wanyu/IteraTeR_full_sent huggingface dataset:
Original:  It automatically extracts useful meta-paths for each node from all possible meta-paths (within a length limit determined by the model depth ), which brings good model interpretability.
Revised:  It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each node from all possible meta-paths (within a length limit determined by the model depth ), which brings good model interpretability.
Edit intent: meaning-changed
Original:  Thus, it is much more efficient than previous methods. We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability.
Revised:  We provide theoretical analysis about the proposed ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability.
Edit intent: meaning-changed
Original:  We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability.
Revised:  We formally prove ie-HGCN in terms of evaluating the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability.
Edit intent: clarity
Original:  We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability.
Revised:  We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths , its connection to the spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability.
Edit intent: meaning-changed
Original:  We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability.
Revised:  We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and its quasi-linear scalability.
Edit intent: coherence
Original:  We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear scalability. Extensive experimental results on three real-world networks demonstrate the superiority of ie-HGCN over  state-of-the-art methods.
Revised:  We formally prove ie-HGCN evaluates the usefulness of all possible meta-paths within a length limit (model depth), show it intrinsically performs spectral graph convolution on HINs, and analyze the time complexity to verify its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over state-of-the-art methods.
Edit intent: clarity
Original:  The approach further helps us to analyze the original model equations. We show that the original model equations provide a very good fit with the United Kingdom data for the cumulative number of infections .
Revised:  The model can also be used to forecast further progression of the disease. In an effort to find optimized parameter values compatible with the United Kingdom coronavirus data, we first determine the relative importance of the various transition rates participating in the original model. Using this we show that the original model equations provide a very good fit with the United Kingdom data for the cumulative number of infections .
Edit intent: meaning-changed
Original:  We show that the original model equations provide a very good fit with the United Kingdom data for the cumulative number of infections . The active infected population of the model is seen to exhibit a turning point around mid-May, suggesting the beginning of a slow-down in the spread of infections.
Revised:  We show that the original model equations provide a very good fit with the United Kingdom data for the cumulative number of infections and the daily new cases. The fact that the model calculated daily new cases exhibits a turning point around mid-May, suggesting the beginning of a slow-down in the spread of infections.
Edit intent: meaning-changed
Original:  However,  the rate of slowing down beyond the turning point is small and therefore the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around early or mid July, provided the lock-down conditions continue to prevail .
Revised:  However, since the rate of slowing down beyond the turning point is small and therefore the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around early or mid July, provided the lock-down conditions continue to prevail .
Edit intent: coherence
Original:  However,  the rate of slowing down beyond the turning point is small and therefore the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around early or mid July, provided the lock-down conditions continue to prevail .
Revised:  However, the rate of slowing down beyond the turning point is small , the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around early or mid July, provided the lock-down conditions continue to prevail .
Edit intent: coherence
Original:  However,  the rate of slowing down beyond the turning point is small and therefore the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around early or mid July, provided the lock-down conditions continue to prevail .
Revised:  However, the rate of slowing down beyond the turning point is small and therefore the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around late July, provided the lock-down conditions continue to prevail .
Edit intent: meaning-changed
Original:  However,  the rate of slowing down beyond the turning point is small and therefore the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around early or mid July, provided the lock-down conditions continue to prevail . Noting that the fits obtained from the reduced logistic equation and the full model equations are equally good. The model and the procedure adopted here are expected to be useful in fitting the data for other countries and forecasting the progression of the disease .
Revised:  However, the rate of slowing down beyond the turning point is small and therefore the cumulative number of infections is likely to saturate to about 3.52 \times 10^5 around early or mid July, provided the lock-down conditions continue to prevail .
Edit intent: coherence
Original: Many key variablesin finance, economics and risk management, including financial returns and foreign exchange rates , exhibit nonlinear dependence, heterogeneity and heavy-tailedness of some usually largely unknown type. The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness may make problematic the analysis of (non-)efficiency , volatility clustering and predictive regressions in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions (ACFs) of returns and their squares.
Revised: Many key variablesin finance, economics and risk management, including financial returns and foreign exchange rates , exhibit nonlinear dependence, heterogeneity and heavy-tailedness . These properties may make problematic the analysis of (non-)efficiency , volatility clustering and predictive regressions in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions (ACFs) of returns and their squares.
Edit intent: clarity
Original:  The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness may make problematic the analysis of (non-)efficiency , volatility clustering and predictive regressions in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions (ACFs) of returns and their squares.
Revised:  The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness may make problematic the analysis of (non-)efficiency and volatility clustering in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions (ACFs) of returns and their squares.
Edit intent: clarity
Original:  The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness may make problematic the analysis of (non-)efficiency , volatility clustering and predictive regressions in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions (ACFs) of returns and their squares.
Revised:  The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness may make problematic the analysis of (non-)efficiency , volatility clustering and predictive regressions in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions of returns and their squares.
Edit intent: clarity
Original:  The paper provides asymptotic theory for sample analogues of the above measures in the case of general time series, including GARCH-type processes. It further develops new approaches to robust inference on them in the case of general  GARCH-type processes exhibiting heavy-tailedness properties .
Revised:  We further provide new approaches to robust inference on them in the case of general GARCH-type processes exhibiting heavy-tailedness properties .
Edit intent: clarity
Original:  The approaches are based on robust inference methods exploiting conservativeness properties of t-statistics Ibragimov and Muller (2010,2016) and several new results on their applicability in the settings considered .
Revised:  The approaches are based on robust inference methods exploiting conservativeness properties of t-statistics Ibragimov and Muller (2010,2016) and several new results on their applicability are presented .
Edit intent: clarity
Original: This paper describes and develops a fast and accurate  algorithm that computes the field of values boundary curve for every conceivable complex  square matrix A , i. e., for all matrices, those with or without repeated eigenvalues and with or without Jordan block structures, with ill-conditioned eigenvalues or ill-conditioned ones and so forth.
Revised: This paper describes and develops a fast and accurate path following algorithm that computes the field of values boundary curve for every conceivable complex square matrix A , i. e., for all matrices, those with or without repeated eigenvalues and with or without Jordan block structures, with ill-conditioned eigenvalues or ill-conditioned ones and so forth.
Edit intent: meaning-changed
Original: This paper describes and develops a fast and accurate  algorithm that computes the field of values boundary curve for every conceivable complex  square matrix A , i. e., for all matrices, those with or without repeated eigenvalues and with or without Jordan block structures, with ill-conditioned eigenvalues or ill-conditioned ones and so forth.
Revised: This paper describes and develops a fast and accurate algorithm that computes the field of values boundary curve for every conceivable complex or real square matrix A , i. e., for all matrices, those with or without repeated eigenvalues and with or without Jordan block structures, with ill-conditioned eigenvalues or ill-conditioned ones and so forth.
Edit intent: meaning-changed
Original: This paper describes and develops a fast and accurate  algorithm that computes the field of values boundary curve for every conceivable complex  square matrix A , i. e., for all matrices, those with or without repeated eigenvalues and with or without Jordan block structures, with ill-conditioned eigenvalues or ill-conditioned ones and so forth.
Revised: This paper describes and develops a fast and accurate algorithm that computes the field of values boundary curve for every conceivable complex square matrix A .
Edit intent: clarity
Original:  It relies on a matrix flow decomposition method that finds a  block-diagonal flow representation for the  hermitean matrix flow H\!K {\cal  _A(t) = \cos(t) H + \sin(t) K if this is possible.
Revised:  It relies on a matrix flow decomposition method that finds a proper block-diagonal flow representation for the hermitean matrix flow H\!K {\cal _A(t) = \cos(t) H + \sin(t) K if this is possible.
Edit intent: meaning-changed
Original:  It relies on a matrix flow decomposition method that finds a  block-diagonal flow representation for the  hermitean matrix flow H\!K {\cal  _A(t) = \cos(t) H + \sin(t) K if this is possible.
Revised:  It relies on a matrix flow decomposition method that finds a block-diagonal flow representation for the associated hermitean matrix flow H\!K {\cal _A(t) = \cos(t) H + \sin(t) K if this is possible.
Edit intent: meaning-changed
Original:  It relies on a matrix flow decomposition method that finds a  block-diagonal flow representation for the  hermitean matrix flow H\!K {\cal  _A(t) = \cos(t) H + \sin(t) K if this is possible.
Revised:  It relies on a matrix flow decomposition method that finds a block-diagonal flow representation for the hermitean matrix flow {\cal _A(t) = \cos(t) H + \sin(t) K if this is possible.
Edit intent: coherence
Original:  It relies on a matrix flow decomposition method that finds a  block-diagonal flow representation for the  hermitean matrix flow H\!K {\cal  _A(t) = \cos(t) H + \sin(t) K if this is possible.
Revised:  It relies on a matrix flow decomposition method that finds a block-diagonal flow representation for the hermitean matrix flow H\!K {\cal F _A(t) = \cos(t) H + \sin(t) K if this is possible.
Edit intent: meaning-changed
Original:  It relies on a matrix flow decomposition method that finds a  block-diagonal flow representation for the  hermitean matrix flow H\!K {\cal  _A(t) = \cos(t) H + \sin(t) K if this is possible. Here H\!K{\cal  _A(t) is a 1-parameter varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.
Revised:  It relies on a matrix flow decomposition method that finds a block-diagonal flow representation for the hermitean matrix flow H\!K {\cal _A(t) = \cos(t) H + \sin(t) K . Here{\cal _A(t) is a 1-parameter varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.
Edit intent: clarity
Original:  Here H\!K{\cal  _A(t) is a 1-parameter varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.
Revised:  Here H\!K{\cal F _A(t) is a 1-parameter varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.
Edit intent: meaning-changed
Original:  Here H\!K{\cal  _A(t) is a 1-parameter varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.
Revised:  Here H\!K{\cal _A(t) is a 1-parameter-varying linear combination of the real and skew part matrices H = (A+A^*)/2 and K = (A-A^*)/(2i) of A.
Edit intent: fluency
Original:  For decomposing flows H\!K {\cal  _A(t), the algorithm decomposes the given dense general matrix A unitarily into  U^*AU = \text { diag} (A_j) with  diagonal blocks A_j that conform in size with those of H\!K_A .
Revised:  For decomposing flows {\cal _A(t), the algorithm decomposes the given dense general matrix A unitarily into U^*AU = \text { diag} (A_j) with diagonal blocks A_j that conform in size with those of H\!K_A .
Edit intent: meaning-changed
Original:  For decomposing flows H\!K {\cal  _A(t), the algorithm decomposes the given dense general matrix A unitarily into  U^*AU = \text { diag} (A_j) with  diagonal blocks A_j that conform in size with those of H\!K_A .
Revised:  For decomposing flows H\!K {\cal F _A(t), the algorithm decomposes the given dense general matrix A unitarily into U^*AU = \text { diag} (A_j) with diagonal blocks A_j that conform in size with those of H\!K_A .
Edit intent: meaning-changed
Original:  For decomposing flows H\!K {\cal  _A(t), the algorithm decomposes the given dense general matrix A unitarily into  U^*AU = \text { diag} (A_j) with  diagonal blocks A_j that conform in size with those of H\!K_A .
Revised:  For decomposing flows H\!K {\cal _A(t), the algorithm decomposes a given dense general matrix A unitarily into U^*AU = \text { diag} (A_j) with diagonal blocks A_j that conform in size with those of H\!K_A .
Edit intent: fluency
Original:  For decomposing flows H\!K {\cal  _A(t), the algorithm decomposes the given dense general matrix A unitarily into  U^*AU = \text { diag} (A_j) with  diagonal blocks A_j that conform in size with those of H\!K_A .
Revised:  For decomposing flows H\!K {\cal _A(t), the algorithm decomposes the given dense general matrix A unitarily into block-diagonal form U^*AU = \text { diag} (A_j) with diagonal blocks A_j that conform in size with those of H\!K_A .
Edit intent: meaning-changed
Original:  For decomposing flows H\!K {\cal  _A(t), the algorithm decomposes the given dense general matrix A unitarily into  U^*AU = \text { diag} (A_j) with  diagonal blocks A_j that conform in size with those of H\!K_A .
Revised:  For decomposing flows H\!K {\cal _A(t), the algorithm decomposes the given dense general matrix A unitarily into U^*AU = \text { diag} (A_j) with j > 1 diagonal blocks A_j that conform in size with those of H\!K_A .
Edit intent: meaning-changed
Original:  For decomposing flows H\!K {\cal  _A(t), the algorithm decomposes the given dense general matrix A unitarily into  U^*AU = \text { diag} (A_j) with  diagonal blocks A_j that conform in size with those of H\!K_A .
Revised:  For decomposing flows H\!K {\cal _A(t), the algorithm decomposes the given dense general matrix A unitarily into U^*AU = \text { diag} (A_j) with diagonal blocks A_j whose individual sizes add up to the size of A .
Edit intent: clarity
Original:  The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices A due to possible eigencurve crossings of H\!K {\cal  _A(t).
Revised:  The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices A due to possible eigencurve crossings of H\!K {\cal F _A(t).
Edit intent: meaning-changed
Original:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal  _A(t_k) for every chosen t_k \in {[} 0,2\pi{]}  .
Revised:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's Francis QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal _A(t_k) for every chosen t_k \in {[} 0,2\pi{]} .
Edit intent: fluency
Original:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal  _A(t_k) for every chosen t_k \in {[} 0,2\pi{]}  .
Revised:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bendixon rectangle based method that computes complete eigenanalyses of H\!K {\cal _A(t_k) for every chosen t_k \in {[} 0,2\pi{]} .
Edit intent: fluency
Original:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal  _A(t_k) for every chosen t_k \in {[} 0,2\pi{]}  .
Revised:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of {\cal _A(t_k) for every chosen t_k \in {[} 0,2\pi{]} .
Edit intent: coherence
Original:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal  _A(t_k) for every chosen t_k \in {[} 0,2\pi{]}  .
Revised:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal F _A(t_k) for every chosen t_k \in {[} 0,2\pi{]} .
Edit intent: clarity
Original:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal  _A(t_k) for every chosen t_k \in {[} 0,2\pi{]}  .
Revised:  Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and very fast when compared with Johnson's global QR eigenvalue and Bedixon rectangle based method that computes complete eigenanalyses of H\!K {\cal _A(t_k) for every chosen t_k \in {[} 0,2\pi{]} more slowly .
Edit intent: meaning-changed
Original: We recall that if A is an invertible and symmetric real m\times m matrix, then it is diagonalisable. Therefore, if we denote by \mathcal{E^{+}(A)\subset R^m (respectively E^{-}(A)\subset R^m) to be the vector subspace generated by eigenvectors with positive eigenvalues of A (correspondingly the vector subspace generated by eigenvectors with negative eigenvalues of A), then we have an orthogonal decomposition R^m=E^{+}(A)\oplus E^{-}(A).
Revised: We ^{+}(A)\subset R^m (respectively E^{-}(A)\subset R^m) to be the vector subspace generated by eigenvectors with positive eigenvalues of A (correspondingly the vector subspace generated by eigenvectors with negative eigenvalues of A), then we have an orthogonal decomposition R^m=E^{+}(A)\oplus E^{-}(A).
Edit intent: coherence
Original:  Let \Delta = \{\delta _0,\delta _1,\delta _2,\ldots \} be a countable set of real numbers which has at least m+1 elements.
Revised:  The update rule for the simplest version is x_{n+1 = \{\delta _0,\delta _1,\delta _2,\ldots \} be a countable set of real numbers which has at least m+1 elements.
Edit intent: meaning-changed