wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Thus, our result has several direct applications, including polynomial-time algorithms 1)  to sample from  matrix Langevin distributions studied in statistics, 2)  to sample from continuous maximum entropy distributions with applications to quantum inference , and 3)  for differentially private low-rank approximation.
Revised:  Thus, our result has several direct applications, including polynomial-time algorithms 1) to sample from complex versions of matrix Langevin distributions studied in statistics, 2) to sample from continuous maximum entropy distributions with applications to quantum inference , and 3) for differentially private low-rank approximation.
Edit intent: meaning-changed
Original:  Thus, our result has several direct applications, including polynomial-time algorithms 1)  to sample from  matrix Langevin distributions studied in statistics, 2)  to sample from continuous maximum entropy distributions with applications to quantum inference , and 3)  for differentially private low-rank approximation.
Revised:  Thus, our result has several direct applications, including polynomial-time algorithms 1) to sample from matrix Langevin distributions studied in statistics, 2) an efficient algorithm to sample from continuous maximum entropy distributions with applications to quantum inference , and 3) for differentially private low-rank approximation.
Edit intent: meaning-changed
Original:  Thus, our result has several direct applications, including polynomial-time algorithms 1)  to sample from  matrix Langevin distributions studied in statistics, 2)  to sample from continuous maximum entropy distributions with applications to quantum inference , and 3)  for differentially private low-rank approximation.
Revised:  Thus, our result has several direct applications, including polynomial-time algorithms 1) to sample from matrix Langevin distributions studied in statistics, 2) to sample from continuous max-entropy distributions on unitary orbits, which implies an efficient algorithm to sample a pure quantum state from the entropy-maximizing ensemble representing a given density matrix , and 3) for differentially private low-rank approximation.
Edit intent: meaning-changed
Original:  Thus, our result has several direct applications, including polynomial-time algorithms 1)  to sample from  matrix Langevin distributions studied in statistics, 2)  to sample from continuous maximum entropy distributions with applications to quantum inference , and 3)  for differentially private low-rank approximation.
Revised:  Thus, our result has several direct applications, including polynomial-time algorithms 1) to sample from matrix Langevin distributions studied in statistics, 2) to sample from continuous maximum entropy distributions with applications to quantum inference , and 3) an efficient algorithm for differentially private low-rank approximation.
Edit intent: meaning-changed
Original:  Thus, our result has several direct applications, including polynomial-time algorithms 1)  to sample from  matrix Langevin distributions studied in statistics, 2)  to sample from continuous maximum entropy distributions with applications to quantum inference , and 3)  for differentially private low-rank approximation. The key obstacle in sampling from an HCIZ density is that the domain is an algebraic manifold and the entries of the sample matrix are highly correlated. To overcome this, we consider a mapping that sends each Hermitian matrix X to a natural ordering of the eigenvalues of all leading principal minors of X. The image of each \mathrm{U(n)-orbit under this map is a convex polytope, and the mapping reveals a recursive structure of \mathrm{U}(n)-orbits.
Revised:  Thus, our result has several direct applications, including polynomial-time algorithms 1) to sample from matrix Langevin distributions studied in statistics, 2) to sample from continuous maximum entropy distributions with applications to quantum inference , and 3) for differentially private (n)-orbit under this map is a convex polytope, and the mapping reveals a recursive structure of \mathrm{U}(n)-orbits.
Edit intent: meaning-changed
Original: With the enhancement of algorithms, cryo-EM  has become the most efficient technique to solve structures of molecules . Take a recent event for example, after the outbreak of COVID-19 in January, the first structure of 2019-nCoV Spike trimer was published in Marchusing cryo-EM, which has provided crucial medical insight for developing vaccines.
Revised: With the enhancement of algorithms, cryo-EM has become the most efficient technique to solve structures of molecules in solution, which has been recently demonstrated by the determination of COVID-19 in January, the first structure of 2019-nCoV Spike trimer was published in Marchusing cryo-EM, which has provided crucial medical insight for developing vaccines.
Edit intent: meaning-changed
Original:  Take a recent event for example, after the outbreak of COVID-19 in January, the first structure of 2019-nCoV Spike trimer was published in Marchusing cryo-EM, which has provided crucial medical insight for developing vaccines. The enabler behind this efficiency is the GPU-accelerated computation which shortens the whole analysis process to 12 days. However, the data characteristics include strong noise, huge dimension, large sample size and high heterogeneity with unknown orientations have made analysis very challenging. Though, the popular GPU-accelerated Bayesian approach has been shown to be successful in 3D refinement. It is noted that the traditional method based on multireference alignment may better differentiate subtle structure differences under low signal to noise ratio (SNR).
Revised:  Take a recent event for example, after the outbreak of COVID-19 spike protein in March, shortly after its breakout in late January 2020. This rapidity is critical for vaccine development in response to emerging pandemic. This explains why a 2D classification approach based on multi-reference alignment (MRA) is not as popular as the Bayesian-based approach despite that the former has advantage in differentiating subtle structural variations under low signal-to-noise ratio (SNR).
Edit intent: meaning-changed
Original:  In this work, a modular GPU-accelerated alignment library called Cryo-RALib is proposed. The library contains both reference-free alignment and multireference alignment that can be widely used to accelerate state-of-the-art classification algorithms.
Revised:  In this work, a modular GPU-accelerated alignment library called Cryo-RALib that contains GPU-accelerated modular routines for accelerating MRA-based classification algorithms.
Edit intent: meaning-changed
Original:  In addition, we connect the cryo-EM image analysis with the python data science stack which enables users to perform data analysis , visualization and inference more easily. Benchmark on the TaiWan Computing Cloud container, our implementation can accelerate the computation by one order of magnitude.
Revised:  In addition, we connect the cryo-EM image analysis with the python data science stack which enables users to perform data analysis and visualization. Benchmarking on the TaiWan Computing Cloud container, our implementation can accelerate the computation by one order of magnitude.
Edit intent: coherence
Original:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Revised:  This paper proposes a novel motion planning approach using the well-known Rapidly Exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Edit intent: clarity
Original:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Revised:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm that enforces both CBF and the robot Kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Edit intent: clarity
Original:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Revised:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path . The proposed algorithm also outputs the corresponding control signals that resulted in the obstacle-free path. The approach also allows considering model uncertainties by incorporating the robust CBF constraints into the proposed framework. Thus, the resulting path is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Edit intent: meaning-changed
Original:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Revised:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles and accounts for the model uncertainty from robot dynamics as well as perception.
Edit intent: coherence
Original:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics as well as perception.
Revised:  This paper proposes a novel motion planning approach using Rapidly exploring Random Trees (RRT) algorithm to enforce the robust CBF and kinodynamic constraints to generate a safety-critical path that is free of any obstacles while taking into account the model uncertainty from robot dynamics and perception.
Edit intent: coherence
Original:  We present numerical validation of the algorithm on the Hamster V7 robot car, a micro autonomous Unmanned Ground Vehicle , where it performs dynamic navigation on an obstacle-ridden path with various uncertainties in perception noises , and robot dynamics.
Revised:  We present numerical validation of the algorithm on the Hamster V7 robot car, a micro autonomous Unmanned Ground Vehicle that performs dynamic navigation on an obstacle-ridden path with various uncertainties in perception noises , and robot dynamics.
Edit intent: clarity
Original:  We present numerical validation of the algorithm on the Hamster V7 robot car, a micro autonomous Unmanned Ground Vehicle , where it performs dynamic navigation on an obstacle-ridden path with various uncertainties in perception noises , and robot dynamics.
Revised:  We present numerical validation of the algorithm on the Hamster V7 robot car, a micro autonomous Unmanned Ground Vehicle , where it performs dynamic navigation on an obstacle-ridden path with various uncertainties in perception noises and robot dynamics.
Edit intent: fluency
Original:  Many approaches have been explored to improve the performance of thismodel especially in low resource languages where the amount of parallel data is not sufficient to train an acceptable backward model . Among such works are the use of self-learning and the iterative back-translation. These methods were shown to perform better than the standard back-translation.
Revised:  Despite this, only the forward model is improved on the monolingual target data in standard back-translation.
Edit intent: coherence
Original:  This work presents the iterative self-training approach as an improvement over the self-learning approach to further enhance the performance of the backward model.
Revised:  A previous study proposed an iterative back-translation approach for improving both models over several iterations. But unlike in the traditional back-translation, it relied on both the target and source monolingual data. This work, therefore, proposes a novel approach that enables both the backward and forward models to benefit from the monolingual target data through a hybrid of self-learning approach to further enhance the performance of the backward model.
Edit intent: meaning-changed
Original:  This work presents the iterative self-training approach as an improvement over the self-learning approach to further enhance the performance of the backward model. Over several iterations, the synthetic datagenerated by the backward model is used to improve its performance through forward translation.
Revised:  This work presents the iterative self-training approach as an improvement over the self-learning and back-translation respectively. Experimental results have shown the synthetic datagenerated by the backward model is used to improve its performance through forward translation.
Edit intent: clarity
Original:  Over several iterations, the synthetic datagenerated by the backward model is used to improve its performance through forward translation. Experiments have shown that the method outperforms both the standard back-translation and self-learning approach on IWSLT'14 English German low resource NMT. While the method also outperforms the iterative back-translation , though slightly, the number of models required to be trained is reduced exactly by the number of iterations .
Revised:  Over several iterations, the superiority of the proposed approach over the traditional back-translation and self-learning approach on IWSLT'14 English German low resource NMT. While the method also outperforms the iterative back-translation , though slightly, the number of models required to be trained is reduced exactly by the number of iterations .
Edit intent: clarity
Original:  Experiments have shown that the method outperforms both the standard back-translation and self-learning approach on IWSLT'14 English German low resource NMT. While the method also outperforms the iterative back-translation , though slightly, the number of models required to be trained is reduced exactly by the number of iterations .
Revised:  Experiments have shown that the method outperforms both the standard back-translation method on English-German low resource neural machine translation. We also proposed an iterative self-learning approach that outperforms the iterative back-translation , though slightly, the number of models required to be trained is reduced exactly by the number of iterations .
Edit intent: clarity
Original:  Experiments have shown that the method outperforms both the standard back-translation and self-learning approach on IWSLT'14 English German low resource NMT. While the method also outperforms the iterative back-translation , though slightly, the number of models required to be trained is reduced exactly by the number of iterations .
Revised:  Experiments have shown that the method outperforms both the standard back-translation and self-learning approach on IWSLT'14 English German low resource NMT. While the method also outperforms the iterative back-translation while also relying only on the monolingual target data and require the training of less models .
Edit intent: meaning-changed
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they {\em unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em {\em .
Edit intent: fluency
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating , piece-wisely, generalized logistic functions: they {\em unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em {\em .
Edit intent: coherence
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, from generalized logistic functions: they {\em unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em {\em .
Edit intent: coherence
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they ensure{\em unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em {\em .
Edit intent: coherence
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they {\em exact unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em {\em .
Edit intent: fluency
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they {\em (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms; moreover they unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em {\em .
Edit intent: meaning-changed
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they {\em unveil a useful feature, that in fact , at least with very strict approximation, is also owned by the (numerical) solutions of the exact equations {\em {\em .
Edit intent: meaning-changed
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they {\em unveil a useful feature, that in fact is also owned by the (numerical) solutions of the {\em {\em .
Edit intent: clarity
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they {\em unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em exact {\em .
Edit intent: fluency
Original:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely,  generalized logistic functions: they {\em   unveil a useful feature, that in fact  is also owned by the (numerical) solutions of the exact equations {\em  {\em   .
Revised:  In the present paper , those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, namely , piece-wisely, generalized logistic functions: they {\em unveil a useful feature, that in fact is also owned by the (numerical) solutions of the exact equations {\em equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations; the easy and practical formulation of the final approximate solutions; the mentioned useful feature, never disclosed before. The work's method and result prove to be robust over a range of values of the well known non-dimensional parameter called{\em .
Edit intent: meaning-changed