Pub Date : 2022-01-01DOI: 10.48550/arXiv.2204.02253
M. Herty, E. Iacomini, G. Visconti
Abstract Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in view of the limit for infinitely particles and extensions towards stability analysis and multi–objective optimization. We illustrate the performance of the method by using test inverse problems from the literature.
{"title":"Recent Trends on Nonlinear Filtering for Inverse Problems","authors":"M. Herty, E. Iacomini, G. Visconti","doi":"10.48550/arXiv.2204.02253","DOIUrl":"https://doi.org/10.48550/arXiv.2204.02253","url":null,"abstract":"Abstract Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in view of the limit for infinitely particles and extensions towards stability analysis and multi–objective optimization. We illustrate the performance of the method by using test inverse problems from the literature.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"10 - 20"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44400297","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}
Abstract Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean–field limit and show well–posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings.
{"title":"Continuous limits of residual neural networks in case of large input data","authors":"M. Herty, Anna Thünen, T. Trimborn, G. Visconti","doi":"10.2478/caim-2022-0008","DOIUrl":"https://doi.org/10.2478/caim-2022-0008","url":null,"abstract":"Abstract Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean–field limit and show well–posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"96 - 120"},"PeriodicalIF":1.3,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45703796","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}
Abstract The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchho material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400.
{"title":"Fluid-structure interaction simulations with a LES filtering approach in solids4Foam","authors":"M. Girfoglio, A. Quaini, G. Rozza","doi":"10.2478/caim-2021-0002","DOIUrl":"https://doi.org/10.2478/caim-2021-0002","url":null,"abstract":"Abstract The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchho material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"12 1","pages":"13 - 28"},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48540884","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}
Abstract Bioinformatic techniques targeting gene expression data require specific analysis pipelines with the aim of studying properties, adaptation, and disease outcomes in a sample population. Present investigation compared together results of four numerical experiments modeling survival rates from bladder cancer genetic profiles. Research showed that a sequence of two discretization phases produced remarkable results compared to a classic approach employing one discretization of gene expression data. Analysis involving two discretization phases consisted of a primary discretizer followed by refinement or pre-binning input values before the main discretization scheme. Among all tests, the best model encloses a sequence of data transformation to compensate skewness, data discretization phase with class-attribute interdependence maximization algorithm, and final classification by voting feature intervals, a classifier that also provides discrete interval optimization.
{"title":"Double-stage discretization approaches for biomarker-based bladder cancer survival modeling","authors":"M. Nascimben, M. Venturin, L. Rimondini","doi":"10.2478/caim-2021-0003","DOIUrl":"https://doi.org/10.2478/caim-2021-0003","url":null,"abstract":"Abstract Bioinformatic techniques targeting gene expression data require specific analysis pipelines with the aim of studying properties, adaptation, and disease outcomes in a sample population. Present investigation compared together results of four numerical experiments modeling survival rates from bladder cancer genetic profiles. Research showed that a sequence of two discretization phases produced remarkable results compared to a classic approach employing one discretization of gene expression data. Analysis involving two discretization phases consisted of a primary discretizer followed by refinement or pre-binning input values before the main discretization scheme. Among all tests, the best model encloses a sequence of data transformation to compensate skewness, data discretization phase with class-attribute interdependence maximization algorithm, and final classification by voting feature intervals, a classifier that also provides discrete interval optimization.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"12 1","pages":"29 - 47"},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49234720","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}
Abstract The basic investigation is the existence and the (numerical) observability of propagating fronts in the framework of the so-called Epithelial-to-Mesenchymal Transition and its reverse Mesenchymal-to-Epithelial Transition, which are known to play a crucial role in tumor development. To this aim, we propose a simplified one-dimensional hyperbolic-parabolic PDE model composed of two equations, one for the representative of the epithelial phenotype, and the second describing the mesenchymal phenotype. The system involves two positive constants, the relaxation time and a measure of invasiveness, moreover an essential feature is the presence of a nonlinear reaction function, typically assumed to be S-shaped. An identity characterizing the speed of propagation of the fronts is proven, together with numerical evidence of the existence of traveling waves. The latter is obtained by discretizing the system by means of an implicit-explicit finite difference scheme, then the algorithm is validated by checking the capability of the so-called LeVeque–Yee formula to reproduce the value of the speed furnished by the above cited identity. Once such justification has been achieved, we concentrate on numerical experiments relative to Riemann initial data connecting two stable stationary states of the underlying ODE model. In particular, we detect an explicit transition threshold separating regression regimes from invasive ones, which depends on critical values of the invasiveness parameter. Finally, we perform an extensive sensitivity analysis with respect to the system parameters, exhibiting a subtle dependence for those close to the threshold values, and we postulate some conjectures on the propagating fronts.
{"title":"Phase transitions of biological phenotypes by means of a prototypical PDE model","authors":"C. Mascia, P. Moschetta, C. Simeoni","doi":"10.2478/caim-2020-0001","DOIUrl":"https://doi.org/10.2478/caim-2020-0001","url":null,"abstract":"Abstract The basic investigation is the existence and the (numerical) observability of propagating fronts in the framework of the so-called Epithelial-to-Mesenchymal Transition and its reverse Mesenchymal-to-Epithelial Transition, which are known to play a crucial role in tumor development. To this aim, we propose a simplified one-dimensional hyperbolic-parabolic PDE model composed of two equations, one for the representative of the epithelial phenotype, and the second describing the mesenchymal phenotype. The system involves two positive constants, the relaxation time and a measure of invasiveness, moreover an essential feature is the presence of a nonlinear reaction function, typically assumed to be S-shaped. An identity characterizing the speed of propagation of the fronts is proven, together with numerical evidence of the existence of traveling waves. The latter is obtained by discretizing the system by means of an implicit-explicit finite difference scheme, then the algorithm is validated by checking the capability of the so-called LeVeque–Yee formula to reproduce the value of the speed furnished by the above cited identity. Once such justification has been achieved, we concentrate on numerical experiments relative to Riemann initial data connecting two stable stationary states of the underlying ODE model. In particular, we detect an explicit transition threshold separating regression regimes from invasive ones, which depends on critical values of the invasiveness parameter. Finally, we perform an extensive sensitivity analysis with respect to the system parameters, exhibiting a subtle dependence for those close to the threshold values, and we postulate some conjectures on the propagating fronts.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"11 1","pages":"1 - 17"},"PeriodicalIF":1.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44404065","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}
L. Meacci, G. Buscaglia, F. Mut, R. Ausas, M. Primicerio
Abstract This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.
{"title":"A new two-component approach in modeling red blood cells","authors":"L. Meacci, G. Buscaglia, F. Mut, R. Ausas, M. Primicerio","doi":"10.2478/caim-2020-0004","DOIUrl":"https://doi.org/10.2478/caim-2020-0004","url":null,"abstract":"Abstract This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":" ","pages":"55 - 71"},"PeriodicalIF":1.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45812249","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}
L. Meacci, G. Buscaglia, F. Mut, R. Ausas, M. Primicerio
Abstract This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.
{"title":"A new two-component approach in modeling red blood cells","authors":"L. Meacci, G. Buscaglia, F. Mut, R. Ausas, M. Primicerio","doi":"10.1515/caim-2020-0004","DOIUrl":"https://doi.org/10.1515/caim-2020-0004","url":null,"abstract":"Abstract This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"11 1","pages":"55 - 71"},"PeriodicalIF":1.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42298805","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}
Abstract The recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) device is an important issue because, when applying an external voltage, the membrane deforms with the consequent risk of touching the upper plate of the device (a condition that should be avoided). Then, during the deformation of the membrane, it is useful to know if this movement admits stable equilibrium configurations. In such a context, our present work analyze the behavior of an electrostatic 1D membrane MEMS device when an external electric voltage is applied. In particular, starting from a well-known second-order elliptical semi-linear di erential model, obtained considering the electrostatic field inside the device proportional to the curvature of the membrane, the only possible equilibrium position is obtained, and its stability is analyzed. Moreover, considering that the membrane has an inertia in moving and taking into account that it must not touch the upper plate of the device, the range of possible values of the applied external voltage is obtained, which accounted for these two particular operating conditions. Finally, some calculations about the variation of potential energy have identified optimal control conditions.
{"title":"Curvature Dependent Electrostatic Field in the Deformable MEMS Device: Stability and Optimal Control","authors":"P. di Barba, L. Fattorusso, M. Versaci","doi":"10.2478/caim-2020-0003","DOIUrl":"https://doi.org/10.2478/caim-2020-0003","url":null,"abstract":"Abstract The recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) device is an important issue because, when applying an external voltage, the membrane deforms with the consequent risk of touching the upper plate of the device (a condition that should be avoided). Then, during the deformation of the membrane, it is useful to know if this movement admits stable equilibrium configurations. In such a context, our present work analyze the behavior of an electrostatic 1D membrane MEMS device when an external electric voltage is applied. In particular, starting from a well-known second-order elliptical semi-linear di erential model, obtained considering the electrostatic field inside the device proportional to the curvature of the membrane, the only possible equilibrium position is obtained, and its stability is analyzed. Moreover, considering that the membrane has an inertia in moving and taking into account that it must not touch the upper plate of the device, the range of possible values of the applied external voltage is obtained, which accounted for these two particular operating conditions. Finally, some calculations about the variation of potential energy have identified optimal control conditions.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":" 77","pages":"35 - 54"},"PeriodicalIF":1.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41252385","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}
Abstract In this work, we consider a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. We propose some numerical methods to approximate the solution of the system which are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our experimental approach, we present some tests and a detailed description of the numerical solutions’ behaviour obtained by varying the values of the system’s characteristic parameters.
{"title":"Numerical methods for a system of coupled Cahn-Hilliard equations","authors":"Mattia Martini, G. E. Sodini","doi":"10.2478/caim-2021-0001","DOIUrl":"https://doi.org/10.2478/caim-2021-0001","url":null,"abstract":"Abstract In this work, we consider a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. We propose some numerical methods to approximate the solution of the system which are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our experimental approach, we present some tests and a detailed description of the numerical solutions’ behaviour obtained by varying the values of the system’s characteristic parameters.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"272 ","pages":"1 - 12"},"PeriodicalIF":1.3,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41280476","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}
Abstract We present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameter vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an “optimize-then-reduce” approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, the cost functional, its gradient and the optimal solution. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows.
{"title":"A certified RB method for PDE-constrained parametric optimization problems","authors":"A. Manzoni, S. Pagani","doi":"10.2478/caim-2019-0017","DOIUrl":"https://doi.org/10.2478/caim-2019-0017","url":null,"abstract":"Abstract We present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameter vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an “optimize-then-reduce” approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, the cost functional, its gradient and the optimal solution. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"123 - 152"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45150277","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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