wanyu/IteraTeR_full_sent huggingface dataset:
Original:  This problem is APX-hard in the general and metric cases but admits efficient approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by some vector norm.
Revised:  This problem is APX-hard in the general and metric cases but admits approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by some vector norm.
Edit intent: clarity
Original:  In fact, the suggested algorithm implements a scheme EPTAS : for any fixed \varepsilon\in(0,1), it computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Revised:  In fact, the proposed algorithm implements a scheme EPTAS : for any fixed \varepsilon\in(0,1), it computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Edit intent: fluency
Original:  In fact, the suggested algorithm implements a scheme EPTAS : for any fixed \varepsilon\in(0,1), it computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Revised:  In fact, the suggested algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), it computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Edit intent: clarity
Original:  In fact, the suggested algorithm implements a scheme EPTAS : for any fixed \varepsilon\in(0,1), it computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Revised:  In fact, the suggested algorithm implements a scheme EPTAS : for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Edit intent: clarity
Original:  This problem is APX-hard in the general and metric cases but admits approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by some vector norm .
Revised:  This problem is APX-hard in the general metric case but admits polynomial-time approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by some vector norm .
Edit intent: meaning-changed
Original:  This problem is APX-hard in the general and metric cases but admits approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by some vector norm . In this paper, we propose the first polynomial-time approximation scheme for Max TSP in  arbitrary metric space of fixed doubling dimension.
Revised:  This problem is APX-hard in the general and metric cases but admits approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by a vector norm in fixed-dimensional real space. We propose the first polynomial-time approximation scheme for Max TSP in arbitrary metric space of fixed doubling dimension.
Edit intent: clarity
Original:  In fact, the proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Revised:  The proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Edit intent: coherence
Original:  In fact, the proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Revised:  In fact, the proposed algorithm implements an efficient PTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Edit intent: clarity
Original:  In fact, the proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Revised:  In fact, the proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Edit intent: clarity
Original:  In fact, the proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
Revised:  In fact, the proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the problem in cubic time.
Edit intent: clarity
Original:  This foundation should include a collection of suitable elements (usually hypercubes, simplices, or closely related polytopes), numerical interpolation procedures (usually orthonormal polynomial bases), and numerical integration procedures (usually quadrature /cubature rules).
Revised:  This foundation should include a collection of suitable elements (usually hypercubes, simplices, or closely related polytopes), numerical interpolation procedures (usually orthonormal polynomial bases), and numerical integration procedures (usually quadrature rules).
Edit intent: fluency
Original:  The branching model is used to derive  analytical results for the trade-offs between the different mitigation strategies . The most important and perhaps surprising result from this analytical exercise is that a community's stability to disease outbreaks is independent of its underlying network structure .
Revised:  The branching model is used to derive analytical results for the trade-offs between the different mitigation strategies , with the surprising result that a community's stability to disease outbreaks is independent of its underlying network structure .
Edit intent: clarity
Original:  There has been increasing literature suggesting that superspreading, the significant variability in number of new infections caused by individuals, plays an important role in the spread of COVID-19 . In this paper, we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases.
Revised:  There has been increasing literature suggesting that superspreading, the significant variability in number of new infections caused by individuals, plays an important role in the spread of SARS-CoV-2 . In this paper, we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases.
Edit intent: meaning-changed
Original:  Through experiments on the JackRabbot dataset with two detector models, DROW3 and DR-SPAAM, we show that self-supervised detectors, trained or fine-tuned with pseudo-labels, outperform detectors trained using manual annotations from a different dataset.
Revised:  Through experiments on the JackRabbot dataset with two detector models, DROW3 and DR-SPAAM, we show that self-supervised detectors, trained or fine-tuned with pseudo-labels, outperform detectors trained only on a different dataset.
Edit intent: clarity
Original:  We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct an evolutionary scenario that explains a given LDT.
Revised:  We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct a relaxed scenario that explains a given LDT.
Edit intent: clarity
Original:  A 400 example mixed language English-Romanian dataset is created for cross-lingual transfer learning evaluation .
Revised:  The goal is building multilingual systems that retrieve in evidence-rich languages to verify claims in evidence-poor languages that are more commonly targeted by disinformation. To this end, our EnmBERT fact verification system shows evidence of transfer learning ability and 400 example mixed language English-Romanian dataset is created for cross-lingual transfer learning evaluation .
Edit intent: meaning-changed
Original:  We argue that under many circumstances the smaller and lighter models fit better for AI-pivoting businesses and that we call for more research into low-cost models, especially for under-resourced languages.
Revised:  We show the trade-off between performance gain and the cost across the models to give more insights for AI-pivoting businesses and that we call for more research into low-cost models, especially for under-resourced languages.
Edit intent: meaning-changed
Original:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)  gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization  while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%%  . We also obtain an improvement for simulating the Fermi-Hubbard model.
Revised:  We show that it suffices to use \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%% . We also obtain an improvement for simulating the Fermi-Hubbard model.
Edit intent: fluency
Original:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)  gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization  while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%%  . We also obtain an improvement for simulating the Fermi-Hubbard model.
Revised:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right) n^{o(1) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%% . We also obtain an improvement for simulating the Fermi-Hubbard model.
Edit intent: meaning-changed
Original:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)  gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization  while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%%  . We also obtain an improvement for simulating the Fermi-Hubbard model.
Revised:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons , improving the best previous result in second quantization while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%% . We also obtain an improvement for simulating the Fermi-Hubbard model.
Edit intent: clarity
Original:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)  gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization  while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%%  . We also obtain an improvement for simulating the Fermi-Hubbard model.
Revised:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%% . We also obtain an improvement for simulating the Fermi-Hubbard model.
Edit intent: fluency
Original:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)  gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization  while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%%  . We also obtain an improvement for simulating the Fermi-Hubbard model.
Revised:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization while outperforming the first-quantized simulation when n= }%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%% . We also obtain an improvement for simulating the Fermi-Hubbard model.
Edit intent: meaning-changed
Original:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)  gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization  while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%%  . We also obtain an improvement for simulating the Fermi-Hubbard model.
Revised:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% %DIFDELCMD < \right)%%% . We also obtain an improvement for simulating the Fermi-Hubbard model.
Edit intent: meaning-changed
Original:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)  gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization  while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%%  . We also obtain an improvement for simulating the Fermi-Hubbard model.
Revised:  We show that it suffices to use \mathcal{O \left(n^{5/3}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and \eta electrons up to a negligible factor , improving the best previous result in second quantization while outperforming the first-quantized simulation when n= \mathcal{O}%DIFDELCMD < \left(%%% \eta^2%DIFDELCMD < \right)%%% \eta^{2-o(1) . We also obtain an improvement for simulating the Fermi-Hubbard model.
Edit intent: meaning-changed
Original:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent (n \geq 3) . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the n-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Revised:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct multi-block generalization of ADMM is not necessarily convergent (n \geq 3) . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the n-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Edit intent: meaning-changed
Original:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent (n \geq 3) . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the n-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Revised:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the n-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Edit intent: coherence
Original:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent (n \geq 3) . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the n-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Revised:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent (n \geq 3) . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the n-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Edit intent: fluency
Original:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent (n \geq 3) . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the n-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Revised:  has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent (n \geq 3) . Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the multi-block extension of ADMM, from the theoretical point of view, it can ensure just the convergence in expectation , which may not be a good indicator of its robustness and efficiency.
Edit intent: clarity
Original:  In this work, analysing the strongly convex quadratic programming case, we interpret the n-block Gauss-Seidel sweep performed by  ADMM in the context of the inexact Augmented Lagrangian Method.
Revised:  In this work, analysing the strongly convex quadratic programming case, we interpret the block Gauss-Seidel sweep performed by ADMM in the context of the inexact Augmented Lagrangian Method.
Edit intent: clarity
Original:  In this work, analysing the strongly convex quadratic programming case, we interpret the n-block Gauss-Seidel sweep performed by  ADMM in the context of the inexact Augmented Lagrangian Method.
Revised:  In this work, analysing the strongly convex quadratic programming case, we interpret the n-block Gauss-Seidel sweep performed by the multi-block ADMM in the context of the inexact Augmented Lagrangian Method.
Edit intent: meaning-changed
Original:  Using the proposed analysis, we are able to outline an alternative technique to those present in literature which, supported from stronger theoretical guarantees, is able to ensure the convergence of the n-block generalization of the ADMM method.
Revised:  Using the proposed analysis, we are able to outline an alternative technique to those present in literature which, supported from stronger theoretical guarantees, is able to ensure the convergence of the multi-block generalization of the ADMM method.
Edit intent: meaning-changed
Original:  We show through  simulations that our approach enables decentralized and communication-free navigation by a multi-robot system to a goal position, avoiding obstacles and collisions, while also maintaining connectivity .
Revised:  We show through simulations that our approach enables decentralized and communication-free navigation by a multi-robot system to a goal position, avoiding obstacles and collisions, maintain connectivity, and respond robustly to sensor noise .
Edit intent: meaning-changed
Original:  A standard approach is to reduce the problem to a finite set of marginal moment conditions and apply the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be unwieldy and impractical if we use a growing sieve of moments .
Revised:  A standard approach is to reduce the problem to a finite set of marginal moment conditions and apply the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be theoretically efficient but practically unwieldy if we use a growing sieve of moments .
Edit intent: clarity
Original:  A standard approach is to reduce the problem to a finite set of marginal moment conditions and apply the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be unwieldy and impractical if we use a growing sieve of moments .
Revised:  A standard approach is to reduce the problem to a finite set of marginal moment conditions and apply the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be unwieldy and impractical if we use a growing sieve of moment conditions .
Edit intent: fluency
Original:  We provide a detailed theoretical analysis of multiple VMM estimators, including  based on kernel methods and neural networks , and provide appropriate conditions under which these estimators are consistent, asymptotically normal, and semiparametrically efficient in the full conditional moment model.
Revised:  We provide a detailed theoretical analysis of multiple VMM estimators, including ones based on kernel methods and neural networks , and provide appropriate conditions under which these estimators are consistent, asymptotically normal, and semiparametrically efficient in the full conditional moment model.
Edit intent: clarity
Original:  We provide a detailed theoretical analysis of multiple VMM estimators, including  based on kernel methods and neural networks , and provide appropriate conditions under which these estimators are consistent, asymptotically normal, and semiparametrically efficient in the full conditional moment model.
Revised:  We provide a detailed theoretical analysis of multiple VMM estimators, including based on kernel methods and neural nets , and provide appropriate conditions under which these estimators are consistent, asymptotically normal, and semiparametrically efficient in the full conditional moment model.
Edit intent: fluency