wanyu/IteraTeR_v2 huggingface dataset:
Original:  A critical graph of r(H_1,H_2,\ldots,H_c) is an edge-colored complete graph on r(H_1,H_2,\ldots,H_c)-1 vertices with c colors which contains no subgraph isomorphic to H_{i} in color i for any i\in \{1,2,\ldots,c\}.
Revised:  A critical graph of r(H_1,H_2,\ldots,H_c) is an edge-colored complete graph on r(H_1,H_2,\ldots,H_c)-1 vertices with c colors which contain no subgraphs in color i isomorphic to H_{i} in color i for any i\in \{1,2,\ldots,c\}.
Edit intent: clarity
Original:  Math. Soc. 19 {\it   (1975)  252--256.) showed that r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2})=n_{1}+1+ \sumi=1^c(n_{i}-1), in which n_{i}K_{2} is a matching of size n_{i}.
Revised:  Math. Soc. 19 {\it 19 (1975) 252--256.) showed that r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2})=n_{1}+1+ \sumi=1^c(n_{i}-1), in which n_{i}K_{2} is a matching of size n_{i}.
Edit intent: fluency
Original:  Math. Soc. 19 {\it   (1975)  252--256.) showed that r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2})=n_{1}+1+ \sumi=1^c(n_{i}-1), in which n_{i}K_{2} is a matching of size n_{i}.
Revised:  Math. Soc. 19 {\it (1975) , 252--256.) showed that r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2})=n_{1}+1+ \sumi=1^c(n_{i}-1), in which n_{i}K_{2} is a matching of size n_{i}.
Edit intent: fluency
Original:  In this paper, using Gallai-Edmonds Structure Theorem, we give a new proof on the value of r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2}) which also characterized all critical graphs .
Revised:  Using the Gallai-Edmonds Structure Theorem, we give a new proof on the value of r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2}) which also characterized all critical graphs .
Edit intent: clarity
Original:  In this paper, using Gallai-Edmonds Structure Theorem, we give a new proof on the value of r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2}) which also characterized all critical graphs .
Revised:  In this paper, using Gallai-Edmonds Theorem, we give a new proof on the value of r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2}) which also characterized all critical graphs .
Edit intent: clarity
Original:  In this paper, using Gallai-Edmonds Structure Theorem, we give a new proof on the value of r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2}) which also characterized all critical graphs .
Revised:  In this paper, using Gallai-Edmonds Structure Theorem, we characterized all the critical graphs for r(n_{1}K_{2},n_{2}K_{2},\ldots,n_{c}K_{2}) which also characterized all critical graphs .
Edit intent: clarity
Original:  It is fully convolutional and obtains about 46.7 times speed-up over  Deep Voice 3 at synthesis while maintaining comparable speech qualityusing a WaveNet vocoder.
Revised:  It is fully convolutional and brings 46.7 times speed-up over Deep Voice 3 at synthesis while maintaining comparable speech qualityusing a WaveNet vocoder.
Edit intent: clarity
Original:  Furthermore, we build the first fully parallel neural text-to-speech system by applying the inverse autoregressive flow~(IAF) as the parallel neural vocoder.
Revised:  Furthermore, we build the parallel text-to-speech system by applying the inverse autoregressive flow~(IAF) as the parallel neural vocoder.
Edit intent: clarity
Original: We propose  guaranteed and fully computable upper bound on the energy norm of the error in low rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems.
Revised: We propose a guaranteed and fully computable upper bound on the energy norm of the error in low rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems.
Edit intent: fluency
Original: We propose  guaranteed and fully computable upper bound on the energy norm of the error in low rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems.
Revised: We propose guaranteed and fully computable upper bound on the energy norm of the error in low-rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems.
Edit intent: fluency
Original:  The error bound is obtained from Euler--Lagrange equations for a complementary flux reconstruction problem, which are solved in the low rank TT representation using the block Alternating Linear Scheme.
Revised:  The error bound is obtained from Euler-Lagrange equations for a complementary flux reconstruction problem, which are solved in the low rank TT representation using the block Alternating Linear Scheme.
Edit intent: fluency
Original:  The error bound is obtained from Euler--Lagrange equations for a complementary flux reconstruction problem, which are solved in the low rank TT representation using the block Alternating Linear Scheme.
Revised:  The error bound is obtained from Euler--Lagrange equations for a complementary flux reconstruction problem, which are solved in the low-rank TT representation using the block Alternating Linear Scheme.
Edit intent: fluency
Original:  This bound is guaranteed to be above the energy norm of the total error, including the discretization error, the tensor approximation error, and the error in the solver of linear algebraic equations  . Numerical examples with the Poisson equation and the Schr\"odinger equation with the Henon-Heiles potential in up to 40 dimensions are presented to illustrate the efficiency of this approach.
Revised:  This bound is guaranteed to be above the energy norm of the total error, including the discretization error, the tensor approximation error, and the error in the solver of linear algebraic equations . Numerical examples with the Poisson equation and the Schroedinger equation with the Henon-Heiles potential in up to 40 dimensions are presented to illustrate the efficiency of this approach.
Edit intent: fluency
Original: We present BrainPainter, a software that automatically generates images of highlighted brain structures given a simple list of numbers corresponding to the output colours of each region.
Revised: We present BrainPainter, a software that automatically generates images of highlighted brain structures given a list of numbers corresponding to the output colours of each region.
Edit intent: clarity
Original:  Compared to existing visualisation software ( e.g. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analsys tools, (2) it can visualise  subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain , without requiring the user to write additional software code .
Revised:  Compared to existing visualisation software ( i.e. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analsys tools, (2) it can visualise subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain , without requiring the user to write additional software code .
Edit intent: fluency
Original:  Compared to existing visualisation software ( e.g. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analsys tools, (2) it can visualise  subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain , without requiring the user to write additional software code .
Revised:  Compared to existing visualisation software ( e.g. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analysis tools, (2) it can visualise subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain , without requiring the user to write additional software code .
Edit intent: fluency
Original:  Compared to existing visualisation software ( e.g. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analsys tools, (2) it can visualise  subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain , without requiring the user to write additional software code .
Revised:  Compared to existing visualisation software ( e.g. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analsys tools, (2) it can visualise both cortical and subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain , without requiring the user to write additional software code .
Edit intent: clarity
Original:  Compared to existing visualisation software ( e.g. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analsys tools, (2) it can visualise  subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain , without requiring the user to write additional software code .
Revised:  Compared to existing visualisation software ( e.g. Freesurfer, SPM, 3d slicer), our software has three key advantages: (1) it does not require the input data to be in a specialised format, allowing it to be used in combination with any neuroimaging analsys tools, (2) it can visualise subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain .
Edit intent: coherence
Original:  We highlight three demonstrations of BrainPainter in existing scientific studies: visualisation of (1) the extent of atrophy through interpolation along a user-defined gradient of colours,  as well as ( 2-3) progression of pathology in cortical and subcortical regions through snapshots.
Revised:  We highlight three use cases where BrainPainter was used in existing neuroimaging studies: (1) the extent of atrophy through interpolation along a user-defined gradient of colours, as well as ( 2-3) progression of pathology in cortical and subcortical regions through snapshots.
Edit intent: clarity
Original:  We highlight three demonstrations of BrainPainter in existing scientific studies: visualisation of (1) the extent of atrophy through interpolation along a user-defined gradient of colours,  as well as ( 2-3) progression of pathology in cortical and subcortical regions through snapshots.
Revised:  We highlight three demonstrations of BrainPainter in existing scientific studies: visualisation of (1) visualisation of the degree of atrophy through interpolation along a user-defined gradient of colours, as well as ( 2-3) progression of pathology in cortical and subcortical regions through snapshots.
Edit intent: clarity
Original:  We highlight three demonstrations of BrainPainter in existing scientific studies: visualisation of (1) the extent of atrophy through interpolation along a user-defined gradient of colours,  as well as ( 2-3) progression of pathology in cortical and subcortical regions through snapshots.
Revised:  We highlight three demonstrations of BrainPainter in existing scientific studies: visualisation of (1) the extent of atrophy through interpolation along a user-defined gradient of colours, as well as ( 3) visualisation of pathology in cortical and subcortical regions through snapshots.
Edit intent: clarity
Original: Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE constrained optimization.
Revised: Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization.
Edit intent: fluency
Original:  In this paper, we focus on the efficient numerical solution to minimizing a convex and smooth tracking-type functional subject to a linear partial differential equation with random coefficients and box constraints.
Revised:  In this paper, we focus on the efficient numerical minimization of a convex and smooth tracking-type functional subject to a linear partial differential equation with random coefficients and box constraints.
Edit intent: clarity
Original:  The approach we take is based on stochastic approximation , where in place of a true gradient, a stochastic gradient is chosen using one sample from a known probability distribution.
Revised:  The approach we take is based on stochastic approximation where, in place of a true gradient, a stochastic gradient is chosen using one sample from a known probability distribution.
Edit intent: fluency
Original:  In the application of this method to PDE constrained optimization under uncertainty, new challenges arise.
Revised:  In the application of this method to PDE-constrained optimization under uncertainty, new challenges arise.
Edit intent: fluency
Original: The network reconstruction problem is one of the challenging problems in network science .
Revised: A challenging problem in complex networks is the network reconstruction problem from data .
Edit intent: clarity
Original:  We develop a methodology to reconstruct conserved networks from flows by combining these graph properties with learning techniques , with polynomial time complexity.
Revised:  We develop a methodology to reconstruct conserved networks from flow data by exploiting graph theoretic properties of conserved networks combined with learning techniques , with polynomial time complexity.
Edit intent: clarity
Original:  We also examine ]  steady-state performance.
Revised:  We also examine ] the steady-state performance.
Edit intent: fluency
Original:  The results  reveal explicitly the influence of the gradient noise, data characteristics, and subspace constraints, on the network performance.
Revised:  The results will reveal explicitly the influence of the gradient noise, data characteristics, and subspace constraints, on the network performance.
Edit intent: fluency
Original:  The results  also show that in the small step-size regime, the iterates generated by the distributed algorithm achieve the centralized steady-state performance .
Revised:  The results will also show that in the small step-size regime, the iterates generated by the distributed algorithm achieve the centralized steady-state performance .
Edit intent: clarity
Original:  Nowadays, Graphics Processing Units (GPUs) are in a variety of systems from supercomputers to mobile phones and tablets.
Revised:  Graphics Processing Units (GPUs) are in a variety of systems from supercomputers to mobile phones and tablets.
Edit intent: coherence
Original:  Nowadays, Graphics Processing Units (GPUs) are in a variety of systems from supercomputers to mobile phones and tablets.
Revised:  Nowadays, Graphics Processing Units (GPUs) are now present in supercomputers to mobile phones and tablets.
Edit intent: clarity
Original:  They are not only used for graphics operations but rather as general-purpose special hardware (GPGPUs) to boost the performance of compute-intensive applications.
Revised:  GPUs are used for graphics operations but rather as general-purpose special hardware (GPGPUs) to boost the performance of compute-intensive applications.
Edit intent: clarity
Original:  They are not only used for graphics operations but rather as general-purpose special hardware (GPGPUs) to boost the performance of compute-intensive applications.
Revised:  They are not only used for graphics operations as well as general-purpose special hardware (GPGPUs) to boost the performance of compute-intensive applications.
Edit intent: clarity
Original:  They are not only used for graphics operations but rather as general-purpose special hardware (GPGPUs) to boost the performance of compute-intensive applications.
Revised:  They are not only used for graphics operations but rather as general-purpose computing (GPGPUs) to boost the performance of compute-intensive applications.
Edit intent: clarity
Original:  However, the percentage of undisclosed characteristics beyond what vendors provide is  small.
Revised:  However, the percentage of undisclosed characteristics beyond what vendors provide is not small.
Edit intent: coherence
Original:  We also show the impact of the possible optimizations a CUDA compiler have over the various latencies.
Revised:  We also show the impact of the various optimizations the CUDA compiler can perform over the various latencies.
Edit intent: clarity
Original:  We run our evaluation on seven different high-end NVIDIA GPUs from five different generations/architectures namely : Kepler, Maxwell, Pascal, Volta, and Turing.
Revised:  We perform our evaluation on seven different high-end NVIDIA GPUs from five different generations/architectures namely : Kepler, Maxwell, Pascal, Volta, and Turing.
Edit intent: clarity
Original:  We run our evaluation on seven different high-end NVIDIA GPUs from five different generations/architectures namely : Kepler, Maxwell, Pascal, Volta, and Turing.
Revised:  We run our evaluation on seven different high-end NVIDIA GPUs from five different generations/architectures : Kepler, Maxwell, Pascal, Volta, and Turing.
Edit intent: coherence
Original:  We believe that this work would help architects have an accurate characterization of the latencies of these GPUs, which would subsequently help in modeling the hardware accurately.
Revised:  The results in this paper can help architects to have an accurate characterization of the latencies of these GPUs, which would subsequently help in modeling the hardware accurately.
Edit intent: clarity
Original:  We believe that this work would help architects have an accurate characterization of the latencies of these GPUs, which would subsequently help in modeling the hardware accurately.
Revised:  We believe that this work would help architects have an accurate characterization of the latencies of these GPUs, which will help in modeling the hardware accurately.
Edit intent: coherence
Original:  In addition, this would also make application developers more aware of how to optimize their applications.
Revised:  Also, software developers can perform informed optimizations to their applications.
Edit intent: coherence
Original: In this paper, we provide a system theoretic treatment of a new class of multilinear time invariant (MLTI) systems in which the states, inputs and outputs are tensors, and the system evolution is governed by multilinear operators.
Revised: In this paper, we provide a system theoretic treatment of a new class of multilinear time-invariant (MLTI) systems in which the states, inputs and outputs are tensors, and the system evolution is governed by multilinear operators.
Edit intent: fluency
Original:  There is a particular tensor unfolding which gives rise to an isomorphism from this tensor space to the general linear group, i.e.  group of invertible matrices.
Revised:  There is a particular tensor unfolding which gives rise to an isomorphism from this tensor space to the general linear group, i.e. the group of invertible matrices.
Edit intent: fluency
Original:  By leveraging this unfolding operation, one can extend classical linear time invariant (LTI) system notions including stability, reachability and observability to MLTI systems.
Revised:  By leveraging this unfolding operation, one can extend classical linear time-invariant (LTI) system notions including stability, reachability and observability to MLTI systems.
Edit intent: fluency
Original:  While the unfolding based formulation is a powerful theoretical construct, the computational advantages of MLTI systems can only be fully realized while working with the tensor form, where hidden patterns/structures (e.g. redundancy/correlations) can be exploited for efficient representations and computations.
Revised:  While the unfolding based formulation is a powerful theoretical construct, the computational advantages of MLTI systems can only be fully realized while working with the tensor form, where hidden patterns/structures can be exploited for efficient representations and computations.
Edit intent: clarity
Original:  In addition, we develop the generalized CANDECOMP/PARAFAC decomposition and tensor train decomposition based model reduction framework, which can significantly reduce the number of MLTI system parameters .
Revised:  In addition, we develop a generalized CANDECOMP/PARAFAC decomposition and tensor train decomposition based model reduction framework, which can significantly reduce the number of MLTI system parameters .
Edit intent: fluency
Original: The Kaczmarz algorithm is one of the most popular methods for solving large-scale over-determined linear systems due to its speed and simplicity .
Revised: The Kaczmarz algorithm is one of the most popular methods for solving large-scale over-determined linear systems due to its simplicity and computational efficiency .
Edit intent: clarity
Original: Recent work on "learned indexes" has revolutionized the way we look at the decades-old field of DBMS indexing.
Revised: Recent work on "learned indexes" has changed the way we look at the decades-old field of DBMS indexing.
Edit intent: clarity
Original:  The key idea is that indexes are "models" that predict the position of a key in a dataset.
Revised:  The key idea is that indexes can be thought of as "models" that predict the position of a key in a dataset.
Edit intent: clarity
Original:  The original work by Kraska et al. shows surprising results in terms of search performance and space requirements: A learned index beats a B+Tree by a factor of up to three in search time and by an order of magnitude in memory footprint , however it is limited to static, read-only workloads.
Revised:  The original work by Kraska et al. shows that a learned index beats a B+Tree by a factor of up to three in search time and by an order of magnitude in memory footprint , however it is limited to static, read-only workloads.
Edit intent: clarity
Original:  The original work by Kraska et al. shows surprising results in terms of search performance and space requirements: A learned index beats a B+Tree by a factor of up to three in search time and by an order of magnitude in memory footprint , however it is limited to static, read-only workloads.
Revised:  The original work by Kraska et al. shows surprising results in terms of search performance and space requirements: A learned index beats a B+Tree by a factor of up to three in search time and by an order of magnitude in memory footprint . However, it is limited to static, read-only workloads.
Edit intent: fluency
Original:  This paperpresents a new class of learned indexes called ALEX which addresses  issues that arise when implementing dynamic, updatable learned indexes . Compared to the learned index from Kraska et al. , ALEX has up to 3000X lower space requirements, but has up to 2.7X higher search performance on static workloads.
Revised:  In this paper, we present a new learned index called ALEX which addresses issues that arise when implementing dynamic, updatable learned indexes . Compared to the learned index from Kraska et al. , ALEX has up to 3000X lower space requirements, but has up to 2.7X higher search performance on static workloads.
Edit intent: clarity
Original:  Our detailed experiments show that ALEX presents a key step towards making learned indexes practical for a broader class of database workloads with dynamic updates.
Revised:  We believe ALEX presents a key step towards making learned indexes practical for a broader class of database workloads with dynamic updates.
Edit intent: clarity