wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our paper proposes a model to use the decentralized file storage system of IPFS, and the integrity preservation properties of the Blockchain, to store and distribute data on the Web.
Revised:  Our paper proposes a model that uses the decentralized file storage system of IPFS, and the integrity preservation properties of the Blockchain, to store and distribute data on the Web.
Edit intent: fluency
Original:  We investigate the relationship between this problem and its single-period counterpart .
Revised:  The problem arises in several applications, such as emergency services, in which vehicles can be relocated in anticipation of traffic congestion. First, we analyze the problem structure and its relationship with its single-period counterpart .
Edit intent: coherence
Original:  The insight gained with this analysis is then used to devise a two-stage heuristic.
Revised:  Then, the insight gained with this analysis is then used to devise a two-stage heuristic.
Edit intent: coherence
Original:  The insight gained with this analysis is then used to devise a two-stage heuristic.
Revised:  The insight gained with this analysis is used to devise a two-stage heuristic.
Edit intent: coherence
Original: In this work, we  study stability and robustness to noise in deterministic SIS epidemics over large networks by using the spectral properties of graphons .
Revised: In this work, we use the spectral properties of graphons to study stability and robustness to noise in deterministic SIS epidemics over large networks by using the spectral properties of graphons .
Edit intent: fluency
Original: In this work, we  study stability and robustness to noise in deterministic SIS epidemics over large networks by using the spectral properties of graphons .
Revised: In this work, we study stability and sensitivity to noise of deterministic SIS epidemics over large networks by using the spectral properties of graphons .
Edit intent: clarity
Original: In this work, we  study stability and robustness to noise in deterministic SIS epidemics over large networks by using the spectral properties of graphons .
Revised: In this work, we study stability and robustness to noise in deterministic SIS epidemics over large networks .
Edit intent: clarity
Original:  We derive a noise index to evaluate the deviation from the disease-free state due to noise.
Revised:  We derive a noise index to quantify the deviation from the disease-free state due to noise.
Edit intent: clarity
Original:  For finite graphs, the index depends on the adjacency eigenvalues of the graphs.
Revised:  For finite networks, we show that the index depends on the adjacency eigenvalues of the graphs.
Edit intent: clarity
Original:  Using the eigenvalues of the associated graphon operator, we are able to find an approximation of the index that is tight when the network size goes to infinity.
Revised:  Using the eigenvalues of the associated graphon operator, we find an approximation of the index that is tight when the network size goes to infinity.
Edit intent: coherence
Original: For an edge-colored graph G, a set F of edges of G is called aproper edge-cut if F is an edge-cut of G and any pair of adjacent edges in F are assigned by different colors.
Revised: proper edge-cut if F is an edge-cut of G and any pair of adjacent edges in F are assigned by different colors.
Edit intent: clarity
Original: For an edge-colored graph G, a set F of edges of G is called aproper edge-cut if F is an edge-cut of G and any pair of adjacent edges in F are assigned by different colors.
Revised: For an edge-colored graph G, a set F of edges of G is called a if F is an edge-cut of G and any pair of adjacent edges in F are assigned by different colors.
Edit intent: coherence
Original:  An edge-colored graph is calledproper disconnected if for each pair of distinct vertices of G there exists a proper edge-cut separating them.
Revised:  An edge-colored graph is called if for each pair of distinct vertices of G there exists a proper edge-cut separating them.
Edit intent: fluency
Original:  For a connected graph G, theproper disconnection number of G, denoted by pd(G), is defined as the minimum number of colors that are needed to make G proper disconnected .
Revised:  For a connected graph G, the of G, denoted by pd(G), is defined as the minimum number of colors that are needed to make G proper disconnected .
Edit intent: clarity
Original:  In this paper, we first show that it is NP-complete to decide whether a given k-edge-colored graph G with  \Delta(G)=4 is proper disconnected.
Revised:  In this paper, we first show that it is NP-complete to decide whether a given edge-colored graph G with \Delta(G)=4 is proper disconnected.
Edit intent: clarity
Original:  Finally , we show that for a general graph G, deciding whether pd(G)=1 is NP-complete, even if G  is bipartite.
Revised:  Furthermore , we show that for a general graph G, deciding whether pd(G)=1 is NP-complete, even if G is bipartite.
Edit intent: coherence
Original: In this paper, based on the matrix polar decomposition, we propose a general algorithmic framework to solve a class of optimization problems on the product of Stiefel manifolds .
Revised: In this paper, we propose a general algorithmic framework to solve a class of optimization problems on the product of Stiefel manifolds .
Edit intent: coherence
Original:  We establish the weak convergence and global convergence of this general algorithmic approach based on the ojasiewicz gradient inequality  .
Revised:  We establish the weak convergence and global convergence of this general algorithmic approach using the ojasiewicz gradient inequality .
Edit intent: fluency
Original:  This symmetric variant and its convergence results are applied to the best symmetric rank-1 approximation and low rank symmetric orthogonal approximation  for higher order  tensors.
Revised:  This symmetric variant and its convergence results are applied to the best symmetric rank-1 approximation and low rank symmetric orthogonal approximation and best symmetric rank-1 approximation for higher order tensors.
Edit intent: coherence
Original:  It turns out that well-known algorithms such as HOPM, S-HOPM, LROAT, S-LROAT  are all special cases of this general algorithmic framework and its symmetric variant  .
Revised:  It turns out that well-known algorithms such as LROAT, S-LROAT are all special cases of this general algorithmic framework and its symmetric variant .
Edit intent: coherence
Original: The problem of predicting links in large networks is a crucial task in a variety of practical applications, including social sciences, biology and computer security.
Revised: The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security.
Edit intent: clarity
Original:  The probabilities of links are obtained by fusing information at multiple levels of resolution: time series models are used to score connections at the edge level, and spectral methods provide estimates of latent positions for each node  .
Revised:  The probabilities of links are obtained by fusing information at two stages: spectral methods provide estimates of latent positions for each node .
Edit intent: clarity
Original:  The methods presented in this article are applied to a number of simulated and real-world computer network graphs, showing promising results.
Revised:  The methods presented in this article are applied to a number of simulated and real-world graphs, showing promising results.
Edit intent: clarity
Original:  Let \mathcal{H be real Hilbert spaces, b\in \mathcal{K and T\inB( \mathcal{H closed range and Moore-Penrose inverse T^\dagger.
Revised:  Let \mathcal{H be real Hilbert spaces, b\in \mathcal K and T\inB( \mathcal{H closed range and Moore-Penrose inverse T^\dagger.
Edit intent: fluency
Original:  Based on the well-known characterization of proximity operators by Moreau, we prove that for any proximity operator Prox\colon \mathcal{K \to \mathcal{K the operator T^\dagger\,\text{Prox} (T\cdot +b) is a proximity operator on \mathcal{H equipped with a suitable norm.
Revised:  Based on the well-known characterization of proximity operators by Moreau, we prove that for any proximity operator Prox\colon \mathcal K \to \mathcal{K the operator T^\dagger\,\text{Prox} (T\cdot +b) is a proximity operator on \mathcal{H equipped with a suitable norm.
Edit intent: fluency
Original:  Based on the well-known characterization of proximity operators by Moreau, we prove that for any proximity operator Prox\colon \mathcal{K \to \mathcal{K the operator T^\dagger\,\text{Prox} (T\cdot +b) is a proximity operator on \mathcal{H equipped with a suitable norm.
Revised:  Based on the well-known characterization of proximity operators by Moreau, we prove that for any proximity operator Prox\colon \mathcal{K \to \mathcal K the operator T^\dagger\,\text{Prox} (T\cdot +b) is a proximity operator on \mathcal{H equipped with a suitable norm.
Edit intent: fluency
Original:  Based on the well-known characterization of proximity operators by Moreau, we prove that for any proximity operator Prox\colon \mathcal{K \to \mathcal{K the operator T^\dagger\,\text{Prox} (T\cdot +b) is a proximity operator on \mathcal{H equipped with a suitable norm.
Revised:  Based on the well-known characterization of proximity operators by Moreau, we prove that for any proximity operator Prox\colon \mathcal{K \to \mathcal{K the operator T^\dagger\,\text{Prox} (T\cdot +b) is a proximity operator on \mathcal H equipped with a suitable norm.
Edit intent: fluency
Original:  In particular, it follows for the frequently applied soft shrinkage operator \text{Prox} = S_{\lambda}\colon\ell_2 \rightarrow\ell_2 and any frame analysis operator T\colon \mathcal{H \to\ell_2 , that the frame shrinkage operator T^\dagger\, S_\lambda\,T is a proximity operator in a suitable Hilbert space.
Revised:  In particular, it follows for the frequently applied soft shrinkage operator \text{Prox} = S_{\lambda}\colon\ell_2 \rightarrow\ell_2 and any frame analysis operator T\colon \mathcal H \to\ell_2 , that the frame shrinkage operator T^\dagger\, S_\lambda\,T is a proximity operator in a suitable Hilbert space.
Edit intent: fluency
Original:  In particular, it follows for the frequently applied soft shrinkage operator \text{Prox} = S_{\lambda}\colon\ell_2 \rightarrow\ell_2 and any frame analysis operator T\colon \mathcal{H \to\ell_2 , that the frame shrinkage operator T^\dagger\, S_\lambda\,T is a proximity operator in a suitable Hilbert space.
Revised:  In particular, it follows for the frequently applied soft shrinkage operator \text{Prox} = S_{\lambda}\colon\ell_2 \rightarrow\ell_2 and any frame analysis operator T\colon \mathcal{H \to\ell_2 that the frame shrinkage operator T^\dagger\, S_\lambda\,T is a proximity operator in a suitable Hilbert space.
Edit intent: fluency
Original:  In particular, it follows for the frequently applied soft shrinkage operator \text{Prox} = S_{\lambda}\colon\ell_2 \rightarrow\ell_2 and any frame analysis operator T\colon \mathcal{H \to\ell_2 , that the frame shrinkage operator T^\dagger\, S_\lambda\,T is a proximity operator in a suitable Hilbert space.
Revised:  In particular, it follows for the frequently applied soft shrinkage operator \text{Prox} = S_{\lambda}\colon\ell_2 \rightarrow\ell_2 and any frame analysis operator T\colon \mathcal{H \to\ell_2 , that the frame shrinkage operator T^\dagger\, S_\lambda\,T is a proximity operator on a suitable Hilbert space.
Edit intent: clarity
Original:  Further, the concatenation of proximity operators on \mathbb R^d equipped with different norms establishes a PNN.
Revised:  The concatenation of proximity operators on \mathbb R^d equipped with different norms establishes a PNN.
Edit intent: coherence
Original:  If the network arises from Parseval frame analysis or synthesis operators,  it forms an averaged operator , called PPNN.
Revised:  If the network arises from Parseval frame analysis or synthesis operators, then it forms an averaged operator , called PPNN.
Edit intent: coherence
Original:  The involved linear operators , respectively their transposed operators, are in a Stiefel manifold , so that minimization methods on Stiefel manifolds can be applied for training such networks .
Revised:  The involved linear operators are in a Stiefel manifold , so that minimization methods on Stiefel manifolds can be applied for training such networks .
Edit intent: coherence
Original:  The involved linear operators , respectively their transposed operators, are in a Stiefel manifold , so that minimization methods on Stiefel manifolds can be applied for training such networks .
Revised:  The involved linear operators , respectively their transposed operators, are in a Stiefel manifold and corresponding minimization methods can be applied for training such networks .
Edit intent: coherence
Original:  The involved linear operators , respectively their transposed operators, are in a Stiefel manifold , so that minimization methods on Stiefel manifolds can be applied for training such networks .
Revised:  The involved linear operators , respectively their transposed operators, are in a Stiefel manifold , so that minimization methods on Stiefel manifolds can be applied for training .
Edit intent: clarity
Original: The "flexible boundary condition method "  , introduced by Sinclair and coworkers in the 1970s, remains among the most popular methods for simulating isolated two-dimensional crystalline defects, embedded in an effectively infinite atomistic domain.
Revised: The "flexible boundary condition " , introduced by Sinclair and coworkers in the 1970s, remains among the most popular methods for simulating isolated two-dimensional crystalline defects, embedded in an effectively infinite atomistic domain.
Edit intent: clarity
Original:  Here we develop a new data reduction method for genome-wide open chromatin data toward cell type classification.
Revised:  Here we give a clustering algorithm for genome-wide open chromatin data toward cell type classification.
Edit intent: clarity
Original:  Form the pure math point of view, this can be seen as the 1-dimensional first step into the theory of simplicial sets.
Revised:  From the pure math point of view, this can be seen as the 1-dimensional first step into the theory of simplicial sets.
Edit intent: fluency
Original: Intelligent reflecting surface (IRS) has emerged as a promising technology to engineer the radio signal propagation for catering to wireless communication, by leveraging a massive number of low-cost passive reflecting elements.
Edit intent: coherence
Original:  To address these issues , we consider in this paper an IRS-aided single-user communication system with discrete phase shifts and propose a new joint design framework for progressive IRS channel estimation and passive beamforming . Specifically, we consider the practical block-based transmission, where each block has a finite  number of training symbols for channel estimation.
Revised:  To address them , we consider in this paper an IRS-aided single-user communication system with discrete phase shifts and propose a new joint design framework for progressive IRS channel estimation and passive beamforming . Specifically, we consider the practical block-based transmission, where each block has a finite number of training symbols for channel estimation.
Edit intent: coherence
Original:  To address these issues , we consider in this paper an IRS-aided single-user communication system with discrete phase shifts and propose a new joint design framework for progressive IRS channel estimation and passive beamforming . Specifically, we consider the practical block-based transmission, where each block has a finite  number of training symbols for channel estimation.
Revised:  To address these issues , we consider in this paper an IRS-aided single-user communication system with discrete phase shifts and propose a new joint design framework for progressive IRS channel estimation and passive beamforming . Specifically, we consider a practical block-based transmission, where each block has a finite number of training symbols for channel estimation.
Edit intent: fluency
Original:  channel estimation, i.e., the channels of all IRS elements are estimated at one time which inevitably causes long delay for data transmission, we propose a novel hierarchical training reflection design for IRS such that by properly partitioning its reflecting elementsinto groups/subgroups and assigning each group/subgroup of elements differently-combined discrete phase shifts over multiple blocks , all IRS elements'
Revised:  channel estimation, i.e., the channels of all IRS elements are estimated at one time which inevitably causes long delay for data transmission, we propose a novel hierarchical training reflection design is proposed to progressively estimate IRS elements' channels over multiple blocks , all IRS elements'
Edit intent: clarity
Original:  The stability and quantification of the rate of convergence of the Mapper to the Reeb space has been studied a lot in recent works ~\mbox{ Brown2019, Carriere2018a, Carriere2018, Munch2016  focusing on the case where a scalar-valued filter is used for the computation of Mapper.
Revised:  The stability and quantification of the rate of convergence of the Mapper to the Reeb space has been studied a lot in recent works ~\mbox{ Brown2019, Carriere2018a, Carriere2018, Munch2016 , focusing on the case where a scalar-valued filter is used for the computation of Mapper.
Edit intent: fluency
Original:  On the other hand, much less is known in the multivariate case, where the domain of the filter is  in \mathbb R^d instead of \mathbb R.
Revised:  On the other hand, much less is known in the multivariate case, when the codomain of the filter is in \mathbb R^d instead of \mathbb R.
Edit intent: clarity
Original:  In this article, we present an approximation result for the Reeb space in the multivariate case using a Mapper-based estimator, which is a slight modification of the usual Mapper construction .
Revised:  In this article, we introduce a slight modification of the usual Mapper construction .
Edit intent: coherence
Original:  Moreover, our approximation is stated with respect to a pseudometric that is an extension of the usual%DIFDELCMD < {\em %DIFDELCMD < %%% interleaving distance between persistence modules~\mbox{ Chazal2016\hspace{0pt} . Finally, we apply our results to the case }  where the filter function used to compute the Mapper is estimated from the data.
Revised:  Moreover, our approximation is stated with respect to a pseudometric that is an extension of the usual%DIFDELCMD < {\em %DIFDELCMD < %%% between persistence modules~\mbox{ Chazal2016\hspace{0pt} . Finally, we apply our results to the case } where the filter function used to compute the Mapper is estimated from the data.
Edit intent: clarity
Original:  Moreover, our approximation is stated with respect to a pseudometric that is an extension of the usual%DIFDELCMD < {\em %DIFDELCMD < %%% interleaving distance between persistence modules~\mbox{ Chazal2016\hspace{0pt} . Finally, we apply our results to the case }  where the filter function used to compute the Mapper is estimated from the data.
Revised:  Moreover, our approximation is stated with respect to a pseudometric that is an extension of the usual%DIFDELCMD < {\em %DIFDELCMD < %%% interleaving distance \hspace{0pt} . Finally, we apply our results to the case } where the filter function used to compute the Mapper is estimated from the data.
Edit intent: clarity
Original:  We ] provide applications of this setting in statistics and machine learning and probability for different kinds of target filters, as well as numerical experiments that demonstrate the relevance of our approach .
Revised:  We ] provide applications of this setting in statistics and machine learning for different kinds of target filters, as well as numerical experiments that demonstrate the relevance of our approach .
Edit intent: clarity
Original:  We ] provide applications of this setting in statistics and machine learning and probability for different kinds of target filters, as well as numerical experiments that demonstrate the relevance of our approach .
Revised:  We ] provide applications of this setting in statistics and machine learning and probability for different kinds of target filters, as well as numerical experiments that demonstrate the relevance of our approach 
Edit intent: fluency
Original:  In this paper, we resolve the question on how to handle commitment requirements which enforce that a scheduler has to guarantee at a certain point in time the completion of admitted jobs.
Revised:  In this paper, we answer the question on how to handle commitment requirements which enforce that a scheduler has to guarantee at a certain point in time the completion of admitted jobs.
Edit intent: clarity
Original:  This is very relevant, e.g., in providing cloud-computing services  and disallows last-minute rejections of critical tasks.
Revised:  This is very relevant, e.g., in providing cloud-computing services , and disallows last-minute rejections of critical tasks.
Edit intent: fluency
Original:  We give an algorithm with an optimal competitive ratio of \Theta(1/\varepsilon) for the online throughput maximization problem when a\big(\varepsilon}\big ) scheduler must commit upon starting a job.
Revised:  We present an algorithm for unrelated machines that is \Theta\big(\varepsilon}\big ) scheduler must commit upon starting a job.
Edit intent: clarity
Original:  For the latter commitment model, it is known that no (randomized) online algorithms does admit any bounded competitive ratio.
Revised:  For the latter commitment model, it is known that no (randomized) online algorithm admits any bounded competitive ratio.
Edit intent: clarity
Original: In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST) which is made of a single detector rotating around a fixed source.
Revised: In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST) . This new system is made of a single detector rotating around a fixed source.
Edit intent: clarity
Original:  Unlike some previous CST  no collimator is used at the detector , such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the new Radon transform is a family of double circular arcs.
Revised:  Unlike some previous CST , no collimator is used at the detector , such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the new Radon transform is a family of double circular arcs.
Edit intent: fluency
Original:  Unlike some previous CST  no collimator is used at the detector , such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the new Radon transform is a family of double circular arcs.
Revised:  Unlike some previous CST no collimator is used at the detector . Such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the new Radon transform is a family of double circular arcs.
Edit intent: fluency
Original:  Unlike some previous CST  no collimator is used at the detector , such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the new Radon transform is a family of double circular arcs.
Revised:  Unlike some previous CST no collimator is used at the detector , such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the associated Radon transform is a family of double circular arcs.
Edit intent: clarity
Original:  As first main theoretical result, an analytic inverse formula is established for this new Radon transform.
Revised:  As first main theoretical result, an analytic inversion formula is established for this new Radon transform.
Edit intent: fluency