wanyu/IteraTeR_v2 huggingface dataset:
Original:  Hence, by using only subsampling and the incomplete Cholesky decomposition , we obtain  at nearly linear complexity  the compression, inversion and approximate PCA of a large class of covariance matrices.
Revised:  Hence, by using only subsampling and the incomplete Cholesky decomposition , we obtain at nearly linear complexity , the compression, inversion and approximate PCA of a large class of covariance matrices.
Edit intent: fluency
Original:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) }  \log^{2d}( N /\epsilon) ) in time.
Revised:  By inverting the order of the Cholesky factorization we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) } \log^{2d}( N /\epsilon) ) in time.
Edit intent: clarity
Original:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) }  \log^{2d}( N /\epsilon) ) in time.
Revised:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) } \log^{2d}( N /\epsilon) ) in time.
Edit intent: fluency
Original:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) }  \log^{2d}( N /\epsilon) ) in time.
Revised:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) } \log^{2d}( N /\epsilon) ) in time.
Edit intent: fluency
Original:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) }  \log^{2d}( N /\epsilon) ) in time.
Revised:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and ( N \log^{2}( N ) } \log^{2d}( N /\epsilon) ) in time.
Edit intent: fluency
Original:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) }  \log^{2d}( N /\epsilon) ) in time.
Revised:  By inverting the order of the Cholesky decomposition we also obtain a solver for elliptic PDE with complexity \mathcal{O ( N \log ( N ) \log ^{d}( N /\epsilon) ) in space and \mathcal{O ( N \log^{2}( N ) } O ( N \log^{2d}( N /\epsilon) ) in time.
Edit intent: coherence
Original: In this paper we revisit matrix completion for recommender systems from the point of view of link prediction on graphs.
Revised: We consider matrix completion for recommender systems from the point of view of link prediction on graphs.
Edit intent: clarity
Original:  Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges representing observed ratings.
Revised:  Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges denoting observed ratings.
Edit intent: clarity
Original:  Our model achieves competitive performance on standard collaborative filtering benchmarks , significantly outperforming related methodsin a recommendation task with side information .
Revised:  Our model achieves competitive performance on standard collaborative filtering benchmarks . In settings where complimentary feature information or structured data such as a social network is available, our framework outperforms recent state-of-the-art methods .
Edit intent: clarity
Original:  This article focus on that issue putting on evidence some misconception related with future generations of machines and the understanding of the brain.
Revised:  This article focuses on that issue putting on evidence some misconception related with future generations of machines and the understanding of the brain.
Edit intent: fluency
Original:  We prove a lower bound on c_{n,k, similar to the lower bound in \mbox{ polymath2010moser}0pt , but with better dependency on k.
Revised:  We , similar to the lower bound in \mbox{ polymath2010moser}0pt , but with better dependency on k.
Edit intent: clarity
Original:  In addition, we show }  that for k \ge 3 the density Hales-Jewett number c_{n,k} is equal to the maximal size of a cylinder intersection in the problem Part_{n,k} of testing whether k subsets of [n] form a partition.
Revised:  In addition, we show } show that for k \ge 3 the density Hales-Jewett number c_{n,k} is equal to the maximal size of a cylinder intersection in the problem Part_{n,k} of testing whether k subsets of [n] form a partition.
Edit intent: fluency
Original:  Thus, Tesson's bound on the problem using the Hales-Jewett theorem \mbox{ \cite{tessonapplication }\hspace{0pt} } is in fact tight, and the density Hales-Jewett number can be thought of as a quantity in communication complexity , similar to the lower bound in \mbox{ \cite{polymath2010moser} }\hspace{0pt} which is roughly c_{n,k}/k^n }\ge  .
Revised:  Thus, Tesson's bound on the problem using the Hales-Jewett theorem }\hspace{0pt} } is in fact tight, and the density Hales-Jewett number can be thought of as a quantity in communication complexity , similar to the lower bound in \mbox{ \cite{polymath2010moser} }\hspace{0pt} which is roughly c_{n,k}/k^n }\ge .
Edit intent: fluency
Original: We investigate a set of discrete-spin statistical physics models for opinion spread in social networks and explore how suitable they are for  predicting real-world belief change on both the individual and group levels.
Revised: We investigate a set of discrete-spin statistical physics models , and explore how suitable they are for predicting real-world belief change on both the individual and group levels.
Edit intent: clarity
Original: We investigate a set of discrete-spin statistical physics models for opinion spread in social networks and explore how suitable they are for  predicting real-world belief change on both the individual and group levels.
Revised: We investigate a set of discrete-spin statistical physics models for opinion spread in social networks and explore how suitable they are for understanding and predicting real-world belief change on both the individual and group levels.
Edit intent: clarity
Original:  We investigate the effects of different social interaction rules (voter, majority, and expert rule), a variety of both artificial and realistic social network structures , different distributions of initial information, dependence on clustering of intrinsic preferences, the effects of having only two choices vs.~multiple choices, and different weightings of social information input relative to intrinsic preferences.
Revised:  We investigate the effects of different social interaction rules that people use, network structures in which they are embedded, distributions of initial information, dependence on clustering of intrinsic preferences, the effects of having only two choices vs.~multiple choices, and different weightings of social information input relative to intrinsic preferences.
Edit intent: clarity
Original:  We investigate the effects of different social interaction rules (voter, majority, and expert rule), a variety of both artificial and realistic social network structures , different distributions of initial information, dependence on clustering of intrinsic preferences, the effects of having only two choices vs.~multiple choices, and different weightings of social information input relative to intrinsic preferences.
Revised:  We investigate the effects of different social interaction rules (voter, majority, and expert rule), a variety of both artificial and realistic social network structures , different distributions of initial beliefs and intrinsic preferences, the effects of having only two choices vs.~multiple choices, and different weightings of social information input relative to intrinsic preferences.
Edit intent: clarity
Original:  We investigate the effects of different social interaction rules (voter, majority, and expert rule), a variety of both artificial and realistic social network structures , different distributions of initial information, dependence on clustering of intrinsic preferences, the effects of having only two choices vs.~multiple choices, and different weightings of social information input relative to intrinsic preferences.
Revised:  We investigate the effects of different social interaction rules (voter, majority, and expert rule), a variety of both artificial and realistic social network structures , different distributions of initial information, dependence on clustering of intrinsic preferences, and the relative importance of social information and intrinsic preferences.
Edit intent: clarity
Original:  We then compare the predictions of these models to empirical social science studies , one done at MIT on 80~individuals living in a dorm during the 2008 presidential election season, and another conducted online by us with 94~participants  during the 2016 presidential election primary season.
Revised:  We then compare the predictions of these models to empirical social science studies , one done at MIT on 80~individuals living in a dorm during the 2008 presidential election season, and another on 94~participants during the 2016 presidential election primary season.
Edit intent: clarity
Original:  We find that these relatively simple statistical physics-based models contain predictive value on both the individual and group levels.
Revised:  We find that simple statistical physics-based models contain predictive value on both the individual and group levels.
Edit intent: clarity
Original:  The results underscore the sensitivity of opinion spread to the underlying social network structure and the number of available belief options, and to a somewhat lesser (but still relevant) degree to the social interaction rules.
Revised:  The results underscore the sensitivity of opinion spread to the underlying social network structure and the social interaction rules.
Edit intent: clarity
Original: Determining the principal energy pathways occurring in biomolecules as a result of thermal motion  remains challenging due to the intrinsic complexity of the systems involved.
Revised: Determining the principal energy pathways occurring in biomolecules as a result of thermal motion , remains challenging due to the intrinsic complexity of the systems involved.
Edit intent: fluency
Original:  Typically, performing just a molecular dynamics simulation is not enough to reveal these pathways and further post-processing analysis of the trajectories becomes strictly necessary .
Revised:  Graph theory provides an approach for making sense of such complexity, where allosteric proteins can be represented as networks of amino acids .
Edit intent: clarity
Original: Initially proposed as part of the cypherpunk-esque rebellion started by Bitcoin, the Ripple credit network is dramatically reshaping the financial and remittance industries.
Revised: The Ripple credit network is dramatically reshaping the financial and remittance industries.
Edit intent: coherence
Original:  These path-based settlements set Ripple apart from the cryptocurrency space (such as Bitcoin and altcoins)both conceptually and in terms of applicability .
Revised:  These path-based IOweYou (IOU) settlements across different (crypto)currencies conceptually distinguishes the Ripple blockchain from cryptocurrencies, and makes it highly suitable to an orthogonal yet vast set of applications in the remittance world for cross-border transactions and beyond .
Edit intent: clarity
Original:  This work takes an in-depth look at the Ripple network since its inception in order to un derstand its structure, evolution, and vulnerability to attacks.
Revised:  This work studies the structure and evolution of the Ripple network since its inception in order to un derstand its structure, evolution, and vulnerability to attacks.
Edit intent: clarity
Original:  From the security point of view, although the core of the network is well-connected and provides high liquidity to users, there is a user base of around 50 ,000 wallets prone to disruption by as few as 10 highly connected wallets.
Revised:  From the security point of view, although the core of the network is well-connected and provides high liquidity to users, there is a user base of around 50 ,000 wallets that can be financially isolated by as few as 10 highly connected wallets.
Edit intent: clarity
Original: Deep neural networks (DNN) have been successfully applied for music classification including music tagging.
Revised: Deep neural networks (DNN) have been successfully applied to music classification including music tagging.
Edit intent: fluency
Original:  However, there are several open questions regarding generalisation and best practices in the choice of network architectures, hyper-parameters and input representations .
Revised:  However, there are several open questions regarding the training, evaluation, and analysis of DNNs .
Edit intent: clarity
Original:  We perform comprehensive experiments involving audio preprocessing using different time-frequency representations, logarithmic magnitude compression, frequency weighting and scaling.
Edit intent: coherence
Original:  The results highlight several import aspects of music tagging and neural networks.
Revised:  The results highlight several important aspects of music tagging and neural networks.
Edit intent: fluency
Original:  We show that networks can be effective despite of relatively large error rates in groundtruth datasets .
Revised:  We show that networks can be effective despite relatively large error rates in groundtruth datasets .
Edit intent: fluency
Original: The whole enterprise of Clebsch-Gordan decomposition (CGD) of an arbitrary collection of SU(2) spin representations can be recast as a simple enumerative combinatoric problem .
Revised: The whole enterprise of spin compositions can be recast as a simple enumerative combinatoric problem .
Edit intent: clarity
Original: The whole enterprise of Clebsch-Gordan decomposition (CGD) of an arbitrary collection of SU(2) spin representations can be recast as a simple enumerative combinatoric problem .
Revised: The whole enterprise of Clebsch-Gordan decomposition (CGD) of an arbitrary collection of SU(2) spin representations can be recast as simple enumerative combinatoric problem .
Edit intent: fluency
Original: The whole enterprise of Clebsch-Gordan decomposition (CGD) of an arbitrary collection of SU(2) spin representations can be recast as a simple enumerative combinatoric problem .
Revised: The whole enterprise of Clebsch-Gordan decomposition (CGD) of an arbitrary collection of SU(2) spin representations can be recast as a simple enumerative combinatoric problems .
Edit intent: fluency
Original:  We show here that enumerative combinatorics (EC)book:Stanley-2011 is a natural setting for CGD , and easily leads to very general analytic formulae -- so far not present in the literature.
Revised:  We show here that enumerative combinatorics (EC)book:Stanley-2011 is a natural setting for CGD , and easily leads to very general analytic formulae -- many of which hitherto not present in the literature.
Edit intent: clarity
Original:  Borodin and Ivanova Discrete Math. 340 (2017) 2234--2242%DIFDELCMD < ] %%% proved that \Omega_{\Delta \leq \Delta + 29 for \Delta \geq 13.
Revised:  Borodin and Ivanova %DIFDELCMD < ] %%% proved that \Omega_{\Delta \leq \Delta + 29 for \Delta \geq 13.
Edit intent: coherence
Original:  They also asked: what's the minimum integer 0 such that \Delta \leq \Delta + 28 whenever \Delta \geq 0? } {\em   In this paper, we give two descriptions of minor 5-stars in plane graphs with minimum degree at least five, the first one refines Borodin and Ivanova's result and the second one partially gives an answer of Borodin and Ivanova's question .
Revised:  They also asked: what's the minimum integer 0 such that \Delta \leq \Delta + 28 whenever \Delta \geq 0? } . The{\em In this paper, we give two descriptions of minor 5-stars in plane graphs with minimum degree at least five, the first one refines Borodin and Ivanova's result and the second one partially gives an answer of Borodin and Ivanova's question .
Edit intent: coherence
Original:  They also asked: what's the minimum integer 0 such that \Delta \leq \Delta + 28 whenever \Delta \geq 0? } {\em   In this paper, we give two descriptions of minor 5-stars in plane graphs with minimum degree at least five, the first one refines Borodin and Ivanova's result and the second one partially gives an answer of Borodin and Ivanova's question .
Revised:  They also asked: what's the minimum integer 0 such that \Delta \leq \Delta + 28 whenever \Delta \geq 0? } {\em height In this paper, we give two descriptions of minor 5-stars in plane graphs with minimum degree at least five, the first one refines Borodin and Ivanova's result and the second one partially gives an answer of Borodin and Ivanova's question .
Edit intent: fluency
Original:  Public health responses should be tailored to the size and timing of any ongoing outbreak.
Revised:  Effective responses rely on the timely understanding of the magnitude and the evolution of an outbreak.
Edit intent: clarity
Original:  These data are both readily available and have the potential to provide powerful information for inferring and predicting the features of seasonal and pandemic influenza.
Revised:  These data are both readily available and have the potential to provide valuable information to estimate and predict the key transmission features of seasonal and pandemic influenza.
Edit intent: clarity
Original:  We propose an epidemic model which links the underlying transmission dynamic process to data on severe influenza cases.
Revised:  We propose an epidemic model that links the underlying transmission dynamic process to data on severe influenza cases.
Edit intent: fluency
Original:  Within a Bayesian framework, we infer  the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including  the effective reproduction number , initial susceptibility, the probability of admission to Intensive Care given infectionand the attack rate.
Revised:  Within a Bayesian framework, we infer the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including : the effective reproduction number , initial susceptibility, the probability of admission to Intensive Care given infectionand the attack rate.
Edit intent: fluency
Original:  Within a Bayesian framework, we infer  the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including  the effective reproduction number , initial susceptibility, the probability of admission to Intensive Care given infectionand the attack rate.
Revised:  Within a Bayesian framework, we infer the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including the effective reproduction number ; the initial susceptibility; the probability of admission to Intensive Care given infectionand the attack rate.
Edit intent: fluency
Original:  This paper suggests that severe case data may be effectively exploited to estimate epidemiological characteristics and to predict the further evolution of an epidemic  .
Revised:  This paper suggests that severe case data can be effectively used to estimate epidemiological characteristics and to predict the further evolution of an epidemic .
Edit intent: clarity
Original:  This paper suggests that severe case data may be effectively exploited to estimate epidemiological characteristics and to predict the further evolution of an epidemic  .
Revised:  This paper suggests that severe case data may be effectively exploited to estimate epidemiological characteristics and to predict the evolution of an epidemic .
Edit intent: clarity
Original: Common-sense or background knowledge is required to understand natural language, but in most neural natural language understanding (NLU) systems, the requisite background knowledge is indirectly acquired from static corpora .
Revised: Common-sense and background knowledge is required to understand natural language, but in most neural natural language understanding (NLU) systems, the requisite background knowledge is indirectly acquired from static corpora .
Edit intent: fluency
Original:  A new task-agnostic reading module provides refined word representations to a task-specific NLU architecture by processing background knowledge in the form of free-text statements , together with the task-specific inputs.
Revised:  A general-purpose reading module reads background knowledge in the form of free-text statements , together with the task-specific inputs.
Edit intent: clarity
Original:  A new task-agnostic reading module provides refined word representations to a task-specific NLU architecture by processing background knowledge in the form of free-text statements , together with the task-specific inputs.
Revised:  A new task-agnostic reading module provides refined word representations to a task-specific NLU architecture by processing background knowledge in the form of free-text statements (together with task-specific inputs.
Edit intent: fluency
Original:  Strong performance on the tasks of document question answering (DQA) and recognizing textual entailment (RTE) demonstrate the effectiveness and flexibility of our approach.
Revised:  Strong performance on the tasks of document question answering (DQA) and recognizing textual entailment (RTE) demonstrate the effectiveness and flexibility of the approach.
Edit intent: fluency
Original:  Analysis shows that our models learn to exploit knowledge selectively and in a semantically appropriate way.
Revised:  Analysis shows that our model learns to exploit knowledge selectively and in a semantically appropriate way.
Edit intent: fluency
Original:  Analysis shows that our models learn to exploit knowledge selectively and in a semantically appropriate way.
Revised:  Analysis shows that our models learn to exploit knowledge in a semantically appropriate way.
Edit intent: clarity
Original:  One fundamental issue is that the spike activity is naturally non-differentiable which causes great difficulties in training SNNs. To this end, we build an iterative LIF model that is more friendly for gradient descent training.
Revised:  Another fundamental issue is that the spike activity is naturally non-differentiable which causes great difficulties in training SNNs. To this end, we build an iterative LIF model that is more friendly for gradient descent training.
Edit intent: fluency
Original:  Our purpose is to propose an efficient layer formulation that extends this property to any domain  described by a graph.
Revised:  Our purpose is to propose an efficient layer formulation that extends this property to any domain that can be described by a graph.
Edit intent: clarity
Original:  It also empowers new memory designs for executing tasks not traditionally associated with memories.
Revised:  This technology also empowers new memory designs for executing tasks not traditionally associated with memories.
Edit intent: clarity
Original:  Although several studies have taken advantage of the novel architecture of HMC, they have not fully explored either its characteristics in terms of latency and bandwidth or their correlation with temperature and power consumption  .
Revised:  Although several studies have taken advantage of the novel architecture of HMC, its characteristics in terms of latency and bandwidth or their correlation with temperature and power consumption .
Edit intent: clarity