In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation49(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of $mgeq 1$ possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of $m$ sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2.
在通常的冲击模型中，冲击来自单一来源。Bozbulut and Eryilmaz[2020]。广义极端冲击模型及其应用。统计通讯-模拟与计算[49(1):110-120]在冲击来自$mgeq 1$可能来源之一时介绍了两种类型的极端冲击模型。在模型1中，随着时间的推移，冲击来自不同的来源。在模型2中，最初，冲击随机地来自$m$源之一，并且冲击继续从同一源到达。本文证明了在通常的随机排序下，模型1的寿命小于模型2。我们进一步证明，如果冲击到达间隔时间具有递增的故障率分布，则通常的随机排序可以推广到危害率排序。我们使用多数化的概念研究了模型2的寿命相对于冲击严重程度的随机行为。我们应用新的随机排序结果表明，模型1下的年龄替代政策比模型2下的成本更高。
{"title":"On stochastic ordering among extreme shock models","authors":"Sirous Fathi Manesh, Muhyiddin Izadi, Baha-Eldin Khaledi","doi":"10.1017/s0269964822000328","DOIUrl":"https://doi.org/10.1017/s0269964822000328","url":null,"abstract":"\u0000 In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation49(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of \u0000 \u0000 \u0000 $mgeq 1$\u0000 \u0000 possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of \u0000 \u0000 \u0000 $m$\u0000 \u0000 sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76064069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1017/s0269964822000390
{"title":"PES volume 36 issue 4 Cover and Back matter","authors":"","doi":"10.1017/s0269964822000390","DOIUrl":"https://doi.org/10.1017/s0269964822000390","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91254895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1017/s0269964822000389
{"title":"PES volume 36 issue 4 Cover and Front matter","authors":"","doi":"10.1017/s0269964822000389","DOIUrl":"https://doi.org/10.1017/s0269964822000389","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91014649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-23DOI: 10.1017/s0269964822000304
Hong-Jie Sun, Yu Chen
For a bivariate random vector $(X, Y)$ , suppose $X$ is some interesting loss variable and $Y$ is a benchmark variable. This paper proposes a new variability measure called the joint tail-Gini functional, which considers not only the tail event of benchmark variable $Y$ , but also the tail information of $X$ itself. It can be viewed as a class of tail Gini-type variability measures, which also include the recently proposed tail-Gini functional. It is a challenging and interesting task to measure the tail variability of $X$ under some extreme scenarios of the variables by extending the Gini's methodology, and the two tail variability measures can serve such a purpose. We study the asymptotic behaviors of these tail Gini-type variability measures, including tail-Gini and joint tail-Gini functionals. The paper conducts this study under both tail dependent and tail independent cases, which are modeled by copulas with so-called tail order property. Some examples are also shown to illuminate our results. In particular, a generalization of the joint tail-Gini functional is considered to provide a more flexible version.
{"title":"Extreme Behaviors of the Tail Gini-Type Variability Measures","authors":"Hong-Jie Sun, Yu Chen","doi":"10.1017/s0269964822000304","DOIUrl":"https://doi.org/10.1017/s0269964822000304","url":null,"abstract":"\u0000 For a bivariate random vector \u0000 \u0000 \u0000 $(X, Y)$\u0000 \u0000 , suppose \u0000 \u0000 \u0000 $X$\u0000 \u0000 is some interesting loss variable and \u0000 \u0000 \u0000 $Y$\u0000 \u0000 is a benchmark variable. This paper proposes a new variability measure called the joint tail-Gini functional, which considers not only the tail event of benchmark variable \u0000 \u0000 \u0000 $Y$\u0000 \u0000 , but also the tail information of \u0000 \u0000 \u0000 $X$\u0000 \u0000 itself. It can be viewed as a class of tail Gini-type variability measures, which also include the recently proposed tail-Gini functional. It is a challenging and interesting task to measure the tail variability of \u0000 \u0000 \u0000 $X$\u0000 \u0000 under some extreme scenarios of the variables by extending the Gini's methodology, and the two tail variability measures can serve such a purpose. We study the asymptotic behaviors of these tail Gini-type variability measures, including tail-Gini and joint tail-Gini functionals. The paper conducts this study under both tail dependent and tail independent cases, which are modeled by copulas with so-called tail order property. Some examples are also shown to illuminate our results. In particular, a generalization of the joint tail-Gini functional is considered to provide a more flexible version.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87532975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-23DOI: 10.1017/s0269964822000316
S. Izadkhah, Ebrahim Amini-Seresht, N. Balakrishnan
This paper examines the preservation of several aging classes of lifetime distributions in the formation of coherent and mixed systems with independent and identically distributed (i.i.d.) or identically distributed (i.d.) component lifetimes. The increasing mean inactivity time class and the decreasing mean time to failure class are developed for the lifetime of systems with possibly dependent and i.d. component lifetimes. The increasing likelihood ratio property is also discussed for the lifetime of a coherent system with i.i.d. component lifetimes. We present sufficient conditions satisfied by the signature of a coherent system with i.i.d. components with exponential distribution, under which the decreasing mean remaining lifetime, the increasing mean inactivity time, and the decreasing mean time to failure are all satisfied by the lifetime of the system. Illustrative examples are presented to support the established results.
{"title":"Preservation properties of some reliability classes by lifetimes of coherent and mixed systems and their signatures","authors":"S. Izadkhah, Ebrahim Amini-Seresht, N. Balakrishnan","doi":"10.1017/s0269964822000316","DOIUrl":"https://doi.org/10.1017/s0269964822000316","url":null,"abstract":"This paper examines the preservation of several aging classes of lifetime distributions in the formation of coherent and mixed systems with independent and identically distributed (i.i.d.) or identically distributed (i.d.) component lifetimes. The increasing mean inactivity time class and the decreasing mean time to failure class are developed for the lifetime of systems with possibly dependent and i.d. component lifetimes. The increasing likelihood ratio property is also discussed for the lifetime of a coherent system with i.i.d. component lifetimes. We present sufficient conditions satisfied by the signature of a coherent system with i.i.d. components with exponential distribution, under which the decreasing mean remaining lifetime, the increasing mean inactivity time, and the decreasing mean time to failure are all satisfied by the lifetime of the system. Illustrative examples are presented to support the established results.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85520659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.1017/S0269964822000298
Yang Yang, Jiayi Xie, Zhimin Zhang
In this paper, we consider some dividend problems in the perturbed compound Poisson model under a constant barrier dividend strategy. We approximate the expected present value of dividend payments before ruin and the expected discounted penalty function based on the COS method, and construct some nonparametric estimators by using a random sample on claim number and individual claim sizes. Under a large sample size setting, we perform an error analysis of the estimators. We also provide some simulation results to verify the effectiveness of this estimation method when the sample size is finite.
{"title":"Nonparametric estimation of some dividend problems in the perturbed compound Poisson model","authors":"Yang Yang, Jiayi Xie, Zhimin Zhang","doi":"10.1017/S0269964822000298","DOIUrl":"https://doi.org/10.1017/S0269964822000298","url":null,"abstract":"In this paper, we consider some dividend problems in the perturbed compound Poisson model under a constant barrier dividend strategy. We approximate the expected present value of dividend payments before ruin and the expected discounted penalty function based on the COS method, and construct some nonparametric estimators by using a random sample on claim number and individual claim sizes. Under a large sample size setting, we perform an error analysis of the estimators. We also provide some simulation results to verify the effectiveness of this estimation method when the sample size is finite.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85331422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-26DOI: 10.1017/s026996482200047x
S. Kattumannil, E. Sreedevi, N. Balakrishnan
In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative past extropy are also established. We then show that several entropy and extropy measures discussed here can be brought into the framework of probability weighted moments, which would facilitate finding estimators of these measures.
{"title":"Relationships between cumulative entropy/extropy, Gini mean difference and probability weighted moments","authors":"S. Kattumannil, E. Sreedevi, N. Balakrishnan","doi":"10.1017/s026996482200047x","DOIUrl":"https://doi.org/10.1017/s026996482200047x","url":null,"abstract":"\u0000 In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative past extropy are also established. We then show that several entropy and extropy measures discussed here can be brought into the framework of probability weighted moments, which would facilitate finding estimators of these measures.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73049748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-25DOI: 10.1017/s0269964823000098
Arpan Mukhopadhyay
We consider a model of binary opinion dynamics where one opinion is inherently “superior” than the other, and social agents exhibit a “bias” toward the superior alternative. Specifically, it is assumed that an agent updates its choice to the superior alternative with probability α > 0 irrespective of its current opinion and opinions of other agents. With probability $1-alpha$ , it adopts majority opinion among two randomly sampled neighbors and itself. We are interested in the time it takes for the network to converge to a consensus on the superior alternative. In a complete graph of size n, we show that irrespective of the initial configuration of the network, the average time to reach consensus scales as $Theta(n,log n)$ when the bias parameter α is sufficiently high, that is, $alpha gt alpha_c$ where α c is a threshold parameter that is uniquely characterized. When the bias is low, that is, when $alpha in (0,alpha_c]$ , we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold $p_c(alpha)$ . If this is not the case, then we show that the network takes $Omega(exp(Theta(n)))$ time on average to reach consensus.
我们考虑了一个二元意见动态模型，其中一种意见本质上比另一种意见“优越”，社会代理人表现出对优越选择的“偏见”。具体地说，假设一个智能体以α > 0的概率更新其选择，而不考虑它当前的意见和其他智能体的意见。概率为$1-alpha$，它在两个随机抽样的邻居和它自己之间采用多数意见。我们感兴趣的是网络在更好的替代方案上达成共识所需的时间。在大小为n的完整图中，我们表明，无论网络的初始配置如何，当偏差参数α足够高时，达到共识的平均时间为$Theta(n,log n)$，即$alpha gt alpha_c$，其中α c是唯一表征的阈值参数。当偏差较低时，即$alpha in (0,alpha_c]$，我们表明，只有当具有优越意见的代理的初始比例高于一定阈值$p_c(alpha)$时，才能实现相同的收敛速度。如果不是这样，那么我们表明网络平均需要$Omega(exp(Theta(n)))$时间来达成共识。
{"title":"Phase transitions in biased opinion dynamics with 2-choices rule","authors":"Arpan Mukhopadhyay","doi":"10.1017/s0269964823000098","DOIUrl":"https://doi.org/10.1017/s0269964823000098","url":null,"abstract":"\u0000 We consider a model of binary opinion dynamics where one opinion is inherently “superior” than the other, and social agents exhibit a “bias” toward the superior alternative. Specifically, it is assumed that an agent updates its choice to the superior alternative with probability α > 0 irrespective of its current opinion and opinions of other agents. With probability \u0000 \u0000 \u0000 $1-alpha$\u0000 \u0000 , it adopts majority opinion among two randomly sampled neighbors and itself. We are interested in the time it takes for the network to converge to a consensus on the superior alternative. In a complete graph of size n, we show that irrespective of the initial configuration of the network, the average time to reach consensus scales as \u0000 \u0000 \u0000 $Theta(n,log n)$\u0000 \u0000 when the bias parameter α is sufficiently high, that is, \u0000 \u0000 \u0000 $alpha gt alpha_c$\u0000 \u0000 where α\u0000 c\u0000 is a threshold parameter that is uniquely characterized. When the bias is low, that is, when \u0000 \u0000 \u0000 $alpha in (0,alpha_c]$\u0000 \u0000 , we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold \u0000 \u0000 \u0000 $p_c(alpha)$\u0000 \u0000 . If this is not the case, then we show that the network takes \u0000 \u0000 \u0000 $Omega(exp(Theta(n)))$\u0000 \u0000 time on average to reach consensus.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78138848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-12DOI: 10.1017/s0269964822000250
Jianping Yang, Tian Zhou, Weiwei Zhuang
Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.
{"title":"Almost first-order stochastic dominance by distorted expectations","authors":"Jianping Yang, Tian Zhou, Weiwei Zhuang","doi":"10.1017/s0269964822000250","DOIUrl":"https://doi.org/10.1017/s0269964822000250","url":null,"abstract":"Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89806508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-12DOI: 10.1017/S0269964822000249
Ran Xu
In this paper, we extend the optimal dividend and capital injection problem with affine penalty at ruin in (Xu, R. & Woo, J.K. (2020). Insurance: Mathematics and Economics 92: 1–16) to the case with singular dividend payments. The asymptotic relationships between our value function to the one with bounded dividend density are studied, which also help to verify that our value function is a viscosity solution to the associated Hamilton–Jacob–Bellman Quasi-Variational Inequality (HJBQVI). We also show that the value function is the smallest viscosity supersolution within certain functional class. A modified comparison principle is proved to guarantee the uniqueness of the value function as the viscosity solution within the same functional class. Finally, a band-type dividend and capital injection strategy is constructed based on four crucial sets; and the optimality of such band-type strategy is proved by using fixed point argument. Numerical examples of the optimal band-type strategies are provided at the end when the claim size follows exponential and gamma distribution, respectively.
在本文中，我们扩展了(Xu, R. & Woo, J.K.(2020))中具有仿射惩罚的最优股利和资本注入问题。保险:数学与经济92:1-16)的情况下的单一股息支付。研究了我们的值函数与有界红利密度的值函数之间的渐近关系，这也有助于验证我们的值函数是相关的hamilton - jack - bellman拟变分不等式(HJBQVI)的粘滞解。在一定的泛函类中，值函数是最小的黏度超解。证明了一种改进的比较原理，保证了值函数作为黏度解在同一函数类内的唯一性。最后，基于四个关键集合，构建了带式股利注资策略;并利用不动点论证证明了这种带型策略的最优性。最后给出了索赔规模分别服从指数分布和伽马分布时最优带型策略的数值算例。
{"title":"Optimal singular dividend control with capital injection and affine penalty payment at ruin","authors":"Ran Xu","doi":"10.1017/S0269964822000249","DOIUrl":"https://doi.org/10.1017/S0269964822000249","url":null,"abstract":"In this paper, we extend the optimal dividend and capital injection problem with affine penalty at ruin in (Xu, R. & Woo, J.K. (2020). Insurance: Mathematics and Economics 92: 1–16) to the case with singular dividend payments. The asymptotic relationships between our value function to the one with bounded dividend density are studied, which also help to verify that our value function is a viscosity solution to the associated Hamilton–Jacob–Bellman Quasi-Variational Inequality (HJBQVI). We also show that the value function is the smallest viscosity supersolution within certain functional class. A modified comparison principle is proved to guarantee the uniqueness of the value function as the viscosity solution within the same functional class. Finally, a band-type dividend and capital injection strategy is constructed based on four crucial sets; and the optimality of such band-type strategy is proved by using fixed point argument. Numerical examples of the optimal band-type strategies are provided at the end when the claim size follows exponential and gamma distribution, respectively.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88192787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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