wanyu/IteraTeR_v2 huggingface dataset:
Original:  Efficient  solutions use the shift-invariance property of Krylov subspaces .
Revised:  Efficient iterative solutions use the shift-invariance property of Krylov subspaces .
Edit intent: clarity
Original:  Efficient  solutions use the shift-invariance property of Krylov subspaces .
Revised:  Efficient solutions use the shift-invariance property of Krylov subspaces 
Edit intent: fluency
Original:  The Hermitian Lanczos method reduces a given vector and matrix to a Jacobi matrix ( a real symmetric tridiagonal matrix with positive super and sub-diagonal entries) and approximates the quadratic form with the Jacobi matrix.
Revised:  The Hermitian Lanczos method reduces a given vector and matrix to a Jacobi matrix ( real symmetric tridiagonal matrix with positive super and sub-diagonal entries) and approximates the quadratic form with the Jacobi matrix.
Edit intent: fluency
Original:  The Hermitian Lanczos method reduces a given vector and matrix to a Jacobi matrix ( a real symmetric tridiagonal matrix with positive super and sub-diagonal entries) and approximates the quadratic form with the Jacobi matrix.
Revised:  The Hermitian Lanczos method reduces a given vector and matrix to a Jacobi matrix ( a real symmetric tridiagonal matrix with positive super and sub-diagonal entries) and approximates the quadratic form using the Jacobi matrix.
Edit intent: fluency
Original:  This study develops a shifted Lanczos method that deals directly with the Hermitian matrix resolvent to extend the scope of problems that the Lanczos method can solve .
Revised:  This study develops a shifted Lanczos method that deals directly with the Hermitian matrix resolvent .
Edit intent: clarity
Original:  We show the moment-matching property of the shifted Lanczos method and give a sufficient condition such that the method does not break down  . Numerical experiments on matrices drawn from real-world applications compare the proposed method with previous methods and show that the proposed method outperforms a well-established method in solving some problems.
Revised:  We show the moment-matching property of the shifted Lanczos method and give a sufficient condition such that the method does not break down . Numerical experiments on matrices drawn from real-world applications compare the proposed method with previous methods and show that the proposed method outperforms well-established method in solving some problems.
Edit intent: fluency
Original:  We show the moment-matching property of the shifted Lanczos method and give a sufficient condition such that the method does not break down  . Numerical experiments on matrices drawn from real-world applications compare the proposed method with previous methods and show that the proposed method outperforms a well-established method in solving some problems.
Revised:  We show the moment-matching property of the shifted Lanczos method and give a sufficient condition such that the method does not break down . Numerical experiments on matrices drawn from real-world applications compare the proposed method with previous methods and show that the proposed method outperforms a well-established methods in solving some problems.
Edit intent: fluency
Original: We give a local search based algorithm for k-median ( k-means ) clustering from the perspective of individual fairness.
Revised: We give a local search based algorithm for k-median and k-means ) clustering from the perspective of individual fairness.
Edit intent: fluency
Original:  In this work, we show how to get an approximately optimal such fair k-clustering .
Revised:  In this work, we show how to get an approximately optimal such fair k-clustering :
Edit intent: fluency
Original:  We take the softmax layer from the style classifier as style embedding and then apply this style embedding extraction model to generate soft style labels for our unlabelled internal TTS dataset .
Revised:  We take the softmax layer from the style classifier as style embedding and then apply this style embedding extraction model to create style labels for our unlabelled internal TTS dataset .
Edit intent: clarity
Original:  We then show that an implicit representation for the PDAWG can be built in O(n \log (|\Pi| + |\Sigma|)) time and O(n) space from left to right.
Edit intent: coherence
Original:  This makes the obtained neighborhoods  more reliable in the sense that connectivity also depends on the orientation of the point set.
Revised:  This makes the obtained neighborhoods to be more reliable in the sense that connectivity also depends on the orientation of the point set.
Edit intent: clarity
Original:  For example, these neighborhoods grow on a comparably flat part of the geometry and do not include points on a nearby surface patch with differently oriented normals.
Edit intent: coherence
Original:  We utilize a sigmoid to define a neighborhood weighting scheme based on the normal variation.
Revised:  We utilize a sigmoid to define the weights based on the normal variation.
Edit intent: clarity
Original:  For its evaluation , we turn to a Shannon entropy model for feature separation  . Based on this model, we apply our weight terms to a large scale of clean and to several real world models.
Revised:  For an evaluation of the weighting scheme , we turn to a Shannon entropy model for feature separation . Based on this model, we apply our weight terms to a large scale of clean and to several real world models.
Edit intent: clarity
Original:  For its evaluation , we turn to a Shannon entropy model for feature separation  . Based on this model, we apply our weight terms to a large scale of clean and to several real world models.
Revised:  For its evaluation , we turn to a Shannon entropy model for feature separation . Based on this model, we evaluate our weighting terms on a large scale of clean and to several real world models.
Edit intent: clarity
Original:  For its evaluation , we turn to a Shannon entropy model for feature separation  . Based on this model, we apply our weight terms to a large scale of clean and to several real world models.
Revised:  For its evaluation , we turn to a Shannon entropy model for feature separation . Based on this model, we apply our weight terms to a large scale of both clean and real-world models.
Edit intent: clarity
Original:  Our weighting takes the shape of the geometry, i.e.  the normal information, into account.
Revised:  Our weighting takes the shape of the geometry, i.e. , the normal information, into account.
Edit intent: fluency
Original:  For an evaluation of the weighting scheme, we turn to a Shannon entropy model for feature separation and rigorously prove its non-degeneracy for our family of weights.
Revised:  For an evaluation of the weighting scheme, we turn to a Shannon entropy model for feature classification that can be proven to be non-degenerate for our family of weights.
Edit intent: clarity
Original:  This is in contrast to current general practice in the field of geometry processing .
Revised:  Finally, we highlight the applicability of our weighting scheme withing the application context of denoising .
Edit intent: clarity
Original: In this work, a flexible , fully space-time adaptive finite element approximation of a prototype multi-physics system coupling fluid flow and convection-dominated transport  is developed and studied.
Revised: In this work, a flexible , fully space-time adaptive finite element approximation of convection-dominated transport is developed and studied.
Edit intent: clarity
Original:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization  which facilitates the simultaneous adjustment of the time and space mesh  .
Revised:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization of the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization which facilitates the simultaneous adjustment of the time and space mesh .
Edit intent: fluency
Original:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization  which facilitates the simultaneous adjustment of the time and space mesh  .
Revised:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture . The error estimate allows the separation of effects of temporal and spatial discretization which facilitates the simultaneous adjustment of the time and space mesh .
Edit intent: coherence
Original:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization  which facilitates the simultaneous adjustment of the time and space mesh  .
Revised:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of the temporal and spatial discretization which facilitates the simultaneous adjustment of the time and space mesh .
Edit intent: clarity
Original:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization  which facilitates the simultaneous adjustment of the time and space mesh  .
Revised:  Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization error contributions which facilitates the simultaneous adjustment of the time and space mesh .
Edit intent: fluency
Original:  To date, the range of reference values for cardiovascular and metabolic risk factors is therefore incomplete.
Edit intent: coherence
Original:  The approach requires no manual intervention or ground truth segmentations  for training.
Revised:  The approach requires no manual intervention or ground truth segmentations are required for training.
Edit intent: clarity
Original:   The standardized framework achieved a close fit to the target values (median R^2 > 0.97) in 7-fold cross-validation with the ResNet50 .
Revised:  Results: The standardized framework achieved a close fit to the target values (median R^2 > 0.97) in 7-fold cross-validation with the ResNet50 .
Edit intent: fluency
Original:   The standardized framework achieved a close fit to the target values (median R^2 > 0.97) in 7-fold cross-validation with the ResNet50 .
Revised:  The standardized framework achieved a close fit to the target values (median R^2 > 0.97) .
Edit intent: coherence
Original:  Interpretation of aggregated saliency maps suggests that the network correctly targets specific body regions and limbs, and learned to emulate different modalities.
Revised:  Interpretation of aggregated saliency maps indicates that the network correctly targets specific body regions and limbs, and learned to emulate different modalities.
Edit intent: fluency
Original:  Methods: The UK Biobank study has successfully imaged more than 32,000 volunteer participants with neck-to-knee body MRI . Each scan is linked to extensive metadata, providing a comprehensive  survey of imaged anatomy and related health states.
Revised:  Methods: The UK Biobank study has successfully imaged more than 32,000 volunteer participants with magnetic resonance imaging (MRI) . Each scan is linked to extensive metadata, providing a comprehensive survey of imaged anatomy and related health states.
Edit intent: clarity
Original:  No manual intervention or ground truth segmentations are required for training.
Revised:  No manual intervention or direct access to reference segmentations for training.
Edit intent: clarity
Original:  Results: The standardized framework achieved a close fit to the target values (median R^2 > 0.97)  . Interpretation of aggregated saliency maps indicates that the network correctly targets specific body regions and limbs, and learned to emulate different modalities.
Revised:  Results: The standardized framework achieved a close fit to the target values (median R^2 > 0.97) . Interpretation of aggregated saliency maps suggests that the network correctly targets specific body regions and limbs, and learned to emulate different modalities.
Edit intent: clarity
Original:  We show how such a stabbing set can be computed for n convex polygons of constant size in the plane  in O((p-q+1)n^{4/3}\log^{ 2  + \epsilon%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (n ) + p^2\log(p) ) expected time.
Revised:  We show how such a stabbing set can be computed for a family of convex polygons in the plane in O((p-q+1)n^{4/3}\log^{ 2 + \epsilon%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (n ) + p^2\log(p) ) expected time.
Edit intent: clarity
Original:  The first is a blocked version of column pivoted Householder QR, organized as a `` left-looking '' method to minimize the number of write operations (which are more expensive than read operations on a spinning disk drive).
Revised:  The first is a blocked version of column pivoted Householder QR, organized as a " left-looking '' method to minimize the number of write operations (which are more expensive than read operations on a spinning disk drive).
Edit intent: fluency
Original:  The first is a blocked version of column pivoted Householder QR, organized as a `` left-looking '' method to minimize the number of write operations (which are more expensive than read operations on a spinning disk drive).
Revised:  The first is a blocked version of column pivoted Householder QR, organized as a `` left-looking " method to minimize the number of write operations (which are more expensive than read operations on a spinning disk drive).
Edit intent: fluency
Original:  Specifically, after a certain limit, an increase of N has a very small effect on h, which contradicts a rational expectation.
Edit intent: coherence
Original:  The best correlation , for 100 citations, is not linear, and numerous data points deviate from the general trend.
Revised:  The best correlation is for the 100 citations, is not linear, and numerous data points deviate from the general trend.
Edit intent: fluency
Original:  The best correlation , for 100 citations, is not linear, and numerous data points deviate from the general trend.
Revised:  The best correlation , for 100 threshold but numerous data points deviate from the general trend.
Edit intent: clarity
Original:  In contrast with the h index, the total number of citations in the series shows a high linear correlation with the number of papers exceeding the thresholds of 10 and 50 citations . Dividing by N, the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations.
Revised:  In contrast with the h index, the total number of citations shows a high linear correlation with the number of papers exceeding the thresholds of 10 and 50 citations . Dividing by N, the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations.
Edit intent: clarity
Original:  In contrast with the h index, the total number of citations in the series shows a high linear correlation with the number of papers exceeding the thresholds of 10 and 50 citations . Dividing by N, the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations.
Revised:  In contrast with the h index, the total number of citations in the series shows a high correlation with the number of papers exceeding the thresholds of 10 and 50 citations . Dividing by N, the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations.
Edit intent: clarity
Original:  In contrast with the h index, the total number of citations in the series shows a high linear correlation with the number of papers exceeding the thresholds of 10 and 50 citations . Dividing by N, the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations.
Revised:  In contrast with the h index, the total number of citations in the series shows a high linear correlation with the number of papers exceeding the thresholds of 10 and 50 citations ; the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations.
Edit intent: coherence
Original:  The dependence is never linear, but for the thresholds of 20 and 30 citations, the deviation from linearity is low.
Edit intent: coherence
Original:  Most notably, we can accelerate the inference by 46X on Criteo dataset and 27X on Avazu dataset without  loss on the prediction accuracy.
Revised:  Most notably, we can accelerate the inference by 46X on Criteo dataset and 27X on Avazu dataset without any loss on the prediction accuracy.
Edit intent: clarity
Original:  In addition, the deep model acceleration makes an efficient model ensemble possible with low latency and significant gains on the performance .
Revised:  This paves the way for successfully deploying complicated embedding-based neural networks in production for ad serving .
Edit intent: clarity
Original: An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large networks .
Revised: An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs .
Edit intent: clarity
Original:  Empirical evaluation demonstrates its competitiveness in terms of  accuracy with state-of-the-art methods  for link prediction and network reconstruction .
Revised:  Empirical evaluation demonstrates competitiveness in terms of accuracy with state-of-the-art methods for link prediction and network reconstruction .
Edit intent: clarity
Original:  Most of the available GAN based methods use the combination of the adversarial and the pixel-wise losses (like L1 or L2 ) as the objective function for training.
Revised:  Most of the available GAN based methods use the combination of the adversarial and the pixel-wise losses (like L_1 or L_2 ) as the objective function for training.
Edit intent: fluency
Original:  The code is available at : URL
Revised:  The code is available at URL
Edit intent: fluency
Original: Background: Alternative to epidemiological models for transmission dynamics of Covid-19 in China, we propose the artificial intelligence (AI)-inspired methods for real-time forecasting of Covid-19 across China to estimate the size, lengths and ending time of Covid-19 across China.
Revised: BACKGROUND An alternative to epidemiological models for transmission dynamics of Covid-19 in China, we propose the artificial intelligence (AI)-inspired methods for real-time forecasting of Covid-19 across China to estimate the size, lengths and ending time of Covid-19 across China.
Edit intent: clarity
Original: Background: Alternative to epidemiological models for transmission dynamics of Covid-19 in China, we propose the artificial intelligence (AI)-inspired methods for real-time forecasting of Covid-19 across China to estimate the size, lengths and ending time of Covid-19 across China.
Revised: Background: Alternative to epidemiological models for transmission dynamics of Covid-19 in China, we propose the artificial intelligence (AI)-inspired methods for real-time forecasting of Covid-19 to estimate the size, lengths and ending time of Covid-19 across China.
Edit intent: fluency
Original:  Method: We developed modified stacked auto-encoder for modeling the transmission dynamics of the epidemics.
Revised:  METHODS We developed a modified stacked auto-encoder for modeling the transmission dynamics of the epidemics.
Edit intent: clarity
Original:  We applied it to real-time forecasting the lab confirmed cases of Covid-19 across China.
Revised:  We applied this model to real-time forecasting the lab confirmed cases of Covid-19 across China.
Edit intent: clarity
Original:  We applied it to real-time forecasting the lab confirmed cases of Covid-19 across China.
Revised:  We applied it to real-time forecasting the confirmed cases of Covid-19 across China.
Edit intent: clarity
Original:  Results: We forecasted curves of cumulative confirmed cases of Covid-19 across China from January 20, 2020 to April 30 , 2020.
Revised:  RESULTS We forecasted curves of cumulative confirmed cases of Covid-19 across China from January 20, 2020 to April 30 , 2020.
Edit intent: fluency
Original:  Results: We forecasted curves of cumulative confirmed cases of Covid-19 across China from January 20, 2020 to April 30 , 2020.
Revised:  Results: We forecasted curves of cumulative confirmed cases of Covid-19 across China from Jan 20, 2020 to April 30 , 2020.
Edit intent: fluency
Original:  Results: We forecasted curves of cumulative confirmed cases of Covid-19 across China from January 20, 2020 to April 30 , 2020.
Revised:  Results: We forecasted curves of cumulative confirmed cases of Covid-19 across China from January 20, 2020 to April 20 , 2020.
Edit intent: clarity
Original:  We used the multiple-step forecasting to estimate that the accuracies of one-step, 2-step, 3-step, 4-step and 5-step forecasting were -0.48\%, 0.18\%, 0.46\%, 0.22\%and 1.55 \%, respectively.
Revised:  Using the multiple-step forecasting to estimate that the accuracies of one-step, 2-step, 3-step, 4-step and 5-step forecasting were -0.48\%, 0.18\%, 0.46\%, 0.22\%and 1.55 \%, respectively.
Edit intent: coherence
Original:  We grouped 34 provinces/cities  into 9 clusters.
Revised:  The 34 provinces/cities into 9 clusters.
Edit intent: clarity
Original:  We grouped 34 provinces/cities  into 9 clusters.
Revised:  We grouped 34 provinces/cities were grouped into 9 clusters.
Edit intent: clarity
Original:  Conclusions: The accuracy of the AI-based methods for forecasting the trajectory of Covid-19 was high.
Revised:  CONCLUSIONS The accuracy of the AI-based methods for forecasting the trajectory of Covid-19 was high.
Edit intent: fluency
Original:  If the data are reliable and there are no second transmission , we can accurately forecast the transmission dynamics of the Covid-19 across the provinces/cities in China.
Revised:  If the data are reliable and there are no second transmissions , we can accurately forecast the transmission dynamics of the Covid-19 across the provinces/cities in China.
Edit intent: fluency
Original: The St. Petersburg Paradox was proposed before two centuries .
Revised: The St. Petersburg Paradox was proposed two centuries ago .
Edit intent: clarity
Original:  In the paper we proposed a new pricing theory with several rules to solve the paradox and state that the fair pricing should be judged by buyer and seller independently.
Revised:  In the paper , we propose a new pricing theory with several rules to solve the paradox and state that the fair pricing should be judged by buyer and seller independently.
Edit intent: fluency