wanyu/IteraTeR_v2 huggingface dataset:
Original:  It is merited to choose classical orthogonal polynomials as basis sets of polynomial space with degree at most L. As  node sets we use zeros of orthogonal polynomials such as Chebyshev points of the first kind, Legendre points.
Revised:  It is merited to choose classical orthogonal polynomials as basis sets of polynomial space with degree at most L. As to the node sets we use zeros of orthogonal polynomials such as Chebyshev points of the first kind, Legendre points.
Edit intent: clarity
Original:  As a matter of fact, these approximation polynomials can be expressed in the form of barycentric interpolation  when the interpolation condition is satisfied.
Revised:  As a matter of fact, these approximation polynomials can be expressed in the form of barycentric interpolation formula when the interpolation condition is satisfied.
Edit intent: clarity
Original:  It is merited to choose classical orthogonal polynomials as basis sets of polynomial space with degree at most L. As to the node sets we use zeros of orthogonal polynomials such as Chebyshev points of the first kind, Legendre points .
Revised:  It is merited to choose classical orthogonal polynomials as basis sets of polynomial space with degree at most L. As to the node sets we use zeros of orthogonal polynomials ) .
Edit intent: coherence
Original:  The number of nodes, say N+ 1, is chosen to ensure L \leq2N+ 1. With the aid of Gauss quadrature, we obtain approximation polynomials of degree L in closed form without solving linear algebra or optimization problem.
Revised:  The number of nodes, say N+ 1. For 2L \leq2N+ 1. With the aid of Gauss quadrature, we obtain approximation polynomials of degree L in closed form without solving linear algebra or optimization problem.
Edit intent: coherence
Original:  The number of nodes, say N+ 1, is chosen to ensure L \leq2N+ 1. With the aid of Gauss quadrature, we obtain approximation polynomials of degree L in closed form without solving linear algebra or optimization problem.
Revised:  The number of nodes, say N+ 1, is chosen to ensure L \leq2N+ 1, with the aid of Gauss quadrature, we obtain approximation polynomials of degree L in closed form without solving linear algebra or optimization problem.
Edit intent: coherence
Original:  We then study the approximation quality of \ell_2 -regularization approximation polynomial in terms of the Lebesgue constants, and the sparsity of \ell_1 -regularization approximation polynomial, respectively.
Revised:  We then study the approximation quality of \ell_2 -regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of \ell_1 -regularization approximation polynomial, respectively.
Edit intent: fluency
Original:  We then study the approximation quality of \ell_2 -regularization approximation polynomial in terms of the Lebesgue constants, and the sparsity of \ell_1 -regularization approximation polynomial, respectively.
Revised:  We then study the approximation quality of \ell_2 -regularization approximation polynomial in terms of the Lebesgue constants, and the sparsity of \ell_1 -regularized approximation polynomial, respectively.
Edit intent: fluency
Original: We consider polynomial approximation over the interval [-1,1] by a class of regularized weighted discrete least squares methods with \ell_2 -regularization and \ell_1-regularization terms , respectively.
Revised: We consider polynomial approximation over the interval [-1,1] by regularized weighted discrete least squares methods with \ell_2 -regularization and \ell_1-regularization terms , respectively.
Edit intent: clarity
Original: We consider polynomial approximation over the interval [-1,1] by a class of regularized weighted discrete least squares methods with \ell_2 -regularization and \ell_1-regularization terms , respectively.
Revised: We consider polynomial approximation over the interval [-1,1] by a class of regularized weighted discrete least squares methods with \ell_2 - or \ell_1-regularization terms , respectively.
Edit intent: fluency
Original: We consider polynomial approximation over the interval [-1,1] by a class of regularized weighted discrete least squares methods with \ell_2 -regularization and \ell_1-regularization terms , respectively.
Revised: We consider polynomial approximation over the interval [-1,1] by a class of regularized weighted discrete least squares methods with \ell_2 -regularization and \ell_1-regularization , respectively.
Edit intent: clarity
Original:  As nodes set we use Gauss quadrature points ( that are the zeros of orthogonal polynomials).
Revised:  As the set of nodes we use Gauss quadrature points ( that are the zeros of orthogonal polynomials).
Edit intent: clarity
Original:  As nodes set we use Gauss quadrature points ( that are the zeros of orthogonal polynomials).
Revised:  As nodes set we use Gauss quadrature points ( which are zeros of orthogonal polynomials).
Edit intent: fluency
Original:  As a matter of fact, these approximation polynomials can be expressed in the form of  barycentric interpolation formula (Berrut and Trefethen, 2004) when the interpolation condition is satisfied.
Revised:  As a matter of fact, these approximation polynomials can be expressed in the form of the barycentric interpolation formula (Berrut and Trefethen, 2004) when the interpolation condition is satisfied.
Edit intent: fluency
Original:  As a matter of fact, these approximation polynomials can be expressed in the form of  barycentric interpolation formula (Berrut and Trefethen, 2004) when the interpolation condition is satisfied.
Revised:  As a matter of fact, these approximation polynomials can be expressed in the form of barycentric interpolation formula when an interpolation condition is satisfied.
Edit intent: coherence
Original:  We then study the approximation quality of  \ell_2-regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of  \ell_1-regularized approximation polynomial , respectively .
Revised:  We then study the approximation quality of the \ell_2-regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of \ell_1-regularized approximation polynomial , respectively .
Edit intent: fluency
Original:  We then study the approximation quality of  \ell_2-regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of  \ell_1-regularized approximation polynomial , respectively .
Revised:  We then study the approximation quality of \ell_2-regularized approximation polynomial in terms of Lebesgue constants, and the sparsity of \ell_1-regularized approximation polynomial , respectively .
Edit intent: fluency
Original:  We then study the approximation quality of  \ell_2-regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of  \ell_1-regularized approximation polynomial , respectively .
Revised:  We then study the approximation quality of \ell_2-regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of the \ell_1-regularized approximation polynomial , respectively .
Edit intent: fluency
Original:  We then study the approximation quality of  \ell_2-regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of  \ell_1-regularized approximation polynomial , respectively .
Revised:  We then study the approximation quality of \ell_2-regularized approximation polynomial in terms of the Lebesgue constants, and the sparsity of \ell_1-regularized approximation polynomial .
Edit intent: coherence
Original:  Finally, we give numerical examples to illustrate these theoretical results and show that  well-chosen regularization parameter can provide good performanceapproximation , with or without contaminated data.
Revised:  Finally, we give numerical examples to illustrate these theoretical results and show that a well-chosen regularization parameter can provide good performanceapproximation , with or without contaminated data.
Edit intent: fluency
Original:  Finally, we give numerical examples to illustrate these theoretical results and show that  well-chosen regularization parameter can provide good performanceapproximation , with or without contaminated data.
Revised:  Finally, we give numerical examples to illustrate these theoretical results and show that well-chosen regularization parameter can lead to good performance , with or without contaminated data.
Edit intent: clarity
Original:  We provide algorithms and hardness results for the task of increasing the matching preclusion number from one to two in bipartite graphs at minimal cost .
Revised:  We consider the task of increasing the matching preclusion number from one to two in bipartite graphs at minimal cost .
Edit intent: clarity
Original:  For the unit weight problem we provide a deterministic \log_2 n-factor approximation algorithm , as well as polynomial-time algorithms for graphs of bounded treewidth and chordal-bipartite graphs.
Revised:  For the unit weight problem we provide a \log_2 n-factor approximation algorithm , as well as polynomial-time algorithms for graphs of bounded treewidth and chordal-bipartite graphs.
Edit intent: clarity
Original:  For the unit weight problem we provide a deterministic \log_2 n-factor approximation algorithm , as well as polynomial-time algorithms for graphs of bounded treewidth and chordal-bipartite graphs.
Revised:  For the unit weight problem we provide a deterministic \log_2 n-factor approximation algorithm and a polynomial-time algorithms for graphs of bounded treewidth and chordal-bipartite graphs.
Edit intent: coherence
Original:  For the unit weight problem we provide a deterministic \log_2 n-factor approximation algorithm , as well as polynomial-time algorithms for graphs of bounded treewidth and chordal-bipartite graphs.
Revised:  For the unit weight problem we provide a deterministic \log_2 n-factor approximation algorithm , as well as polynomial-time algorithm for chordal-bipartite graphs.
Edit intent: clarity
Original: It is a long-standing open problem whether there exists an output-polynomial algorithm enumerating all minimal hitting sets of a hypergraph.
Revised: We devise a method to enumerate the inclusion-wise minimal hitting sets of a hypergraph.
Edit intent: clarity
Original:  Additionally, we prove that the extension problem of minimal hitting sets is W 3%DIFDELCMD < ]%%% -complete when parameterised by the size of the set which is to be extended .
Revised:  Additionally, we prove that the extension problem of minimal hitting sets 3%DIFDELCMD < ]%%% -complete when parameterised by the size of the set which is to be extended .
Edit intent: clarity
Original:  The algorithm ]  has delay O(m^{k^*+1} \, n^2) on n-vertex, m-edge hypergraphs, where k^* is the rank of the transversal hypergraph, i.e., the cardinality of the largest minimal solution.
Revised:  The algorithm ] has delay O(m^{k^*+1} n^2) on n-vertex, m-edge hypergraphs, where k^* is the rank of the transversal hypergraph, i.e., the cardinality of the largest minimal solution.
Edit intent: coherence
Original:  We show that this problem, parameterised by the cardinality of the set which is to be extended, is one of the first natural  W[3] -complete problems .
Revised:  We show that this is one of the first natural W[3] -complete problems .
Edit intent: clarity
Original:  We show that this problem, parameterised by the cardinality of the set which is to be extended, is one of the first natural  W[3] -complete problems .
Revised:  We show that this problem, parameterised by the cardinality of the set which is to be extended, is one of the first natural W[3] .
Edit intent: clarity
Original:  We give an algorithm for the subroutine that is optimal under the assumption that W 2%DIFDELCMD < ] %DIFDELCMD < %%% \neq \mathrm{FPT unique column combinations .
Revised:  We give an algorithm for the 2%DIFDELCMD < ] %DIFDELCMD < %%% \neq \mathrm{FPT unique column combinations .
Edit intent: clarity
Original: Recently, spiking neural network (SNN) has received significant attentions for its biological plausibility.
Revised: Spiking neural networks (SNNs) have received significant attention for their biological plausibility.
Edit intent: clarity
Original:  SNN theoretically has at least the same computational power as traditional artificial neural networks (ANNs) , and it has the potential to achieve revolutionary energy-efficiency  .
Revised:  SNNs theoretically have at least the same computational power as traditional artificial neural networks (ANNs) , and it has the potential to achieve revolutionary energy-efficiency .
Edit intent: fluency
Original:  SNN theoretically has at least the same computational power as traditional artificial neural networks (ANNs) , and it has the potential to achieve revolutionary energy-efficiency  .
Revised:  SNN theoretically has at least the same computational power as traditional artificial neural networks (ANNs) . They possess potential of achieving energy-efficiency .
Edit intent: clarity
Original:  However, at current stage, it is still a big challenge to train a very deep SNN. In this paper, we propose an efficient approach to build a spiking version of deep residual network (ResNet) , which represents the state-of-the-art convolutional neural networks (CNNs).
Revised:  However, it is still a big challenge to train a very deep SNN. In this paper, we propose an efficient approach to build a spiking version of deep residual network (ResNet) , which represents the state-of-the-art convolutional neural networks (CNNs).
Edit intent: coherence
Original:  We employ the idea of converting a trained ResNet to a network of spiking neurons  named Spiking ResNet .
Revised:  We employ the idea of converting a trained ResNet to a network of spiking neurons , named Spiking ResNet .
Edit intent: fluency
Original:  To address the conversion problem, we propose a shortcut normalisation mechanism to appropriately scale continuous-valued activations to match firing rates in SNN, and a layer-wise error compensation approach to reduce the error caused by discretisation.
Revised:  To address the conversion problem, we propose a shortcut conversion model to appropriately scale continuous-valued activations to match firing rates in SNN, and a layer-wise error compensation approach to reduce the error caused by discretisation.
Edit intent: clarity
Original:  To address the conversion problem, we propose a shortcut normalisation mechanism to appropriately scale continuous-valued activations to match firing rates in SNN, and a layer-wise error compensation approach to reduce the error caused by discretisation.
Revised:  To address the conversion problem, we propose a shortcut normalisation mechanism to appropriately scale continuous-valued activations to match firing rates in SNN, and a compensation mechanism to reduce the error caused by discretisation.
Edit intent: coherence
Original:  Experimental results on MNIST, CIFAR-10, and CIFAR-100 demonstrate thatthe proposed Spiking ResNet yields the state-of-the-art performance of SNNs .
Revised:  Experimental results demonstrate that, compared with the state-of-the-art SNN approaches, the proposed Spiking ResNet yields the state-of-the-art performance of SNNs .
Edit intent: clarity
Original:  Timelines provide an intuitive way to facilitate an overview of events related to a query entity - i.e.  an entity or an event of user interest - over a certain period of time.
Revised:  Timelines provide an intuitive way to facilitate an overview of events related to a query entity - i.e. an entity or an event of user interest - over a certain period of time.
Edit intent: fluency
Original:  Timelines provide an intuitive way to facilitate an overview of events related to a query entity - i.e.  an entity or an event of user interest - over a certain period of time.
Revised:  Timelines provide an intuitive way to facilitate an overview of events related to a query entity - i.e. , an entity or an event of user interest - over a certain period of time.
Edit intent: fluency
Original:  The line-based halftoning principle called `hatching` is applied to the line patterns naturally occuring in FDM prints, which are built up in a layer-by-layer fashion.
Revised:  The line-based halftoning principle called 'hatching' is applied to the line patterns naturally occuring in FDM prints, which are built up in a layer-by-layer fashion.
Edit intent: fluency
Original:  The proposed halftoning technique isn ` t limited by the challenges existing techniques face;
Revised:  The proposed halftoning technique isn ' t limited by the challenges existing techniques face;
Edit intent: fluency
Original: To address modeling problems of brain-inspired intelligence, this thesis is focused on researching in the semantic-oriented framework design for image, audio, language and video .
Revised: To address modeling problems of brain-inspired intelligence, this thesis is focused on researching in the semantic-oriented framework design for multimedia and multimodal information .
Edit intent: clarity
Original:  Furthermore, the semantic-oriented hierarchical Cross-media Neural Cognitive Computing (CNCC) framework was proposed based on MNCC  , and formal description and analysis for CNCC  was given.
Revised:  Furthermore, the semantic-oriented hierarchical Cross-media Neural Cognitive Computing (CNCC) framework was proposed based on MNCC model , and formal description and analysis for CNCC was given.
Edit intent: clarity
Original:  Furthermore, the semantic-oriented hierarchical Cross-media Neural Cognitive Computing (CNCC) framework was proposed based on MNCC  , and formal description and analysis for CNCC  was given.
Revised:  Furthermore, the semantic-oriented hierarchical Cross-media Neural Cognitive Computing (CNCC) framework was proposed based on MNCC , and formal description and analysis for CNCC framework was given.
Edit intent: coherence
Original: We investigate the behavior of a simple majority dynamics on network topologies that exhibit a clustered structure.
Revised: We investigate the behavior of a simple majority dynamics on networks of agents whose interaction topology exhibits a community structure.
Edit intent: clarity
Original:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Revised:  By leveraging recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Edit intent: fluency
Original:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Revised:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Edit intent: clarity
Original:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Revised:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized , the system rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Edit intent: clarity
Original:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Revised:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the communities maintain internal consensus on two different states.
Edit intent: clarity
Original:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on two different states.
Revised:  By leveraging on recent advancements in the analysis of dynamics, we prove that, when the initial states of the nodes are randomly initialized or when they satisfy a slight bias condition, the network rapidly and stably converges to a configuration in which the clusters maintain internal consensus on different states.
Edit intent: clarity
Original:   In the context of the study of Label Propagation Algorithms, a class of widely used heuristics for clustering in data mining , it represents the first theoretical result on the behavior of a  label propagation algorithm with quasilinear message complexity.
Revised:  In the context of Label Propagation Algorithms, a class of widely used heuristics for clustering in data mining , it represents the first theoretical result on the behavior of a label propagation algorithm with quasilinear message complexity.
Edit intent: clarity
Original:   In the context of the study of Label Propagation Algorithms, a class of widely used heuristics for clustering in data mining , it represents the first theoretical result on the behavior of a  label propagation algorithm with quasilinear message complexity.
Revised:  In the context of the study of Label Propagation Algorithms, a class of widely used heuristics for clustering in data mining , it represents the first theoretical result on the behavior of a distributed label propagation algorithm with quasilinear message complexity.
Edit intent: clarity
Original:   In the context of the study of Label Propagation Algorithms, a class of widely used heuristics for clustering in data mining , it represents the first theoretical result on the behavior of a  label propagation algorithm with quasilinear message complexity.
Revised:  In the context of the study of Label Propagation Algorithms, a class of widely used heuristics for clustering in data mining , it represents the first theoretical result on the behavior of a label propagation algorithm with quasi-linear message complexity.
Edit intent: fluency
Original:  Our results  shows that, when the probability of adoption of a given mutation by a node of the evolutionary graph depends super-linearly on the frequency of the mutation in the neighborhood of the node , and the underlying evolutionary graph has a clustered structure, there is a non-negligible probability for species differentiation to occur.
Revised:  Our results shows that, when the probability of adoption of a given mutation by a node of the evolutionary graph depends super-linearly on the frequency of the mutation in the neighborhood of the node and the underlying evolutionary graph has a clustered structure, there is a non-negligible probability for species differentiation to occur.
Edit intent: fluency