wanyu/IteraTeR_v2 huggingface dataset:
Original:  We show that assuming that G has bounded in-degree, bounded c-components  , and that the observational distribution is identifiable and satisfies certain strong positivity condition : 1. Evaluation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using }  m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Revised:  We show that assuming that G has bounded in-degree, bounded c-components , and that the observational distribution is identifiable and satisfies certain strong positivity condition Evaluation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using } m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Edit intent: coherence
Original:  We show that assuming that G has bounded in-degree, bounded c-components  , and that the observational distribution is identifiable and satisfies certain strong positivity condition : 1. Evaluation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using }  m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Revised:  We show that assuming that G has bounded in-degree, bounded c-components , and that the observational distribution is identifiable and satisfies certain strong positivity condition : 1. %DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using } m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Edit intent: fluency
Original:  We show that assuming that G has bounded in-degree, bounded c-components  , and that the observational distribution is identifiable and satisfies certain strong positivity condition : 1. Evaluation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using }  m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Revised:  We show that assuming that G has bounded in-degree, bounded c-components , and that the observational distribution is identifiable and satisfies certain strong positivity condition : 1. Evaluation%DIFDELCMD < ] %%% , we give an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using } m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Edit intent: clarity
Original:  We show that assuming that G has bounded in-degree, bounded c-components  , and that the observational distribution is identifiable and satisfies certain strong positivity condition : 1. Evaluation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using }  m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Revised:  We show that assuming that G has bounded in-degree, bounded c-components , and that the observational distribution is identifiable and satisfies certain strong positivity condition : 1. Evaluation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P' that satisfies d_{tv(P_x, P') \leq \epsilon using } takes m=O(n\epsilon^{-2}) samples from P and O(mn) time .
Edit intent: clarity
Original:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a  distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Revised:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. %DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Edit intent: fluency
Original:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a  distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Revised:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% , and outputs with high probability a distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Edit intent: clarity
Original:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a  distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Revised:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a description of a distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Edit intent: clarity
Original:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a  distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Revised:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a distribution P such that d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Edit intent: clarity
Original:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a  distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Revised:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon %DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Edit intent: clarity
Original:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a  distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Revised:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 Evaluation] \hat{P} ( mn) time .
Edit intent: fluency
Original:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a  distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] \hat{P} ( mn) time .
Revised:  The evaluator can return in O(n) time the probability P'(v) for any assignment v to V. 2. Generation%DIFDELCMD < ] %%% There is an algorithm that outputs with probability 2/3 a sampler for a distribution P that satisfies d _{ tv }(P_x, \hat{P}) \leq \epsilon using m=%DIFDELCMD < \tilde{O}%%% (n\epsilon^{-2 ] the description can return in O(n) time the probability\hat{P} ( mn) time .
Edit intent: clarity
Original:  The sampler returns \vec{v}\vec{v} \vec{V}  ]  an iid sample from \hat{P} with probability 1-\delta in O(n \epsilon^{-1 \log\delta^{-1}} ) time.
Revised:  The sampler returns \vec{v}\vec{v} to\vec{V} ] an iid sample from \hat{P} with probability 1-\delta in O(n \epsilon^{-1 \log\delta^{-1}} ) time.
Edit intent: clarity
Original:  The sampler returns \vec{v}\vec{v} \vec{V}  ]  an iid sample from \hat{P} with probability 1-\delta in O(n \epsilon^{-1 \log\delta^{-1}} ) time.
Revised:  The sampler returns \vec{v}\vec{v} \vec{V} Generation] an iid sample from \hat{P} with probability 1-\delta in O(n \epsilon^{-1 \log\delta^{-1}} ) time.
Edit intent: fluency
Original:  The sampler returns \vec{v}\vec{v} \vec{V}  ]  an iid sample from \hat{P} with probability 1-\delta in O(n \epsilon^{-1 \log\delta^{-1}} ) time.
Revised:  The sampler returns \vec{v}\vec{v} \vec{V} ] an iid sample from \hat{P} in O(n \epsilon^{-1 \log\delta^{-1}} ) time.
Edit intent: clarity
Original:  We also show lower bounds for the sample complexity showing that our sample complexity has  optimal dependence on the parameters n and \epsilon  as well as  the strong positivity parameter.
Revised:  We also show lower bounds for the sample complexity showing that our sample complexity has an optimal dependence on the parameters n and \epsilon as well as the strong positivity parameter.
Edit intent: fluency
Original:  We also show lower bounds for the sample complexity showing that our sample complexity has  optimal dependence on the parameters n and \epsilon  as well as  the strong positivity parameter.
Revised:  We also show lower bounds for the sample complexity showing that our sample complexity has optimal dependence on the parameters n and \epsilon , as well as the strong positivity parameter.
Edit intent: fluency
Original: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and some trigonometric polynomial \varphi_j.
Revised: We study approximation properties of general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and some trigonometric polynomial \varphi_j.
Edit intent: fluency
Original: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and some trigonometric polynomial \varphi_j.
Revised: We study approximation properties of the general multivariate periodic quasi-interpolation %DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and some trigonometric polynomial \varphi_j.
Edit intent: clarity
Original: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and some trigonometric polynomial \varphi_j.
Revised: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% operators, which are generated by distributions / function \varphi_j and some trigonometric polynomial \varphi_j.
Edit intent: clarity
Original: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and some trigonometric polynomial \varphi_j.
Revised: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / functions \varphi_j and some trigonometric polynomial \varphi_j.
Edit intent: fluency
Original: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and some trigonometric polynomial \varphi_j.
Revised: We study approximation properties of the general multivariate periodic quasi-interpolation operator Q_j(f, \varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j), which is generated by the distribution / function \varphi_j and trigonometric polynomials \varphi_j.
Edit intent: clarity
Original:  Under different compatibility conditions on \widetilde\varphi_j and \varphi_j, we obtain upper and lower  estimates for the L_p-error of approximation by operators Q_j(f,\varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j) in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, K-functionals, and other terms.
Revised:  Under different compatibility conditions on \widetilde\varphi_j and \varphi_j, we obtain upper and lower bound estimates for the L_p-error of approximation by operators Q_j(f,\varphi_j,%DIFDELCMD < \widetilde%%% \varphi_j) in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, K-functionals, and other terms.
Edit intent: clarity
Original:  We highlight in particular the reliance of the benefits on the search space itself  .
Revised:  In particular we highlight the impact of the search space itself .
Edit intent: clarity
Original:  Because our method uses a L0 constraint instead of the L1 penalty, it does not introduce any bias in the training parameters or filter channels.
Revised:  Because our method uses a L0 constraint instead of the L_1 penalty, it does not introduce any bias in the training parameters or filter channels.
Edit intent: fluency
Original:  Finally, experimental validation on  synthetic and real datasets both show that the proposed method obtains better or competitive performance compared to other states of art network pruning methods.
Revised:  Finally, experimental validation on extensive synthetic and real datasets both show that the proposed method obtains better or competitive performance compared to other states of art network pruning methods.
Edit intent: clarity
Original:  Finally, experimental validation on  synthetic and real datasets both show that the proposed method obtains better or competitive performance compared to other states of art network pruning methods.
Revised:  Finally, experimental validation on synthetic and real vision datasets show that the proposed method obtains better or competitive performance compared to other states of art network pruning methods.
Edit intent: clarity
Original:  Our  method is based on a  genetic algorithm with customization addressing problem characteristics.
Revised:  Our proposed method is based on a genetic algorithm with customization addressing problem characteristics.
Edit intent: clarity
Original:  We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and  a custom repair operation to avoid the evaluation of infeasible solutions.
Revised:  We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and use a custom repair operation to avoid the evaluation of infeasible solutions.
Edit intent: coherence
Original:  We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and  a custom repair operation to avoid the evaluation of infeasible solutions.
Revised:  We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and a custom repair operator to avoid the evaluation of infeasible solutions.
Edit intent: fluency
Original:  Moreover, the independent variables of the TSP and KP components are unified to a real variable representation by using a biased random-key approach.
Edit intent: coherence
Original:  The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance of each solution .
Revised:  The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance .
Edit intent: clarity
Original:  Furthermore, we provide a comprehensive study which shows the influence of hyperparameters on the performance of our method and investigate the performance of each hyperparameter combination over time.
Revised:  Furthermore, we provide a comprehensive study showing the influence of hyperparameters on the performance of our method and investigate the performance of each hyperparameter combination over time.
Edit intent: coherence
Original:  Furthermore, we provide a comprehensive study which shows the influence of hyperparameters on the performance of our method and investigate the performance of each hyperparameter combination over time.
Revised:  Furthermore, we provide a comprehensive study which shows the influence of each parameter on the performance of our method and investigate the performance of each hyperparameter combination over time.
Edit intent: fluency
Original:  In addition to our experiments , we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019  conferences where our method has won first and second place , respectively, thus proving its ability to find high-quality solutions consistently.
Revised:  In addition to our experiments , we discuss the results of the BI-TTP competitions at EMO-2019 conferences where our method has won first and second place , respectively, thus proving its ability to find high-quality solutions consistently.
Edit intent: clarity
Original:  In addition to our experiments , we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019  conferences where our method has won first and second place , respectively, thus proving its ability to find high-quality solutions consistently.
Revised:  In addition to our experiments , we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second places , respectively, thus proving its ability to find high-quality solutions consistently.
Edit intent: fluency
Original:  Finally, we discuss the results of the BI-TTP competitions at EMO-2019 andGECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.
Revised:  Finally, we discuss the results of the BI-TTP competitions at andGECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.
Edit intent: clarity
Original:  Finally, we discuss the results of the BI-TTP competitions at EMO-2019 andGECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.
Revised:  Finally, we discuss the results of the BI-TTP competitions at EMO-2019 GECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.
Edit intent: fluency
Original:  Finally, we discuss the results of the BI-TTP competitions at EMO-2019 andGECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.
Revised:  Finally, we discuss the results of the BI-TTP competitions at EMO-2019 andEMO-2019 and GECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.
Edit intent: fluency
Original: Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex  discrete systems and  analyzing their experimental recordings.
Revised: Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex , discrete systems and analyzing their experimental recordings.
Edit intent: fluency
Original: Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex  discrete systems and  analyzing their experimental recordings.
Revised: Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex discrete systems and for analyzing their experimental recordings.
Edit intent: fluency
Original:  Many variants of the classical naive and TAP (i.e., second-order) mean field approximations have been proposed, each of which makes unique assumptions about time evolution of the system's correlation structure.
Revised:  Many variants of the classical naive and TAP (i.e., second-order) mean field approximations have been proposed, each of which makes unique assumptions about the temporal evolution of the system's correlation structure.
Edit intent: fluency
Original:  This disparity of methods makes it difficult to systematically advance the mean field approach over previous contributions.
Revised:  This disparity of methods makes it difficult to systematically advance mean field approaches beyond previous contributions.
Edit intent: clarity
Original:  This approach not only unifies previous methods but  allows us to define novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Revised:  This view not only unifies previous methods but allows us to define novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Edit intent: clarity
Original:  This approach not only unifies previous methods but  allows us to define novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Revised:  This approach not only unifies previous methods but also allows us to define novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Edit intent: fluency
Original:  This approach not only unifies previous methods but  allows us to define novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Revised:  This approach not only unifies previous methods but allows us to propose novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Edit intent: clarity
Original:  Many variants of the classical naive and TAP (i.e., second-order) mean field approximations have been proposed , each of which makes unique assumptions about the temporal evolution of the system's correlation structure .
Revised:  Many variants of the classical naive and TAP (i.e., second-order) mean field approximations have been proposed , each of which makes unique assumptions about the system's correlation structure .
Edit intent: clarity
Original:  Many variants of the classical naive and TAP (i.e., second-order) mean field approximations have been proposed , each of which makes unique assumptions about the temporal evolution of the system's correlation structure .
Revised:  Many variants of the classical naive and TAP (i.e., second-order) mean field approximations have been proposed , each of which makes unique assumptions about the temporal evolution of the system's temporal evolution .
Edit intent: clarity