Pub Date : 2001-09-11DOI: 10.1109/PNPM.2001.953360
A. Miner
The solution of a generalized stochastic Petri net (GSPN) is severely restricted by the size of its underlying continuous-time Markov chain. In recent work (G. Ciardo and A.S. Miner, 1999), matrix diagrams built from a Kronecker expression for the transition rate matrix of certain types of GSPNs were shown to allow for more efficient solution; however, the GSPN model requires a special form, so that the transition rate matrix has a Kronecker expression. In this paper, we extend the earlier results to GSPN models with partitioned sets of places. Specifically, we give a more restrictive definition for matrix diagrams and show that the new form is canonical. We then present an algorithm that builds a canonical matrix diagram representation for an arbitrary non-negative matrix, given encodings for the sets of rows and columns. Using this algorithm, a Kronecker expression is not required to construct the matrix diagram. The efficient matrix diagram algorithms for numerical solution presented earlier are still applicable. We apply our technique to several example GSPNs.
{"title":"Efficient solution of GSPNs using canonical matrix diagrams","authors":"A. Miner","doi":"10.1109/PNPM.2001.953360","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953360","url":null,"abstract":"The solution of a generalized stochastic Petri net (GSPN) is severely restricted by the size of its underlying continuous-time Markov chain. In recent work (G. Ciardo and A.S. Miner, 1999), matrix diagrams built from a Kronecker expression for the transition rate matrix of certain types of GSPNs were shown to allow for more efficient solution; however, the GSPN model requires a special form, so that the transition rate matrix has a Kronecker expression. In this paper, we extend the earlier results to GSPN models with partitioned sets of places. Specifically, we give a more restrictive definition for matrix diagrams and show that the new form is canonical. We then present an algorithm that builds a canonical matrix diagram representation for an arbitrary non-negative matrix, given encodings for the sets of rows and columns. Using this algorithm, a Kronecker expression is not required to construct the matrix diagram. The efficient matrix diagram algorithms for numerical solution presented earlier are still applicable. We apply our technique to several example GSPNs.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121895518","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953364
M. Gribaudo, A. Horváth
Fluid (or hybrid) Petri nets with flush-out arcs are Petri net based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. For this kind of formalism, equations can be automatically derived from the model. Such equations, however, are often too complex to be solved analytically and simple discretization techniques usually can be successfully applied only to simple cases. We present a particular numerical technique for transient solution that makes use of Kronecker-algebra.
{"title":"Fluid stochastic Petri nets augmented with flush-out arcs: a transient analysis technique","authors":"M. Gribaudo, A. Horváth","doi":"10.1109/PNPM.2001.953364","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953364","url":null,"abstract":"Fluid (or hybrid) Petri nets with flush-out arcs are Petri net based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. For this kind of formalism, equations can be automatically derived from the model. Such equations, however, are often too complex to be solved analytically and simple discretization techniques usually can be successfully applied only to simple cases. We present a particular numerical technique for transient solution that makes use of Kronecker-algebra.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123769548","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953368
P. Buchholz
Equivalence is a basic concept in many modeling formalisms to compare different realizations of a system or to compute for a given system a minimal equivalent representation. We present two different equivalence relations for a class of generalized stochastic Petri nets (GSPNs) with labeled transitions (LGSPNs), namely trace equivalence and bisimulation equivalence. In contrast to most other approaches we allow labeling of timed and immediate transitions and thus have to define equivalence for a stochastic process with exponentially timed and immediate transitions. For this class of GSPNs it is possible to compose nets via timed and immediate transitions which has also been introduced for superposed generalized stochastic Petri nets (SGSPNs). We describe under which conditions the proposed equivalences are congruences according to the composition of nets. The congruence condition is easily to achieve for timed transitions but it is shown that some additional restrictions are necessary to obtain a congruence relation which is preserved under composition via immediate transitions. However, if such a congruence is defined, then component state spaces can be reduced by aggregation before composition. This aggregation includes an elimination of some immediate transitions in LGSPNs composed via immediate transitions which has not been considered yet.
{"title":"Equivalence and aggregation of GSPNs with labeled transitions","authors":"P. Buchholz","doi":"10.1109/PNPM.2001.953368","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953368","url":null,"abstract":"Equivalence is a basic concept in many modeling formalisms to compare different realizations of a system or to compute for a given system a minimal equivalent representation. We present two different equivalence relations for a class of generalized stochastic Petri nets (GSPNs) with labeled transitions (LGSPNs), namely trace equivalence and bisimulation equivalence. In contrast to most other approaches we allow labeling of timed and immediate transitions and thus have to define equivalence for a stochastic process with exponentially timed and immediate transitions. For this class of GSPNs it is possible to compose nets via timed and immediate transitions which has also been introduced for superposed generalized stochastic Petri nets (SGSPNs). We describe under which conditions the proposed equivalences are congruences according to the composition of nets. The congruence condition is easily to achieve for timed transitions but it is shown that some additional restrictions are necessary to obtain a congruence relation which is preserved under composition via immediate transitions. However, if such a congruence is defined, then component state spaces can be reduced by aggregation before composition. This aggregation includes an elimination of some immediate transitions in LGSPNs composed via immediate transitions which has not been considered yet.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126188619","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953355
D. Tutsch, J. Sokol
An important feature of the next generation Internet will be the ubiquitous access of mobile users dealing with real-time applications. A recently introduced architecture, called USAIA by J. Sokol and J. Widmer (2001), is considered to provide both for realtime traffic, fast handoffs and a high probability for QoS support during movement of the mobile nodes. This paper examines the performance of the wireless cell level of the USAIA architecture with means of a Petri net model. The design allows a detailed investigation of various model parameters. Therefore, the model is able to assist in optimizing the framework in terms of network design, protocol processing, and resource utilization.
{"title":"Petri net based performance evaluation of USAIA's bandwidth partitioning for the wireless cell level","authors":"D. Tutsch, J. Sokol","doi":"10.1109/PNPM.2001.953355","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953355","url":null,"abstract":"An important feature of the next generation Internet will be the ubiquitous access of mobile users dealing with real-time applications. A recently introduced architecture, called USAIA by J. Sokol and J. Widmer (2001), is considered to provide both for realtime traffic, fast handoffs and a high probability for QoS support during movement of the mobile nodes. This paper examines the performance of the wireless cell level of the USAIA architecture with means of a Petri net model. The design allows a detailed investigation of various model parameters. Therefore, the model is able to assist in optimizing the framework in terms of network design, protocol processing, and resource utilization.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117349218","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953353
A. Bobbio, G. Franceschinis, R. Gaeta, L. Portinale
The case-study presented in this paper is aimed at assessing the dependability of a Programmable Logic Controller (PLC) devoted to safety functions. This case study has been brought to our attention by a national environmental agency and has been partially abstracted and anonymized to protect proprietary information. The PLC consists of a triplicated channel with a (2:3) majority voting logic and is modeled by means of a recently proposed extension of the classical Fault Tree (FT) formalism called Parametric Fault Tree (PFT). In the PFT replicated units are folded and parameterized so that only one representative of the various similar replicas is explicitly included in the model. The quantitative analysis of the PFT assumes s-independence among components and is based on combinatorial formulas. In order to include dependencies both in the failure and repair process, the PFT is directly converted into a particular class of High Level Petri Nets, called SWN. The paper illustrates the PFT formalism and the automatic conversion algorithm from a PFT into a SWN Moreover, it is shown how various kind of dependencies can be accommodated in the obtained SWN model.
{"title":"Dependability assessment of an industrial Programmable Logic Controller via Parametric Fault-Tree and High Level Petri net","authors":"A. Bobbio, G. Franceschinis, R. Gaeta, L. Portinale","doi":"10.1109/PNPM.2001.953353","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953353","url":null,"abstract":"The case-study presented in this paper is aimed at assessing the dependability of a Programmable Logic Controller (PLC) devoted to safety functions. This case study has been brought to our attention by a national environmental agency and has been partially abstracted and anonymized to protect proprietary information. The PLC consists of a triplicated channel with a (2:3) majority voting logic and is modeled by means of a recently proposed extension of the classical Fault Tree (FT) formalism called Parametric Fault Tree (PFT). In the PFT replicated units are folded and parameterized so that only one representative of the various similar replicas is explicitly included in the model. The quantitative analysis of the PFT assumes s-independence among components and is based on combinatorial formulas. In order to include dependencies both in the failure and repair process, the PFT is directly converted into a particular class of High Level Petri Nets, called SWN. The paper illustrates the PFT formalism and the automatic conversion algorithm from a PFT into a SWN Moreover, it is shown how various kind of dependencies can be accommodated in the obtained SWN model.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130711851","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953374
D. Deavours, W. Sanders
This paper gives an overview of the Mobius framework, and gives a formal specification for defining atomic models within the framework. The framework is designed to be capable of incorporating multiple modeling formalisms, including atomic models (e.g, SPNs), composition formalisms (e.g., Replicate/Join), measure specification formalisms, connection formalisms, and solvers. We focus on atomic models, which are composed of actions, state variables, and properties. We argue that these are sufficient to specify a large number of atomic model formalisms in the Mobius framework. The framework serves as a basis for the Mobius tool.
{"title":"Mobius: framework and atomic models","authors":"D. Deavours, W. Sanders","doi":"10.1109/PNPM.2001.953374","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953374","url":null,"abstract":"This paper gives an overview of the Mobius framework, and gives a formal specification for defining atomic models within the framework. The framework is designed to be capable of incorporating multiple modeling formalisms, including atomic models (e.g, SPNs), composition formalisms (e.g., Replicate/Join), measure specification formalisms, connection formalisms, and solvers. We focus on atomic models, which are composed of actions, state variables, and properties. We argue that these are sufficient to specify a large number of atomic model formalisms in the Mobius framework. The framework serves as a basis for the Mobius tool.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132846942","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953356
L. Wells, S. Christensen, L. Kristensen, K. Mortensen
This paper presents a general framework for modeling distributed computing environments for performance analysis by means of Timed Hierarchical Coloured Petri Nets. The proposed framework was used to build and analyze a Coloured Petri Net model of a HTTP web server. Analysis of the performance of the web server model reveals how the web server will respond to changes in the arrival rate of requests, and alternative configurations of the web server model are examined. These are the results of a research project conducted in cooperation between the CPN Centre and Hewlett-Packard Corporation on capacity planning and performance analysis of distributed computing environments.
{"title":"Simulation based performance analysis of web servers","authors":"L. Wells, S. Christensen, L. Kristensen, K. Mortensen","doi":"10.1109/PNPM.2001.953356","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953356","url":null,"abstract":"This paper presents a general framework for modeling distributed computing environments for performance analysis by means of Timed Hierarchical Coloured Petri Nets. The proposed framework was used to build and analyze a Coloured Petri Net model of a HTTP web server. Analysis of the performance of the web server model reveals how the web server will respond to changes in the arrival rate of requests, and alternative configurations of the web server model are examined. These are the results of a research project conducted in cooperation between the CPN Centre and Hewlett-Packard Corporation on capacity planning and performance analysis of distributed computing environments.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128251505","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953351
G. Ciardo
Petri nets and stochastic Petri nets have been widely adopted as one of the best tools to model the logical and timing behavior of discrete-state systems. However, their practical applicability is limited by the state-space explosion problem. We survey some of the techniques that have been used to cope with large state spaces, starting from early explicit methods, which require data structures of size proportional to the number of states or state-to-state transitions, then moving to implicit methods, which borrow ideas from symbolic model checking (binary decision diagrams) and numerical linear algebra (Kronecker operators) to drastically reduce the computational requirements. Next, we describe the structural decomposition approach which has been the topic of our research in the last few years. This method only requires to specify a partition of the places in the net and, combining decision diagrams and Kronecker operators with the new concepts of event locality and node saturation, achieves fundamental gains in both memory and time efficiency. At the same, the approach is applicable to a wide range of models. We conclude by considering several research directions that could further push the range of solvable models, eventually leading to an even greater industrial acceptance of this simple yet powerful modeling formalism.
{"title":"What a structural world [structural decomposition]","authors":"G. Ciardo","doi":"10.1109/PNPM.2001.953351","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953351","url":null,"abstract":"Petri nets and stochastic Petri nets have been widely adopted as one of the best tools to model the logical and timing behavior of discrete-state systems. However, their practical applicability is limited by the state-space explosion problem. We survey some of the techniques that have been used to cope with large state spaces, starting from early explicit methods, which require data structures of size proportional to the number of states or state-to-state transitions, then moving to implicit methods, which borrow ideas from symbolic model checking (binary decision diagrams) and numerical linear algebra (Kronecker operators) to drastically reduce the computational requirements. Next, we describe the structural decomposition approach which has been the topic of our research in the last few years. This method only requires to specify a partition of the places in the net and, combining decision diagrams and Kronecker operators with the new concepts of event locality and node saturation, achieves fundamental gains in both memory and time efficiency. At the same, the approach is applicable to a wide range of models. We conclude by considering several research directions that could further push the range of solvable models, eventually leading to an even greater industrial acceptance of this simple yet powerful modeling formalism.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123841982","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953362
Simona Bernardi, G. Balbo
Concurrent generalized Petri nets (CGPNs) are a subclass of Markov regenerative stochastic Petri nets, characterized by timed transitions with general distributed firing times (GEN transitions), that become enabled simultaneously while no other GEN transitions can be activated during their enabling periods. In their original definition, CGPNs were identified through a study of their state space; hence they are recognized only after the construction of their tangible reachability graphs. In this paper, we present sufficient conditions representing a first step in the definition of an alternative method for the characterization of this type of models. The method is based on the structural analysis of the net, it does not require the generation of its tangible reachability graph, and is thus computationally convenient. Moreover, an advantage of this method is that it can also be applied in the case of models characterized by large state spaces, and is hence prone to be analysed via simulation using regenerative techniques. The criteria that we propose represent the basis for a preliminary analysis of the model in order to verify its membership of the class of CGPNs whose numerical solution always requires the construction of the tangible reachability graph and the characterization of the underlying Markov regenerative process.
{"title":"Concurrent generalized Petri nets: regenerative conditions","authors":"Simona Bernardi, G. Balbo","doi":"10.1109/PNPM.2001.953362","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953362","url":null,"abstract":"Concurrent generalized Petri nets (CGPNs) are a subclass of Markov regenerative stochastic Petri nets, characterized by timed transitions with general distributed firing times (GEN transitions), that become enabled simultaneously while no other GEN transitions can be activated during their enabling periods. In their original definition, CGPNs were identified through a study of their state space; hence they are recognized only after the construction of their tangible reachability graphs. In this paper, we present sufficient conditions representing a first step in the definition of an alternative method for the characterization of this type of models. The method is based on the structural analysis of the net, it does not require the generation of its tangible reachability graph, and is thus computationally convenient. Moreover, an advantage of this method is that it can also be applied in the case of models characterized by large state spaces, and is hence prone to be analysed via simulation using regenerative techniques. The criteria that we propose represent the basis for a preliminary analysis of the model in order to verify its membership of the class of CGPNs whose numerical solution always requires the construction of the tangible reachability graph and the characterization of the underlying Markov regenerative process.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121187132","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 : 2001-09-11DOI: 10.1109/PNPM.2001.953361
G. Chiola, R. Carvajal-Schiaffino
The construction of the reachability graph presents the problem that its size may grow exponentially with respect to the size of the Petri-net model. For this reason, all available tools suffer restrictions due to the limitation of the available computational resources. We present a new, efficient algorithm based on a data structure that encodes canonical firing count vectors starting from the initial marking rather than token distributions. Our new algorithm applies to bounded and consistent Petri-net models. We define the main concept for this new marking representation, then we present performance results in terms of comparisons of space and time resources against the standard GreatSPN (Great Stochastic Petri Nets) solver.
{"title":"A reachability graph construction algorithm based on canonical transition firing count vectors","authors":"G. Chiola, R. Carvajal-Schiaffino","doi":"10.1109/PNPM.2001.953361","DOIUrl":"https://doi.org/10.1109/PNPM.2001.953361","url":null,"abstract":"The construction of the reachability graph presents the problem that its size may grow exponentially with respect to the size of the Petri-net model. For this reason, all available tools suffer restrictions due to the limitation of the available computational resources. We present a new, efficient algorithm based on a data structure that encodes canonical firing count vectors starting from the initial marking rather than token distributions. Our new algorithm applies to bounded and consistent Petri-net models. We define the main concept for this new marking representation, then we present performance results in terms of comparisons of space and time resources against the standard GreatSPN (Great Stochastic Petri Nets) solver.","PeriodicalId":364695,"journal":{"name":"Proceedings 9th International Workshop on Petri Nets and Performance Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2001-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122642806","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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