This paper presents a survey on some of the recent progress on numerical solutions for controlled switching diffusions. We begin by recalling the basics of switching diffusions and controlled switching diffusions. We then present regular controls and singular controls. The main objective of this paper is to provide a survey on some recent advances on Markov chain approximation methods for solving stochastic control problems numerically. A number of applications in insurance, mathematical biology, epidemiology, and economics are presented. Several numerical examples are provided for demonstration.
{"title":"A survey of numerical solutions for stochastic control problems: Some recent progress","authors":"Zhu Jin, Mingxue Qiu, K. Tran, G. Yin","doi":"10.3934/naco.2022004","DOIUrl":"https://doi.org/10.3934/naco.2022004","url":null,"abstract":"This paper presents a survey on some of the recent progress on numerical solutions for controlled switching diffusions. We begin by recalling the basics of switching diffusions and controlled switching diffusions. We then present regular controls and singular controls. The main objective of this paper is to provide a survey on some recent advances on Markov chain approximation methods for solving stochastic control problems numerically. A number of applications in insurance, mathematical biology, epidemiology, and economics are presented. Several numerical examples are provided for demonstration.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73796242","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}
D. Chalishajar, K. Ravikumar, K. Ramkumar, A. Anguraj
This paper assesses a class of nonlocal Hilfer fractional stochastic differential equations (NHFSDEs) governed by fractional Brownian motion (fBm). New sufficient condition of exact null controllability for this stochastic setting has been investigated using fractional calculus, fixed point theory and a theory of resolvent operator. The derived result is new because it generalizes several of previously published results. However, the obtained results are proven by an illustration using stochastic partial differential equations to demonstrate the present application characteristic of null controllability. A filter example is demonstrated to make use of resolvent operator in a practical way.
{"title":"Null controllability of Hilfer fractional stochastic differential equations with nonlocal conditions","authors":"D. Chalishajar, K. Ravikumar, K. Ramkumar, A. Anguraj","doi":"10.3934/naco.2022029","DOIUrl":"https://doi.org/10.3934/naco.2022029","url":null,"abstract":"This paper assesses a class of nonlocal Hilfer fractional stochastic differential equations (NHFSDEs) governed by fractional Brownian motion (fBm). New sufficient condition of exact null controllability for this stochastic setting has been investigated using fractional calculus, fixed point theory and a theory of resolvent operator. The derived result is new because it generalizes several of previously published results. However, the obtained results are proven by an illustration using stochastic partial differential equations to demonstrate the present application characteristic of null controllability. A filter example is demonstrated to make use of resolvent operator in a practical way.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80381863","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}
In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method can be considered as an combination of Ishikawa's process with the proximal point algorithm, the extragradient algorithm with or without linesearch. Under certain conditions on parameters, the iteration sequences generated by the proposed methods are proved to be weakly convergent to a solution of the problem. These results extend the previous results given in the literature. A numerical example is also provided to illustrate the proposed algorithms.
{"title":"Weak convergence theorems for symmetric generalized hybrid mappings and equilibrium problems","authors":"Do Sang Kim, N. N. Hai, B. Dinh","doi":"10.3934/naco.2021051","DOIUrl":"https://doi.org/10.3934/naco.2021051","url":null,"abstract":"In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method can be considered as an combination of Ishikawa's process with the proximal point algorithm, the extragradient algorithm with or without linesearch. Under certain conditions on parameters, the iteration sequences generated by the proposed methods are proved to be weakly convergent to a solution of the problem. These results extend the previous results given in the literature. A numerical example is also provided to illustrate the proposed algorithms.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87910341","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}
The object of this work is to construct an explicit linear operators begin{document}$ A $end{document} and begin{document}$ B $end{document} which generate a nilpotent Lie algebra for the bracket begin{document}$ left[A,Bright] = AB-BA $end{document} of degree 2 in infinite dimensional spaces. This construction can be applied to give an exact optimal solution for a class of infinite dimensional bilinear systems.
The object of this work is to construct an explicit linear operators begin{document}$ A $end{document} and begin{document}$ B $end{document} which generate a nilpotent Lie algebra for the bracket begin{document}$ left[A,Bright] = AB-BA $end{document} of degree 2 in infinite dimensional spaces. This construction can be applied to give an exact optimal solution for a class of infinite dimensional bilinear systems.
{"title":"Optimal control problem governed by an infinite dimensional two-nilpotent bilinear systems","authors":"A. Aib, N. Bensalem","doi":"10.3934/naco.2022018","DOIUrl":"https://doi.org/10.3934/naco.2022018","url":null,"abstract":"<p style='text-indent:20px;'>The object of this work is to construct an explicit linear operators <inline-formula><tex-math id=\"M1\">begin{document}$ A $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M2\">begin{document}$ B $end{document}</tex-math></inline-formula> which generate a nilpotent Lie algebra for the bracket <inline-formula><tex-math id=\"M3\">begin{document}$ left[A,Bright] = AB-BA $end{document}</tex-math></inline-formula> of degree 2 in infinite dimensional spaces. This construction can be applied to give an exact optimal solution for a class of infinite dimensional bilinear systems.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86117634","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}
The transportation problem is a particular type of linear programming problem in which the main objective is to minimize the cost. In marked contrast to the classical real-world transportation model, shipping supplies from one source to a destination cause several costs and benefits, each of which is incomparable to another. The extended transportation problem was first introduced in a study conducted by Amirteimoori [1]. In contrast, many important questions regarding the production possibility set, the place of costs, the benefits, and the essence of these costs were not fully addressed yet. Therefore, this paper focuses on transportation models that do not provide explicit output. This method is helpful because it is designed for a specific purpose: to send goods and supply-demand at the lowest cost and decision-maker; does not suffer from the confusion of costs and the various consequences of placing them costs and outputs. Furthermore, this model improves the contradiction between the essence of the problem and the input/output-oriented data envelopment analysis. In this paper, previous models that can not incorporate all the sources of inefficiency have been solved. We apply the slack-based measure(SBM) to calculate all identified inefficiency sources. A numerical example is considered to show the approach's applicability, as mentioned above, to actual life situations. As a result, the optimal costs achieved via the proposed method are more realistic and accurate by obtaining a more representative efficiency assessment. This example proved our proposed approach's efficiency, providing a more efficient solution by corporate all sources inefficiency and presenting efficient costs for each path.
{"title":"A two-stage data envelopment analysis approach to solve extended transportation problem with non-homogenous costs","authors":"Aliyeh Hadi, S. Mehrabian","doi":"10.3934/naco.2022006","DOIUrl":"https://doi.org/10.3934/naco.2022006","url":null,"abstract":"The transportation problem is a particular type of linear programming problem in which the main objective is to minimize the cost. In marked contrast to the classical real-world transportation model, shipping supplies from one source to a destination cause several costs and benefits, each of which is incomparable to another. The extended transportation problem was first introduced in a study conducted by Amirteimoori [1]. In contrast, many important questions regarding the production possibility set, the place of costs, the benefits, and the essence of these costs were not fully addressed yet. Therefore, this paper focuses on transportation models that do not provide explicit output. This method is helpful because it is designed for a specific purpose: to send goods and supply-demand at the lowest cost and decision-maker; does not suffer from the confusion of costs and the various consequences of placing them costs and outputs. Furthermore, this model improves the contradiction between the essence of the problem and the input/output-oriented data envelopment analysis. In this paper, previous models that can not incorporate all the sources of inefficiency have been solved. We apply the slack-based measure(SBM) to calculate all identified inefficiency sources. A numerical example is considered to show the approach's applicability, as mentioned above, to actual life situations. As a result, the optimal costs achieved via the proposed method are more realistic and accurate by obtaining a more representative efficiency assessment. This example proved our proposed approach's efficiency, providing a more efficient solution by corporate all sources inefficiency and presenting efficient costs for each path.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73000036","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}
In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index begin{document}$ m $end{document}. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.
In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index begin{document}$ m $end{document}. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.
{"title":"Drazin theta and theta Drazin matrices","authors":"Divya P. Shenoy","doi":"10.3934/naco.2022023","DOIUrl":"https://doi.org/10.3934/naco.2022023","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index <inline-formula><tex-math id=\"M3\">begin{document}$ m $end{document}</tex-math></inline-formula>. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79106442","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}
We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with exact penalization and running maximum or integral cost. The method is then extended to the common noise setting. Our work extends (Bokanowski, Picarelli, and Zidani, SIAM J. Control Optim. 54.5 (2016), pp. 2568--2593) and (Bokanowski, Picarelli, and Zidani, Appl. Math. Optim. 71 (2015), pp. 125--163) to a mean-field setting. The reformulation as an unconstrained problem is particularly suitable for the numerical resolution of the problem, that is achieved from an extension of a machine learning algorithm from (Carmona, Lauri{`e}re, arXiv:1908.01613 to appear in Ann. Appl. Prob., 2019). A first application concerns the storage of renewable electricity in the presence of mean-field price impact and another one focuses on a mean-variance portfolio selection problem with probabilistic constraints on the wealth. We also illustrate our approach for a direct numerical resolution of the primal Markowitz continuous-time problem without relying on duality.
我们考虑具有概率状态约束的McKean-Vlasov动力学控制(或称平均场控制)。我们依赖于一种水平集方法，它将约束问题表示为具有精确惩罚和运行最大或积分成本的无约束问题。然后将该方法推广到常见的噪声设置。我们的工作扩展了(Bokanowski, Picarelli, and Zidani, SIAM J. Control Optim. 54.5 (2016)， pp. 2568—2593)和(Bokanowski, Picarelli, and Zidani, apple .)。数学。Optim. 71 (2015)， pp. 125—163)到平均场设置。作为无约束问题的重新表述特别适合于问题的数值解决，这是通过扩展(Carmona, Lauri{ ' e}re, arXiv:1908.01613)的机器学习算法实现的，并出现在Ann中。达成。概率。, 2019)。第一个应用涉及平均场价格影响下可再生电力的存储，另一个应用侧重于对财富有概率约束的平均方差投资组合选择问题。我们还说明了不依赖对偶的原始马科维茨连续时间问题的直接数值解决方法。
{"title":"A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection","authors":"Maximilien Germain, H. Pham, X. Warin","doi":"10.3934/naco.2022033","DOIUrl":"https://doi.org/10.3934/naco.2022033","url":null,"abstract":"We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with exact penalization and running maximum or integral cost. The method is then extended to the common noise setting. Our work extends (Bokanowski, Picarelli, and Zidani, SIAM J. Control Optim. 54.5 (2016), pp. 2568--2593) and (Bokanowski, Picarelli, and Zidani, Appl. Math. Optim. 71 (2015), pp. 125--163) to a mean-field setting. The reformulation as an unconstrained problem is particularly suitable for the numerical resolution of the problem, that is achieved from an extension of a machine learning algorithm from (Carmona, Lauri{`e}re, arXiv:1908.01613 to appear in Ann. Appl. Prob., 2019). A first application concerns the storage of renewable electricity in the presence of mean-field price impact and another one focuses on a mean-variance portfolio selection problem with probabilistic constraints on the wealth. We also illustrate our approach for a direct numerical resolution of the primal Markowitz continuous-time problem without relying on duality.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81622617","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}
A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized objective functional to compute a descent direction and, second, a stepsize choice based on an Armijo-like condition to ensure sufficient descent in every iteration. We provide several convergence results. Under mild assumptions, the method generates sequences of iterates which converge, on subsequences, towards minimizers. Moreover, a sublinear rate of convergence for the objective functional values is derived. Second, we show that the method enjoys improved rates of convergence if the partially linearized problem fulfills certain growth estimates. Most notably these results do not require strong convexity of the objective functional. Numerical tests on a variety of challenging PDE-constrained optimization problems confirm the practical efficiency of the proposed algorithm.
{"title":"On fast convergence rates for generalized conditional gradient methods with backtracking stepsize","authors":"K. Kunisch, Daniel Walter","doi":"10.3934/naco.2022026","DOIUrl":"https://doi.org/10.3934/naco.2022026","url":null,"abstract":"A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized objective functional to compute a descent direction and, second, a stepsize choice based on an Armijo-like condition to ensure sufficient descent in every iteration. We provide several convergence results. Under mild assumptions, the method generates sequences of iterates which converge, on subsequences, towards minimizers. Moreover, a sublinear rate of convergence for the objective functional values is derived. Second, we show that the method enjoys improved rates of convergence if the partially linearized problem fulfills certain growth estimates. Most notably these results do not require strong convexity of the objective functional. Numerical tests on a variety of challenging PDE-constrained optimization problems confirm the practical efficiency of the proposed algorithm.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75554921","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}
This work establishes the equivalence between Mean Field Game and a class of PDE systems closely related to compressible Navier-Stokes equations. The solvability of the PDE system via the existence of the Nash Equilibrium of the Mean Field Game is provided under a set of conditions.
{"title":"From mean field games to Navier-Stokes equations","authors":"T. Luo, Q. Song","doi":"10.3934/naco.2022020","DOIUrl":"https://doi.org/10.3934/naco.2022020","url":null,"abstract":"<p style='text-indent:20px;'>This work establishes the equivalence between Mean Field Game and a class of PDE systems closely related to compressible Navier-Stokes equations. The solvability of the PDE system via the existence of the Nash Equilibrium of the Mean Field Game is provided under a set of conditions.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73252981","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}
Harbir Antil, Thomas S. Brown, R. Lohner, F. Togashi, Deepanshu Verma
For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to 'train' or 'learn' the network are faced with a very large number (in the millions even for small networks) of equivalent optimal solutions in the parameter space. To the best of our knowledge, this observation is absent in the literature. In order to narrow down the parameter search space, a novel technique is introduced in order to fix the bias vector configurations to be monotonically increasing. This is achieved by augmenting a typical learning problem with inequality constraints on the bias vectors in each layer. A Moreau-Yosida regularization based algorithm is proposed to handle these inequality constraints and a theoretical convergence of this algorithm is established. Applications of the proposed approach to standard trigonometric functions and more challenging stiff ordinary differential equations arising in chemically reacting flows clearly illustrate the benefits of the proposed approach. Further application of the approach on the MNIST dataset within TensorFlow, illustrate that the presented approach can be incorporated in any of the existing machine learning libraries.
{"title":"Deep neural nets with fixed bias configuration","authors":"Harbir Antil, Thomas S. Brown, R. Lohner, F. Togashi, Deepanshu Verma","doi":"10.3934/naco.2022016","DOIUrl":"https://doi.org/10.3934/naco.2022016","url":null,"abstract":"For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to 'train' or 'learn' the network are faced with a very large number (in the millions even for small networks) of equivalent optimal solutions in the parameter space. To the best of our knowledge, this observation is absent in the literature. In order to narrow down the parameter search space, a novel technique is introduced in order to fix the bias vector configurations to be monotonically increasing. This is achieved by augmenting a typical learning problem with inequality constraints on the bias vectors in each layer. A Moreau-Yosida regularization based algorithm is proposed to handle these inequality constraints and a theoretical convergence of this algorithm is established. Applications of the proposed approach to standard trigonometric functions and more challenging stiff ordinary differential equations arising in chemically reacting flows clearly illustrate the benefits of the proposed approach. Further application of the approach on the MNIST dataset within TensorFlow, illustrate that the presented approach can be incorporated in any of the existing machine learning libraries.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82930534","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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