wanyu/IteraTeR_v2 huggingface dataset:
Original:  In the Fair-PCA problem , the input data is divided into k groups, and the goal is to find a single d-dimensional representation for all groups for which the maximum reconstruction error of any one group is minimized .
Revised:  In the Fair-PCA problem , the input data is divided into k groups, and the goal is to find a single d-dimensional representation for all groups for which the minimum variance of any one group is minimized .
Edit intent: clarity
Original:  In the Fair-PCA problem , the input data is divided into k groups, and the goal is to find a single d-dimensional representation for all groups for which the maximum reconstruction error of any one group is minimized .
Revised:  In the Fair-PCA problem , the input data is divided into k groups, and the goal is to find a single d-dimensional representation for all groups for which the maximum reconstruction error of any one group is maximized .
Edit intent: fluency
Original:  In NSW  the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensinal space.
Revised:  In NSW , the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensinal space.
Edit intent: fluency
Original:  In NSW  the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensinal space.
Revised:  In NSW the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensional space.
Edit intent: fluency
Original:  As an application of this result, we obtain a polynomial time algorithm for Fair-PCA for k=2 groups , resolving an open problem of Samadi, et. al. 2018, and a polynomial time algorithm for NSW objective for k=2 groups.
Revised:  As an application of this result, we obtain a polynomial time algorithm for Fair-PCA for k=2 groups and a polynomial time algorithm for NSW objective for k=2 groups.
Edit intent: coherence
Original:  We conclude with experiments indicating the effectiveness of algorithms based on extreme point solutions of semi-definite programs on several real-world datasets .
Revised:  We conclude with experiments indicating the effectiveness of algorithms based on extreme point solutions of semi-definite programs on several real-world data sets .
Edit intent: clarity
Original:  The recent rise of cloud applications, representinglarge complex modern distributed services, has made perfor-mance monitoring a major issue and a critical process for bothcloud providers and cloud customers.
Revised:  The recent rise of complex cloud applications has made performance monitoring a major issue and a critical process for bothcloud providers and cloud customers.
Edit intent: clarity
Original:  To better understandthe feasibility of this approach, this paper explores severalapproaches how application monitoring can be integrated intoSDN . In particular, we combine port mirroring with tunneling toenable message filtering and reformatting, and we propose a cus-tomized port sniffing approach.
Revised:  This paper explores several approaches for supporting application monitoring through SDN . In particular, we combine port mirroring with tunneling toenable message filtering and reformatting, and we propose a cus-tomized port sniffing approach.
Edit intent: clarity
Original:  We provide their implementationbased on OVS, analyze their advantages and disadvantages, andprovide a  comprehensive performance evaluation to understandthe trade-offs and to show that moving application monitoringto the network is an attractive option .
Revised:  We provide their implementationbased on OVS, analyze their advantages and disadvantages, andprovide a comprehensive performance evaluation to analyze advantages and disadvantages of our approach, and highlight the trade-offs .
Edit intent: clarity
Original:  For a further introductory note and motivation on the theoretical concept we refer to 1 . A very detailed methodological overview of the concept of a smart derivative contract can be found in 3 .
Revised:  For a further introductory note and motivation on the theoretical concept we refer to URL . A very detailed methodological overview of the concept of a smart derivative contract can be found in 3 .
Edit intent: coherence
Original:  Methods: Approval for this study was obtained by the responsible ethics committees and written informed consent was obtained from all accrued subjects.
Revised:  Methods: 
Edit intent: coherence
Original:  We also give improved sequential algorithms for alias table construction and for sampling with replacement . Experiments on shared-memory parallel machines with up to 158 threads show near linear speedups both for construction and queries  .
Revised:  We also give improved sequential algorithms for alias table construction and for sampling with replacement show near linear speedups both for construction and queries .
Edit intent: clarity
Original:  In the latter case a mean-field critical transition is expected and here we provide numerial results for the synchonization/desynchonization duration distributions.
Revised:  In the latter case a mean-field critical transition is expected and here we provide numerical results for the synchonization/desynchonization duration distributions.
Edit intent: fluency
Original:  At this crossover point we observe power-law--tailed desynchronization durations, with \tau_t \simeq 1.2(1), away from experimental values for the brain.
Revised:  At this crossover point we observe power-law--tailed synchronization durations, with \tau_t \simeq 1.2(1), away from experimental values for the brain.
Edit intent: fluency
Original:  Additionally, we changed the signs of outgoing weights of 20%DIFDELCMD < \\%%% %DIF < of randomly selected nodes, to mimic a model with inhibitory interactions.
Revised:  %DIFDELCMD < \\%%% %DIF < of randomly selected nodes, to mimic a model with inhibitory interactions.
Edit intent: coherence
Original:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Revised:  This paper 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Edit intent: clarity
Original:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Revised:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method %DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Edit intent: coherence
Original:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Revised:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Edit intent: coherence
Original:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Revised:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Edit intent: coherence
Original:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood 20%DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Revised:  This paper presents a new geometric interpretation of the randomize-then-optimize (RTO) method 1%DIFDELCMD < ] %%% and a unified transport-map interpretation of RTO and other optimization-based samplers, i. e., implicit sampling 19%DIFDELCMD < ] %%% and randomized-maximum-likelihood %DIFDELCMD < ]%%% . We then introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension.
Edit intent: coherence
Original:  We thus formalize a function-space version of RTO and establish sufficient conditions for it to produce a valid Metropolis-Hastings proposal, yielding dimension-independent sampling performance.
Revised:  We thus formalize a function space version of RTO and establish sufficient conditions for it to produce a valid Metropolis-Hastings proposal, yielding dimension-independent sampling performance.
Edit intent: fluency
Original:  A major limitation of these approaches is that they take source code as simple tokens of text and ignore its contextual, syntaxtual and structural dependencies.
Revised:  A major limitation of these approaches is that they take source code as simple tokens of text and ignore its contextual, syntactical and structural dependencies.
Edit intent: fluency
Original:  In this work, we present CodeGRU, a Gated Recurrent Unit based source code language model that is capable of capturing contextual, syntaxtual and structural dependencies for modeling the source code.
Revised:  In this work, we present CodeGRU, a gated recurrent unit based source code language model that is capable of capturing contextual, syntaxtual and structural dependencies for modeling the source code.
Edit intent: fluency
Original:  In this work, we present CodeGRU, a Gated Recurrent Unit based source code language model that is capable of capturing contextual, syntaxtual and structural dependencies for modeling the source code.
Revised:  In this work, we present CodeGRU, a Gated Recurrent Unit based source code language model that is capable of capturing source code's contextual, syntactical and structural dependencies for modeling the source code.
Edit intent: fluency
Original:  We evaluated CodeGRU with real-world dataset and it shows that CodeGRU can effectively capture contextual, syntaxtual and structural dependencies which previous works fails.
Revised:  We evaluated CodeGRU with real-world data set and it shows that CodeGRU can effectively capture contextual, syntaxtual and structural dependencies which previous works fails.
Edit intent: clarity
Original:  Our proposed AQR generator provides orders of magnitude reduction in area while offering 6-fold reduced power dissipation, on average, compared to the state-of-the-art non-uniform clock generators.
Revised:  Our proposed AQR generator provides orders of magnitude reduction in area , on average, while offering ~ 6-fold reduced power dissipation, on average, compared to the state-of-the-art non-uniform clock generators.
Edit intent: clarity
Original: Rust is a major advancement in industrial programming languages due in large part to its success in bridging the gap between low-level systems programming and high-level application programming.
Revised: Rust claims to advance industrial programming by bridging the gap between low-level systems programming and high-level application programming.
Edit intent: clarity
Original:  This success has ultimately empowered programmers to more easily build reliable and efficient software , and at its heart lies a novel approach to ownership that balances type system expressivity with usability.
Revised:  At the heart of the argument that this enables programmers to build more reliable and efficient software , and at its heart lies a novel approach to ownership that balances type system expressivity with usability.
Edit intent: clarity
Original:  This success has ultimately empowered programmers to more easily build reliable and efficient software , and at its heart lies a novel approach to ownership that balances type system expressivity with usability.
Revised:  This success has ultimately empowered programmers to more easily build reliable and efficient software , and at its heart lies a novel approach to ownership that aims to balance type system expressivity with usability.
Edit intent: clarity
Original:  To that end, we present Oxide, a formalized programming language close to source-level Rust (but with fully-annotated types).
Revised:  We present Oxide, a formalized programming language close to source-level Rust (but with fully-annotated types).
Edit intent: coherence
Original:  This presentation takes a new view of lifetimes as approximate provenances of references, and our type system is able to automatically compute this information through a flow-sensitive substructural typing judgment for which we prove syntactic type safety using progress and preservation.
Revised:  This presentation takes a new view of lifetimes as an approximation of the provenances of references, and our type system is able to automatically compute this information through a flow-sensitive substructural typing judgment for which we prove syntactic type safety using progress and preservation.
Edit intent: fluency
Original:  This presentation takes a new view of lifetimes as approximate provenances of references, and our type system is able to automatically compute this information through a flow-sensitive substructural typing judgment for which we prove syntactic type safety using progress and preservation.
Revised:  This presentation takes a new view of lifetimes as approximate provenances of references, and our type system is able to automatically compute this information through a substructural typing judgment for which we prove syntactic type safety using progress and preservation.
Edit intent: clarity
Original:  The result is a simpler formulation of borrow checking - including recent features such as non-lexical lifetimes - that we hope researchers will be able to use as the basis for work on Rust.
Revised:  Oxide is a simpler formulation of borrow checking - including recent features such as non-lexical lifetimes - that we hope researchers will be able to use as the basis for work on Rust.
Edit intent: clarity
Original:  While the randomized case is\hat  well-understood,  the main work in the deterministic case is the work of Merhi et al.
Revised:  While the randomized case is\hat well-understood, while the main work in the deterministic case is the work of Merhi et al.
Edit intent: coherence
Original:  While the randomized case is\hat  well-understood,  the main work in the deterministic case is the work of Merhi et al.
Revised:  While the randomized case is\hat well-understood, the main work in the deterministic case is that of Merhi et al.
Edit intent: clarity
Original: 5}n) samples and  similar runtime with the \ell_2/\ell_1 guarantee.
Revised: 5}n) samples and a similar runtime with the \ell_2/\ell_1 guarantee.
Edit intent: fluency
Original:  We focus on the stronger \ell _\infty /\ell_1 guarantee and the closely related problem of incoherent matrices.
Revised:  We focus on the stronger \ell _{\infty /\ell_1 guarantee and the closely related problem of incoherent matrices.
Edit intent: fluency
Original:  Our constructions match previous constructions by DeVore (J Complexity 2007), Amini and Marvasti (IEEE Trans Info Theory 2011) and Nelson, Nguyen and Woodruff (RANDOM  12), where there was no constraint on the form of the incoherent matrix.
Revised:  Our constructions match previous constructions by DeVore (J Complexity 2007), Amini and Marvasti (IEEE Trans Info Theory 2011) and Nelson, Nguyen and Woodruff (RANDOM ' 12), where there was no constraint on the form of the incoherent matrix.
Edit intent: fluency
Original:  Our algorithms are nearly sample optimal , since a lower bound of \Omega (k^2 + k log n) is known, even for the case where the sensing matrix can be arbitrarily designed.
Revised:  Our algorithms are nearly sample-optimal , since a lower bound of \Omega (k^2 + k log n) is known, even for the case where the sensing matrix can be arbitrarily designed.
Edit intent: fluency
Original:  Our algorithms are nearly sample optimal , since a lower bound of \Omega (k^2 + k log n) is known, even for the case where the sensing matrix can be arbitrarily designed.
Revised:  Our algorithms are nearly sample optimal , since a lower bound of \Omega (k^2 + k log n) is known, even for the case where the sensing matrix can be arbitrarily designed.
Edit intent: fluency
Original:  Similarly, for incoherent matrices, a lower bound of \Omega (k^2 log n/ log k) is known , indicating that our constructions are nearly optimal .
Revised:  Similarly, for incoherent matrices, a lower bound of \Omega (k^2 log n/ log k) is known , indicating that our constructions are nearly optimal .
Edit intent: fluency
Original:  Similarly, for incoherent matrices, a lower bound of \Omega (k^2 log n/ log k) is known , indicating that our constructions are nearly optimal .
Revised:  Similarly, for incoherent matrices, a lower bound of \Omega (k^2 log n/ log k) is known for incoherent matrices .
Edit intent: clarity
Original: In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained Regularized Nuclear Norm Minimization (RNNM) framework.
Revised: In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework.
Edit intent: fluency
Original:  Our theoretical findings show that, one can robustly recover any matrix X  from its few noisy measurements \mathbf{b =A(X)+ \mathbf{n with a bounded constraint \| \mathbf{n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Revised:  Our theoretical findings show that, the RNNM method is able to provide a robust recovery of any matrix X from its few noisy measurements \mathbf{b =A(X)+ \mathbf{n with a bounded constraint \| \mathbf{n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Edit intent: clarity
Original:  Our theoretical findings show that, one can robustly recover any matrix X  from its few noisy measurements \mathbf{b =A(X)+ \mathbf{n with a bounded constraint \| \mathbf{n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Revised:  Our theoretical findings show that, one can robustly recover any matrix X from its few noisy measurements b =A(X)+ \mathbf{n with a bounded constraint \| \mathbf{n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Edit intent: fluency
Original:  Our theoretical findings show that, one can robustly recover any matrix X  from its few noisy measurements \mathbf{b =A(X)+ \mathbf{n with a bounded constraint \| \mathbf{n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Revised:  Our theoretical findings show that, one can robustly recover any matrix X from its few noisy measurements \mathbf{b =A(X)+ n with a bounded constraint \| \mathbf{n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Edit intent: fluency
Original:  Our theoretical findings show that, one can robustly recover any matrix X  from its few noisy measurements \mathbf{b =A(X)+ \mathbf{n with a bounded constraint \| \mathbf{n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Revised:  Our theoretical findings show that, one can robustly recover any matrix X from its few noisy measurements \mathbf{b =A(X)+ \mathbf{n with a bounded constraint \| n \| _2 \leq%DIFDELCMD < \epsilonthrough %%% the RNNM, if the linear map A satisfies Restricted Isometry Property (RIP)
Edit intent: fluency
Original:  with%DIFDELCMD < align* %DIFDELCMD < tk<\frac{t-1{t}} align* %%% for certain fixed\leq\epsilon, provided that the tk-order restricted isometry constant (RIC) of A satisfies a certain constraint related to } t> 1. Recently, this condition for t%DIFDELCMD < \geq4%%%  /3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained Nuclear Norm Minimization (NNM).
Revised:  with%DIFDELCMD < align* %DIFDELCMD < tk<\frac{t-1{t}} align* %%% for certain fixed\leq\epsilon, provided that the tk-order restricted isometry constant (RIC) of A satisfies a certain constraint related to } t> %DIFDELCMD < \geq4%%% /3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained Nuclear Norm Minimization (NNM).
Edit intent: coherence
Original:  with%DIFDELCMD < align* %DIFDELCMD < tk<\frac{t-1{t}} align* %%% for certain fixed\leq\epsilon, provided that the tk-order restricted isometry constant (RIC) of A satisfies a certain constraint related to } t> 1. Recently, this condition for t%DIFDELCMD < \geq4%%%  /3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained Nuclear Norm Minimization (NNM).
Revised:  with%DIFDELCMD < align* %DIFDELCMD < tk<\frac{t-1{t}} align* %%% for certain fixed\leq\epsilon, provided that the tk-order restricted isometry constant (RIC) of A satisfies a certain constraint related to } t> 1. Recently, this condition for t%DIFDELCMD < \geq4%%% /3 has been proved by Cai and Zhang (2014) to guarantee the exact recovery of any rank-k matrices via the constrained Nuclear Norm Minimization (NNM).
Edit intent: clarity