Pub Date : 2004-12-01DOI: 10.1109/CDC.2004.1430234
M. Chyba, H. J. Sussmann, H. Maurer, Gottfried Vossen
We consider the minimum time problem for a class of underwater vehicles. We focus on the situation of initial and final configurations at rest satisfying x/sub 0/ /spl ne/ x/sub f/, z/sub 0/ = z/sub f/, /spl Theta//sub 0/ /spl Theta//sub f/ = 0. We supplement our theory with a numerical study of optimal bang-bang and singular solutions and include a discussion on a possible Fuller-like phenomenon.
{"title":"Underwater vehicles: the minimum time problem","authors":"M. Chyba, H. J. Sussmann, H. Maurer, Gottfried Vossen","doi":"10.1109/CDC.2004.1430234","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430234","url":null,"abstract":"We consider the minimum time problem for a class of underwater vehicles. We focus on the situation of initial and final configurations at rest satisfying x/sub 0/ /spl ne/ x/sub f/, z/sub 0/ = z/sub f/, /spl Theta//sub 0/ /spl Theta//sub f/ = 0. We supplement our theory with a numerical study of optimal bang-bang and singular solutions and include a discussion on a possible Fuller-like phenomenon.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124304610","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 : 2004-12-01DOI: 10.1109/CDC.2004.1430323
N. C. Martins, M. Dahleh, N. Elia
We study the stabilizability of uncertain systems in the presence of finite capacity feedback. Motivated by the structure of communication networks, we consider a stochastic digital link that sends words whose size is governed by a random process. Such link is used to transmit state measurements between the plant and the controller. We derive necessary and sufficient conditions for the internal and the external stabilizability of the feedback loop. In accordance with previous publications, stabilizability of unstable plants is possible if and only if the link's average transmission rate is above a positive critical value. In our formulation the plant and the link can be stochastic. In addition, stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We show that the critical average transmission rate, for stabilizability, depends on the description of uncertainty and the statistical properties of the plant as well as the link.
{"title":"Feedback stabilization of uncertain systems using a stochastic digital link","authors":"N. C. Martins, M. Dahleh, N. Elia","doi":"10.1109/CDC.2004.1430323","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430323","url":null,"abstract":"We study the stabilizability of uncertain systems in the presence of finite capacity feedback. Motivated by the structure of communication networks, we consider a stochastic digital link that sends words whose size is governed by a random process. Such link is used to transmit state measurements between the plant and the controller. We derive necessary and sufficient conditions for the internal and the external stabilizability of the feedback loop. In accordance with previous publications, stabilizability of unstable plants is possible if and only if the link's average transmission rate is above a positive critical value. In our formulation the plant and the link can be stochastic. In addition, stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We show that the critical average transmission rate, for stabilizability, depends on the description of uncertainty and the statistical properties of the plant as well as the link.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114980422","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 : 2004-12-01DOI: 10.1109/CDC.2004.1430330
D. Paley, Naomi Ehrich Leonard, R. Sepulchre
This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to bistability and hysteresis. We also present behavior primitives that enable piecewise-linear network trajectory tracking.
{"title":"Collective motion: bistability and trajectory tracking","authors":"D. Paley, Naomi Ehrich Leonard, R. Sepulchre","doi":"10.1109/CDC.2004.1430330","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430330","url":null,"abstract":"This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to bistability and hysteresis. We also present behavior primitives that enable piecewise-linear network trajectory tracking.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133386928","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 : 2004-12-01DOI: 10.1109/CDC.2004.1430211
Dongjun Lee, Perry Y. Li
We propose a general control framework for multiple mechanical systems interacting with environments and/or humans under coordination requirements. The key innovation is the passive decomposition which enables us to achieve the two requirements of such systems simultaneously: motion coordination and energetic passivity of the closed-loop system. It decomposes the system dynamics into shape system addressing the coordination aspect, locked system representing overall dynamics of the coordinated system, and dynamic couplings between the locked and shape systems. The dynamic couplings can be cancelled out without violating passivity. Thus, the coordination aspect (shape system) and the dynamics of the coordinated system (locked system) can be decoupled from each other while enforcing passivity. Also, by designing the locked and shape controls to enforce passivity of their respective systems, passivity of the closed-loop system is guaranteed. We analyze and exhibit geometry of the passive decomposition and the locked and shape systems.
{"title":"Passive decomposition of multiple mechanical systems under coordination requirements","authors":"Dongjun Lee, Perry Y. Li","doi":"10.1109/CDC.2004.1430211","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430211","url":null,"abstract":"We propose a general control framework for multiple mechanical systems interacting with environments and/or humans under coordination requirements. The key innovation is the passive decomposition which enables us to achieve the two requirements of such systems simultaneously: motion coordination and energetic passivity of the closed-loop system. It decomposes the system dynamics into shape system addressing the coordination aspect, locked system representing overall dynamics of the coordinated system, and dynamic couplings between the locked and shape systems. The dynamic couplings can be cancelled out without violating passivity. Thus, the coordination aspect (shape system) and the dynamics of the coordinated system (locked system) can be decoupled from each other while enforcing passivity. Also, by designing the locked and shape controls to enforce passivity of their respective systems, passivity of the closed-loop system is guaranteed. We analyze and exhibit geometry of the passive decomposition and the locked and shape systems.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116352793","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 : 2004-12-01DOI: 10.1109/CDC.2004.1428976
G. Zhai, Hai Lin, Xuping Xu, A. Michel
In this paper, we study stability property for a class of switched systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time. When all continuous-time subsystems are Hurwitz stable and all discrete-time subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for the subsystems and that the switched system is exponentially stable under arbitrary switching. When unstable subsystems are involved, we show that given a desired decay rate of the system, if the activation time ratio between unstable subsystems and stable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.
{"title":"Stability analysis and design of switched normal systems","authors":"G. Zhai, Hai Lin, Xuping Xu, A. Michel","doi":"10.1109/CDC.2004.1428976","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428976","url":null,"abstract":"In this paper, we study stability property for a class of switched systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time. When all continuous-time subsystems are Hurwitz stable and all discrete-time subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for the subsystems and that the switched system is exponentially stable under arbitrary switching. When unstable subsystems are involved, we show that given a desired decay rate of the system, if the activation time ratio between unstable subsystems and stable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"512 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132285288","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 : 2004-12-01DOI: 10.1109/CDC.2004.1430277
K. Fujimoto
This paper is devoted to a characterization of singular values of nonlinear operators. Although eigenvalue and spectrum analysis for nonlinear operators has been studied by many researchers in mathematics literature, singular value analysis has not been investigated so much. In this paper, a framework of singular value analysis is proposed which is closely related to the operator gain. The proposed singular value analysis is based on the eigenvalue analysis of a special class of nonlinear operators called differentially self-adjoint. Some properties of those operators are clarified which are natural generalization of the linear case results. Furthermore, a sufficient condition for the existence of singular values is provided. The proposed analysis tools are expected to play an important role in nonlinear control systems theory as in the linear case.
{"title":"What are singular values of nonlinear operators?","authors":"K. Fujimoto","doi":"10.1109/CDC.2004.1430277","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430277","url":null,"abstract":"This paper is devoted to a characterization of singular values of nonlinear operators. Although eigenvalue and spectrum analysis for nonlinear operators has been studied by many researchers in mathematics literature, singular value analysis has not been investigated so much. In this paper, a framework of singular value analysis is proposed which is closely related to the operator gain. The proposed singular value analysis is based on the eigenvalue analysis of a special class of nonlinear operators called differentially self-adjoint. Some properties of those operators are clarified which are natural generalization of the linear case results. Furthermore, a sufficient condition for the existence of singular values is provided. The proposed analysis tools are expected to play an important role in nonlinear control systems theory as in the linear case.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132295486","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 : 2004-12-01DOI: 10.1109/CDC.2004.1428882
Chang-Woo Yang, S. Shakkottai
In this paper we look at the shortest-remaining-processing-time (SRPT) scheduling algorithm. It has been long thought that although it exhibits optimal mean packet delay, the larger sized packets will "suffer" a very large delay. In this paper, we consider this scheduling rule for a discrete-time queueing system that is accessed by a large number of flows (a many flows regime). In such an asymptotic regime where the number of flows are large, we derive expressions for the packet delay distributions for batch arrival processes, and with bounded packet sizes. Using these results, we compare the delay asymptote (i.e., for any finite delay, and asymptotic in the number of flows) of the SRPT scheduler with that of a FIFO (first in first out) scheduler, when there is a mix of packet sizes. In particular, we apply the asymptotic delay result to a system accessed by packets which are one of two sizes: '1' or 'k', and the arrival process is i.i.d. in time. We show that the difference in rate function of the delay asymptote between SRPT and FIFO for the size 'k' packet decays as 1/k. Thus, for large packets, the delay distributions under FIFO and SRPT look similar. On the other hand, for the size '1' packet, the delay rate function under SRPT is invariant with k. However for FIFO, the delay rate function for the size '1' packet decays as 1/k. This indicates that for size '1' packets, SRPT performs increasingly better as the range in packet size increases. Thus, these results indicate that SRPT is a good policy to implement for Web-servers, where empirical evidence suggests a large variability in packet sizes.
{"title":"Delay asymptotics of the SRPT scheduler","authors":"Chang-Woo Yang, S. Shakkottai","doi":"10.1109/CDC.2004.1428882","DOIUrl":"https://doi.org/10.1109/CDC.2004.1428882","url":null,"abstract":"In this paper we look at the shortest-remaining-processing-time (SRPT) scheduling algorithm. It has been long thought that although it exhibits optimal mean packet delay, the larger sized packets will \"suffer\" a very large delay. In this paper, we consider this scheduling rule for a discrete-time queueing system that is accessed by a large number of flows (a many flows regime). In such an asymptotic regime where the number of flows are large, we derive expressions for the packet delay distributions for batch arrival processes, and with bounded packet sizes. Using these results, we compare the delay asymptote (i.e., for any finite delay, and asymptotic in the number of flows) of the SRPT scheduler with that of a FIFO (first in first out) scheduler, when there is a mix of packet sizes. In particular, we apply the asymptotic delay result to a system accessed by packets which are one of two sizes: '1' or 'k', and the arrival process is i.i.d. in time. We show that the difference in rate function of the delay asymptote between SRPT and FIFO for the size 'k' packet decays as 1/k. Thus, for large packets, the delay distributions under FIFO and SRPT look similar. On the other hand, for the size '1' packet, the delay rate function under SRPT is invariant with k. However for FIFO, the delay rate function for the size '1' packet decays as 1/k. This indicates that for size '1' packets, SRPT performs increasingly better as the range in packet size increases. Thus, these results indicate that SRPT is a good policy to implement for Web-servers, where empirical evidence suggests a large variability in packet sizes.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134364849","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 : 2004-12-01DOI: 10.1109/CDC.2004.1429384
P. Voulgaris, C. Hadjicostis
In this paper we further explore our deterministic worst-case framework for perfect reconstruction of discrete data transmissions through dispersive communication channels. Specifically, we are concerned with perfect reconstruction when the data can be processed in a way that does not increase the energy per-symbol (power). We obtain necessary and sufficient conditions for perfect reconstructability with power-limited preprocessing for two distinct cases: (i) the case of a single source-destination pair and (ii) the case of a single source with multiple destinations. In both cases, our conditions for perfect reconstructability are irrespective of the receiver structure. We also discuss via an example the trade-off that arises between the rate of transmission and the minimal power that is required for perfect reconstruction.
{"title":"Optimal preprocessing strategies for perfect reconstruction of binary signals under power-constrained transmission","authors":"P. Voulgaris, C. Hadjicostis","doi":"10.1109/CDC.2004.1429384","DOIUrl":"https://doi.org/10.1109/CDC.2004.1429384","url":null,"abstract":"In this paper we further explore our deterministic worst-case framework for perfect reconstruction of discrete data transmissions through dispersive communication channels. Specifically, we are concerned with perfect reconstruction when the data can be processed in a way that does not increase the energy per-symbol (power). We obtain necessary and sufficient conditions for perfect reconstructability with power-limited preprocessing for two distinct cases: (i) the case of a single source-destination pair and (ii) the case of a single source with multiple destinations. In both cases, our conditions for perfect reconstructability are irrespective of the receiver structure. We also discuss via an example the trade-off that arises between the rate of transmission and the minimal power that is required for perfect reconstruction.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"31 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132915635","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 : 2004-12-01DOI: 10.1109/cdc.2004.1428981
R. Guha, Carl A. Gunter, S. Sarkar
Several power aware routing schemes have been developed under the assumption that nodes are willing to sacrifice their power reserves in the interest of the network as a whole. But, in several applications of practical utility, nodes are organized in groups, and as a result a node is willing to sacrifice in the interest of other nodes in its group but not necessarily for nodes outside its group. Such groups arise naturally as sets of nodes associated with a single owner or task. We consider the premise that groups will share resources with other groups only if each group experiences a reduction in power consumption. When this is the case the groups may form a coalition in which they route each other's packets. We demonstrate that sharing between groups has different properties from sharing between individuals and investigate fair mutually-beneficial sharing between groups. In particular, we propose a Pareto-efficient condition for group sharing based on max-min fairness called fair coalition routing. We propose distributed algorithms for computing the fair coalition routing. Using these algorithms we demonstrate that fair coalition routing allows different groups to mutually beneficially share their resources.
{"title":"Fair coalitions for power-aware routing in wireless networks","authors":"R. Guha, Carl A. Gunter, S. Sarkar","doi":"10.1109/cdc.2004.1428981","DOIUrl":"https://doi.org/10.1109/cdc.2004.1428981","url":null,"abstract":"Several power aware routing schemes have been developed under the assumption that nodes are willing to sacrifice their power reserves in the interest of the network as a whole. But, in several applications of practical utility, nodes are organized in groups, and as a result a node is willing to sacrifice in the interest of other nodes in its group but not necessarily for nodes outside its group. Such groups arise naturally as sets of nodes associated with a single owner or task. We consider the premise that groups will share resources with other groups only if each group experiences a reduction in power consumption. When this is the case the groups may form a coalition in which they route each other's packets. We demonstrate that sharing between groups has different properties from sharing between individuals and investigate fair mutually-beneficial sharing between groups. In particular, we propose a Pareto-efficient condition for group sharing based on max-min fairness called fair coalition routing. We propose distributed algorithms for computing the fair coalition routing. Using these algorithms we demonstrate that fair coalition routing allows different groups to mutually beneficially share their resources.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124863308","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 : 2004-12-01DOI: 10.1109/CDC.2004.1430379
O. Junge, J. Marsden, I. Mezić
This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R/sub 2/ to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large-scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.
{"title":"Uncertainty in the dynamics of conservative maps","authors":"O. Junge, J. Marsden, I. Mezić","doi":"10.1109/CDC.2004.1430379","DOIUrl":"https://doi.org/10.1109/CDC.2004.1430379","url":null,"abstract":"This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R/sub 2/ to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large-scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129576014","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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