Pub Date : 1900-01-01DOI: 10.1137/1.9781611974072.54
E. Grigorieva, E. Khailov
A SEIR type model for the spread of Ebola epidemic in a population of constant size is considered. In order to control the spread of infection and prevent such epidemics, we add to the model four bounded controls. Three of them represent the efforts that reduce the contact between the susceptible and infectious individuals, between the susceptible and hospitalized, and, lastly, between susceptible and buried individuals. The fourth control represents the burial efforts. We state the optimal control problem of minimizing the number of the infectious individuals at the given terminal time. The corresponding optimal solutions are obtained with the use of the Pontryagin maximum principle. Such values of the model parameters and control constraints are used, for which the optimal controls are bang-bang. Their types are found and investigated analytically. An approach for estimating the number of zeros of the corresponding switching functions, different from the one that was used in our previous papers, is applied. The resulting estimates enable us to reduce the optimal control problem to a considerably simpler problem of the finite-dimensional constrained minimization.
{"title":"Analytical Study of Optimal Control Intervention Strategies for Ebola Epidemic Model","authors":"E. Grigorieva, E. Khailov","doi":"10.1137/1.9781611974072.54","DOIUrl":"https://doi.org/10.1137/1.9781611974072.54","url":null,"abstract":"A SEIR type model for the spread of Ebola epidemic in a population of constant size is considered. In order to control the spread of infection and prevent such epidemics, we add to the model four bounded controls. Three of them represent the efforts that reduce the contact between the susceptible and infectious individuals, between the susceptible and hospitalized, and, lastly, between susceptible and buried individuals. The fourth control represents the burial efforts. We state the optimal control problem of minimizing the number of the infectious individuals at the given terminal time. The corresponding optimal solutions are obtained with the use of the Pontryagin maximum principle. Such values of the model parameters and control constraints are used, for which the optimal controls are bang-bang. Their types are found and investigated analytically. An approach for estimating the number of zeros of the corresponding switching functions, different from the one that was used in our previous papers, is applied. The resulting estimates enable us to reduce the optimal control problem to a considerably simpler problem of the finite-dimensional constrained minimization.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115154524","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 : 1900-01-01DOI: 10.1137/1.9781611974072.50
E. Zattoni
Disturbance decoupling — i.e., the problem of making the output of a dynamical system insensitive to undesired inputs — is a classical problem of control theory and a main concern in control applications. Hence, it has been solved for many classes of dynamical systems, considering both structural and stability requirements. As to decoupling in linear switching systems, several definitions of stability apply. The aim of this contribution is investigating different decoupling problems with progressively more stringent stability requirements: from structural decoupling to decoupling with local input-to-state stability. A convex procedure for the computation of the switching compensator is presented, based on the fact that quadratic stability under arbitrary switching guarantees global uniform asymptotic stability and the latter implies local input-to-state stability. Measurable and inaccessible disturbances are considered in a unified setting. The work is focused on discrete-time systems, although all the results hold for continuous-time systems as well, with the obvious modifications.
{"title":"Stability issues in disturbance decoupling for switching linear systems","authors":"E. Zattoni","doi":"10.1137/1.9781611974072.50","DOIUrl":"https://doi.org/10.1137/1.9781611974072.50","url":null,"abstract":"Disturbance decoupling — i.e., the problem of making the output of a dynamical system insensitive to undesired inputs — is a classical problem of control theory and a main concern in control applications. Hence, it has been solved for many classes of dynamical systems, considering both structural and stability requirements. As to decoupling in linear switching systems, several definitions of stability apply. The aim of this contribution is investigating different decoupling problems with progressively more stringent stability requirements: from structural decoupling to decoupling with local input-to-state stability. A convex procedure for the computation of the switching compensator is presented, based on the fact that quadratic stability under arbitrary switching guarantees global uniform asymptotic stability and the latter implies local input-to-state stability. Measurable and inaccessible disturbances are considered in a unified setting. The work is focused on discrete-time systems, although all the results hold for continuous-time systems as well, with the obvious modifications.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125051407","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 : 1900-01-01DOI: 10.1137/1.9781611973273.13
Anshu Narang-Siddarth, J. Valasek
It is well understood that an open-loop Lyapunov stable nonaffine-in-control nonlinear system can be asymptotically stabilized through feedback. But stabilizing an open-loop unstable nonaffine system remains an open research question. This paper derives the necessary conditions required to render a general open-loop unstable nonlinear system passive through static feedback. It is shown that this is possible only if the system under consideration has relative degree one and is weakly minimum phase through an appropriate output definition. Unlike feedback passivation for affine-incontrol nonlinear systems this result is not sufficient. The developments and the essential ideas of the paper are verified for a continuously stirred tank reactor.
{"title":"Necessary Conditions for Feedback Passivation of Nonaffine-in-Control Systems","authors":"Anshu Narang-Siddarth, J. Valasek","doi":"10.1137/1.9781611973273.13","DOIUrl":"https://doi.org/10.1137/1.9781611973273.13","url":null,"abstract":"It is well understood that an open-loop Lyapunov stable nonaffine-in-control nonlinear system can be asymptotically stabilized through feedback. But stabilizing an open-loop unstable nonaffine system remains an open research question. This paper derives the necessary conditions required to render a general open-loop unstable nonlinear system passive through static feedback. It is shown that this is possible only if the system under consideration has relative degree one and is weakly minimum phase through an appropriate output definition. Unlike feedback passivation for affine-incontrol nonlinear systems this result is not sufficient. The developments and the essential ideas of the paper are verified for a continuously stirred tank reactor.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129750562","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 : 1900-01-01DOI: 10.1137/1.9781611974072.18
V. Mai, Dipankar Maity, B. Ramasubramanian, M. Rotkowitz
This paper considers optimization problems which are convex, except for a constraint on the rank of a matrix variable. Minimizing or penalizing the nuclear norm of a matrix has proven to be an effective method for generally keeping its rank small, and a vast amount of recent work has focused on this technique; however, many problems require finding a matrix whose rank is constrained to be a particular value. We present a new method for these problems, introducing a convex constraint that forces the rank to be at least the desired value, while using the nuclear norm penalty to keep the rank from rising above that value. This results in a convex optimization problem that will attempt to satisfy the constraints, to minimize the objective, and will usually produce the desired rank. We further study the choice of parameter used with the nuclear norm penalty, both with and without the constraint. It is shown that another convex optimization problem can be formulated from the dual problem which will find the best parameter in some cases, and will still produce a useful result in other cases. We find that considering parameters which are negative, that is, considering rewarding the nuclear norm, as well as penalizing it, can result in better performance with the desired rank. The methods developed are demonstrated on rank-constrained semidefinite programming problems (SDPs). The first three authors contributed equally to this work. Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:vsmai@umd.edu Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:dmaity@umd.edu Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:rbhaskar@umd.edu Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:mcrotk@umd.edu
{"title":"Convex Methods for Rank-Constrained Optimization Problems","authors":"V. Mai, Dipankar Maity, B. Ramasubramanian, M. Rotkowitz","doi":"10.1137/1.9781611974072.18","DOIUrl":"https://doi.org/10.1137/1.9781611974072.18","url":null,"abstract":"This paper considers optimization problems which are convex, except for a constraint on the rank of a matrix variable. Minimizing or penalizing the nuclear norm of a matrix has proven to be an effective method for generally keeping its rank small, and a vast amount of recent work has focused on this technique; however, many problems require finding a matrix whose rank is constrained to be a particular value. We present a new method for these problems, introducing a convex constraint that forces the rank to be at least the desired value, while using the nuclear norm penalty to keep the rank from rising above that value. This results in a convex optimization problem that will attempt to satisfy the constraints, to minimize the objective, and will usually produce the desired rank. We further study the choice of parameter used with the nuclear norm penalty, both with and without the constraint. It is shown that another convex optimization problem can be formulated from the dual problem which will find the best parameter in some cases, and will still produce a useful result in other cases. We find that considering parameters which are negative, that is, considering rewarding the nuclear norm, as well as penalizing it, can result in better performance with the desired rank. The methods developed are demonstrated on rank-constrained semidefinite programming problems (SDPs). The first three authors contributed equally to this work. Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:vsmai@umd.edu Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:dmaity@umd.edu Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:rbhaskar@umd.edu Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20740. email:mcrotk@umd.edu","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126023825","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 : 1900-01-01DOI: 10.1137/1.9781611973273.6
Hui Xie, R. T. Fomena, Alan Francis Lynch
The problem of Structure and Motion Estimation in machine vision can be addressed by designing observers for dynamic systems. We propose an observer for feature point depth and camera linear velocity. The camera’s angular velocity is assumed known. As well, we require two feature points with known displacement. Relative to previous work, we do not require linear acceleration measurements. The local exponential stability of the observer is proven using a converse Lyapunov theorem. We assume the camera motion satisfies a persistency of excitation condition and the linear acceleration is bounded and has finite energy.
{"title":"Reduced-order Observer Design for Structure and Motion Estimation","authors":"Hui Xie, R. T. Fomena, Alan Francis Lynch","doi":"10.1137/1.9781611973273.6","DOIUrl":"https://doi.org/10.1137/1.9781611973273.6","url":null,"abstract":"The problem of Structure and Motion Estimation in machine vision can be addressed by designing observers for dynamic systems. We propose an observer for feature point depth and camera linear velocity. The camera’s angular velocity is assumed known. As well, we require two feature points with known displacement. Relative to previous work, we do not require linear acceleration measurements. The local exponential stability of the observer is proven using a converse Lyapunov theorem. We assume the camera motion satisfies a persistency of excitation condition and the linear acceleration is bounded and has finite energy.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130459573","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 : 1900-01-01DOI: 10.1137/1.9781611973273.2
L. Ning, T. Georgiou
We consider the problem of approximating a (nonnegative definite) covariance matrix by the sum of two structured covariances –one which is diagonal and one which has low-rank. Such an additive decomposition follows the dictum of factor analysis where linear relations are sought between variables corrupted by independent measurement noise. We use as distance the Wasserstein metric between their respective distributions (assumed Gaussian) which induces a metric between nonnegative definite matrices, in general. The rank-constraint renders the optimization non-convex. We propose alternating between optimization with respect to each of the two summands. Properties of these optimization problems and the performance of the approach are being analyzed.
{"title":"The Wasserstein metric in Factor Analysis","authors":"L. Ning, T. Georgiou","doi":"10.1137/1.9781611973273.2","DOIUrl":"https://doi.org/10.1137/1.9781611973273.2","url":null,"abstract":"We consider the problem of approximating a (nonnegative definite) covariance matrix by the sum of two structured covariances –one which is diagonal and one which has low-rank. Such an additive decomposition follows the dictum of factor analysis where linear relations are sought between variables corrupted by independent measurement noise. We use as distance the Wasserstein metric between their respective distributions (assumed Gaussian) which induces a metric between nonnegative definite matrices, in general. The rank-constraint renders the optimization non-convex. We propose alternating between optimization with respect to each of the two summands. Properties of these optimization problems and the performance of the approach are being analyzed.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"40 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132537063","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 : 1900-01-01DOI: 10.1137/1.9781611974072.41
Marco Torres-Reyna, D. Martinez-Vazquez, E. Licéaga-Castro
Abstract What shape should an aircraft have to give certain desirable properties? Nonlinear Inverse Dynamics (NID) may be one of the necessary tools needed to find an answer to this question. In flight dynamics NID is usually applied to define flight trajectories calculations and flight control systems design. The underlying concept behind inverse dynamics applications is the definition of a desired manoeuvre, usually defined by a dynamical model or a pre-established trajectory. By forcing a aircraft whose dynamics are described by a set of nonlinear differential equations to behave like a prescribed model -non necessarily linearflight control systems are designed. This technique is referred to as nonlinear model matching. As follows NID is used to assist the preliminary design of aircraft. From a set of flight characteristics defined by customer specifications the parameters which define the shape and size, such as: wing span, weight, wing aerofoil selection, engine characteristics and wing polar are estimated.
{"title":"Aircraft Preliminary Design Using Nonlinear Inverse Dynamics","authors":"Marco Torres-Reyna, D. Martinez-Vazquez, E. Licéaga-Castro","doi":"10.1137/1.9781611974072.41","DOIUrl":"https://doi.org/10.1137/1.9781611974072.41","url":null,"abstract":"Abstract What shape should an aircraft have to give certain desirable properties? Nonlinear Inverse Dynamics (NID) may be one of the necessary tools needed to find an answer to this question. In flight dynamics NID is usually applied to define flight trajectories calculations and flight control systems design. The underlying concept behind inverse dynamics applications is the definition of a desired manoeuvre, usually defined by a dynamical model or a pre-established trajectory. By forcing a aircraft whose dynamics are described by a set of nonlinear differential equations to behave like a prescribed model -non necessarily linearflight control systems are designed. This technique is referred to as nonlinear model matching. As follows NID is used to assist the preliminary design of aircraft. From a set of flight characteristics defined by customer specifications the parameters which define the shape and size, such as: wing span, weight, wing aerofoil selection, engine characteristics and wing polar are estimated.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125033358","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 : 1900-01-01DOI: 10.1137/1.9781611974072.42
Dimitri Scheftelowitsch
We consider Markov decision processes with uncertain transition probabilities and two optimization problems in this context: the finite horizon problem which asks to find an optimal policy for a finite number of transitions and the percentile optimization problem for a wide class of uncertain Markov decision processes which asks to find a policy with the optimal probability to reach a given reward objective. To the best of our knowledge, unlike other optimality criteria, the finite horizon problem has not been considered for the case of bounded-parameter Markov decision processes, and the percentile optimization problem has only been considered for very special cases. Unlike most problems in the Markov decision process research context, dynamic programming is not applicable, as the usual subdivision in independent subproblems in each state is not anymore possible. Justified by this observation, we establish NP-hardness results for these problems by showing appropriate reductions.
{"title":"The Complexity of Uncertainty in Markov Decision Processes","authors":"Dimitri Scheftelowitsch","doi":"10.1137/1.9781611974072.42","DOIUrl":"https://doi.org/10.1137/1.9781611974072.42","url":null,"abstract":"We consider Markov decision processes with uncertain transition probabilities and two optimization problems in this context: the finite horizon problem which asks to find an optimal policy for a finite number of transitions and the percentile optimization problem for a wide class of uncertain Markov decision processes which asks to find a policy with the optimal probability to reach a given reward objective. To the best of our knowledge, unlike other optimality criteria, the finite horizon problem has not been considered for the case of bounded-parameter Markov decision processes, and the percentile optimization problem has only been considered for very special cases. Unlike most problems in the Markov decision process research context, dynamic programming is not applicable, as the usual subdivision in independent subproblems in each state is not anymore possible. Justified by this observation, we establish NP-hardness results for these problems by showing appropriate reductions.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124520113","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 : 1900-01-01DOI: 10.1137/1.9781611974072.53
W. Halter, Nico Kress, Konrad Otte, Sabrina Reich, B. Hauer, F. Allgöwer
Bio-chemical reaction networks are more and more adapted to be used for the production of fine chemicals. Due to the appearance of intermediate species which influence the single reaction steps, a single compartment approach for the implementation of such a reaction may not be optimal. Multi-compartment approaches however might have the potential to increase the yield of desired product if the coupling of the compartments is chosen appropriately. A model based approach is presented to identify and analyze such coupling schemes for a specific enzyme cascade as an example system.
{"title":"Yield-Analysis of Different Coupling Schemes for Interconnected Bio-Reactors","authors":"W. Halter, Nico Kress, Konrad Otte, Sabrina Reich, B. Hauer, F. Allgöwer","doi":"10.1137/1.9781611974072.53","DOIUrl":"https://doi.org/10.1137/1.9781611974072.53","url":null,"abstract":"Bio-chemical reaction networks are more and more adapted to be used for the production of fine chemicals. Due to the appearance of intermediate species which influence the single reaction steps, a single compartment approach for the implementation of such a reaction may not be optimal. Multi-compartment approaches however might have the potential to increase the yield of desired product if the coupling of the compartments is chosen appropriately. A model based approach is presented to identify and analyze such coupling schemes for a specific enzyme cascade as an example system.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133215442","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 : 1900-01-01DOI: 10.1137/1.9781611973273.25
Jiacheng Wu, K. Cassel
A theoretical model of a potential treatment for intimal hyperplasia due to hemodialysis is proposed. This model consists of two parts. The first part is modeling the development of intimal hyperplasia as a diffusion process of muscle cells from the media to the lumen, for which the governing equation is a partial differential equation. The second part is designing an observer-based feedback controller to stabilize the equilibrium point of the system, corresponding to no intimal hyperplasia. Simulation results show that the intimal hyperplasia can be reduced by 90% in nearly 30 days of treatment.
{"title":"Observer-Based Feedback Control of a Mathematical Model of Intimal Hyperplasia","authors":"Jiacheng Wu, K. Cassel","doi":"10.1137/1.9781611973273.25","DOIUrl":"https://doi.org/10.1137/1.9781611973273.25","url":null,"abstract":"A theoretical model of a potential treatment for intimal hyperplasia due to hemodialysis is proposed. This model consists of two parts. The first part is modeling the development of intimal hyperplasia as a diffusion process of muscle cells from the media to the lumen, for which the governing equation is a partial differential equation. The second part is designing an observer-based feedback controller to stabilize the equilibrium point of the system, corresponding to no intimal hyperplasia. Simulation results show that the intimal hyperplasia can be reduced by 90% in nearly 30 days of treatment.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130569702","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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