Pub Date : 2024-07-23DOI: 10.1186/s13362-024-00148-7
Richard Kwame Ansah, Alex Akwasi Opoku, Kassim Tawiah, Richard Kena Boadi, Bridget Nana-Ama Gana, Sampson Tackie, Maud Avevor Ayornu, Stephen Manu Ampofo Mills
This paper employs a statistical mechanical model as a framework to investigate how socioeconomic factors of individuals such as gender and place of residence influence their decision when deciding between comprehensive and third-party motor insurance policies in Ghana. Data from a general insurance firm was used for this investigation taking five years’ worth of transactions into account. The methods of partial least squares and the ordinary least squares are, respectively, used to estimate the parameters of the interacting and the non-interacting models in the Multipopulation Currie-Weiss model in a discrete choice framework. The findings showed that both location and gender have discernible influences on how people choose their motor insurance. We encourage insurance companies to intensify their campaign on the importance of motor insurance to all vehicle/car owners, especially those in rural areas in order to reduce the risk and associated losses in vehicular accidents on Ghanaian roads.
{"title":"Mathematical modelling of decision making: the case of motor insurance choices","authors":"Richard Kwame Ansah, Alex Akwasi Opoku, Kassim Tawiah, Richard Kena Boadi, Bridget Nana-Ama Gana, Sampson Tackie, Maud Avevor Ayornu, Stephen Manu Ampofo Mills","doi":"10.1186/s13362-024-00148-7","DOIUrl":"https://doi.org/10.1186/s13362-024-00148-7","url":null,"abstract":"This paper employs a statistical mechanical model as a framework to investigate how socioeconomic factors of individuals such as gender and place of residence influence their decision when deciding between comprehensive and third-party motor insurance policies in Ghana. Data from a general insurance firm was used for this investigation taking five years’ worth of transactions into account. The methods of partial least squares and the ordinary least squares are, respectively, used to estimate the parameters of the interacting and the non-interacting models in the Multipopulation Currie-Weiss model in a discrete choice framework. The findings showed that both location and gender have discernible influences on how people choose their motor insurance. We encourage insurance companies to intensify their campaign on the importance of motor insurance to all vehicle/car owners, especially those in rural areas in order to reduce the risk and associated losses in vehicular accidents on Ghanaian roads.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"425 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780921","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 : 2024-07-22DOI: 10.1186/s13362-024-00149-6
Willem Jansen, Martijn Anthonissen, Jan ten Thije Boonkkamp, Wilbert IJzerman
Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase-space description of an optical system. Phase space is the set of position and direction coordinates of light rays intersecting a surface. The original algorithm (Filosa, ten Thije Boonkkamp and IJzerman in J Math Ind 11(1):4, 2021) is limited to optical systems consisting of only straight surfaces; we generalize it to accommodate curved surfaces. The algorithm is applied to a standard optical system, the compound parabolic concentrator. We compare the accuracy and speed of the generalized algorithm, the original algorithm and Monte Carlo ray tracing. The results show that the generalized algorithm outperforms both other methods.
串联后向光线映射是二维光线追踪的一种替代方法。它基于光学系统的相空间描述。相空间是光线与曲面相交的位置和方向坐标集。最初的算法（Filosa、ten Thije Boonkkamp 和 IJzerman 在 J Math Ind 11(1):4, 2021）仅限于由直线表面组成的光学系统；我们将其推广到曲面。我们将该算法应用于标准光学系统--复合抛物面聚光器。我们比较了广义算法、原始算法和蒙特卡洛射线追踪的精度和速度。结果表明，广义算法优于其他两种方法。
{"title":"Concatenated backward ray mapping on the compound parabolic concentrator","authors":"Willem Jansen, Martijn Anthonissen, Jan ten Thije Boonkkamp, Wilbert IJzerman","doi":"10.1186/s13362-024-00149-6","DOIUrl":"https://doi.org/10.1186/s13362-024-00149-6","url":null,"abstract":"Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase-space description of an optical system. Phase space is the set of position and direction coordinates of light rays intersecting a surface. The original algorithm (Filosa, ten Thije Boonkkamp and IJzerman in J Math Ind 11(1):4, 2021) is limited to optical systems consisting of only straight surfaces; we generalize it to accommodate curved surfaces. The algorithm is applied to a standard optical system, the compound parabolic concentrator. We compare the accuracy and speed of the generalized algorithm, the original algorithm and Monte Carlo ray tracing. The results show that the generalized algorithm outperforms both other methods.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"25 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141754063","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 : 2024-07-11DOI: 10.1186/s13362-024-00147-8
John Inge Asperheim, Prerana Das, Bjørnar Grande, Dietmar Hömberg, Thomas Petzold
In the present paper the high-frequency induction welding process is studied numerically. The mathematical model comprises a harmonic vector potential formulation of the Maxwell equations and a quasi-static, convection dominated heat equation coupled through the Joule heat term and nonlinear constitutive relations. Its main novelties are a new analytic approach which permits to compute a spatially varying feed velocity depending on the angle of the Vee-opening and additional spring-back effects. Moreover, a numerical stabilization approach for the finite element discretization allows to consider realistic weld-line speeds and thus a fairly comprehensive three-dimensional simulation of the tube welding process.
本文对高频感应焊接过程进行了数值研究。数学模型包括麦克斯韦方程的谐波矢量势公式，以及通过焦耳热项和非线性构成关系耦合的准静态对流主导热方程。它的主要创新之处在于采用了一种新的分析方法，可以根据 Vee 开口角度和额外的回弹效应计算空间变化的进给速度。此外，有限元离散化的数值稳定方法允许考虑现实的焊接线速度，从而对管材焊接过程进行相当全面的三维模拟。
{"title":"Numerical simulation of high-frequency induction welding in longitudinal welded tubes","authors":"John Inge Asperheim, Prerana Das, Bjørnar Grande, Dietmar Hömberg, Thomas Petzold","doi":"10.1186/s13362-024-00147-8","DOIUrl":"https://doi.org/10.1186/s13362-024-00147-8","url":null,"abstract":"In the present paper the high-frequency induction welding process is studied numerically. The mathematical model comprises a harmonic vector potential formulation of the Maxwell equations and a quasi-static, convection dominated heat equation coupled through the Joule heat term and nonlinear constitutive relations. Its main novelties are a new analytic approach which permits to compute a spatially varying feed velocity depending on the angle of the Vee-opening and additional spring-back effects. Moreover, a numerical stabilization approach for the finite element discretization allows to consider realistic weld-line speeds and thus a fairly comprehensive three-dimensional simulation of the tube welding process.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614950","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 : 2024-07-10DOI: 10.1186/s13362-024-00152-x
Ihsan Arharas, Mohamed El Fatini, Mohammed Louriki, Roger Pettersson
In epidemic modeling, interpretation of compartment quantities, such as s, i, and r in relevant equations, is not always straightforward. Ambiguities regarding whether these quantities represent numbers or fractions of individuals in each compartment rise questions about significance of the involved parameters. In this paper, we address these challenges by considering a density-dependent epidemic modelling by a birth-death process approach inspired by Kurtz from 1970s’. In contrast to existing literature, which employs population size scaling under constant population condition, we scale with respect to the area. Namely, under the assumption of spatial homogeneity of the population, we consider the quantities of susceptible, infective and recovered per unit area. This spatial scaling allows diffusion approximation for birth-death type epidemic models with varying population size. By adopting this approach, we anticipate to contribute to a clear and transparent description of compartment quantities and parameters in epidemic modeling.
在流行病建模中，对相关方程中的 s、i 和 r 等分区量的解释并不总是很直接。这些量代表的是每个分区中个体的数量还是分数，这一点含糊不清，引发了对相关参数重要性的质疑。本文受 20 世纪 70 年代库尔茨（Kurtz）的启发，采用出生-死亡过程方法对依赖密度的流行病进行建模，从而解决了这些难题。与现有文献在恒定种群条件下采用种群规模缩放的方法不同，我们采用的是与区域相关的缩放方法。也就是说，在人口空间均质性假设下，我们考虑单位面积内的易感人群、感染人群和康复人群的数量。这种空间缩放方法可以对人口数量不同的出生-死亡型流行病模型进行扩散近似。通过采用这种方法，我们希望能对流行病模型中的分区数量和参数做出清晰透明的描述。
{"title":"Epidemic modelling by birth-death processes with spatial scaling","authors":"Ihsan Arharas, Mohamed El Fatini, Mohammed Louriki, Roger Pettersson","doi":"10.1186/s13362-024-00152-x","DOIUrl":"https://doi.org/10.1186/s13362-024-00152-x","url":null,"abstract":"In epidemic modeling, interpretation of compartment quantities, such as s, i, and r in relevant equations, is not always straightforward. Ambiguities regarding whether these quantities represent numbers or fractions of individuals in each compartment rise questions about significance of the involved parameters. In this paper, we address these challenges by considering a density-dependent epidemic modelling by a birth-death process approach inspired by Kurtz from 1970s’. In contrast to existing literature, which employs population size scaling under constant population condition, we scale with respect to the area. Namely, under the assumption of spatial homogeneity of the population, we consider the quantities of susceptible, infective and recovered per unit area. This spatial scaling allows diffusion approximation for birth-death type epidemic models with varying population size. By adopting this approach, we anticipate to contribute to a clear and transparent description of compartment quantities and parameters in epidemic modeling.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"29 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572896","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 : 2024-07-05DOI: 10.1186/s13362-024-00150-z
Bernd Kugelmann, Roland Pulch
Mathematical modelling of a dengue epidemic with two serotypes including a temporary cross-immunity yields a nonlinear system consisting of ordinary differential equations (ODEs). We investigate an optimal control problem, where the integral of the infected humans is minimised within a time interval. The controls represent human actions to decrease the number of mosquitos in the model. An integral constraint is added, which takes a limitation on the sum of the human actions into account. On the one hand, we derive and apply a direct approach to solve the optimal control problem. Therein, a discretisation of the controls is constructed using spline interpolation in time. Consequently, a finite-dimensional constrained minimisation problem can be solved. On the other hand, we employ an indirect approach, where necessary conditions for an optimal solution are considered. This technique yields a multipoint boundary value problem of a larger system of ODEs including adjoint equations. We present results of numerical computations, where the two methods are compared.
{"title":"Optimal control of a dengue model with cross-immunity","authors":"Bernd Kugelmann, Roland Pulch","doi":"10.1186/s13362-024-00150-z","DOIUrl":"https://doi.org/10.1186/s13362-024-00150-z","url":null,"abstract":"Mathematical modelling of a dengue epidemic with two serotypes including a temporary cross-immunity yields a nonlinear system consisting of ordinary differential equations (ODEs). We investigate an optimal control problem, where the integral of the infected humans is minimised within a time interval. The controls represent human actions to decrease the number of mosquitos in the model. An integral constraint is added, which takes a limitation on the sum of the human actions into account. On the one hand, we derive and apply a direct approach to solve the optimal control problem. Therein, a discretisation of the controls is constructed using spline interpolation in time. Consequently, a finite-dimensional constrained minimisation problem can be solved. On the other hand, we employ an indirect approach, where necessary conditions for an optimal solution are considered. This technique yields a multipoint boundary value problem of a larger system of ODEs including adjoint equations. We present results of numerical computations, where the two methods are compared.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549792","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 : 2024-06-20DOI: 10.1186/s13362-024-00146-9
Wolfgang Rannetbauer, Simon Hubmer, Carina Hambrock, Ronny Ramlau
Thermal spray coating is a critical process in many industries, involving the application of coatings to surfaces to enhance their functionality. This paper proposes a framework for modelling and predicting critical target variables in thermal spray coating processes, based on the application of statistical design of experiments (DoE) and the modelling of the data using generalized linear models (GLMs) with a particular emphasis on gamma regression. Experimental data obtained from thermal spray coating trials are used to validate the presented approach, demonstrating that it is able to accurately model and predict critical target variables. As such, the framework has significant potential for the optimization of thermal spray coating processes, and can contribute to the development of more efficient and effective coating technologies in various industries.
{"title":"Predictive modelling of critical variables for improving HVOF coating using gamma regression models","authors":"Wolfgang Rannetbauer, Simon Hubmer, Carina Hambrock, Ronny Ramlau","doi":"10.1186/s13362-024-00146-9","DOIUrl":"https://doi.org/10.1186/s13362-024-00146-9","url":null,"abstract":"Thermal spray coating is a critical process in many industries, involving the application of coatings to surfaces to enhance their functionality. This paper proposes a framework for modelling and predicting critical target variables in thermal spray coating processes, based on the application of statistical design of experiments (DoE) and the modelling of the data using generalized linear models (GLMs) with a particular emphasis on gamma regression. Experimental data obtained from thermal spray coating trials are used to validate the presented approach, demonstrating that it is able to accurately model and predict critical target variables. As such, the framework has significant potential for the optimization of thermal spray coating processes, and can contribute to the development of more efficient and effective coating technologies in various industries.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"65 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501734","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 : 2024-04-30DOI: 10.1186/s13362-024-00145-w
Samson Worku, Pratik Mullick
The escalating process of urbanization has raised concerns about incidents arising from overcrowding, necessitating a deep understanding of large human crowd behavior and the development of effective crowd management strategies. This study employs computational methods to analyze real-world crowd behaviors, emphasizing self-organizing patterns. Notably, the intersection of two streams of individuals triggers the spontaneous emergence of striped patterns, validated through both simulations and live human experiments. Addressing a gap in computational methods for studying these patterns, previous research utilized the pattern-matching technique, employing the Nelder-Mead Simplex algorithm for fitting a two-dimensional sinusoidal function to pedestrian coordinates. This paper advances the pattern-matching procedure by introducing Simulated Annealing as the optimization algorithm and employing a two-dimensional square wave for data fitting. The amalgamation of Simulated Annealing and the square wave significantly enhances pattern fitting quality, validated through statistical hypothesis tests. The study concludes by outlining potential applications of this method across diverse scenarios.
{"title":"Detecting self-organising patterns in crowd motion: effect of optimisation algorithms","authors":"Samson Worku, Pratik Mullick","doi":"10.1186/s13362-024-00145-w","DOIUrl":"https://doi.org/10.1186/s13362-024-00145-w","url":null,"abstract":"The escalating process of urbanization has raised concerns about incidents arising from overcrowding, necessitating a deep understanding of large human crowd behavior and the development of effective crowd management strategies. This study employs computational methods to analyze real-world crowd behaviors, emphasizing self-organizing patterns. Notably, the intersection of two streams of individuals triggers the spontaneous emergence of striped patterns, validated through both simulations and live human experiments. Addressing a gap in computational methods for studying these patterns, previous research utilized the pattern-matching technique, employing the Nelder-Mead Simplex algorithm for fitting a two-dimensional sinusoidal function to pedestrian coordinates. This paper advances the pattern-matching procedure by introducing Simulated Annealing as the optimization algorithm and employing a two-dimensional square wave for data fitting. The amalgamation of Simulated Annealing and the square wave significantly enhances pattern fitting quality, validated through statistical hypothesis tests. The study concludes by outlining potential applications of this method across diverse scenarios.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"13 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140836087","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 : 2024-03-28DOI: 10.1186/s13362-024-00144-x
Audrius Kabašinskas
Pension funds are an essential part of retirement planning, and their performance and risks play a significant role in ensuring financial stability for retirees. This study aims to analyse the connectedness and spillover effects in the Lithuanian second-pillar pension fund market. The findings of this study provide insight on the interdependence within the second-pillar pension funds market and with other financial markets, and contribute to a better understanding of the risk-return trade-off of pension funds, especially during high-volatility periods. Differently from other studies in this paper market regimes are identified using Hidden Markov Models (HMM). Interdependence (including multivariate and non-linear) and causality between pension funds are analysed in different market regimes. Finally, returns spillover in different regimes is estimated using VAR and VECM models. The results of this paper are expected to be useful for pension fund managers, participants, and pension system supervisors in making decisions about investment strategies and in practices of systemic risk management regulation.
养老基金是退休规划的重要组成部分，其业绩和风险在确保退休人员的财务稳定方面发挥着重要作用。本研究旨在分析立陶宛第二支柱养老基金市场的关联性和溢出效应。研究结果有助于深入了解第二支柱养老基金市场内部以及与其他金融市场之间的相互依存关系，有助于更好地理解养老基金的风险收益权衡，尤其是在高波动时期。与其他研究不同的是，本文使用隐马尔可夫模型（HMM）来识别市场制度。本文分析了不同市场制度下养老基金之间的相互依存关系（包括多变量和非线性）和因果关系。最后，使用 VAR 和 VECM 模型估算了不同制度下的收益溢出效应。本文的研究结果将有助于养老基金管理者、参与者和养老金系统监管者做出投资战略决策，并有助于系统风险管理监管实践。
{"title":"Systemic risk assessment of Lithuanian second-pillar pension funds through connectedness and spillover","authors":"Audrius Kabašinskas","doi":"10.1186/s13362-024-00144-x","DOIUrl":"https://doi.org/10.1186/s13362-024-00144-x","url":null,"abstract":"Pension funds are an essential part of retirement planning, and their performance and risks play a significant role in ensuring financial stability for retirees. This study aims to analyse the connectedness and spillover effects in the Lithuanian second-pillar pension fund market. The findings of this study provide insight on the interdependence within the second-pillar pension funds market and with other financial markets, and contribute to a better understanding of the risk-return trade-off of pension funds, especially during high-volatility periods. Differently from other studies in this paper market regimes are identified using Hidden Markov Models (HMM). Interdependence (including multivariate and non-linear) and causality between pension funds are analysed in different market regimes. Finally, returns spillover in different regimes is estimated using VAR and VECM models. The results of this paper are expected to be useful for pension fund managers, participants, and pension system supervisors in making decisions about investment strategies and in practices of systemic risk management regulation.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315713","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 : 2024-03-22DOI: 10.1186/s13362-024-00142-z
Roshdey Mareay
Soft rough based on covering $mathcal {S}RC$ theory has become a useful and well-known area of research in theories of uncertainty. The present work follows up on this flourishing research topic. We introduce a new model of $mathcal {S}RC$ in a fusion of soft set theory $mathcal {S}ST$ and rough set depending on covering $mathcal {C}RS$ . We put forth a definition of soft rough covering approximation space $mathcal {S}CAS$ via neighborhood concept. Some axiomatic systems of our model of $mathcal {S}RC$ are discussed. We study the relationship between our model of $mathcal {S}RC$ and three other $mathcal {S}RC$ -models. An algorithm for reduction of the attributes of the information systems using $mathcal {S}CAS$ is established. Based on the theoretical discussion, we set forth some applications of our model which will be helpful in decision making process via $mathcal {S}RC$ theory.
{"title":"Soft rough sets based on covering and their applications","authors":"Roshdey Mareay","doi":"10.1186/s13362-024-00142-z","DOIUrl":"https://doi.org/10.1186/s13362-024-00142-z","url":null,"abstract":"Soft rough based on covering $mathcal {S}RC$ theory has become a useful and well-known area of research in theories of uncertainty. The present work follows up on this flourishing research topic. We introduce a new model of $mathcal {S}RC$ in a fusion of soft set theory $mathcal {S}ST$ and rough set depending on covering $mathcal {C}RS$ . We put forth a definition of soft rough covering approximation space $mathcal {S}CAS$ via neighborhood concept. Some axiomatic systems of our model of $mathcal {S}RC$ are discussed. We study the relationship between our model of $mathcal {S}RC$ and three other $mathcal {S}RC$ -models. An algorithm for reduction of the attributes of the information systems using $mathcal {S}CAS$ is established. Based on the theoretical discussion, we set forth some applications of our model which will be helpful in decision making process via $mathcal {S}RC$ theory.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140202964","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 : 2024-03-19DOI: 10.1186/s13362-024-00141-0
Maja Rudolph, Stefan Kurz, Barbara Rakitsch
Design patterns provide a systematic way to convey solutions to recurring modeling challenges. This paper introduces design patterns for hybrid modeling, an approach that combines modeling based on first principles with data-driven modeling techniques. While both approaches have complementary advantages there are often multiple ways to combine them into a hybrid model, and the appropriate solution will depend on the problem at hand. In this paper, we provide four base patterns that can serve as blueprints for combining data-driven components with domain knowledge into a hybrid approach. In addition, we also present two composition patterns that govern the combination of the base patterns into more complex hybrid models. Each design pattern is illustrated by typical use cases from application areas such as climate modeling, engineering, and physics.
{"title":"Hybrid modeling design patterns","authors":"Maja Rudolph, Stefan Kurz, Barbara Rakitsch","doi":"10.1186/s13362-024-00141-0","DOIUrl":"https://doi.org/10.1186/s13362-024-00141-0","url":null,"abstract":"Design patterns provide a systematic way to convey solutions to recurring modeling challenges. This paper introduces design patterns for hybrid modeling, an approach that combines modeling based on first principles with data-driven modeling techniques. While both approaches have complementary advantages there are often multiple ways to combine them into a hybrid model, and the appropriate solution will depend on the problem at hand. In this paper, we provide four base patterns that can serve as blueprints for combining data-driven components with domain knowledge into a hybrid approach. In addition, we also present two composition patterns that govern the combination of the base patterns into more complex hybrid models. Each design pattern is illustrated by typical use cases from application areas such as climate modeling, engineering, and physics.","PeriodicalId":44012,"journal":{"name":"Journal of Mathematics in Industry","volume":"70 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165588","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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