wanyu/IteraTeR_v2 huggingface dataset:
Original:  To this end we prove a new algebraic dichotomy about the lattice of locally closed clones over the domain { \mathbb{Q } that contain Aut(Q;<).
Revised:  To this end we prove a new algebraic dichotomy about the lattice of locally closed clones over the domain { \mathbb Q } that contain Aut(Q;<).
Edit intent: clarity
Original:  The adaptive immune system's humoral response creates plasma B cells and memory B cells, each with their own goals .
Revised:  The adaptive immune system's humoral response creates plasma B cells and memory B cells, each with their own immunological objectives .
Edit intent: clarity
Original:  We demonstrate how the model is instantiated as a Bayesian network to create a structural digital twin of an unmanned aerial vehicle .
Revised:  We demonstrate how the model is instantiated to enable a structural digital twin of an unmanned aerial vehicle .
Edit intent: clarity
Original:  The graphical model foundation ensures that the digital twin creation and updating process is principled, repeatable , and able to scale to the calibration of an entire fleet of digital twins.
Revised:  The graphical model foundation ensures that the digital twin calibration and updating process is principled, repeatable , and able to scale to the calibration of an entire fleet of digital twins.
Edit intent: clarity
Original:  The graphical model foundation ensures that the digital twin creation and updating process is principled, repeatable , and able to scale to the calibration of an entire fleet of digital twins.
Revised:  The graphical model foundation ensures that the digital twin creation and updating process is principled, unified , and able to scale to the calibration of an entire fleet of digital twins.
Edit intent: clarity
Original:  The graphical model foundation ensures that the digital twin creation and updating process is principled, repeatable , and able to scale to the calibration of an entire fleet of digital twins.
Revised:  The graphical model foundation ensures that the digital twin creation and updating process is principled, repeatable , and able to scale to an entire fleet of digital twins.
Edit intent: clarity
Original:  This approach also leads to a game-theoretic analysis, but in the correlated play that arises from  learning dynamics rather than factored equilibrium behavior .
Revised:  This approach also leads to a game-theoretic analysis, but in the correlated play that arises from learning dynamics rather than factored agent behavior at equilibrium .
Edit intent: clarity
Original:  We present a set of examples illustrating the distinct strengths and weaknesses of each type of equilibrium in the literature, and proving that none subsumes all others.
Revised:  We present a set of examples illustrating the distinct strengths and weaknesses of each type of equilibrium in the literature, and prove that no tractable concept subsumes all others.
Edit intent: clarity
Original:  A novel linear analysis on the extended DG model yields stability constraints on the finite subdomain grid size that get tighter for increasing values of the P\'eclet number.
Revised:  A novel linear analysis on the extended DG model yields unconditional stability with respect to the P\'eclet number.
Edit intent: clarity
Original:  The new algorithm is designed to improve computational efficiency, accuracy and robustness in numerical integration of high-dimensional problems.
Revised:  The new method is designed to improve computational efficiency, accuracy and robustness in numerical integration of high-dimensional problems.
Edit intent: clarity
Original:  In particular, it overcomes well-known computational challenges associated with dynamic tensor integration, including low-rank modeling errors and the need to invert the covariance matrix of the tensor cores at each time step.
Revised:  In particular, it overcomes well-known computational challenges associated with dynamic tensor integration, including low-rank modeling errors and the need to invert covariance matrices of tensor cores at each time step.
Edit intent: fluency
Original: A parallel cut-cell algorithm is described to solve the free boundary problem of the Grad-Shafranov equation.
Revised: A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad-Shafranov equation.
Edit intent: fluency
Original:  The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem  and a Cartesian grid embedded boundary method to handle the complex geometry.
Revised:  The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem , and a Cartesian grid embedded boundary method to handle the complex geometry.
Edit intent: fluency
Original:  Numerical results verify the the accuracy and efficiency of the free-boundary Grad-Shafranov solver.
Revised:  Numerical results verify the accuracy and efficiency of the free-boundary Grad-Shafranov solver.
Edit intent: fluency
Original: The accurate approximation of scalar-valued functions from sample points is a key task in mathematical modeling and computational science.
Revised: Accurate approximation of scalar-valued functions from sample points is a key task in mathematical modeling and computational science.
Edit intent: fluency
Original: The accurate approximation of scalar-valued functions from sample points is a key task in mathematical modeling and computational science.
Revised: The accurate approximation of scalar-valued functions from sample points is a key task in computational science.
Edit intent: clarity
Original:  This problem arises in many science and engineering problems, in particular those involving the solution of parametric Partial Differential Equations (PDEs).
Revised:  This arises in science and engineering problems, in particular those involving the solution of parametric Partial Differential Equations (PDEs).
Edit intent: clarity
Original:  This problem arises in many science and engineering problems, in particular those involving the solution of parametric Partial Differential Equations (PDEs).
Revised:  This problem arises in many science and engineering problems, in particular those involving solution of parametric Partial Differential Equations (PDEs).
Edit intent: fluency
Original:  Second, the domain of the function is usually high dimensional, and third, the range lies in a Hilbert space.
Revised:  Second, the domain of the function is usually high dimensional, and 3) the range lies in a Hilbert space.
Edit intent: coherence
Original:  This result introduces a DNN training procedure and a full theoretical analysis with explicit guarantees on the error and sample complexity.
Revised:  This result introduces a DNN training procedure and full theoretical analysis with explicit guarantees on the error and sample complexity.
Edit intent: fluency
Original:  This result introduces a DNN training procedure and a full theoretical analysis with explicit guarantees on the error and sample complexity.
Revised:  This result introduces a DNN training procedure and a full theoretical analysis with explicit guarantees on error and sample complexity.
Edit intent: fluency
Original:  This error bound is explicit in the three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Revised:  The error bound is explicit in the three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Edit intent: fluency
Original:  This error bound is explicit in the three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Revised:  This error bound is explicit in three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Edit intent: fluency
Original:  This error bound is explicit in the three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Revised:  This error bound is explicit in the three key errors occurring in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Edit intent: fluency
Original:  This error bound is explicit in the three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Revised:  This error bound is explicit in the three key errors occurred in the approximation procedure: the best approximation, measurement, and physical discretization error .
Edit intent: fluency
Original:  This error bound is explicit in the three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization error .
Revised:  This error bound is explicit in the three key errors occurred in the approximation procedure: best approximation error, measurementerror and physical discretization errors .
Edit intent: fluency
Original:   Second, we  provide preliminary numerical results illustrating the practical performance of DNNs on Hilbert-valued functions arising as solutions to parametric PDEs.
Revised:  Second, we provide preliminary numerical results illustrating practical performance of DNNs on Hilbert-valued functions arising as solutions to parametric PDEs.
Edit intent: fluency
Original:   Second, we  provide preliminary numerical results illustrating the practical performance of DNNs on Hilbert-valued functions arising as solutions to parametric PDEs.
Revised:  Second, we provide preliminary numerical results illustrating the practical performance of DNNs on parametric PDEs.
Edit intent: clarity
Original:  We consider different parameters, modify the DNN architecture to achieve better and competitive results and compare these to current best-in-class schemes.
Revised:  We consider different parameters, modifying the DNN architecture to achieve better and competitive results and compare these to current best-in-class schemes.
Edit intent: fluency
Original:  We consider different parameters, modify the DNN architecture to achieve better and competitive results and compare these to current best-in-class schemes.
Revised:  We consider different parameters, modify the DNN architecture to achieve better and competitive results , comparing these to current best-in-class schemes.
Edit intent: coherence
Original: This paper addresses writer identification and  retrieval which is  a challenging problem in the document analysis  field.
Revised: This paper addresses writer identification and retrieval which is considered as a challenging problem in the document analysis field.
Edit intent: clarity
Original:  In this work, a novel pipeline is proposed for the problem  by employing a unified neural network architecture consisting of the ResNet-20 as a feature extractor and an integrated NetVLAD layer, inspired by the vectors of locally aggregated descriptors (VLAD), in the head of the latter part.
Revised:  In this work, a novel pipeline is proposed for the problem at hand by employing a unified neural network architecture consisting of the ResNet-20 as a feature extractor and an integrated NetVLAD layer, inspired by the vectors of locally aggregated descriptors (VLAD), in the head of the latter part.
Edit intent: clarity
Original:  In this work, a novel pipeline is proposed for the problem  by employing a unified neural network architecture consisting of the ResNet-20 as a feature extractor and an integrated NetVLAD layer, inspired by the vectors of locally aggregated descriptors (VLAD), in the head of the latter part.
Revised:  In this work, a novel pipeline is proposed for the problem by employing a unified neural network architecture consisting of the ResNet-20 as a feature extractor and an integrated NetVLAD layer, inspired by the vector of locally aggregated descriptors (VLAD), in the head of the latter part.
Edit intent: fluency
Original:  Having defined this architecture,  triplet semi-hard loss function is used to directly learn an embedding for individual input image patches.
Revised:  Having defined this architecture, the triplet semi-hard loss function is used to directly learn an embedding for individual input image patches.
Edit intent: fluency
Original:  Generalised max-pooling is used for the aggregation of embedded descriptors of each handwritten image.
Revised:  Subsequently, generalized max-pooling is used for the aggregation of embedded descriptors of each handwritten image.
Edit intent: coherence
Original:  Generalised max-pooling is used for the aggregation of embedded descriptors of each handwritten image.
Revised:  Generalised max-pooling technique is employed for the aggregation of embedded descriptors of each handwritten image.
Edit intent: clarity
Original:  In the evaluation part, for identification and retrieval , re-ranking has been done based on query expansion and k-reciprocal nearest neighbours , and it is shown that the pipeline can benefit tremendously from this step.
Revised:  Also, a novel re-ranking strategy is introduced for the task of identification and retrieval , re-ranking has been done based on query expansion and k-reciprocal nearest neighbours , and it is shown that the pipeline can benefit tremendously from this step.
Edit intent: coherence
Original:  In the evaluation part, for identification and retrieval , re-ranking has been done based on query expansion and k-reciprocal nearest neighbours , and it is shown that the pipeline can benefit tremendously from this step.
Revised:  In the evaluation part, for identification and retrieval based on k-reciprocal nearest neighbours , and it is shown that the pipeline can benefit tremendously from this step.
Edit intent: coherence
Original:  In the evaluation part, for identification and retrieval , re-ranking has been done based on query expansion and k-reciprocal nearest neighbours , and it is shown that the pipeline can benefit tremendously from this step.
Revised:  In the evaluation part, for identification and retrieval , re-ranking has been done based on query expansion and k-reciprocal nearest neighbors , and it is shown that the pipeline can benefit tremendously from this step.
Edit intent: fluency
Original:  Experimental evaluation shows that our writer identification and writer retrieval pipeline is superior compared to the state-of-the-art pipelines, as our results on the publicly available ICDAR13 and CVL datasets set new standards by achieving 96.5\% and 98.4\% mAP, respectively .
Revised:  Experimental evaluation shows that our writer identification and writer retrieval pipeline achieves superior performance on the ICDAR 2013 and CVL datasets set new standards by achieving 96.5\% and 98.4\% mAP, respectively .
Edit intent: clarity
Original:  Experimental evaluation shows that our writer identification and writer retrieval pipeline is superior compared to the state-of-the-art pipelines, as our results on the publicly available ICDAR13 and CVL datasets set new standards by achieving 96.5\% and 98.4\% mAP, respectively .
Revised:  Experimental evaluation shows that our writer identification and writer retrieval pipeline is superior compared to the state-of-the-art pipelines, as our results on the publicly available ICDAR13 and CVL datasets in terms of mAP .
Edit intent: clarity
Original:  The experiments include evaluation of model quality, analysis of coverage of distinct topic categories, and the relation between coverage and other  topic model evaluation methods .
Revised:  The experiments include evaluation of model quality, analysis of coverage of distinct topic categories, and the analysis of the relationship between coverage and other topic model evaluation methods .
Edit intent: clarity
Original:  The experiments include evaluation of model quality, analysis of coverage of distinct topic categories, and the relation between coverage and other  topic model evaluation methods .
Revised:  The experiments include evaluation of model quality, analysis of coverage of distinct topic categories, and the relation between coverage and other methods of topic model evaluation methods .
Edit intent: clarity
Original:  The experiments include evaluation of model quality, analysis of coverage of distinct topic categories, and the relation between coverage and other  topic model evaluation methods .
Revised:  The experiments include evaluation of model quality, analysis of coverage of distinct topic categories, and the relation between coverage and other topic model evaluation .
Edit intent: clarity
Original:  The contributions of the paper include the measures of coverage and the recommendations for the use of topic models for topic discovery .
Revised:  The contributions of the paper include new measures of coverage and the recommendations for the use of topic models for topic discovery .
Edit intent: clarity
Original: Topic models are widely used unsupervised models of text capable of learning topics - weighted lists of words and documents - from large collections of text documents.
Revised: Topic models are widely used unsupervised models capable of learning topics - weighted lists of words and documents - from large collections of text documents.
Edit intent: clarity
Original:  The contributions of the paper include new measures of coverage,  insights into both topic models and other methods of model evaluation, and the datasets and code for facilitating future research of both topic coverageand other approaches to topic model evaluation .
Revised:  The contributions of the paper include new measures of coverage, insights into both topic models and different methods of model evaluation, and the datasets and code for facilitating future research of both topic coverageand other approaches to topic model evaluation .
Edit intent: clarity
Original:  The contributions of the paper include new measures of coverage,  insights into both topic models and other methods of model evaluation, and the datasets and code for facilitating future research of both topic coverageand other approaches to topic model evaluation .
Revised:  The contributions of the paper include new measures of coverage, insights into both topic models and other methods of model evaluation, and the datasets and code for facilitating future research on topic coverage .
Edit intent: clarity
Original:  As applications, we apply it to compute expection values determined by classical solutions of SDEs, with improved dependence on precision.
Revised:  As applications, we apply it to compute expectation values determined by classical solutions of SDEs, with improved dependence on precision.
Edit intent: fluency
Original:  In this point of view, we demonstrate to learning process of cellular automata(CA) that could satisfy locality,time-reversibility and the  holographic principle through CNNs. After choosing a rules that satisfy the above three conditions for cells , CNNs architecture that can learn rules were proposed and it was confirmed that accurate inferences were made for simple examples.
Revised:  In this point of view, we demonstrate to learning process of cellular automata(CA) that could satisfy locality,time-reversibility and the certain holographic principle through CNNs. After choosing a rules that satisfy the above three conditions for cells , CNNs architecture that can learn rules were proposed and it was confirmed that accurate inferences were made for simple examples.
Edit intent: coherence
Original:  However , just because the convoultion  expressed in covariant form is obtained , it is not obvious to implement the algorithm corresponding to that expression.
Revised:  However , just because the convoultion expressed in covariant form , it is not obvious to implement the algorithm corresponding to that expression.
Edit intent: clarity
Original:  Therefore, the already known mathematical expression of covariant CNNs can be implemented through feed-forward neural networks .
Revised:  Therefore, in the current situation, it would be best to simplify the problem to satisfy some physical requirements and then see if it is possible to learn with the corresponding neural-networks architecture .
Edit intent: coherence
Original:  In this point of view, we demonstrate to learning process of cellular automata(CA) that could satisfy locality,time-reversibility and the certain holographic principle through conventional CNNs.
Revised:  In this point of view, we demonstrate to learning process of cellular automata(CA) that could satisfy locality,time-reversibility through CNNs.
Edit intent: clarity
Original:  A pandemic crisis like the Covid-19 outbreak is a complex event, involving many aspects of the social lives on many temporal scales.
Revised:  A pandemic crisis like the Covid-19 outbreak is a complex event, involving numerous aspects of the social lives on many temporal scales.
Edit intent: fluency
Original:  A pandemic crisis like the Covid-19 outbreak is a complex event, involving many aspects of the social lives on many temporal scales.
Revised:  A pandemic crisis like the Covid-19 outbreak is a complex event, involving many aspects of the social life on multiple temporal scales.
Edit intent: fluency
Original:  Focusing on the Spanish Twittersphere, we characterize users activity behaviour across the different phases of the Covid-19 first wave.
Revised:  Focusing on the Spanish Twittersphere, we characterized users activity behaviour across the different phases of the Covid-19 first wave.
Edit intent: fluency
Original:  By performing stepwise segmented regression analysis and Bayesian switchpoint analysis on a sample of Spanish Twittersphere userstimeline, we observe that generic Spanish Twitter users and journalists experience an abrupt positive relative increment of their tweeting activity between March the 9th and the 14th , in coincidence with control measures being announced by regional and State level authorities.
Revised:  By performing stepwise segmented regression analysis and Bayesian switchpoint analysis on a sample of Spanish Twittersphere userstimeline, we observe that generic Spanish Twitter users and journalists experience an abrupt positive relative increment of their tweeting activity between March 9 and March 14 , in coincidence with control measures being announced by regional and State level authorities.
Edit intent: fluency
Original:   On the contrary, politicians follow a completely endogenous dynamic determined by institutional agenda  .
Revised:  On the contrary, politicians follow a completely endogenous dynamics determined by institutional agenda .
Edit intent: fluency
Original:  However, some five-year outcomes, such as glycosylated hemoglobin (A1C) , are over 40%DIFDELCMD < \\%%% %DIF < missing data.
Revised:  However, some five-year outcomes, such as glycosylated hemoglobin (A1C) %DIFDELCMD < \\%%% %DIF < missing data.
Edit intent: clarity
Original:  In particular , we extend the Hilbert-Schmidt dependence measure to  this context introducing a new bootstrap procedure in which we prove to be consistent.
Revised:  In particular , we extend the Hilbert-Schmidt dependence measure to this context introducing a new bootstrap procedure , for which we prove to be consistent.
Edit intent: coherence