wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We discover that the atom radius of Ca2+ in conventional force fields is too large for the QM calculation to capture the variation in  coordination geometry of Ca2+ in its ionic form and lead to unphysical charges.
Revised:  We discover that the atom radius of Ca2+ in conventional force fields is too large for the QM calculation to capture the variation in the coordination geometry of Ca2+ in its ionic form and lead to unphysical charges.
Edit intent: fluency
Original:  We discover that the atom radius of Ca2+ in conventional force fields is too large for the QM calculation to capture the variation in  coordination geometry of Ca2+ in its ionic form and lead to unphysical charges.
Revised:  We discover that the atom radius of Ca2+ in conventional force fields is too large for the QM calculation to capture the variation in coordination geometry of Ca2+ in its ionic form , leading to unphysical charges.
Edit intent: coherence
Original: In this paper , we establish an exact expression of the sin\Theta angle for the singular subspace perturbation. This expression clearly characterizes the linear dependence of the sin\Theta angle on the perturbation matrix.
Revised: In this paper , we establish an exact expression of the sin\Theta angles between the perturbed and the original singular subspaces. This formula is expressed in terms of the perturbation matrix and therefore characterizes how the singular vector perturbation is induced by the additive noise. We then use this formula to derive a one-sided version of the sin\Theta angle on the perturbation matrix.
Edit intent: meaning-changed
Original:  This expression clearly characterizes the linear dependence of the sin\Theta angle on the perturbation matrix. It serves as a tool that allows us to study a set of related problems in a more systematical way.In particular, we derive a useful perturbation bound for the Principal Component Analysis , which seems to be missing in the literature.
Revised:  This expression clearly characterizes the linear dependence of the sin\Theta theorem, as well as improve the bound on the \ell_{2,\infty Principal Component Analysis , which seems to be missing in the literature.
Edit intent: meaning-changed
Original:  We derive the perturbation bound for the singular value thresholding operator applied to full-rank matrices. We derive an improved \ell_{2\rightarrow \infty bound on singular vectors, which matches the best-known results for eigenvectors derived under more restricted conditions.
Revised:  We derive the perturbation bound for the singular value thresholding operator \rightarrow \infty bound on singular vectors, which matches the best-known results for eigenvectors derived under more restricted conditions.
Edit intent: meaning-changed
Original: Singular vector perturbation is an important topic in numerical analysis and statistics. The main goal of this paperis to provide a useful tool to tackle matrix perturbation problems. Explicitly , we establish a useful formula for the sin\Theta angles between the perturbed and the original singular subspaces.
Revised: In this paper , we establish a useful formula for the sin\Theta angles between the perturbed and the original singular subspaces.
Edit intent: clarity
Original:  This formula is expressed in terms of the perturbation matrix and therefore characterizes how the singular vector perturbation is induced by the additive noise. We then use thisformula to derive a one-sided version of the sin\Theta theorem, as well as improve the bound on the 2,\infty norm of the singular vector perturbation error.
Revised:  These formulae explicitly show that how the perturbation of the original matrix propagates into singular vectors and singular subspaces, thus providing a direct way of analyzing them. Following this, we derive a collection of new results on SVD perturbation related problems, including a tighter bound on the 2,\infty norm of the singular vector perturbation error.
Edit intent: meaning-changed
Original:  We then use thisformula to derive a one-sided version of the sin\Theta theorem, as well as improve the bound on the 2,\infty norm of the singular vector perturbation error. Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and the stability of the singular value thresholding operator ) can be solved with the help of these new results .
Revised:  We then use thisformula to derive a one-sided version of the sin\Theta theorem, as well as improve the bound on the 2,\infty norm of the singular vector perturbation errors under Gaussian noise, a new stability analysis of the Principal Component Analysis and the stability of the singular value thresholding operator ) can be solved with the help of these new results .
Edit intent: meaning-changed
Original:  Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and the stability of the singular value thresholding operator ) can be solved with the help of these new results .
Revised:  Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and an error bound on the singular value thresholding operator ) can be solved with the help of these new results .
Edit intent: meaning-changed
Original:  Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and the stability of the singular value thresholding operator ) can be solved with the help of these new results .
Revised:  Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and the stability of the singular value thresholding operator . For the latter two, we consider the most general rectangular matrices with full matrix rank .
Edit intent: meaning-changed
Original:  The time-fractional partial differential equation appears in several diffusion problems used in physics and engineering applications . Using some of these ideas we numerical compute solutions of the fractional Black-Scholes formula that is used as a model for valuing call and put options on a paying stock. Time-fractional Black-Scholes models subdiffusive and superdiffusive behavior of the prices at the stock market  .
Revised:  The time-fractional partial differential equation appears in several diffusion problems used in physics and engineering applications , and models subdiffusive and superdiffusive behavior of the prices at the stock market .
Edit intent: coherence
Original:  Time-fractional Black-Scholes models subdiffusive and superdiffusive behavior of the prices at the stock market  .
Revised:  Time-fractional Black-Scholes models subdiffusive and superdiffusive behavior of the prices at the stock market . This work shows the flexibility of the radial basis function scheme to solve multidimensional problems with several types of nodes and it also shows how to reduce the condition number of the matrices involved .
Edit intent: meaning-changed
Original: We introduce a randomized algorithm, namely %DIFDELCMD < {\tt %%% rchol , to construct an approximate Cholesky factorization for a given sparse Laplacian matrix (a.k.a., graph Laplacian).
Revised: We introduce a randomized algorithm, namely %DIFDELCMD < {\tt %%% RCHOL , to construct an approximate Cholesky factorization for a given sparse Laplacian matrix (a.k.a., graph Laplacian).
Edit intent: fluency
Original: We introduce a randomized algorithm, namely %DIFDELCMD < {\tt %%% rchol , to construct an approximate Cholesky factorization for a given sparse Laplacian matrix (a.k.a., graph Laplacian).
Revised: We introduce a randomized algorithm, namely %DIFDELCMD < {\tt %%% rchol , to construct an approximate Cholesky factorization for a given Laplacian matrix (a.k.a., graph Laplacian).
Edit intent: meaning-changed
Original:  For example, our parallel code scaled up to 64 threads on a single node for solving the 3D Poisson equation, discretized with the 7-point stencil on a 1024\times 1024 \times 1024 grid, or \textbf{one billion unknowns.
Revised:  For example, our parallel code scaled up to 64 threads on a single node for solving the 3D Poisson equation, discretized with the 7-point stencil on a 1024\times 1024 \times 1024 grid, or \textbf{one billion unknowns.
Edit intent: fluency
Original:  Numerical experiments demonstrated the robustness and the scalability of RCHOL. For example, our parallel code scaled up to 64 threads on a single node for solving the 3D Poisson equation, discretized with the 7-point stencil on a 1024\times 1024 \times 1024 grid, or one billion unknowns.
Revised:  We report numerical experiments that demonstrate the robustness and the scalability of RCHOL. For example, our parallel code scaled up to 64 threads on a single node for solving the 3D Poisson equation, discretized with the 7-point stencil on a 1024\times 1024 \times 1024 grid, or one billion unknowns.
Edit intent: clarity
Original:  Numerical experiments demonstrated the robustness and the scalability of RCHOL. For example, our parallel code scaled up to 64 threads on a single node for solving the 3D Poisson equation, discretized with the 7-point stencil on a 1024\times 1024 \times 1024 grid, or one billion unknowns.
Revised:  Numerical experiments demonstrated the robustness and the scalability of RCHOL. For example, our parallel code scaled up to 64 threads on a single node for solving the 3D Poisson equation, discretized with the 7-point stencil on a 1024\times 1024 \times 1024 grid, a problem that has one billion unknowns.
Edit intent: clarity
Original:  When using a spatial and vertical temporal discretisation that preserve the skew-symmetric structure of the non-canonical Hamiltonian form of the equations of motion , this scheme allows for the exact balance of all energetic exchanges in space and time.
Revised:  The new HEVI scheme is implemented in conjunction with a mixed mimetic spectral element spatial discretisation and semi-implicit vertical time stepping scheme that both preserve the skew-symmetric structure of the non-canonical Hamiltonian form of the equations of motion , this scheme allows for the exact balance of all energetic exchanges in space and time.
Edit intent: meaning-changed
Original:  When using a spatial and vertical temporal discretisation that preserve the skew-symmetric structure of the non-canonical Hamiltonian form of the equations of motion , this scheme allows for the exact balance of all energetic exchanges in space and time.
Revised:  When using a spatial and vertical temporal discretisation that preserve the skew-symmetric structure of the non-canonical Hamiltonian form of the equations of motion . Within this context the new HEVI scheme allows for the exact balance of all energetic exchanges in space and time.
Edit intent: meaning-changed
Original:  For the non-hydrostatic test case, the vertical upwinding of the potential temperature diagnostic equation is shown to reduce spurious oscillations without altering the energetics of the solution, since this upwinding is performed in an energetically consistent manner  .
Revised:  For the nonhydrostatic test case, the vertical upwinding of the potential temperature diagnostic equation is shown to reduce spurious oscillations without altering the energetics of the solution, since this upwinding is performed in an energetically consistent manner .
Edit intent: fluency
Original:  For the non-hydrostatic test case, the vertical upwinding of the potential temperature diagnostic equation is shown to reduce spurious oscillations without altering the energetics of the solution, since this upwinding is performed in an energetically consistent manner  .
Revised:  For the non-hydrostatic test case, the vertical upwinding of the potential temperature diagnostic equation is shown to reduce spurious oscillations without altering the energetics of the solution, since this upwinding is performed in an energetically consistent manner . For this test case, which is configured on an affine geometry, the exact balance of energy exchanges allows the model to run stably without any form of dissipation .
Edit intent: meaning-changed
Original:  The throughput in terms of processing training samples has been boosted by the use of the IPU in conjunction with grouped convolutions by a factor \sim 3.5 for training of the classifier and a factor of \sim 7 for the regression network.
Revised:  The throughput in terms of processing training samples has been boosted by the use of the IPU in conjunction with grouped convolutions by a factor ~ 3.5 for training of the classifier and a factor of \sim 7 for the regression network.
Edit intent: clarity
Original:  The throughput in terms of processing training samples has been boosted by the use of the IPU in conjunction with grouped convolutions by a factor \sim 3.5 for training of the classifier and a factor of \sim 7 for the regression network.
Revised:  The throughput in terms of processing training samples has been boosted by the use of the IPU in conjunction with grouped convolutions by a factor \sim 3.5 for training of the classifier and a factor of ~ 7 for the regression network.
Edit intent: clarity
Original:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling  and syntactic generalization tests, while using fewer parameters then other models.
Revised:  The model explicitly models the structure with an incremental parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling and syntactic generalization tests, while using fewer parameters then other models.
Edit intent: meaning-changed
Original:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling  and syntactic generalization tests, while using fewer parameters then other models.
Revised:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of a standard language model . Experiments show that SOM can achieve strong results in language modeling and syntactic generalization tests, while using fewer parameters then other models.
Edit intent: fluency
Original:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling  and syntactic generalization tests, while using fewer parameters then other models.
Revised:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model (left-to-right). To train the incremental parser and avoid exposure bias, we also propose a novel dynamic oracle, so that SOM is more robust to wrong parsing decisions. Experiments show that SOM can achieve strong results in language modeling and syntactic generalization tests, while using fewer parameters then other models.
Edit intent: meaning-changed
Original:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling  and syntactic generalization tests, while using fewer parameters then other models.
Revised:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling , incremental parsing and syntactic generalization tests, while using fewer parameters then other models.
Edit intent: meaning-changed
Original:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling  and syntactic generalization tests, while using fewer parameters then other models.
Revised:  The model explicitly models the structure with a one-step look-ahead parser and maintains the conditional probability setting of the standard language model . Experiments show that SOM can achieve strong results in language modeling and syntactic generalization tests, while using fewer parameters than other models.
Edit intent: fluency
Original:  Remarkably, in the bi-stale phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to an irreversible loop dynamics that may cause the loss of the species with shorter dispersal range.
Revised:  Remarkably, in the bi-stable phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to an irreversible loop dynamics that may cause the loss of the species with shorter dispersal range.
Edit intent: fluency
Original:  Remarkably, in the bi-stale phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to an irreversible loop dynamics that may cause the loss of the species with shorter dispersal range.
Revised:  Remarkably, in the bi-stale phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to a half loop dynamics associated to a cusp catastrophe, which causes the irreversible loss of the species with shorter dispersal range.
Edit intent: meaning-changed
Original:  Remarkably, in the bi-stale phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to an irreversible loop dynamics that may cause the loss of the species with shorter dispersal range.
Revised:  Remarkably, in the bi-stale phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to an irreversible loop dynamics that may cause the loss of the species with the shortest dispersal range.
Edit intent: clarity
Original:  Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability g \leq \le 1.
Revised:  Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability g \le 1.
Edit intent: clarity
Original:  While the well-known efficient market hypothesis rules out any possibility of accurate prediction of stock prices, there are formal propositions in the literature demonstrating accurate modeling of the predictive systems  can enable us to predict stock prices with a very high level of accuracy.
Revised:  While the well-known efficient market hypothesis rules out any possibility of accurate prediction of stock prices, there are formal propositions in the literature demonstrating accurate modeling of the predictive systems that can enable us to predict stock prices with a very high level of accuracy.
Edit intent: fluency
Original:  Using these extremely granular stock price data, we build four convolutional neural network (CNN) and five long- and short-term memory (LSTM)-based deep learning models for accurate forecasting of  future stock prices.
Revised:  Using these extremely granular stock price data, we build four convolutional neural network (CNN) and five long- and short-term memory (LSTM)-based deep learning models for accurate forecasting of the future stock prices.
Edit intent: fluency
Original: We design an algorithm for computing connectivity in hypergraphs which runs in time \hat O_r(p + \min\{\lambda  n^2, n^r/\lambda  \}) (the \hat O_r(\cdot) hides the terms subpolynomial in the main parameter and terms that depend only on r) where p is the size, n is the number of vertices, and r is the rank of the hypergraph.
Revised: We design an algorithm for computing connectivity in hypergraphs which runs in time \hat O_r(p + \min\{\lambda ^{\frac{r-3 n^2, n^r/\lambda \}) (the \hat O_r(\cdot) hides the terms subpolynomial in the main parameter and terms that depend only on r) where p is the size, n is the number of vertices, and r is the rank of the hypergraph.
Edit intent: meaning-changed
Original: We design an algorithm for computing connectivity in hypergraphs which runs in time \hat O_r(p + \min\{\lambda  n^2, n^r/\lambda  \}) (the \hat O_r(\cdot) hides the terms subpolynomial in the main parameter and terms that depend only on r) where p is the size, n is the number of vertices, and r is the rank of the hypergraph.
Revised: We design an algorithm for computing connectivity in hypergraphs which runs in time \hat O_r(p + \min\{\lambda n^2, n^r/\lambda ^{r/(r-1) \}) (the \hat O_r(\cdot) hides the terms subpolynomial in the main parameter and terms that depend only on r) where p is the size, n is the number of vertices, and r is the rank of the hypergraph.
Edit intent: meaning-changed
Original:  Our algorithm is faster than existing algorithms when the  connectivity \lambda is \Omega(n^{(r-2)/2 . At the heart of our algorithm is a structural result regarding min-cuts in simple hypergraphs.
Revised:  Our algorithm is faster than existing algorithms when the the rank is constant and the connectivity \lambda is \Omega(n^{(r-2)/2 . At the heart of our algorithm is a structural result regarding min-cuts in simple hypergraphs.
Edit intent: meaning-changed
Original:  Our algorithm is faster than existing algorithms when the  connectivity \lambda is \Omega(n^{(r-2)/2 . At the heart of our algorithm is a structural result regarding min-cuts in simple hypergraphs.
Revised:  Our algorithm is faster than existing algorithms when the connectivity \lambda is \omega(1) . At the heart of our algorithm is a structural result regarding min-cuts in simple hypergraphs.
Edit intent: meaning-changed
Original:  First, we design a short pilot study with few clusters for testing whether base-line interventions are welfare-maximizing, with its rejection motivating larger-scale experimentation .
Revised:  First, we design a short pilot study with few clusters to test whether there exists a welfare-improving treatment configuration and hence worth learning by conducting a larger scale experiment. We propose a practical test that uses information on the marginal effect of the policy on welfare to compare the base-line interventions are welfare-maximizing, with its rejection motivating larger-scale experimentation .
Edit intent: meaning-changed
Original:  In this document , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Revised:  In this paper , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Edit intent: clarity