Pub Date : 2014-12-01DOI: 10.1109/CICA.2014.7013237
S. Mirghasemi, C. Macnab, A. Chu
In a mixed liquor biological wastewater treatment process, the dissolved oxygen level is a very important factor. This paper proposes an adaptive neural network control strategy to maintain a set point in aerated bioreactors. The proposed method prevents weight drift and associated bursting, without sacrificing performance. The controller is tested on a simplified version of the benchmark simulation model number 1, with disturbances in influent. The proposed controller outperforms PI control.
{"title":"Dissolved oxygen control of activated sludge biorectors using neural-adaptive control","authors":"S. Mirghasemi, C. Macnab, A. Chu","doi":"10.1109/CICA.2014.7013237","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013237","url":null,"abstract":"In a mixed liquor biological wastewater treatment process, the dissolved oxygen level is a very important factor. This paper proposes an adaptive neural network control strategy to maintain a set point in aerated bioreactors. The proposed method prevents weight drift and associated bursting, without sacrificing performance. The controller is tested on a simplified version of the benchmark simulation model number 1, with disturbances in influent. The proposed controller outperforms PI control.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125653749","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013253
Joohee Suh, Dean Frederick Hougen
An important, long-term objective of intelligent robotics is to develop robots that can learn about and adapt to new environments. We focus on developing a learning model that can build up new knowledge through direct experience with and feedback from an environment. We designed and constructed Context-based Adaptive Robot Behavior-Learning Model (CARB-LM) which is conceptually inspired by Hebbian and anti-Hebbian learning and by neuromodulation in neural networks. CARB-LM has two types of learning processes: (1) context-based learning and (2) reward-based learning. The former uses past accumulated positive experiences as analogies to current conditions, allowing the robot to infer likely rewarding behaviors, and the latter exploits current reward information so the robot can refine its behaviors based on current experience. The reward is acquired by checking the effect of the robot's behavior in the environment. As a first test of this model, we tasked a simulated TurtleBot robot with moving smoothly around a previously unexplored environment. We simulated this environment using ROS and Gazebo and performed experiments to evaluate the model. The robot showed substantial learning and greatly outperformed both a hand-coded controller and a randomly wandering robot.
{"title":"Context-based adaptive robot behavior learning model (CARB-LM)","authors":"Joohee Suh, Dean Frederick Hougen","doi":"10.1109/CICA.2014.7013253","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013253","url":null,"abstract":"An important, long-term objective of intelligent robotics is to develop robots that can learn about and adapt to new environments. We focus on developing a learning model that can build up new knowledge through direct experience with and feedback from an environment. We designed and constructed Context-based Adaptive Robot Behavior-Learning Model (CARB-LM) which is conceptually inspired by Hebbian and anti-Hebbian learning and by neuromodulation in neural networks. CARB-LM has two types of learning processes: (1) context-based learning and (2) reward-based learning. The former uses past accumulated positive experiences as analogies to current conditions, allowing the robot to infer likely rewarding behaviors, and the latter exploits current reward information so the robot can refine its behaviors based on current experience. The reward is acquired by checking the effect of the robot's behavior in the environment. As a first test of this model, we tasked a simulated TurtleBot robot with moving smoothly around a previously unexplored environment. We simulated this environment using ROS and Gazebo and performed experiments to evaluate the model. The robot showed substantial learning and greatly outperformed both a hand-coded controller and a randomly wandering robot.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115882089","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013251
Li-Xin Wang
We apply the price dynamical model with big buyers and big sellers to the daily closing prices of the top 20 banking and real estate stocks listed in the Hong Kong Stock Exchange. The basic idea is to estimate the strength parameters of the big buyers and the big sellers in the model and make buy/sell decisions based on these parameter estimates. We propose two trading strategies: (i) Follow-the-Big-Buyer which buys when big buyer begins to appear and there is no sign of big sellers, holds the stock as long as the big buyer is still there, and sells the stock once the big buyer disappears; and (ii) Ride-the-Mood which buys as soon as the big buyer strength begins to surpass the big seller strength, and sells the stock once the opposite happens. Based on the testing over 245 two-year intervals uniformly distributed across the seven years from 03-July-2007 to 02-July-2014 which includes a variety of scenarios, the net profits would increase 67% or 120% on average if an investor switched from the benchmark Buy-and-Hold strategy to the Follow-the-Big-Buyer or Ride-the-Mood strategies during this period, respectively.
{"title":"How to detect big buyers in Hong Kong stock market and follow them up to make money","authors":"Li-Xin Wang","doi":"10.1109/CICA.2014.7013251","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013251","url":null,"abstract":"We apply the price dynamical model with big buyers and big sellers to the daily closing prices of the top 20 banking and real estate stocks listed in the Hong Kong Stock Exchange. The basic idea is to estimate the strength parameters of the big buyers and the big sellers in the model and make buy/sell decisions based on these parameter estimates. We propose two trading strategies: (i) Follow-the-Big-Buyer which buys when big buyer begins to appear and there is no sign of big sellers, holds the stock as long as the big buyer is still there, and sells the stock once the big buyer disappears; and (ii) Ride-the-Mood which buys as soon as the big buyer strength begins to surpass the big seller strength, and sells the stock once the opposite happens. Based on the testing over 245 two-year intervals uniformly distributed across the seven years from 03-July-2007 to 02-July-2014 which includes a variety of scenarios, the net profits would increase 67% or 120% on average if an investor switched from the benchmark Buy-and-Hold strategy to the Follow-the-Big-Buyer or Ride-the-Mood strategies during this period, respectively.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116955391","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013233
L. Mozelli, F. O. Souza, E. Mendes
The static output feedback control (SOFC) for Takagi-Sugeno (TS) fuzzy systems is addressed in this paper. Based on Lyapunov theory the proposed methods are formulated as Linear Matrix Inequalities (LMIs). To obtain less conservative conditions the properties of membership functions time-derivative are explored. Wiht this new methodology SOFC with higher H∞ attenuation level can be designed. Moreover, the method is extended to local stabilization using the concepts of invariant ellipsoids and regions of stability. These local conditions overcome some difficulties associated with estimating bounds for the timederivative of the membership functions. Examples are given to illustrate the merits of the proposed approaches.
{"title":"SOFC for TS fuzzy systems: Less conservative and local stabilization conditions","authors":"L. Mozelli, F. O. Souza, E. Mendes","doi":"10.1109/CICA.2014.7013233","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013233","url":null,"abstract":"The static output feedback control (SOFC) for Takagi-Sugeno (TS) fuzzy systems is addressed in this paper. Based on Lyapunov theory the proposed methods are formulated as Linear Matrix Inequalities (LMIs). To obtain less conservative conditions the properties of membership functions time-derivative are explored. Wiht this new methodology SOFC with higher H∞ attenuation level can be designed. Moreover, the method is extended to local stabilization using the concepts of invariant ellipsoids and regions of stability. These local conditions overcome some difficulties associated with estimating bounds for the timederivative of the membership functions. Examples are given to illustrate the merits of the proposed approaches.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126326027","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013228
Wei Li, Hong-gui Han, J. Qiao
This paper proposes a novel input-output clustering approach for structure identification of T-S fuzzy neural networks. This approach consists of two phases. Firstly, k-means clustering method is applied to the input data to provide the initial clusters of the input space. Secondly, check whether the sub-clustering is needed for each input cluster by considering the corresponding output variation and then apply the k-means method to further partition those input clusters needed sub-clustering. Applying the above process recursively leads to the structure identification of a T-S fuzzy neural network and then the parameter identification is completed by using the gradient learning algorithm. The experiments by applying the proposed method to several benchmark problems show better performance compared with many existing methods and then verify the effectiveness and usefulness of the proposed method.
{"title":"An input-output clustering approach for structure identification of T-S fuzzy neural networks","authors":"Wei Li, Hong-gui Han, J. Qiao","doi":"10.1109/CICA.2014.7013228","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013228","url":null,"abstract":"This paper proposes a novel input-output clustering approach for structure identification of T-S fuzzy neural networks. This approach consists of two phases. Firstly, k-means clustering method is applied to the input data to provide the initial clusters of the input space. Secondly, check whether the sub-clustering is needed for each input cluster by considering the corresponding output variation and then apply the k-means method to further partition those input clusters needed sub-clustering. Applying the above process recursively leads to the structure identification of a T-S fuzzy neural network and then the parameter identification is completed by using the gradient learning algorithm. The experiments by applying the proposed method to several benchmark problems show better performance compared with many existing methods and then verify the effectiveness and usefulness of the proposed method.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120950195","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013246
Samronne N. do Carmo, M. O. D. Almeida, F. A. D. Castro, Rafael F. R. Campos, J. M. Araújo, C. Dórea
Control techniques for systems with constraints on control and state are somewhat attractive, mainly in cases where these constraints represent safety or critical points of operation. An important approach for control of constrained linear systems is based on the concept of set invariance, whose main advantages are the inclusion of constraints in the whole design, the non-conservative nature of the controllers and the ability to cope with noise measurement and disturbance entering in the system. Some disadvantage are a possibly high complexity of the control law for higher order systems or the absence of an analytical, off-line control law in some cases, as, for instance, in the output feedback case. The online computation of the control input at each step is ever possible, but the computational cost involved may turn the solution impracticable in the case of systems with fast dynamics. Neural networks, on the other hand, is an interesting alternative for function approximation, and works well in capturing the characteristics of the input-output manifold of the online control law, starting from a training set generated by simulation of the control system. In this paper, neural networks are applied to substitute in an efficient way the online control computation. A real case based example is used to verify the effectiveness of the proposed neural controller.
{"title":"Neural network fitting for input-output manifolds of online control laws in constrained linear systems","authors":"Samronne N. do Carmo, M. O. D. Almeida, F. A. D. Castro, Rafael F. R. Campos, J. M. Araújo, C. Dórea","doi":"10.1109/CICA.2014.7013246","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013246","url":null,"abstract":"Control techniques for systems with constraints on control and state are somewhat attractive, mainly in cases where these constraints represent safety or critical points of operation. An important approach for control of constrained linear systems is based on the concept of set invariance, whose main advantages are the inclusion of constraints in the whole design, the non-conservative nature of the controllers and the ability to cope with noise measurement and disturbance entering in the system. Some disadvantage are a possibly high complexity of the control law for higher order systems or the absence of an analytical, off-line control law in some cases, as, for instance, in the output feedback case. The online computation of the control input at each step is ever possible, but the computational cost involved may turn the solution impracticable in the case of systems with fast dynamics. Neural networks, on the other hand, is an interesting alternative for function approximation, and works well in capturing the characteristics of the input-output manifold of the online control law, starting from a training set generated by simulation of the control system. In this paper, neural networks are applied to substitute in an efficient way the online control computation. A real case based example is used to verify the effectiveness of the proposed neural controller.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123118115","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013248
D. Dubinin, V. Geringer, A. Kochegurov, K. Reif
The essay outlines one particular possibility of efficient evaluating the Performance of edge detector algorithms. Three generally known and published algorithms (Canny, Marr, Shen) were analysed by way of example. The analysis is based on two-dimensional signals created by means of two-dimensional Semi-Markov Model and subsequently provided with an additive Gaussian noise component. Five quality metrics allow an objective comparison of the algorithms.
{"title":"An efficient method to evaluate the performance of edge detection techniques by a two-dimensional Semi-Markov model","authors":"D. Dubinin, V. Geringer, A. Kochegurov, K. Reif","doi":"10.1109/CICA.2014.7013248","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013248","url":null,"abstract":"The essay outlines one particular possibility of efficient evaluating the Performance of edge detector algorithms. Three generally known and published algorithms (Canny, Marr, Shen) were analysed by way of example. The analysis is based on two-dimensional signals created by means of two-dimensional Semi-Markov Model and subsequently provided with an additive Gaussian noise component. Five quality metrics allow an objective comparison of the algorithms.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122893656","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013238
A. K. Deb, D. Guha
The purpose of this paper is to design a dynamic neural network that can effectively estimate all the states of single input non linear plants. Lyapunov's stability theory along with solution of full form Ricatti equation is used to guarantee that the tracking errors are uniformly bounded. No a priori knowledge on the bounds of weights and errors are required. The nonlinear plant and the dynamic neural network models have been simulated by the same input to illustrate the validity of theoretical results.
{"title":"Estimation of states of a nonlinear plant using dynamic neural network","authors":"A. K. Deb, D. Guha","doi":"10.1109/CICA.2014.7013238","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013238","url":null,"abstract":"The purpose of this paper is to design a dynamic neural network that can effectively estimate all the states of single input non linear plants. Lyapunov's stability theory along with solution of full form Ricatti equation is used to guarantee that the tracking errors are uniformly bounded. No a priori knowledge on the bounds of weights and errors are required. The nonlinear plant and the dynamic neural network models have been simulated by the same input to illustrate the validity of theoretical results.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127858392","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013239
H. V. Ayala, L. F. D. Cruz, R. Z. Freire, L. Coelho
This paper presents a procedure for input selection and parameter estimation for system identification based on Radial Basis Functions Neural Networks (RBFNNs) models and Free Search Differential Evolution (FSDE). We adopt a cascaded evolutionary algorithm approach and problem decomposition to define the model orders and the related model parameters based on higher orders correlation functions. Thus, we adopt two distinct populations: the first to select the lags on the inputs and outputs of the system and the second to define the parameters for the RBFNN. We show the results when the proposed methodology is applied to model a coupled drives system with real acquired data. We use to this end the canonical binary genetic algorithm (selection of lags) and the recently proposed FSDE (definition of the model parameters), which is very convenient for the present problem for having few control parameters. The results show the validity of the approach when compared to a classical input selection algorithm.
{"title":"Cascaded free search differential evolution applied to nonlinear system identification based on correlation functions and neural networks","authors":"H. V. Ayala, L. F. D. Cruz, R. Z. Freire, L. Coelho","doi":"10.1109/CICA.2014.7013239","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013239","url":null,"abstract":"This paper presents a procedure for input selection and parameter estimation for system identification based on Radial Basis Functions Neural Networks (RBFNNs) models and Free Search Differential Evolution (FSDE). We adopt a cascaded evolutionary algorithm approach and problem decomposition to define the model orders and the related model parameters based on higher orders correlation functions. Thus, we adopt two distinct populations: the first to select the lags on the inputs and outputs of the system and the second to define the parameters for the RBFNN. We show the results when the proposed methodology is applied to model a coupled drives system with real acquired data. We use to this end the canonical binary genetic algorithm (selection of lags) and the recently proposed FSDE (definition of the model parameters), which is very convenient for the present problem for having few control parameters. The results show the validity of the approach when compared to a classical input selection algorithm.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130405856","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 : 2014-12-01DOI: 10.1109/CICA.2014.7013226
G. Pillai, Pushpak Jagtap, M. Nisha
This paper proposes a new neuro-fuzzy learning machine called extreme learning adaptive neuro-fuzzy inference system (ELANFIS) which can be applied to control of nonlinear systems. The new learning machine combines the learning capabilities of neural networks and the explicit knowledge of the fuzzy systems as in the case of conventional adaptive neuro-fuzzy inference system (ANFIS). The parameters of the fuzzy layer of ELANFIS are not tuned to achieve faster learning speed without sacrificing the generalization capability. The proposed learning machine is used for inverse control and model predictive control of nonlinear systems. Simulation results show improved performance with very less computation time which is much essential for real time control.
{"title":"Extreme learning ANFIS for control applications","authors":"G. Pillai, Pushpak Jagtap, M. Nisha","doi":"10.1109/CICA.2014.7013226","DOIUrl":"https://doi.org/10.1109/CICA.2014.7013226","url":null,"abstract":"This paper proposes a new neuro-fuzzy learning machine called extreme learning adaptive neuro-fuzzy inference system (ELANFIS) which can be applied to control of nonlinear systems. The new learning machine combines the learning capabilities of neural networks and the explicit knowledge of the fuzzy systems as in the case of conventional adaptive neuro-fuzzy inference system (ANFIS). The parameters of the fuzzy layer of ELANFIS are not tuned to achieve faster learning speed without sacrificing the generalization capability. The proposed learning machine is used for inverse control and model predictive control of nonlinear systems. Simulation results show improved performance with very less computation time which is much essential for real time control.","PeriodicalId":340740,"journal":{"name":"2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128315946","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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