wanyu/IteraTeR_v2 huggingface dataset:
Original:  We demonstrate the (theoretical) applicability by deriving some theorems on the characterization n-tier architectures.
Revised:  We demonstrate the applicability of our concepts to theory by deriving theorems on the characterization n-tier architectures.
Edit intent: clarity
Original:  We demonstrate the (theoretical) applicability by deriving some theorems on the characterization n-tier architectures.
Revised:  We demonstrate the (theoretical) applicability by deriving some theorems on the classification of certain types of architectures.
Edit intent: clarity
Original:  We then illustrate the difference between the resulting distributions numerically, using Laplace approximations and dimension-robust MCMC to estimate the unknown velocity field and uncertainty associated with the estimates.
Revised:  We then illustrate the difference between the resulting distributions numerically, using Laplace approximations to estimate the unknown velocity field and uncertainty associated with the estimates.
Edit intent: clarity
Original: The graph matching problem aims to find the latent vertex correspondence between two edge-correlated graphs and has many practical applications .
Revised: Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has many practical applications .
Edit intent: clarity
Original: The graph matching problem aims to find the latent vertex correspondence between two edge-correlated graphs and has many practical applications .
Revised: The graph matching problem aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields .
Edit intent: clarity
Original:  In this work , we study a version of the seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance.
Revised:  In this paper , we study a version of the seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance.
Edit intent: clarity
Original:  In this work , we study a version of the seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance.
Revised:  In this work , we study a seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance.
Edit intent: clarity
Original:   Specifically, consider two correlated graphs whose edges are sampled independently with probability s from a parent \ER graph G(n,p).
Revised:  Specifically, consider two correlated graphs whose edges are sampled independently from a parent \ER graph G(n,p).
Edit intent: clarity
Original:  Furthermore, a mapping between the vertices of the two graphs is provided as seeds, of which an unknown \beta fraction is correct.
Revised:  A mapping between the vertices of the two graphs is provided as seeds, of which an unknown \beta fraction is correct.
Edit intent: coherence
Original:  This problem was first studied in \mbox{ lubars2018correcting0pt where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% \frac{8{3}p,
Revised:  0pt where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% \frac{8{3}p,
Edit intent: coherence
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},45\log{n}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% %DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},45\log{n}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Edit intent: coherence
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},45\log{n}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% {n(1-p)^2s^2}},45\log{n}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Edit intent: coherence
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},45\log{n}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},45\log{n}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% /{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Edit intent: coherence
Original:  In order to improve the matching performance for sparse graphs, we propose a new algorithm that uses "witnesses" in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{ \cite{lubars2018correcting}\hspace{0pt} .
Revised:  In order to improve the matching performance for sparse graphs, we propose a new algorithm that uses "witnesses" in the 2-hop neighborhood, instead of only 1-hop }\hspace{0pt} .
Edit intent: coherence
Original:  Thus, no effective NMR parameters or relaxation superoperators are used for the calculation ofcontinuous NMR spectra.
Revised:  Thus, no effective NMR parameters or relaxation superoperators are used for the calculation of NMR spectra.
Edit intent: clarity
Original:  While the findings are demonstrated for the hydrogen atom , it is  outlined that the approach can be applied to any molecular system for which the electronic structure can be calculated by using a common quantum chemical method.
Revised:  Furthermore , it is outlined that the approach can be applied to any molecular system for which the electronic structure can be calculated by using a common quantum chemical method.
Edit intent: coherence
Original:  While the findings are demonstrated for the hydrogen atom , it is  outlined that the approach can be applied to any molecular system for which the electronic structure can be calculated by using a common quantum chemical method.
Revised:  While the findings are demonstrated for the hydrogen atom , it is outlined that the presented method can be applied to any molecular system for which the electronic structure can be calculated by using a common quantum chemical method.
Edit intent: clarity
Original:  While the findings are demonstrated for the hydrogen atom , it is  outlined that the approach can be applied to any molecular system for which the electronic structure can be calculated by using a common quantum chemical method.
Revised:  While the findings are demonstrated for the hydrogen atom , it is outlined that the approach can be applied to any molecular system for which the electronic structure can be calculated using a common quantum chemical method.
Edit intent: fluency
Original:  Thus , the presented approach has potential for an improved NMR data analysis and more accurate predictions for hyperpolarized Magnetic Resonance Imaging .
Revised:  Therefore , the presented approach has potential for an improved NMR data analysis and more accurate predictions for hyperpolarized Magnetic Resonance Imaging .
Edit intent: fluency
Original: This work improves the concept of conventional NMR theory, in which the positions of the nuclei are limited to fixed points, to the case in which the nuclei can be continuously distributed in space.
Edit intent: coherence
Original:  Experimental NMR data contain highly detailed information about molecular structures which can be reconstructed only relatively roughly with today's NMR theories.
Revised:  Experimental NMR data contain very detailed information about molecular structures which can be reconstructed only relatively roughly with today's NMR theories.
Edit intent: clarity
Original:  Experimental NMR data contain highly detailed information about molecular structures which can be reconstructed only relatively roughly with today's NMR theories.
Revised:  Experimental NMR data contain highly detailed information about molecular structures that can often only be reconstructed relatively roughly with today's NMR theories.
Edit intent: clarity
Original:  Hence, a lot information on spatial distributions of nuclei remain hidden in experimental NMR data.
Revised:  Hence, a lot information on molecular structures remain hidden in experimental NMR data.
Edit intent: clarity
Original:  In this document it is shown how the continuous probability density for the spatial distribution of the nuclei can be investigated and reconstructed from NMR data.
Revised:  In this document it is shown how the continuous probability density for the spatial distribution of the nuclei can be reconstructed from NMR data.
Edit intent: clarity
Original:  This is because the effective spin model  idealizes nuclei as fixed point particles in a lattice L, while bond rotations, vibrations and proton exchange cause  delocalization of nuclei.
Revised:  This is because the effective spin model which idealizes nuclei as fixed point particles in a lattice L, while bond rotations, vibrations and proton exchange cause delocalization of nuclei.
Edit intent: coherence
Original:  This is because the effective spin model  idealizes nuclei as fixed point particles in a lattice L, while bond rotations, vibrations and proton exchange cause  delocalization of nuclei.
Revised:  This is because the effective spin model idealizes nuclei as fixed point particles in a lattice L, while bond rotations, vibrations and proton exchange cause a delocalization of nuclei.
Edit intent: fluency
Original:  Therefore, the presented method may be used to obtain a more detailed molecular structure from NMR data and hence replace the effective spin model which forms the basis for NMR theory since 1950.
Revised:  Therefore, the presented method may replace the effective spin model which forms the basis for NMR theory since 1950.
Edit intent: coherence
Original: We consider the problem of fitting a polynomial  to a set of data points, each data point consisting of a feature vector and a response variable.
Revised: We consider the problem of fitting a polynomial function to a set of data points, each data point consisting of a feature vector and a response variable.
Edit intent: clarity
Original:  In contrast to standard least-squares polynomial regression, we require that the polynomial regressor satisfy shape constraints, such as monotonicity with respect to a variable , Lipschitz-continuity, or convexity over a region.
Revised:  In contrast to standard polynomial regression, we require that the polynomial regressor satisfy shape constraints, such as monotonicity with respect to a variable , Lipschitz-continuity, or convexity over a region.
Edit intent: clarity
Original:  In contrast to standard least-squares polynomial regression, we require that the polynomial regressor satisfy shape constraints, such as monotonicity with respect to a variable , Lipschitz-continuity, or convexity over a region.
Revised:  In contrast to standard least-squares polynomial regression, we require that the polynomial regressor satisfy shape constraints, such as monotonicity , Lipschitz-continuity, or convexity over a region.
Edit intent: clarity
Original:  We further show that, under some assumptions on the generation of the data points, the regressors obtained are consistent estimators of the underlying shape-constrained function that maps the feature vectors to the responses.
Revised:  We then prove that, under some assumptions on the generation of the data points, the regressors obtained are consistent estimators of the underlying shape-constrained function that maps the feature vectors to the responses.
Edit intent: clarity
Original:  We further show that, under some assumptions on the generation of the data points, the regressors obtained are consistent estimators of the underlying shape-constrained function that maps the feature vectors to the responses.
Revised:  We further show that, under some assumptions on the generation of the data points, the regressor obtained is a consistent estimator of the underlying shape-constrained function that maps the feature vectors to the responses.
Edit intent: clarity
Original: We propose a Susceptible-Infected (SI) epidemic spreading model including containment measures.
Revised: We propose a tractable epidemic model that includes containment measures.
Edit intent: clarity
Original:  In  absence of containment measures the epidemics spreads exponentially fast for any value of the infectivity \lambda>0.
Revised:  In the absence of containment measures the epidemics spreads exponentially fast for any value of the infectivity \lambda>0.
Edit intent: fluency
Original:  We consider a wide range of temporal kernels for the effective infectivity and we investigate the effect of the considered containment measures.
Revised:  We consider a wide range of temporal kernels for effective infectivity and we investigate the effect of the considered containment measures.
Edit intent: fluency
Original:  We find that not all kernels are able to push the epidemic dynamics below the epidemic threshold, with some containment measures only able to reduce the rate of the exponential growth of new infected individuals.
Revised:  We find that not all kernels are able to push the epidemic dynamics below the epidemic threshold, with some containment measures only able to reduce the rate of the exponential growth of newly infected individuals.
Edit intent: fluency
Original:  We also propose a model with pandemic caused by a growing number of new separated foci.
Revised:  We also propose a pandemic model caused by a growing number of new separated foci.
Edit intent: fluency
Original:  We here present a  theoretical framework to gauge the effectiveness of a given coarse-grained description by measuring the model's information content.
Revised:  We here present a theoretical framework to gauge the effectiveness of a given simplified representation by measuring its information content.
Edit intent: clarity
Original:  Also, 6G will focus on Quality of Experience (QoE) to provide rich experiences from 6G technology.
Revised:  Also, it will focus on Quality of Experience (QoE) to provide rich experiences from 6G technology.
Edit intent: clarity
Original:  Yet 5G has to be experienced by people  and B5G has to be developed;
Revised:  Yet 5G has to be experienced by people worldwide and B5G has to be developed;
Edit intent: clarity
Original:  We have discussed issues and challenges from all aspects from hardware to the enabling technologies which will be utilized by 6G.
Revised:  We have discussed issues and challenges from every aspect from hardware to the enabling technologies which will be utilized by 6G.
Edit intent: fluency
Original:  These results are instrumental to calibrate the models on power and gas energy European markets and to price spread options written on different underlying assets using Monte Carlo and Fourier techniques.
Revised:  These results are instrumental to calibrate the models on power and gas energy European markets and to price spread options written on different underlying assets using simulations techniques.
Edit intent: clarity
Original: We develop a novel Multilevel Asymptotic-Preserving Monte Carlo ( ML-APMC)method for simulating the kinetic Boltzmann transport equation with  Bhatnagar-Gross-Krook (BGK) collision operator.
Revised: We develop a novel Multilevel Asymptotic-Preserving Monte Carlo ( ML-APMC)method for simulating the kinetic Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collision operator.
Edit intent: fluency
Original:  The main features of our method are a new and improved recipe for correlating particle trajectories with different time step sizes , and a new and more general level selection strategy  .
Revised:  The main features of our method are a new and improved recipe for correlating particle trajectories with different time step sizes . Furthermore, a new and more general level selection strategy .
Edit intent: coherence
Original:  We illustrate the efficiency of our ML-APMC method by applying it to a one-dimensional fusion test case with nonhomogeneous and anisotropic plasma background.
Revised:  We illustrate the efficiency of our ML-APMC method by applying it to a one-dimensional test case with nonhomogeneous and anisotropic plasma background.
Edit intent: clarity
Original:  Next , a back-end deep learning model classifies the spectrogram features into categories of respiratory disease or anomaly . Experiments are conducted over the ICBHI benchmark dataset of respiratory sounds .
Revised:  Next , a back-end deep learning network is used to classify the spectrogram features into categories of respiratory disease or anomaly . Experiments are conducted over the ICBHI benchmark dataset of respiratory sounds .
Edit intent: clarity
Original:  Next , a back-end deep learning model classifies the spectrogram features into categories of respiratory disease or anomaly . Experiments are conducted over the ICBHI benchmark dataset of respiratory sounds .
Revised:  Next , a back-end deep learning model classifies the spectrogram features into categories of respiratory anomaly cycles or diseases. Experiments, conducted over the ICBHI benchmark dataset of respiratory sounds .
Edit intent: clarity
Original:  According to obtained experimental results, we make three main contributions toward lung-sound analysis: Firstly, we provide an extensive analysis on common factors (type of spectrogram, time resolution, cycle length, or data augmentation , etc.) that affect final prediction accuracy in a deep learning based system.
Revised:  According to obtained experimental results, we make three main contributions towards respiratory-sound analysis. Firstly, we provide an extensive analysis on common factors (type of spectrogram, time resolution, cycle length, or data augmentation , etc.) that affect final prediction accuracy in a deep learning based system.
Edit intent: clarity
Original:  According to obtained experimental results, we make three main contributions toward lung-sound analysis: Firstly, we provide an extensive analysis on common factors (type of spectrogram, time resolution, cycle length, or data augmentation , etc.) that affect final prediction accuracy in a deep learning based system.
Revised:  According to obtained experimental results, we make three main contributions toward lung-sound analysis: Firstly, we carry out an extensive exploration of the effect of spectrogram type, spectral-time resolution, overlapped/non-overlapped windows, and data augmentation on final prediction accuracy in a deep learning based system.
Edit intent: clarity
Original:  Finally, we successfully to apply the Teacher-Student scheme to solve the trade-off between model performance and model size that helps to increase ability of building real-time applications.
Revised:  Finally, we apply a Teacher-Student scheme to solve the trade-off between model performance and model size that helps to increase ability of building real-time applications.
Edit intent: coherence
Original:  Finally, we successfully to apply the Teacher-Student scheme to solve the trade-off between model performance and model size that helps to increase ability of building real-time applications.
Revised:  Finally, we successfully to apply the Teacher-Student scheme to achieve a trade-off between model performance and model size that helps to increase ability of building real-time applications.
Edit intent: clarity
Original:  Finally, we successfully to apply the Teacher-Student scheme to solve the trade-off between model performance and model size that helps to increase ability of building real-time applications.
Revised:  Finally, we successfully to apply the Teacher-Student scheme to solve the trade-off between model performance and model complexity which additionally helps to increase ability of building real-time applications.
Edit intent: clarity
Original: Deep speaker embedding has demonstrated state-of-the-art performance in audio speaker recognition (SRE) . However, one potential issue with this approach is that the speaker vectors derived from deep embedding models tend to be non-Gaussian for each individual speaker, and non-homogeneous for distributions of different speakers.
Revised: Deep speaker embedding has demonstrated state-of-the-art performance in speaker recognition tasks . However, one potential issue with this approach is that the speaker vectors derived from deep embedding models tend to be non-Gaussian for each individual speaker, and non-homogeneous for distributions of different speakers.
Edit intent: clarity
Original:  These irregular distributions can seriously impact SRE performance, especially with the popular PLDA scoring method, which assumes homogeneous Gaussian distribution.
Revised:  These irregular distributions can seriously impact speaker recognition performance, especially with the popular PLDA scoring method, which assumes homogeneous Gaussian distribution.
Edit intent: clarity
Original:  However, in most current E2E models for SE, these properties are either not fully considered , or are too complex to be realized.
Revised:  However, in most current E2E models for SE, these properties are either not fully considered or are too complex to be realized.
Edit intent: fluency
Original:  approach that performs enhancement on the embedded features in the hidden layers instead of on the physical spectral features commonly used in speech separation tasks . Experimental results on speech denoising and compressed speech restoration tasks confirm that with the lightweight architecture of SRU and the feature-mapping-based RFM, WaveCRN performs comparably with other state-of-the-art approaches with notably reduced model complexity and inference time.
Revised:  approach that performs enhancement on the feature maps in the hidden layers instead of on the physical spectral features commonly used in speech separation tasks . Experimental results on speech denoising and compressed speech restoration tasks confirm that with the lightweight architecture of SRU and the feature-mapping-based RFM, WaveCRN performs comparably with other state-of-the-art approaches with notably reduced model complexity and inference time.
Edit intent: clarity
Original:  approach that performs enhancement on the embedded features in the hidden layers instead of on the physical spectral features commonly used in speech separation tasks . Experimental results on speech denoising and compressed speech restoration tasks confirm that with the lightweight architecture of SRU and the feature-mapping-based RFM, WaveCRN performs comparably with other state-of-the-art approaches with notably reduced model complexity and inference time.
Revised:  approach that performs enhancement on the embedded features in the hidden layers instead of on the physical spectral features commonly used in speech separation methods . Experimental results on speech denoising and compressed speech restoration tasks confirm that with the lightweight architecture of SRU and the feature-mapping-based RFM, WaveCRN performs comparably with other state-of-the-art approaches with notably reduced model complexity and inference time.
Edit intent: clarity