wanyu/IteraTeR_full_sent huggingface dataset:
Original:  All steps necessary in nonlinear model reduction are covered by our analysis. These are the space discretization by conventional methods, the projection-based model order reduction and the complexity reduction of nonlinearities. Special attention is paid to the structure-preservation on all levels. The proposed reduced models are shown to be locally massconservative, to fulfill energy bounds and to inherit port-Hamiltonian structure. The main ingredients of our analysis are energy-based modeling concepts like the port-Hamiltonian framework and the theory on the Legendre transform, which allow a convenient and general line of argumentation.
Revised:  Our approach is guided throughout by energy-based modeling concepts like the port-Hamiltonian framework and the theory on the Legendre transform, which allow a convenient and general line of argumentation.
Edit intent: coherence
Original:  The main ingredients of our analysis are energy-based modeling concepts like the port-Hamiltonian framework and the theory on the Legendre transform, which allow a convenient and general line of argumentation. Moreover, the case of the barotropic Euler equations is examined in more detail and a well-posedness result is proven for their approximation in our framework .
Revised:  The main ingredients of our analysis are energy-based modeling concepts like the port-Hamiltonian formalism, theory of Legendre transformation), which provide a convenient and general line of reasoning. Under mild assumptions on the approximation, local conservation of mass, an energy bound, and the inheritance of the port-Hamiltonian structure can be shown. Our approach is not limited to conventional space discretization but also covers complexity reduction of the case of the barotropic Euler equations is examined in more detail and a well-posedness result is proven for their approximation in our framework .
Edit intent: meaning-changed
Original:  Moreover, the case of the barotropic Euler equations is examined in more detail and a well-posedness result is proven for their approximation in our framework .
Revised:  Moreover, the nonlinearities by inexact integration. Thus, it can serve as a basis for structure-preserving model reduction. Combined with an energy stable time integration, we numerically demonstrate the applicability and good stability properties of the approach using the Euler equations as an example .
Edit intent: meaning-changed
Original: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971 Turchin1971%DIFDELCMD < ]%%% . In each step  , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Revised: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to Turchin1971%DIFDELCMD < ]%%% . In each step , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Edit intent: fluency
Original: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971 Turchin1971%DIFDELCMD < ]%%% . In each step  , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Revised: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971 %DIFDELCMD < ]%%% . In each step , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Edit intent: coherence
Original: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971 Turchin1971%DIFDELCMD < ]%%% . In each step  , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Revised: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971 Turchin1971%DIFDELCMD < ]%%% Turchin, 1971. In each step , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Edit intent: meaning-changed
Original: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971 Turchin1971%DIFDELCMD < ]%%% . In each step  , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Revised: The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971 Turchin1971%DIFDELCMD < ]%%% . In each step of the Gibbs Sampler , we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all other coordinates.
Edit intent: clarity
Original:  Here we show that for convex bodies in R^{n} with diameter D, the resulting Coordinate Hit-and-Run (CHAR) algorithm mixes in poly(n ,D) steps.
Revised:  Here we show that for a convex body K in R^{n} with diameter D, the resulting Coordinate Hit-and-Run (CHAR) algorithm mixes in poly(n ,D) steps.
Edit intent: meaning-changed
Original:  Here we show that for convex bodies in R^{n} with diameter D, the resulting Coordinate Hit-and-Run (CHAR) algorithm mixes in poly(n ,D) steps.
Revised:  Here we show that for convex bodies in R^{n} with diameter D, the mixing time of the Coordinate Hit-and-Run (CHAR) algorithm mixes in poly(n ,D) steps.
Edit intent: clarity
Original:  Here we show that for convex bodies in R^{n} with diameter D, the resulting Coordinate Hit-and-Run (CHAR) algorithm mixes in poly(n ,D) steps. This is the first polynomial guarantee for this widely-used algorithm.
Revised:  Here we show that for convex bodies in R^{n} with diameter D, the resulting Coordinate Hit-and-Run (CHAR) algorithm on K is polynomial in n and D.
Edit intent: meaning-changed
Original:  framework powered by adding the Total Variation regularizer which promotes gradient-sparsity of the solution . Differently from other existing approaches, we solve the arising minimization problem by using the well known Alternating Direction Method of Multipliers (ADMM)
Revised:  framework and we propose to combine it with a space-variant Total Variation regularizer which promotes gradient-sparsity of the solution . Differently from other existing approaches, we solve the arising minimization problem by using the well known Alternating Direction Method of Multipliers (ADMM)
Edit intent: meaning-changed
Original:  framework powered by adding the Total Variation regularizer which promotes gradient-sparsity of the solution . Differently from other existing approaches, we solve the arising minimization problem by using the well known Alternating Direction Method of Multipliers (ADMM)
Revised:  framework powered by adding the Total Variation regularizer with an automatic estimation of the local regularization parameters . Differently from other existing approaches, we solve the arising minimization problem by using the well known Alternating Direction Method of Multipliers (ADMM)
Edit intent: meaning-changed
Original:  framework powered by adding the Total Variation regularizer which promotes gradient-sparsity of the solution . Differently from other existing approaches, we solve the arising minimization problem by using the well known Alternating Direction Method of Multipliers (ADMM)
Revised:  framework powered by adding the Total Variation regularizer which promotes gradient-sparsity of the solution . Differently from other existing approaches, we solve the arising minimization problem via the flexible Alternating Direction Method of Multipliers (ADMM)
Edit intent: clarity
Original:  framework, decoupling the contribution of the DIP L_{2 . The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed by means of experiments for different image restoration tasks on synthetic as well as on real data .
Revised:  . Furthermore, we provide a specific implementation also for the standard isotropic Total Variation . The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed by means of experiments for different image restoration tasks on synthetic as well as on real data .
Edit intent: meaning-changed
Original:  framework, decoupling the contribution of the DIP L_{2 . The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed by means of experiments for different image restoration tasks on synthetic as well as on real data .
Revised:  framework, decoupling the contribution of the DIP L_{2 . The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed through several experiments on simulated as well as on real data .
Edit intent: clarity
Original:  framework, decoupling the contribution of the DIP L_{2 . The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed by means of experiments for different image restoration tasks on synthetic as well as on real data .
Revised:  framework, decoupling the contribution of the DIP L_{2 . The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed by means of experiments for different image restoration tasks on synthetic as well as real natural and medical corrupted images .
Edit intent: meaning-changed
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised:  MaxIS%DIFDELCMD < }%%% ) problem is a fundamental problem in graph theory, which is NP-hard . Since the underlying graphs are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: coherence
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised: Maximum Independent Set ( %DIFDELCMD < }%%% ) problem is a fundamental problem in graph theory, which is NP-hard . Since the underlying graphs are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: fluency
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% Computing a maximum independent set (MaxIS) is a fundamental problem in graph theory, which is NP-hard . Since the underlying graphs are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: clarity
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental NP-hard problem in graph theory, which is NP-hard . Since the underlying graphs are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: fluency
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental problem in graph theory, which has important applications in a wide range of areas such as social network analysis, graphical information systems and coding theory . Since the underlying graphs are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: meaning-changed
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental problem in graph theory, which is NP-hard . Since the underlying graphs of numerous applications are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: clarity
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental problem in graph theory, which is NP-hard . Since the underlying graphs are always changing MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: clarity
Original: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental  problem in graph theory, which is NP-hard . Since the underlying graphs  are always changing in numerous applications, computing a MaxIS over dynamic graphs has received increasing attention in recent years.
Revised: Maximum Independent Set ( MaxIS%DIFDELCMD < }%%% ) problem is a fundamental problem in graph theory, which is NP-hard . Since the underlying graphs are always changing in numerous applications, computing a continuously, the problem of maintaining a MaxIS over dynamic graphs has received increasing attention in recent years.
Edit intent: meaning-changed
Original:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie .
Revised:  Due to the intractability of maintaining an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie .
Edit intent: clarity
Original:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie .
Revised:  Due to the intractability to compute an exact MaxIS , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie .
Edit intent: clarity
Original:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie .
Revised:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem of maintaining an approximate MaxIS over fully dynamic graphs, where 4 graph update operations are allowed\ie .
Edit intent: meaning-changed
Original:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie .
Revised:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie, adding or deleting a vertex or an edge. Based on swap operation, we present a novel framework for maintaining an approximate maximum independent set which contains no k-swaps and make a deep analysis of performance ratio achieved by it .
Edit intent: meaning-changed
Original:  A framework based on swap operations for resolving this problem is presented and two concrete update algorithms based on one-swappable vertices and two-swappble vertex pairs are designed. Both algorithms can compute high-quality independent sets over dynamic graphs with O(\Delta^3) time for general graphs and with O( 1 ) time for bounded-degree graphs.
Revised:  We implement a dynamic (\frac{\Delta 1 ) time for bounded-degree graphs.
Edit intent: clarity
Original:  Both algorithms can compute high-quality independent sets over dynamic graphs with O(\Delta^3) time for general graphs and with O( 1 ) time for bounded-degree graphs. Moreover, the lower bound of the size of the solution maintained by our algorithms is derived if there is no swappable vertex in it. Then the algorithms are extended under\textit{semi-external setting to maintained a high-quality independent set with limited memory consumption .
Revised:  Both algorithms can compute high-quality independent sets over dynamic graphs with O(\Delta^3) time for general graphs and with O( 1 \textit{semi-external setting to maintained a high-quality independent set with limited memory consumption .
Edit intent: coherence
Original:  In the DMV model, we show that under a well-known condition , it is optimal to sell the first unit deterministically . Under the same sufficient condition, a bundling mechanism (which is deterministic) is optimal in the IMV model.
Revised:  In the DMV model, we show that under a well-known condition , it is optimal to sell the first unit deterministically in the DMV model and (b) it is optimal to bundle (which is a deterministic mechanism) in the IMV model.
Edit intent: coherence
Original:  We say that there is strong learning when beliefs converge to the truth and there is weak learning when equilibrium flows converge to those under complete information. Our main result is a characterization of the  networks for which learning occurs for all increasing cost functions, given highly variable demand .
Revised:  We say that there is strong learning when beliefs converge to the truth and there is weak learning when the equilibrium flow converges to the networks for which learning occurs for all increasing cost functions, given highly variable demand .
Edit intent: clarity
Original: We introduce N-LTP , an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, named entity recognition, dependency parsing, and semantic dependency parsing.
Revised: We introduce N-LTP , an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, named entity recognition, dependency parsing, and semantic dependency parsing.
Edit intent: meaning-changed
Original: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging,  named entity recognition , dependency }   parsing , and semantic dependency parsing.
Revised: We introduce N-LTP, an open-source neural language technology platform supporting six fundamental Chinese NLP tasks: lexical analysis ( Chinese word segmentation, part-of-speech tagging, named entity recognition , dependency } parsing , and semantic dependency parsing.
Edit intent: meaning-changed
Original: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging,  named entity recognition , dependency }   parsing , and semantic dependency parsing.
Revised: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, and named entity recognition , dependency } parsing , and semantic dependency parsing.
Edit intent: meaning-changed
Original: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging,  named entity recognition , dependency }   parsing , and semantic dependency parsing.
Revised: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, named entity recognition ), } parsing , and semantic dependency parsing.
Edit intent: meaning-changed
Original: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging,  named entity recognition , dependency }   parsing , and semantic dependency parsing.
Revised: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, named entity recognition , dependency syntactic parsing} parsing , and semantic dependency parsing.
Edit intent: meaning-changed
Original: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging,  named entity recognition , dependency }   parsing , and semantic dependency parsing.
Revised: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, named entity recognition , dependency } (dependency parsing), and parsing , and semantic dependency parsing.
Edit intent: meaning-changed
Original: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging,  named entity recognition , dependency }   parsing , and semantic dependency parsing.
Revised: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, named entity recognition , dependency } semantic parsing , and semantic dependency parsing.
Edit intent: meaning-changed
Original: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging,  named entity recognition , dependency }   parsing , and semantic dependency parsing.
Revised: We introduce N-LTP, an open-source Python Chinese natural language processing toolkit supporting five basic tasks: Chinese word segmentation, part-of-speech tagging, named entity recognition , dependency } parsing (semantic dependency parsing and semantic role labeling). Unlike the existing state-of-the-art toolkits, such as Stanza, that adopt an independent model for each task,
Edit intent: meaning-changed
Original:  In addition, we propose to use knowledge distillation where  single-task models teach a multi-task model , helping the multi-task model  surpass its single-task teachers . Finally, we provide fundamental tasks API and a visualization tool to make users easier to use and view the processing results directly.
Revised:  In addition, knowledge distillation where single-task models teach a multi-task model , helping the multi-task model surpass its single-task teachers . Finally, we provide fundamental tasks API and a visualization tool to make users easier to use and view the processing results directly.
Edit intent: coherence