wanyu/IteraTeR_v2 huggingface dataset:
Original:  The forward FaVeST which evaluates the Fourier coefficients has computational steps proportional to N\log N for N number of evaluation points.
Revised:  The forward FaVeST which evaluates the Fourier coefficients and has computational cost proportional to N\log N for N number of evaluation points.
Edit intent: clarity
Original:  The adjoint FaVeST which evaluates a linear combination of vector spherical harmonics with degree up to M for M evaluation points is proportional to M\logM.
Revised:  The adjoint FaVeST which evaluates a linear combination of vector spherical harmonics with degree up to M for M evaluation points has cost proportional to M\logM.
Edit intent: clarity
Original: Vector spherical harmonics on the unit sphere of R^3 have wide applications in geophysics, quantum mechanics and astrophysics.
Revised: Vector spherical harmonics on the unit sphere of R^3 have broad applications in geophysics, quantum mechanics and astrophysics.
Edit intent: clarity
Original:  The forward FaVeST evaluates the Fourier coefficients and has  computational cost proportional to N\log N for N number of evaluation points.
Revised:  The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to N\log N for N number of evaluation points.
Edit intent: fluency
Original:  The adjoint FaVeST which evaluates a linear combination of vector spherical harmonics with  degree up to M for M evaluation points has cost proportional to M\logM.
Revised:  The adjoint FaVeST which evaluates a linear combination of vector spherical harmonics with a degree up to M for M evaluation points has cost proportional to M\logM.
Edit intent: fluency
Original:  Numerical examples of simulated tangent fields illustrate the accuracy and efficiency of FaVeST.
Revised:  Numerical examples of simulated tangent fields illustrate the accuracy , efficiency and stability of FaVeST.
Edit intent: clarity
Original:  They typically offload input data to external computing systems (such as cloud servers) for further processing.
Revised:  They typically offload data to external computing systems (such as cloud servers) for further processing.
Edit intent: clarity
Original: Devices comprising the Internet of Things , such as sensors and small cameras, usually have small memories and limited computational power.
Revised: Resource-constrained IoT devices , such as sensors and small cameras, usually have small memories and limited computational power.
Edit intent: clarity
Original:  The proliferation of such resource-constrained devices in recent years  has led to the generation of large quantities of data .
Revised:  The proliferation of such resource-constrained devices in recent years . This has led to the generation of large quantities of data .
Edit intent: coherence
Original:  Deploying machine learning systems on such edge  devices alleviates the above issues by allowing computations to be performed close to the data sources.
Revised:  Deploying machine learning systems on such edge computing devices alleviates the above issues by allowing computations to be performed close to the data sources.
Edit intent: clarity
Original:  This survey describes major research efforts where machine learning has been deployed at the edge of computer networks  .
Revised:  This survey describes major research efforts where machine learning systems have been deployed at the edge of computer networks .
Edit intent: clarity
Original:  Here, we focus on community-structured SAT . Namely,  the set of variables consists of a number of disjoint communities, and clauses tend to consist of variables from the same community.
Revised:  Here, we focus mainly on the aspect of community structure . Namely, the set of variables consists of a number of disjoint communities, and clauses tend to consist of variables from the same community.
Edit intent: clarity
Original:  Here, we focus on community-structured SAT . Namely,  the set of variables consists of a number of disjoint communities, and clauses tend to consist of variables from the same community.
Revised:  Here, we focus on community-structured SAT . Namely, here the set of variables consists of a number of disjoint communities, and clauses tend to consist of variables from the same community.
Edit intent: coherence
Original:  In this paper, we endeavor to study the satisfiability threshold for  random industrial SAT.
Revised:  In this paper, we endeavor to study the satisfiability threshold for the proposed model of random industrial SAT.
Edit intent: clarity
Original:  Our main result is that the threshold of random community-structured SAT tends to be smaller than its counterpart for random SAT.
Revised:  Our main result is that the threshold in this model tends to be smaller than its counterpart for random SAT.
Edit intent: clarity
Original: In this technical report , we present the core calculi for two of the domain specific languages comprising the Aquarium kernel  synthesis project.
Revised: This technical report describes two of the domain specific languages comprising the Aquarium kernel synthesis project.
Edit intent: clarity
Original: In this technical report , we present the core calculi for two of the domain specific languages comprising the Aquarium kernel  synthesis project.
Revised: In this technical report , we present the core calculi for two of the domain specific languages used in the Aquarium kernel synthesis project.
Edit intent: clarity
Original: This technical report describes two of the domain specific languages used in the Aquarium kernel code synthesis project.
Revised: This technical report describes two of the domain-specific languages used in the Aquarium kernel code synthesis project.
Edit intent: fluency
Original:  Alewife is a specification language that can be used to write machine independent specifications for assembly-level instruction blocks.
Revised:  Alewife is a specification language that can be used to write machine-independent specifications for assembly-level instruction blocks.
Edit intent: fluency
Original:  The asymptotic approximation ratio, defined as the ratio of the period of a CH sequence to the lower bound N^2 when N \to \infty, is still 2.5 for the best known CH  in the literature.
Revised:  The asymptotic approximation ratio, defined as the ratio of the period of a CH sequence to the lower bound N^2 when N \to \infty, is still 2.5 for the best known CH sequence in the literature.
Edit intent: fluency
Original: PageRank is a greatly essential ranking algorithm in web information retrieval or search engine .
Revised: PageRank is a widespread model for analysing the relative relevance of nodes within large graphs arising in several applications .
Edit intent: clarity
Original:  In the current paper, we present a cost-effective Hessenberg-type method built upon the Hessenberg process for the computation of PageRank vector, which is better suited than the Arnoldi-type algorithm when the damping factor becomes high and especially the dimension of the search subspace is large.
Revised:  In the current paper, we present a cost-effective Hessenberg-type method built upon the Hessenberg process for the computation of PageRank vector, which is better suited than the Arnoldi-type methods, especially when the damping factor becomes high and especially the dimension of the search subspace is large.
Edit intent: clarity
Original:  In the current paper, we present a cost-effective Hessenberg-type method built upon the Hessenberg process for the computation of PageRank vector, which is better suited than the Arnoldi-type algorithm when the damping factor becomes high and especially the dimension of the search subspace is large.
Revised:  In the current paper, we present a cost-effective Hessenberg-type method built upon the Hessenberg process for the computation of PageRank vector, which is better suited than the Arnoldi-type algorithm when the damping factor is close to 1 and the dimension of the search subspace is large.
Edit intent: clarity
Original:  The convergence and  complexity of the proposed algorithm are also investigated.
Revised:  The convergence and the complexity of the proposed algorithm are also investigated.
Edit intent: fluency
Original:  The convergence and  complexity of the proposed algorithm are also investigated.
Revised:  The convergence and complexity of the proposed algorithm are investigated.
Edit intent: clarity
Original:  Numerical results are reported to show that the proposed method is efficient and faster than some existing related algorithms, in particular when the damping factor is large .
Revised:  Numerical experiments are reported to show that the proposed method is efficient and faster than some existing related algorithms, in particular when the damping factor is large .
Edit intent: clarity
Original:  Numerical results are reported to show that the proposed method is efficient and faster than some existing related algorithms, in particular when the damping factor is large .
Revised:  Numerical results are reported to show the efficiency of the new solver for practical PageRank computations .
Edit intent: clarity
Original:  To this end, we develop a new algorithm for the GOSSIP model that 1\pm \epsilon approximates the p-th frequency moment F_p = i=1^N f_i^p in O(\epsilon^{-2} n^{1-k/p}) rounds, for p >2 \geq2 , when the number of distinct elements F_0 is at most O\left(n^{1/(k-1)}\right).
Revised:  To this end, we develop a new algorithm for the GOSSIP model that 1\pm \epsilon approximates the p-th frequency moment F_p = i=1^N f_i^p in O(\epsilon^{-2} n^{1-k/p}) rounds, for p \geq2 , when the number of distinct elements F_0 is at most O\left(n^{1/(k-1)}\right).
Edit intent: clarity
Original:  During tumor angiogenesis, tumor cells secret a number of chemical substrates called tumor angiogenic factors (TAFs).
Revised:  During tumour angiogenesis, tumour cells secret a number of chemical substrates called tumor angiogenic factors (TAFs).
Edit intent: fluency
Original:  During tumor angiogenesis, tumor cells secret a number of chemical substrates called tumor angiogenic factors (TAFs).
Revised:  During tumor angiogenesis, tumor cells secret a number of chemical substrates called tumour angiogenic factors (TAFs).
Edit intent: fluency
Original:  These factors also create a chemical gradient (chemotaxis) between the tumor and the surrounding blood vessels.
Revised:  These factors also create a chemical gradient (chemotaxis) between the tumour and the surrounding blood vessels.
Edit intent: fluency
Original:  Due to the chemotactic force, the capillary sprouts migrate toward the tumor .
Revised:  Due to the chemotactic force, the capillary sprouts migrate towards the tumour .
Edit intent: fluency
Original:  On the other hand, a haptotactic force  due to fibronectin , secreted by the endothelial cell is also acts on these sprouts.
Revised:  On the other hand, a haptotactic force generated due to fibronectin , secreted by the endothelial cell is also acts on these sprouts.
Edit intent: clarity
Original:  On the other hand, a haptotactic force  due to fibronectin , secreted by the endothelial cell is also acts on these sprouts.
Revised:  On the other hand, a haptotactic force due to fibronectin which is secreted by the endothelial cell is also acts on these sprouts.
Edit intent: coherence
Original:  On the other hand, a haptotactic force  due to fibronectin , secreted by the endothelial cell is also acts on these sprouts.
Revised:  On the other hand, a haptotactic force due to fibronectin , secreted by the endothelial cell , also acts on these sprouts.
Edit intent: fluency
Original:  The process of tumor angiogenesis is not fully understood .
Revised:  Tumour angiogenesis is not fully understood .
Edit intent: clarity
Original:  We use 2-D cellular automata (CA) modeling for studying the behavior of tumor angiogenesis using both Moore and von-Neumann neighborhood.
Revised:  We use 2-D cellular automata (CA) model to study the behavior of tumor angiogenesis using both Moore and von-Neumann neighborhood.
Edit intent: fluency
Original:  We use 2-D cellular automata (CA) modeling for studying the behavior of tumor angiogenesis using both Moore and von-Neumann neighborhood.
Revised:  We use 2-D cellular automata (CA) modeling for studying the behavior of tumour angiogenesis using both Moore and von-Neumann neighborhood.
Edit intent: fluency
Original:  The CA model also captures capillary sprout branching and the fusion of two adjacent sprout tips (anastomoses)  .
Revised:  The CA model also mimics capillary sprout branching and the fusion of two adjacent sprout tips (anastomoses) .
Edit intent: clarity
Original: Accurate day-ahead individual resident load forecasting is very important to various applications of smart grid .
Revised: Accurate day-ahead individual residential load forecasting is very important to various applications of smart grid .
Edit intent: fluency
Original: Accurate day-ahead individual resident load forecasting is very important to various applications of smart grid .
Revised: Accurate day-ahead individual resident load forecasting is of great importance to various applications of smart grid .
Edit intent: clarity
Original:  As a powerful machine learning technology, deep learning has shown great advantages  in load forecasting task .
Revised:  As a powerful machine learning technology, has shown great advantages in load forecasting task .
Edit intent: clarity
Original:  As a powerful machine learning technology, deep learning has shown great advantages  in load forecasting task .
Revised:  As a powerful machine learning technology, deep learning has shown great advantages in load forecasting tasks .
Edit intent: fluency
Original:  However, deep learning is a computationally-hungry method, requires a plenty of training timeand results in considerable energy consumed and a plenty of CO2 emitted.
Revised:  However, deep learning is a computationally-hungry method, and requires high costs (e.g., time, energy and CO2 emitted.
Edit intent: clarity
Original:  This aggravates the energy crisis and incurs a substantial cost to the environment.
Revised:  This aggravates the energy crisis and incurs a substantial burden to the environment.
Edit intent: clarity
Original:  As a result , the deep learning methods are difficult to be popularized and applied in the real smart grid environment.
Revised:  As a consequence , the deep learning methods are difficult to be popularized and applied in the real smart grid environment.
Edit intent: fluency
Original:  In this paper, to reduce training time, energy consumed and CO2 emitted, we propose a efficient green model based on convolutional neural network, namely LoadCNN, for next-day load forecasting of individual resident .
Revised:  In this paper, we propose a efficient green model based on convolutional neural network, namely LoadCNN, for next-day load forecasting of individual resident .
Edit intent: coherence
Original:  In this paper, to reduce training time, energy consumed and CO2 emitted, we propose a efficient green model based on convolutional neural network, namely LoadCNN, for next-day load forecasting of individual resident .
Revised:  In this paper, to reduce training time, energy consumed and CO2 emitted, we propose a low training cost model based on convolutional neural network, namely LoadCNN, for next-day load forecasting of individual resident .
Edit intent: clarity
Original:  The training time, energy consumption, and CO2 emissions of LoadCNN are only approximately 1/ 70 of the corresponding indicators of other state-of-the-art models  . Meanwhile, it achieves state-of-the-art performance in terms of prediction accuracy . LoadCNN is the first load forecasting model which simultaneously considers prediction accuracy , training time, energy efficiency and environment costs.
Revised:  The training time, energy consumption, and CO2 emissions are only approximate 1/ 70 of the corresponding indicators of other state-of-the-art models . Meanwhile, it achieves state-of-the-art performance in terms of prediction accuracy . LoadCNN is the first load forecasting model which simultaneously considers prediction accuracy , training time, energy efficiency and environment costs.
Edit intent: coherence
Original:  The training time, energy consumption, and CO2 emissions of LoadCNN are only approximately 1/ 70 of the corresponding indicators of other state-of-the-art models  . Meanwhile, it achieves state-of-the-art performance in terms of prediction accuracy . LoadCNN is the first load forecasting model which simultaneously considers prediction accuracy , training time, energy efficiency and environment costs.
Revised:  The training time, energy consumption, and CO2 emissions of LoadCNN are only approximately 1/ 70 of the corresponding indicators of other state-of-the-art models . Meanwhile, it achieves state-of-the-art models, making LoadCNN the first load forecasting model which simultaneously considers prediction accuracy , training time, energy efficiency and environment costs.
Edit intent: clarity
Original:  It is a efficient green model that is able to be quickly, cost-effectively and environmental-friendly deployed in a realistic smart grid environment.
Revised:  It is a efficient green model that is able to be quickly, cost-effectively and environmentally-friendly deployed in a realistic smart grid environment.
Edit intent: fluency
Original:  Even though power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them  (e.g.  linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Revised:  Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them (e.g. linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Edit intent: coherence
Original:  Even though power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them  (e.g.  linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Revised:  Even though power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them ~ (e.g. linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Edit intent: fluency
Original:  Even though power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them  (e.g.  linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Revised:  Even though power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them (e.g. ~ linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Edit intent: fluency
Original:  As a solution, we present a novel maximum likelihood estimation approach that exploits the friendship paradox to sample more efficiently from the tail of the degree distribution.
Revised:  As a solution, we present a novel maximum likelihood estimation approach that exploits the friendship paradox to sample more efficiently from the tail of the degree distribution.
Edit intent: fluency
Original:  We analytically show that the proposed method results in a smaller bias, variance and a Cramer-Rao lower bound compared to the maximum-likelihood estimate obtained with uniformly sampled nodes  (which is the most commonly used method in literature).
Revised:  We analytically show that the proposed method results in a smaller bias, variance and a Cramer-Rao lower bound compared to the maximum-likelihood estimate obtained with uniformly sampled nodes ~ (which is the most commonly used method in literature).
Edit intent: fluency
Original:  We analytically show that the proposed method results in a smaller bias, variance and a Cramer-Rao lower bound compared to the maximum-likelihood estimate obtained with uniformly sampled nodes  (which is the most commonly used method in literature).
Revised:  We analytically show that the proposed method results in a smaller bias, variance and a Cramer-Rao lower bound compared to the maximum-likelihood estimate obtained with uniformly sampled nodes (which is the commonly used method in literature).
Edit intent: clarity
Original:  Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them ~ (e.g. ~ linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Revised:  Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them (e.g. ~ linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Edit intent: fluency
Original:  Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them ~ (e.g. ~ linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Revised:  Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them ~ (e.g. linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution.
Edit intent: fluency
Original:  We analytically show that the proposed method results in a smaller bias, variance and a Cram\`{e lower bound compared to the  maximum-likelihood estimate obtained with uniformly sampled nodes ~ (which is the  commonly used method in literature).
Revised:  We analytically show that the proposed method results in a smaller bias, variance and a Cram\`{e lower bound compared to the vanilla maximum-likelihood estimate obtained with uniformly sampled nodes ~ (which is the commonly used method in literature).
Edit intent: fluency
Original:  We analytically show that the proposed method results in a smaller bias, variance and a Cram\`{e lower bound compared to the  maximum-likelihood estimate obtained with uniformly sampled nodes ~ (which is the  commonly used method in literature).
Revised:  We analytically show that the proposed method results in a smaller bias, variance and a Cram\`{e lower bound compared to the maximum-likelihood estimate obtained with uniformly sampled nodes (which is the commonly used method in literature).
Edit intent: fluency
Original:  In the case of the Gross-Pitaevskii eigenvalue problem  we prove global convergence towards an eigenfunction  .
Revised:  In the case of the Gross-Pitaevskii eigenvalue problem , we prove global convergence towards an eigenfunction .
Edit intent: fluency