wanyu/IteraTeR_v2 huggingface dataset:
Original:  for instance, that the order of months in the  Lunar calendar is Corner < Apricot < Peach , and so on .
Revised:  for instance, that the order of months in the Lunar calendar is Corner < Apricot < Peach .
Edit intent: coherence
Original:  We first identify tractable special cases and then proceed towards the most general case, which we prove is NP-complete.
Revised:  We first identify tractable special cases and proceed towards the most general case, which we prove is NP-complete.
Edit intent: coherence
Original:  Nevertheless, we show that the general case  can be effectively handled by a SAT solver.
Revised:  We show that the general case can be effectively handled by a SAT solver.
Edit intent: coherence
Original:  Nevertheless, we show that the general case  can be effectively handled by a SAT solver.
Revised:  Nevertheless, we show that the general case nevertheless can be effectively handled by a SAT solver.
Edit intent: coherence
Original:  We also propose an interestingness measure to rank the discovered implicit domain orders . Finally, we report on the results of an experimental evaluation using real-world datasets .
Revised:  We also devise an interestingness measure to rank the discovered implicit domain orders . Finally, we report on the results of an experimental evaluation using real-world datasets .
Edit intent: clarity
Original: In view of the undisputed success of neural networks and due to the remarkable recent improvements in their ability to solve a huge variety of practical problems, the development of a satisfying and rigorous mathematical understanding of their performance is one of the main challenges in the field of learning theory .
Revised: The development of a satisfying and rigorous mathematical understanding of their performance is one of the main challenges in the field of learning theory .
Edit intent: coherence
Original: In view of the undisputed success of neural networks and due to the remarkable recent improvements in their ability to solve a huge variety of practical problems, the development of a satisfying and rigorous mathematical understanding of their performance is one of the main challenges in the field of learning theory .
Revised: In view of the undisputed success of neural networks and due to the remarkable recent improvements in their ability to solve a huge variety of practical problems, the development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence .
Edit intent: clarity
Original:  In order to find optimum Knapsack solutions, an RNN of depth four and width depending quadratically on the profit of an optimum Knapsack solution is sufficient  .
Revised:  We show that an RNN of depth four and width depending quadratically on the profit of an optimum Knapsack solution is sufficient .
Edit intent: coherence
Original:  In order to find optimum Knapsack solutions, an RNN of depth four and width depending quadratically on the profit of an optimum Knapsack solution is sufficient  .
Revised:  In order to find optimum Knapsack solutions, an RNN of depth four and width depending quadratically on the profit of an optimum Knapsack solution is sufficient to find optimum Knapsack solutions .
Edit intent: fluency
Original:  We also prove the following tradeoff between the size of an RNN and the quality of the computed Knapsack solution: For Knapsack instances consisting of n items, an RNN of depth five and width w computes a solution of value at least 1-O(n^2/w) times the optimum solution value.
Revised:  We also prove the following tradeoff between the size of an RNN and the quality of the computed Knapsack solution: for Knapsack instances consisting of n items, an RNN of depth five and width w computes a solution of value at least 1-O(n^2/w) times the optimum solution value.
Edit intent: fluency
Original:  Our results build upon a  dynamic programming formulation of the Knapsack Problem as well as a careful rounding of profit values that is also at the core of the well-known fully polynomial-time approximation scheme for the Knapsack Problem.
Revised:  Our results build upon a dynamic programming formulation of the Knapsack Problem as well as a careful rounding of profit values that are also at the core of the well-known fully polynomial-time approximation scheme for the Knapsack Problem.
Edit intent: fluency
Original:   Finally, we point out that similar results can be achieved for other optimization problems that can be solved by dynamic programming , such as , e.g., various Shortest Path Problems and the Longest Common Subsequence  Problem.
Revised:  Finally, we point out that our results can be achieved for other optimization problems that can be solved by dynamic programming , such as , e.g., various Shortest Path Problems and the Longest Common Subsequence Problem.
Edit intent: clarity
Original:   Finally, we point out that similar results can be achieved for other optimization problems that can be solved by dynamic programming , such as , e.g., various Shortest Path Problems and the Longest Common Subsequence  Problem.
Revised:  Finally, we point out that similar results can be achieved for other optimization problems that admit dynamic programming solution methods , such as , e.g., various Shortest Path Problems and the Longest Common Subsequence Problem.
Edit intent: clarity
Original:   Finally, we point out that similar results can be achieved for other optimization problems that can be solved by dynamic programming , such as , e.g., various Shortest Path Problems and the Longest Common Subsequence  Problem.
Revised:  Finally, we point out that similar results can be achieved for other optimization problems that can be solved by dynamic programming , such as various Shortest Path Problems and the Longest Common Subsequence Problem.
Edit intent: coherence
Original:   Finally, we point out that similar results can be achieved for other optimization problems that can be solved by dynamic programming , such as , e.g., various Shortest Path Problems and the Longest Common Subsequence  Problem.
Revised:  Finally, we point out that similar results can be achieved for other optimization problems that can be solved by dynamic programming , such as , e.g., various Shortest Path Problems , the Longest Common Subsequence Problem.
Edit intent: fluency
Original: " IMDb.com " as a user-regulating and one the most-visited portal has created an opportunity to create an enormous database.
Revised: `` IMDb.com " as a user-regulating and one the most-visited portal has created an opportunity to create an enormous database.
Edit intent: fluency
Original: " IMDb.com " as a user-regulating and one the most-visited portal has created an opportunity to create an enormous database.
Revised: " IMDb.com '' as a user-regulating and one the most-visited portal has created an opportunity to create an enormous database.
Edit intent: fluency
Original:  Analysis of the information on Internet Movie Database - IMDb, either those related to the movie or provided by users , would help to reveal the determinative factors in the route of success for each movie.
Revised:  Analysis of the information on Internet Movie Database - IMDb, either those related to the movie or provided by users would help to reveal the determinative factors in the route of success for each movie.
Edit intent: fluency
Original:  The present paper is the first paper in a series of papers aiming  the mentioned goals, by a brief description of the created dataset and a demo of data analysis.
Revised:  The present paper is the first paper in a series of papers aiming at the mentioned goals, by a brief description of the created dataset and a demo of data analysis.
Edit intent: fluency
Original: ``IMDb.com'' as a user-regulating and one the most-visited portal has created an opportunity to create an enormous database.
Revised: "IMDb" as a user-regulating and one the most-visited portal has created an opportunity to create an enormous database.
Edit intent: clarity
Original: ``IMDb.com'' as a user-regulating and one the most-visited portal has created an opportunity to create an enormous database.
Revised: ``IMDb.com'' as a user-regulating and one the most-visited portal has provided an opportunity to create an enormous database.
Edit intent: clarity
Original:  The present paper is the first paper in a series of papers aiming at the mentioned goals, by a brief description of the created dataset and a demo of dataanalysis .
Revised:  The present paper is the first paper in a series of papers aiming at the mentioned goals, by a description of the created dataset and a demo of dataanalysis .
Edit intent: clarity
Original:  We suggest an automated approach for finding biophysically plausible plasticity rules based on the definition of task families, associated performance measures and biophysical constraints.
Revised:  We suggest an automated approach for discovering biophysically plausible plasticity rules based on the definition of task families, associated performance measures and biophysical constraints.
Edit intent: fluency
Original:  This approach makes the relative weighting of guiding factors explicit, explores large search spaces, encourages diverse sets of hypotheses, and can discover domain-specific solutions.
Edit intent: coherence
Original:  In this paper, we look at the system of two communities , which are connected by bridge links between a fraction r of bridge nodes, and study the effect of bridge nodes to the final state of the Susceptible-Infected-Recovered model, by mapping it to link percolation.
Revised:  In this paper, we look at the system of two communities which are connected by bridge links between a fraction r of bridge nodes, and study the effect of bridge nodes to the final state of the Susceptible-Infected-Recovered model, by mapping it to link percolation.
Edit intent: fluency
Original:  We provide an algorithm, based on a piecewise linear approximation of the logarithm of epidemic observables, allowing one to monitor the epidemic .
Revised:  We show that the logarithm of each epidemic observable can be approximated by a piecewise linear approximation of the logarithm of epidemic observables, allowing one to monitor the epidemic .
Edit intent: clarity
Original:  We base the design and implementation of BOURBON on empirically grounded principles that we derive through careful analysis of LSM design.
Revised:  We base the design and implementation of BOURBON on empirically-grounded principles that we derive through careful analysis of LSM design.
Edit intent: fluency
Original: The equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device are modelled by a system of second order semi-linear elliptic partial differential equations with non-homogeneous boundary conditions.
Revised: We study a system of semi-linear elliptic partial differential equations with non-homogeneous boundary conditions.
Edit intent: clarity
Original: %DIFDELCMD < {\it %%% A priori and  {\it a posteriori} energy norm analysis is established for a sufficiently large penalization parameter and  sufficiently fine triangulation .
Revised: %DIFDELCMD < {\it %%% A priori and {\it a posteriori} analysis for a sufficiently large penalization parameter and sufficiently fine triangulation .
Edit intent: clarity
Original:  Optimal order%DIFDELCMD < {\it %DIFDELCMD < %%% a priori error estimates in L^2 norm is also established.
Revised:  Optimal order%DIFDELCMD < {\it %DIFDELCMD < %%% error estimates in L^2 norm is also established.
Edit intent: clarity
Original:  We introduce two schemes for task-based information compression (i) Learning-based information compression (LBIC) which leverages reinforcement learning to compactly represent the observation space of the agents, and (ii) State aggregation for information compression (SAIC), for which a state aggregation algorithm is analytically designed.
Revised:  We introduce a scheme for task-based information compression (i) Learning-based information compression (LBIC) which leverages reinforcement learning to compactly represent the observation space of the agents, and (ii) State aggregation for information compression (SAIC), for which a state aggregation algorithm is analytically designed.
Edit intent: clarity
Original:  We introduce two schemes for task-based information compression (i) Learning-based information compression (LBIC) which leverages reinforcement learning to compactly represent the observation space of the agents, and (ii) State aggregation for information compression (SAIC), for which a state aggregation algorithm is analytically designed.
Revised:  We introduce two schemes for task-based information compression titled State aggregation for information compression (SAIC), for which a state aggregation algorithm is analytically designed.
Edit intent: coherence
Original:  The SAIC is shown , conditionally, to be capable of achieving the optimal performance in terms of the attained sum of discounted rewards.
Revised:  The SAIC is shown to be capable of achieving the optimal performance in terms of the attained sum of discounted rewards.
Edit intent: clarity
Original:  The SAIC is shown , conditionally, to be capable of achieving the optimal performance in terms of the attained sum of discounted rewards.
Revised:  The SAIC is shown , conditionally, to be capable of achieving the optimal performance in terms of the achieved sum of discounted rewards.
Edit intent: fluency
Original:  The proposed algorithms are applied to a rendezvous problem and their performance is compared with two benchmarks;
Revised:  The proposed algorithm is applied to a rendezvous problem and their performance is compared with two benchmarks;
Edit intent: fluency
Original:  The proposed algorithms are applied to a rendezvous problem and their performance is compared with two benchmarks;
Revised:  The proposed algorithms are applied to a rendezvous problem and its performance is compared with two benchmarks;
Edit intent: clarity
Original:  Numerical experiments confirm the superiority of the proposed algorithms .
Revised:  Numerical experiments confirm the superiority of the proposed algorithm .
Edit intent: fluency
Original:  The inter-agent communication can tackle the issue of local observability, however, the limited rate of the inter-agent communication prevents the agent from acquiring the precise global state information.
Revised:  Inter-agent communication can tackle the issue of local observability, however, the limited rate of the inter-agent communication prevents the agent from acquiring the precise global state information.
Edit intent: clarity
Original:  The inter-agent communication can tackle the issue of local observability, however, the limited rate of the inter-agent communication prevents the agent from acquiring the precise global state information.
Revised:  The inter-agent communication can tackle the issue of local observability, however, the limited rate of inter-agent communication prevents the agent from acquiring the precise global state information.
Edit intent: fluency
Original:  The inter-agent communication can tackle the issue of local observability, however, the limited rate of the inter-agent communication prevents the agent from acquiring the precise global state information.
Revised:  The inter-agent communication can tackle the issue of local observability, however, the limited rate of the inter-agent communication prevents the agents from acquiring the precise global state information.
Edit intent: fluency
Original:  We show that this problem is equivalent to a form of rate-distortion problem  which we call the task-based information compression  .
Revised:  We show that this problem is equivalent to a form of rate-distortion problem , which we call the task-based information compression .
Edit intent: fluency
Original:  We show that this problem is equivalent to a form of rate-distortion problem  which we call the task-based information compression  .
Revised:  We show that this problem is equivalent to a form of rate-distortion problem which we call task-based information compression .
Edit intent: fluency
Original:  We introduce a scheme for task-based information compression titled State aggregation for information compression (SAIC) , for which a state aggregation algorithm is analytically designed.
Revised:  We introduce state aggregation for information compression (SAIC) , for which a state aggregation algorithm is analytically designed.
Edit intent: clarity
Original:  The SAIC is shown to be capable of achieving near-optimal performance in terms of the achieved sum of discounted rewards.
Revised:  The SAIC is shown to achieve near-optimal performance in terms of the achieved sum of discounted rewards.
Edit intent: clarity
Original: Aquatic biospheres reliant on oxygenic photosynthesis are expected to play an important role on Earth-like planets  with large-scale oceans insofar as carbon fixation (i.e., biosynthesis of organic compounds) is concerned.
Revised: Aquatic biospheres reliant on oxygenic photosynthesis are expected to play an important role on Earth-like planets endowed with large-scale oceans insofar as carbon fixation (i.e., biosynthesis of organic compounds) is concerned.
Edit intent: clarity
Original:  In particular, we estimate how these characteristics evolve with the  ambient ocean temperature (T_W), which is a key environmental variable.
Revised:  In particular, we estimate how these characteristics evolve with the ambient ocean temperature (T_W), the latter of which constitutes a key environmental variable.
Edit intent: clarity
Original:  We conclude by discussing the implications of our analysis for the past and future Earth, and exoplanets orbiting M-dwarfs.
Revised:  We conclude by exploring the implications of our analysis for the past and future Earth, and exoplanets orbiting M-dwarfs.
Edit intent: clarity
Original:  Experimental results on several real-world and synthetic datasets demonstrate that our algorithm runs up to four orders of magnitude faster than existing k-RMS algorithms while returning results of near-equal quality.
Revised:  Experimental results on several real-world and synthetic datasets demonstrate that our algorithm runs up to four orders of magnitude faster than existing k-RMS algorithms while returning results of nearly equal quality.
Edit intent: clarity
Original:  We then detail the application of this result to  a posteriori error analysis of Maxwell's equations discretized with N\'ed\'elec 's finite elements of arbitrary order.
Revised:  We then detail the application of this result to the a posteriori error analysis of Maxwell's equations discretized with N\'ed\'elec 's finite elements of arbitrary order.
Edit intent: fluency
Original:  We then detail the application of this result to  a posteriori error analysis of Maxwell's equations discretized with N\'ed\'elec 's finite elements of arbitrary order.
Revised:  We then detail the application of this result to a posteriori error analysis of Maxwell's equations discretized with N\'ed\'elec finite elements of arbitrary order.
Edit intent: fluency
Original:  The estimators become guaranteed when the regularity pick-up constant is explicitly known.
Revised:  The error estimates become guaranteed when the regularity pick-up constant is explicitly known.
Edit intent: clarity
Original:  In particular, IoT devices (with various communication types and energy constraints)  are assumed to belong the ISP who collects sensing data from IoT devices for its services.
Revised:  In particular, IoT devices (with various communication types and energy constraints) which are assumed to belong the ISP who collects sensing data from IoT devices for its services.
Edit intent: coherence
Original:  Specially, the ISP leads the game by requesting an optimal energy price and service time that maximize its revenue to the ESP.
Revised:  Specially, the ISP leads the game by sending its optimal service time and energy price request (that maximizes its profit) to the ESP.
Edit intent: clarity
Original:  Following the requested deal from the ISP, the ESP supplies an optimized transmission power which satisfies the energy demand of the ISPwhile maximizes its utility .
Revised:  The ESP then optimizes and supplies the transmission power which satisfies the energy demand of the ISPwhile maximizes its utility .
Edit intent: clarity
Original:  Following the requested deal from the ISP, the ESP supplies an optimized transmission power which satisfies the energy demand of the ISPwhile maximizes its utility .
Revised:  Following the requested deal from the ISP, the ESP supplies an optimized transmission power which satisfies the ISP's request (while maximizing ESP's utility) .
Edit intent: clarity
Original:  Then two relaxed schemes (i.e., partial or joint energy price and service time adjustments) based on block coordinate descent (BCD) and convex-concave procedure (CCCP) techniques are proposed to solve the non-convex optimization problem for the ISP . Due to the selfish behavior of both players, we investigate the inefficiency of the proposed approach by proposing two baseline scenarios, i.e., non-negotiated energy trading and social welfare scenarios, and the Price of Anarchy (PoA).
Revised:  Then , to tackle the non-convex optimization problem for the ISP . Due to the selfish behavior of both players, we investigate the inefficiency of the proposed approach by proposing two baseline scenarios, i.e., non-negotiated energy trading and social welfare scenarios, and the Price of Anarchy (PoA).
Edit intent: clarity
Original:  Finally, numerical results reveal that our approach can achieve significant improvements in revenues of both providers compared with conventional transmission methods , e. g., bistatic backscatter, and harvest-then-transmit communication methods .
Revised:  Finally, numerical results reveal that our approach can achieve significant improvements in terms of the ISP's profit compared with those of conventional transmission methods , e. g., bistatic backscatter, and harvest-then-transmit communication methods .
Edit intent: clarity
Original:  This plutocracy is reflected not only in control over execution, but also in the distribution of new wealth, giving rise to " rich get richer " phenomena.
Revised:  This plutocracy is reflected not only in control over execution, but also in the distribution of new wealth, giving rise to `` rich get richer " phenomena.
Edit intent: fluency
Original:  This plutocracy is reflected not only in control over execution, but also in the distribution of new wealth, giving rise to " rich get richer " phenomena.
Revised:  This plutocracy is reflected not only in control over execution, but also in the distribution of new wealth, giving rise to " rich get richer '' phenomena.
Edit intent: fluency
Original:  A single currency community can achieve distributive justice by egalitarian coin minting, where each member mints one coin at every time step.
Revised:  A single currency community can achieve distributive justice by egalitarian coin minting, whereby each member mints one coin at every time step.
Edit intent: clarity
Original:  On these subspaces the method also convergence with optimal rates in terms of the noise level with the discrepancy principle as parameter choice rule.
Revised:  On these subspaces the method also converges with optimal rates in terms of the noise level with the discrepancy principle as parameter choice rule.
Edit intent: fluency
Original:  One account of the informativity effect on duration is that the acoustic details of word reduction are stored as part of a word's  representation.
Revised:  One account of the informativity effect on duration is that the acoustic details of word reduction are stored as part of a word's mental representation.
Edit intent: clarity