doi":"10.3389/fams.2023.1064130","DOIUrl":"https://doi.org/10.3389/fams.2023.1064130","url":null,"abstract":"Tissue-mimicking materials [e.g., polyvinyl alcohol cryogel (PVA-C)] are extensively used in clinical applications such as tissue repair and tissue engineering. Various mechanical testing techniques have been used to assess the biomechanical compatibility of tissue-mimicking materials. This article presents the development of inverse finite element (FE) techniques that are solved using numerical optimization to characterize the mechanical properties of PVA-C specimens. In this study, a numerical analysis where the displacement influence factor was employed in conjunction with a linear elastic model of finite thickness was performed. In the analysis, the effects of Poisson's ratio, specimen aspect ratio, and relative indentation depth were investigated, and a novel mathematical term was introduced to Sneddon's equation. In addition, a robust optimization algorithm was developed in MATLAB that utilized FE modeling for parameter estimation before it was rigorously validated.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47046692","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 : 2023-04-05DOI: 10.3389/fams.2023.1090753
A. Hodgkinson, Aisha Tursynkozha, D. Trucu
The eukaryotic cell cycle comprises 4 phases (G1, S, G2, and M) and is an essential component of cellular health, allowing the cell to repair damaged DNA prior to division. Facilitating this processes, p53 is activated by DNA-damage and arrests the cell cycle to allow for the repair of this damage, while mutations in the p53 gene frequently occur in cancer. As such, this process occurs on the cell-scale but affects the organism on the cell population-scale. Here, we present two models of cell cycle progression: The first of these is concerned with the cell-scale process of cell cycle progression and the temporal biochemical processes, driven by cyclins and underlying progression from one phase to the next. The second of these models concerns the cell population-scale process of cell-cycle progression and its arrest under the influence of DNA-damage and p53-activation. Both systems take advantage of structural modeling conventions to develop novels methods for describing and exploring cell-cycle dynamics on these two divergent scales. The cell-scale model represents the accumulations of cyclins across an internal cell space and demonstrates that such a formalism gives rise to a biological clock system, with definite periodicity. The cell population-scale model allows for the exploration of interactions between various regulating proteins and the DNA-damage state of the system and quantitatively demonstrates the structural dynamics which allow p53 to regulate the G2- to M-phase transition and to prevent the mitosis of genetically damaged cells. A divergent periodicity and clear distribution of transition times is observed, as compared with the single-cell system. Comparison to a system with a reduced genetic repair rate shows a greater delay in cell cycle progression and an increased accumulation of cell in the G2-phase, as a result of the p53 biochemical feedback mechanism.
{"title":"Structured dynamics of the cell-cycle at multiple scales","authors":"A. Hodgkinson, Aisha Tursynkozha, D. Trucu","doi":"10.3389/fams.2023.1090753","DOIUrl":"https://doi.org/10.3389/fams.2023.1090753","url":null,"abstract":"The eukaryotic cell cycle comprises 4 phases (G1, S, G2, and M) and is an essential component of cellular health, allowing the cell to repair damaged DNA prior to division. Facilitating this processes, p53 is activated by DNA-damage and arrests the cell cycle to allow for the repair of this damage, while mutations in the p53 gene frequently occur in cancer. As such, this process occurs on the cell-scale but affects the organism on the cell population-scale. Here, we present two models of cell cycle progression: The first of these is concerned with the cell-scale process of cell cycle progression and the temporal biochemical processes, driven by cyclins and underlying progression from one phase to the next. The second of these models concerns the cell population-scale process of cell-cycle progression and its arrest under the influence of DNA-damage and p53-activation. Both systems take advantage of structural modeling conventions to develop novels methods for describing and exploring cell-cycle dynamics on these two divergent scales. The cell-scale model represents the accumulations of cyclins across an internal cell space and demonstrates that such a formalism gives rise to a biological clock system, with definite periodicity. The cell population-scale model allows for the exploration of interactions between various regulating proteins and the DNA-damage state of the system and quantitatively demonstrates the structural dynamics which allow p53 to regulate the G2- to M-phase transition and to prevent the mitosis of genetically damaged cells. A divergent periodicity and clear distribution of transition times is observed, as compared with the single-cell system. Comparison to a system with a reduced genetic repair rate shows a greater delay in cell cycle progression and an increased accumulation of cell in the G2-phase, as a result of the p53 biochemical feedback mechanism.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43775831","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 : 2023-04-05DOI: 10.3389/fams.2023.1165371
Bernardo Cockburn, Shukai Du, M. Sánchez
We provide a short introduction to the devising of a special type of methods for numerically approximating the solution of Hamiltonian partial differential equations. These methods use Galerkin space-discretizations which result in a system of ODEs displaying a discrete version of the Hamiltonian structure of the original system. The resulting system of ODEs is then discretized by a symplectic time-marching method. This combination results in high-order accurate, fully discrete methods which can preserve the invariants of the Hamiltonian defining the ODE system. We restrict our attention to linear Hamiltonian systems, as the main results can be obtained easily and directly, and are applicable to many Hamiltonian systems of practical interest including acoustics, elastodynamics, and electromagnetism. After a brief description of the Hamiltonian systems of our interest, we provide a brief introduction to symplectic time-marching methods for linear systems of ODEs which does not require any background on the subject. We describe then the case in which finite-difference space-discretizations are used and focus on the popular Yee scheme (1966) for electromagnetism. Finally, we consider the case of finite-element space discretizations. The emphasis is placed on the conservation properties of the fully discrete schemes. We end by describing ongoing work.
{"title":"Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems","authors":"Bernardo Cockburn, Shukai Du, M. Sánchez","doi":"10.3389/fams.2023.1165371","DOIUrl":"https://doi.org/10.3389/fams.2023.1165371","url":null,"abstract":"We provide a short introduction to the devising of a special type of methods for numerically approximating the solution of Hamiltonian partial differential equations. These methods use Galerkin space-discretizations which result in a system of ODEs displaying a discrete version of the Hamiltonian structure of the original system. The resulting system of ODEs is then discretized by a symplectic time-marching method. This combination results in high-order accurate, fully discrete methods which can preserve the invariants of the Hamiltonian defining the ODE system. We restrict our attention to linear Hamiltonian systems, as the main results can be obtained easily and directly, and are applicable to many Hamiltonian systems of practical interest including acoustics, elastodynamics, and electromagnetism. After a brief description of the Hamiltonian systems of our interest, we provide a brief introduction to symplectic time-marching methods for linear systems of ODEs which does not require any background on the subject. We describe then the case in which finite-difference space-discretizations are used and focus on the popular Yee scheme (1966) for electromagnetism. Finally, we consider the case of finite-element space discretizations. The emphasis is placed on the conservation properties of the fully discrete schemes. We end by describing ongoing work.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41932541","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 : 2023-04-04DOI: 10.3389/fams.2023.1100147
Absana Tarammim, M. T. Akter
This research study inspects the effectiveness of synchronization methods such as active control and backstepping control from systematic design procedures of a synchronized Shimizu–Morioka system for the same parameter. It aimed to achieve synchronization between the state variables of two identical Shimizu–Morioka chaotic systems by defining the proposed varieties of the error dynamics coefficient matrix. Furthermore, this study also aimed to designed an active controller that enables the synchronization of these systems. The use of designed recursive backstepping nonlinear controllers was based on the Lyapunov function. Furthermore, it also demonstrated the stability of the synchronization of the nonlinear identical Shimizu–Morioka system. The new virtual state variable and establishment of Lyapunov functionals are used in the backstepping controller to stabilize and reduce errors between the Master (MS)/Drive (DS) systems. For comparison, the complexity of active controllers is verified to be such that the designed controller's effectiveness based on backstepping is attainable in engineering applications. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed synchronization strategy with the Runge–Kutta (RK-4) algorithm of fourth order through MatLab Simulink.
{"title":"Shimizu–Morioka's chaos synchronization: An efficacy analysis of active control and backstepping methods","authors":"Absana Tarammim, M. T. Akter","doi":"10.3389/fams.2023.1100147","DOIUrl":"https://doi.org/10.3389/fams.2023.1100147","url":null,"abstract":"This research study inspects the effectiveness of synchronization methods such as active control and backstepping control from systematic design procedures of a synchronized Shimizu–Morioka system for the same parameter. It aimed to achieve synchronization between the state variables of two identical Shimizu–Morioka chaotic systems by defining the proposed varieties of the error dynamics coefficient matrix. Furthermore, this study also aimed to designed an active controller that enables the synchronization of these systems. The use of designed recursive backstepping nonlinear controllers was based on the Lyapunov function. Furthermore, it also demonstrated the stability of the synchronization of the nonlinear identical Shimizu–Morioka system. The new virtual state variable and establishment of Lyapunov functionals are used in the backstepping controller to stabilize and reduce errors between the Master (MS)/Drive (DS) systems. For comparison, the complexity of active controllers is verified to be such that the designed controller's effectiveness based on backstepping is attainable in engineering applications. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed synchronization strategy with the Runge–Kutta (RK-4) algorithm of fourth order through MatLab Simulink.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42216777","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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