wanyu/IteraTeR_v2 huggingface dataset:
Original:  For the large scale, we introduce the stigmergy mechanism as an indirect communication bridge among the independent learning agents  and carefully design a mathematical representation to indicate the impact of digital pheromone.
Revised:  For the large scale, we introduce the stigmergy mechanism as an indirect communication bridge among the independent learning agents and carefully design a mathematical method to indicate the impact of digital pheromone.
Edit intent: clarity
Original:  Besides, we also present a federal training method to effectively optimize the neural network within each agent in a decentralized manner.
Revised:  In addition, we present a federal training method to effectively optimize the neural network within each agent in a decentralized manner.
Edit intent: coherence
Original:  Besides, we also present a federal training method to effectively optimize the neural network within each agent in a decentralized manner.
Revised:  Besides, we also present a federal training method to effectively optimize the neural network of each agent in a decentralized manner.
Edit intent: clarity
Original:  Finally, we establish a simulation scenario where a number of mobile agents in a certain area move automatically to form a specified target shape , and demonstrate the superiorities of our proposed methods through extensive simulations .
Revised:  Finally, we establish a simulation scenario in which a number of mobile agents in a certain area move automatically to form a specified target shape , and demonstrate the superiorities of our proposed methods through extensive simulations .
Edit intent: fluency
Original:  Finally, we establish a simulation scenario where a number of mobile agents in a certain area move automatically to form a specified target shape , and demonstrate the superiorities of our proposed methods through extensive simulations .
Revised:  Finally, we establish a simulation scenario where a number of mobile agents in a certain area move automatically to form a specified target shape . Extensive simulations demonstrate the effectiveness of our proposed methods through extensive simulations .
Edit intent: clarity
Original:  Finally, we establish a simulation scenario where a number of mobile agents in a certain area move automatically to form a specified target shape , and demonstrate the superiorities of our proposed methods through extensive simulations .
Revised:  Finally, we establish a simulation scenario where a number of mobile agents in a certain area move automatically to form a specified target shape , and demonstrate the superiorities of our proposed method .
Edit intent: clarity
Original:  As a key feature, the framework and its theory have been developed and checked with the unavoidable help of the interactive prover Matita.
Revised:  As a key feature, the framework and its theory have been developed and checked with the valuable help of the interactive prover Matita.
Edit intent: clarity
Original: Structural covariance analysis is a promising and increasingly used structural Magnetic Resonance Imaging (MRI ) analysis method which characterises the co-relations of morphology between brain regions over a group of subjects.
Revised: Structural covariance analysis is a widely used structural MRI analysis method which characterises the co-relations of morphology between brain regions over a group of subjects.
Edit intent: clarity
Original:  However, to our knowledge, little has been investigated in terms of the comparability of results between different data sets of healthy human subjects as well as the reliability of results over  different rescan sessions and FreeSurfer versions.
Revised:  However, to our knowledge, little has been investigated in terms of the comparability of results between different data sets or the reliability of results over different rescan sessions and FreeSurfer versions.
Edit intent: clarity
Original:  Our results show (significant) differences of structural covariance between two data sets of age- and sex-matched healthy human adults.
Revised:  In terms of comparability, our results show substantial differences in the structural covariance matrix between data sets of age- and sex-matched healthy human adults.
Edit intent: clarity
Original:  This low comparability is unaltered by site correction, and is most severe when using average cortical thickness as a measure of cortical morphology.
Revised:  These differences persist after site correction, and is most severe when using average cortical thickness as a measure of cortical morphology.
Edit intent: clarity
Original:  This low comparability is unaltered by site correction, and is most severe when using average cortical thickness as a measure of cortical morphology.
Revised:  This low comparability is unaltered by site correction, they are exacerbated by low sample sizes, and they are most pronounced when using average cortical thickness as a measure of cortical morphology.
Edit intent: clarity
Original:  Similar results of low reliabilitywere found when comparing rescan sessions of the same subjects, and even between different FreeSurfer versions of the same scans.
Revised:  Similar results of low reliabilitywere found when comparing repeated scan sessions of the same subjects, and even between different FreeSurfer versions of the same scans.
Edit intent: clarity
Original:  To our knowledge this study is the first highlight the problem of reliability and comparability in structural covariance . Practically, we suggest that (1)
Revised:  To our knowledge this study is the first highlight the problem of reliability and comparability in structural covariance . Practically, we make the following recommendations (1)
Edit intent: clarity
Original: In this paper, we present an analysis of the effect of penalty term in the mixed discontinuous Galerkin finite element method for the biharmonic equation .
Revised: In this paper, we present a study on the effect of penalty term in the mixed discontinuous Galerkin finite element method for the biharmonic equation .
Edit intent: clarity
Original: In this paper, we present an analysis of the effect of penalty term in the mixed discontinuous Galerkin finite element method for the biharmonic equation .
Revised: In this paper, we present an analysis of the effect of penalty term in the mixed Discontinuous Galerkin Finite Element Method for the biharmonic equation .
Edit intent: fluency
Original:  We prove that choosing the penalty term \alpha_k = \sigma_0 |e_k|^{-1} p^2 < \sigma_0 |e_k|^{-3} p^2 for a sufficiently large \sigma_0, ensures optimal rate of convergence in the L^2 and the energy norm for the approximations u_h and v_h . Finally, we present numerical experiments to validate our theoretical results.
Revised:  We prove that choosing the penalty term proportional to |e_k|^{-1} p^2 < \sigma_0 |e_k|^{-3} p^2 for a sufficiently large \sigma_0, ensures optimal rate of convergence in the L^2 and the energy norm for the approximations u_h and v_h . Finally, we present numerical experiments to validate our theoretical results.
Edit intent: clarity
Original:  We prove that choosing the penalty term \alpha_k = \sigma_0 |e_k|^{-1} p^2 < \sigma_0 |e_k|^{-3} p^2 for a sufficiently large \sigma_0, ensures optimal rate of convergence in the L^2 and the energy norm for the approximations u_h and v_h . Finally, we present numerical experiments to validate our theoretical results.
Revised:  We prove that choosing the penalty term \alpha_k = \sigma_0 |e_k|^{-1} p^2 < \sigma_0 |e_k|^{-3} p^2 for a sufficiently large \sigma_0, ensures optimal rate of convergence for the approximation, including for piecewise linear elements . Finally, we present numerical experiments to validate our theoretical results.
Edit intent: clarity
Original:  We show that Expected Improvement  and the Upper Confidence Bound  always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is never guaranteed to do so and Weighted Expected Improvement does  only for a restricted range of weights.
Revised:  We show that Expected Improvement and the Upper Confidence Bound always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does only for a restricted range of weights.
Edit intent: clarity
Original:  We show that Expected Improvement  and the Upper Confidence Bound  always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is never guaranteed to do so and Weighted Expected Improvement does  only for a restricted range of weights.
Revised:  We show that Expected Improvement and the Upper Confidence Bound always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is never guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights.
Edit intent: fluency
Original:  Extensive empirical evaluation of these together with random search, purely exploratory  and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that \epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions , particularly with a limited budget.
Revised:  Extensive empirical evaluation of these together with random search, purely exploratory , and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that \epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions , particularly with a limited budget.
Edit intent: fluency
Original:  The model is parameterized by  number of nodes, number of communities, distribution of community sizes, and the link probability inside the communities.
Revised:  The model is parameterized by a number of nodes, number of communities, distribution of community sizes, and the link probability inside the communities.
Edit intent: fluency
Original:  The model is parameterized by  number of nodes, number of communities, distribution of community sizes, and the link probability inside the communities.
Revised:  The model is parameterized by number of nodes, number of communities, distribution of community sizes, and the edge probability inside the communities.
Edit intent: clarity
Original:  This model admits sparse parameter regimes with power-law limiting degree distributions, and nonvanishing clustering coeffient .
Revised:  This model admits sparse parameter regimes with power-law limiting degree distributions, and nonvanishing clustering coefficient .
Edit intent: fluency
Original: In this paper, we propose Poq , a runtime assertion scheme for debugging on a quantum computer.
Revised: In this paper, we propose Proq , a runtime assertion scheme for debugging on a quantum computer.
Edit intent: fluency
Original: In this paper, we propose Poq , a runtime assertion scheme for debugging on a quantum computer.
Revised: In this paper, we propose Poq , a runtime assertion scheme for testing and debugging quantum programs on a quantum computer.
Edit intent: clarity
Original:  The predicates in the assertions are represented by projections (or equivalently, closed subspaces of the state space), following Birkhoff-von Neumann quantum logic.
Revised:  The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space), following Birkhoff-von Neumann quantum logic.
Edit intent: clarity
Original:  We compare Poq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Poq by its applications to assert two sophisticated quantum algorithms .
Revised:  We compare Proq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Poq by its applications to assert two sophisticated quantum algorithms .
Edit intent: fluency
Original:  We compare Poq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Poq by its applications to assert two sophisticated quantum algorithms .
Revised:  We compare Poq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Proq by its applications to assert two sophisticated quantum algorithms .
Edit intent: fluency
Original:  At the end of the stream, we post-process the output of the algorithm using any offline algorithm for submodular maximization, and we obtain a solution whose approximation guarantee is \alpha{1+\alpha}- \epsilon , where \alpha is the approximation of the offline algorithm.
Revised:  At the end of the stream, we post-process their data structures using any offline algorithm for submodular maximization, and we obtain a solution whose approximation guarantee is \alpha{1+\alpha}- \epsilon , where \alpha is the approximation of the offline algorithm.
Edit intent: clarity
Original:  At the end of the stream, we post-process the output of the algorithm using any offline algorithm for submodular maximization, and we obtain a solution whose approximation guarantee is \alpha{1+\alpha}- \epsilon , where \alpha is the approximation of the offline algorithm.
Revised:  At the end of the stream, we post-process the output of the algorithm using any offline algorithm for submodular maximization, and obtain a solution whose approximation guarantee is \alpha{1+\alpha}- \epsilon , where \alpha is the approximation of the offline algorithm.
Edit intent: fluency
Original:  we obtain a \frac{1}{2}- \epsilon approximation ,
Revised:  this leads to \frac{1}{2}- \epsilon approximation ,
Edit intent: clarity
Original:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019  that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Revised:  2019 . If we post-process with the algorithm of Buchbinder and Feldman ( Math of OR 2019 that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Edit intent: clarity
Original:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019  that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Revised:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019 ), that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Edit intent: fluency
Original:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019  that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Revised:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019 that achieves the currently best approximation guarantee \alpha=0.385, we obtain 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Edit intent: fluency
Original:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019  that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Revised:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019 that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 -approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Edit intent: clarity
Original:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019  that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Revised:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019 that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Edit intent: coherence
Original:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019  that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to Alaluf-Feldman, 2019%DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Revised:  2019 . If we post-process with the algorithm of Buchbinder-Feldman, Math of OR 2019 that achieves the currently best approximation guarantee \alpha=0.385, we obtain a 0.2779 approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.2335 due to %DIFDELCMD < ]%%% . In addition to its improved approximation guarantee, our algorithm enjoys a fast update time and overall running time .
Edit intent: clarity
Original:  Our main contributions are two single-pass (semi-)streaming algorithms that use (k )\cdot\mathrm{poly / \varepsilon  ) memory, where k is the size constraint.
Revised:  Our main contribution is a single-pass (semi-)streaming algorithms that use (k )\cdot\mathrm{poly / \varepsilon ) memory, where k is the size constraint.
Edit intent: clarity
Original:  Our main contributions are two single-pass (semi-)streaming algorithms that use (k )\cdot\mathrm{poly / \varepsilon  ) memory, where k is the size constraint.
Revised:  Our main contributions are two single-pass (semi-)streaming (k )\cdot\mathrm{poly / \varepsilon ) memory, where k is the size constraint.
Edit intent: clarity
Original:  At the end of the stream, both our algorithms post-process their data structures using any offline algorithm for submodular maximization, and obtain a solution whose approximation guarantee is \alpha{1+\alpha}-\varepsilon, where \alpha is the approximation of the offline algorithm.
Revised:  At the end of the stream, our algorithm post-processes its data structure using any offline algorithm for submodular maximization, and obtain a solution whose approximation guarantee is \alpha{1+\alpha}-\varepsilon, where \alpha is the approximation of the offline algorithm.
Edit intent: clarity
Original:  At the end of the stream, both our algorithms post-process their data structures using any offline algorithm for submodular maximization, and obtain a solution whose approximation guarantee is \alpha{1+\alpha}-\varepsilon, where \alpha is the approximation of the offline algorithm.
Revised:  At the end of the stream, both our algorithms post-process their data structures using any offline algorithm for submodular maximization, and obtains a solution whose approximation guarantee is \alpha{1+\alpha}-\varepsilon, where \alpha is the approximation of the offline algorithm.
Edit intent: fluency
Original:  We aim to answer whether the code works as intended and whether the time-parallelization is as efficient as expected.
Edit intent: coherence
Original: A language over an alphabet B = A \cup A of opening (A) and closing (A) brackets, is balanced if it is a subset of the Dyck language D _{B over B, and it is well-formed if all words are prefixes of words in D _{B . We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time.
Revised: A language over an alphabet B = A \cup A of opening (A) and closing (A) brackets, is balanced if it is a subset of the Dyck language D _B over B, and it is well-formed if all words are prefixes of words in D _{B . We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time.
Edit intent: fluency
Original: A language over an alphabet B = A \cup A of opening (A) and closing (A) brackets, is balanced if it is a subset of the Dyck language D _{B over B, and it is well-formed if all words are prefixes of words in D _{B . We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time.
Revised: A language over an alphabet B = A \cup A of opening (A) and closing (A) brackets, is balanced if it is a subset of the Dyck language D _{B over B, and it is well-formed if all words are prefixes of words in D _B . We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time.
Edit intent: fluency
Original:  These two results enable us to decide in polynomial time for the class 2-TW of non-linear tree transducers with output alphabet B^* whether or not the output language is balanced.
Revised:  These two results enable us to decide in polynomial time for the class 2-TWs of non-linear tree transducers with output alphabet B^* whether or not the output language is balanced.
Edit intent: fluency
Original:  We introduce a new algorithm to estimate the connection probabilities in a network , which is robust to both outlier nodes and missing observations.
Revised:  We introduce a new algorithm to detect outliers in a network , which is robust to both outlier nodes and missing observations.
Edit intent: clarity
Original:  Under fairly general assumptions, this method detects the outliers, and achieves the best known error for the estimation of connection probabilities with polynomial computation cost.
Revised:  Under fairly general assumptions, this method detects the outliers, and achieves the best known error for the prediction of missing links with polynomial computation cost.
Edit intent: clarity
Original:  We provide a simulation study which demonstrates the good behaviour of the method in terms of outliers selection and prediction of the missing links  .
Revised:  We provide a simulation study which demonstrates the good behavior of the algorithm in terms of outliers selection and prediction of the missing links .
Edit intent: clarity