wanyu/IteraTeR_v2 huggingface dataset:
Original:  We study alternation under linear shifts ( when M is the identity matrix) called the shift invariant alternation (denoted by salt(f)).
Revised:  We study alternation under linear shifts ( M is the identity matrix) called the shift invariant alternation (denoted by salt(f)).
Edit intent: clarity
Original:  By a result of Lin and Zhang (2017), it follows that bs(f)%DIFDELCMD < \le %%% O(salt(f)^2s(f)).
Revised:  %DIFDELCMD < \le %%% O(salt(f)^2s(f)).
Edit intent: coherence
Original:  We show an affine transform A, such that the corresponding function g satisfies bs(f,0^n) \le s(g), using which we proving that for F(x,y) : =f(x\land y), the bounded error quantum communication complexity of F with prior entanglement, Q^*_{1/3}(F)=\Omega(bs(f,0^n)).
Revised:  We show an affine transform A, such that the corresponding function g satisfies bs(f,0^n) \le s(g), using which we proving that for F(x,y) =f(x\land y), the bounded error quantum communication complexity of F with prior entanglement, Q^*_{1/3}(F)=\Omega(bs(f,0^n)).
Edit intent: fluency
Original:  Using this, we show, * For a fixed prime p and 0< \epsilon < 1, any f with deg_p(f)%DIFDELCMD < \le %DIFDELCMD < %%% (1-\epsilon)\log n must satisfy Q^*_{1/3(F)
Revised:  We show, * For a fixed prime p and 0< \epsilon < 1, any f with deg_p(f)%DIFDELCMD < \le %DIFDELCMD < %%% (1-\epsilon)\log n must satisfy Q^*_{1/3(F)
Edit intent: coherence
Original:  Using this, we show, * For a fixed prime p and 0< \epsilon < 1, any f with deg_p(f)%DIFDELCMD < \le %DIFDELCMD < %%% (1-\epsilon)\log n must satisfy Q^*_{1/3(F)
Revised:  Using this, we show, * For a prime p and 0< \epsilon < 1, any f with deg_p(f)%DIFDELCMD < \le %DIFDELCMD < %%% (1-\epsilon)\log n must satisfy Q^*_{1/3(F)
Edit intent: clarity
Original:  Using this, we show, * For a fixed prime p and 0< \epsilon < 1, any f with deg_p(f)%DIFDELCMD < \le %DIFDELCMD < %%% (1-\epsilon)\log n must satisfy Q^*_{1/3(F)
Revised:  Using this, we show, * For a fixed prime p and 0< %DIFDELCMD < \le %DIFDELCMD < %%% (1-\epsilon)\log n must satisfy Q^*_{1/3(F)
Edit intent: coherence
Original:  = \Omega}%DIFDELCMD < \left %DIFDELCMD < (%%% \frac{n^{\epsilon/2}{\log n} }%DIFDELCMD < \right )%%% . Here, deg_p(f) denotes the degree of the multilinear polynomial of f over%DIFDELCMD < \F%%% _p . * For f such that there exists primes p and q with deg_q(f)%DIFDELCMD < \ge %DIFDELCMD < %%% \Omega(deg_p(f)^\delta) for \delta >(F) = \Omega(n^{\epsilon/2}{\log n}).
Revised:  = \Omega}%DIFDELCMD < \left %DIFDELCMD < (%%% }{\log n} }%DIFDELCMD < \right )%%% . Here, deg_p(f) denotes the degree of the multilinear polynomial of f over%DIFDELCMD < \F%%% _p . * For f such that there exists primes p and q with deg_q(f)%DIFDELCMD < \ge %DIFDELCMD < %%% \Omega(deg_p(f)^\delta) for \delta >(F) = \Omega(n^{\epsilon/2}{\log n}).
Edit intent: clarity
Original: As shown in 3 , the usual update modes of Boolean networks (BNs), including synchronous and (generalized) asynchronous, fail to capture behaviours introduced by multivalued refinements.
Revised: As shown in , the usual update modes of Boolean networks (BNs), including synchronous and (generalized) asynchronous, fail to capture behaviours introduced by multivalued refinements.
Edit intent: coherence
Original: As shown in 3 , the usual update modes of Boolean networks (BNs), including synchronous and (generalized) asynchronous, fail to capture behaviours introduced by multivalued refinements.
Revised: As shown in 3 URL the usual update modes of Boolean networks (BNs), including synchronous and (generalized) asynchronous, fail to capture behaviours introduced by multivalued refinements.
Edit intent: fluency
Original: As shown in 3 , the usual update modes of Boolean networks (BNs), including synchronous and (generalized) asynchronous, fail to capture behaviours introduced by multivalued refinements.
Revised: As shown in 3 , the usual update modes of Boolean networks (BNs), including synchronous and (generalized) asynchronous, fail to capture behaviors introduced by multivalued refinements.
Edit intent: fluency
Original:  This semantics subsumes all the usual updating modes, while enabling new behaviours achievable by more concrete models.
Revised:  It subsumes all the usual updating modes, while enabling new behaviours achievable by more concrete models.
Edit intent: clarity
Original:  This semantics subsumes all the usual updating modes, while enabling new behaviours achievable by more concrete models.
Revised:  This semantics subsumes all the usual updating modes, while enabling new behaviors achievable by more concrete models.
Edit intent: fluency
Original: In this paper we analyze the Friedkin-Johnsen model of opinions 1 when the coefficients weighting the agent susceptibilities to interpersonal influence approach 1.
Revised: In this paper we analyze the Friedkin-Johnsen model of opinions when the coefficients weighting the agent susceptibilities to interpersonal influence approach 1.
Edit intent: fluency
Original:  In general the achieved consensus value will be different to the one obtained by the corresponding DeGroot model 2 .
Revised:  In general the achieved consensus value will be different to the one obtained by the corresponding DeGroot model 2 
Edit intent: fluency
Original:  Furthermore, we present deterministic oversampling strategies that select points by descending in directions of eigenvectors corresponding to sampling point updates and by establishing connections between sampling point selection and k-means clustering.
Revised:  Furthermore, we discuss deterministic oversampling strategies that select points by descending in directions of eigenvectors corresponding to sampling point updates and by establishing connections between sampling point selection and k-means clustering.
Edit intent: clarity
Original:  Furthermore, we present deterministic oversampling strategies that select points by descending in directions of eigenvectors corresponding to sampling point updates and by establishing connections between sampling point selection and k-means clustering.
Revised:  Furthermore, we present deterministic oversampling strategies that select points by descending in directions of eigenvectors corresponding to sampling point updates and by establishing connections between sampling point selection and clustering.
Edit intent: clarity
Original:  Our probabilistic analysis shows that randomized oversampling stabilizes empirical interpolation in the presence of Gaussian noise.
Revised:  We demonstrate with a probabilistic analysis that randomized oversampling stabilizes empirical interpolation in the presence of Gaussian noise.
Edit intent: clarity
Original:  Our probabilistic analysis shows that randomized oversampling stabilizes empirical interpolation in the presence of Gaussian noise.
Revised:  Our probabilistic analysis shows that randomized oversampling stabilizes empirical interpolation in the presence of noise.
Edit intent: clarity
Original:  Our numerical results demonstrate on synthetic and diffusion-reaction problems that randomized and deterministic oversampling with our approach stabilizes empirical interpolation in the presence of noise.
Revised:  Numerical experiments with synthetic and diffusion-reaction problems that randomized and deterministic oversampling with our approach stabilizes empirical interpolation in the presence of noise.
Edit intent: clarity
Original:  Our numerical results demonstrate on synthetic and diffusion-reaction problems that randomized and deterministic oversampling with our approach stabilizes empirical interpolation in the presence of noise.
Revised:  Our numerical results demonstrate on synthetic and diffusion-reaction problems demonstrate the stability of oversampled empirical interpolation in the presence of noise.
Edit intent: clarity
Original: This work investigates randomized and deterministic oversampling in (discrete) empirical interpolation for nonlinear model reduction  . Empirical interpolation derives approximations of nonlinear terms from a few samples  via interpolation in low-dimensional spaces.
Revised: This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction . Empirical interpolation derives approximations of nonlinear terms from a few samples via interpolation in low-dimensional spaces.
Edit intent: clarity
Original: This work investigates randomized and deterministic oversampling in (discrete) empirical interpolation for nonlinear model reduction  . Empirical interpolation derives approximations of nonlinear terms from a few samples  via interpolation in low-dimensional spaces.
Revised: This work investigates randomized and deterministic oversampling in (discrete) empirical interpolation for nonlinear model reduction . Empirical interpolation derives approximations from a few samples via interpolation in low-dimensional spaces.
Edit intent: clarity
Original:  It has been demonstrated that empirical interpolation can become unstable if the samples from the nonlinear terms are perturbed due to, e.g., noise, turbulence, and numerical inaccuracies.
Revised:  It has been observed that empirical interpolation can become unstable if the samples from the nonlinear terms are perturbed due to, e.g., noise, turbulence, and numerical inaccuracies.
Edit intent: clarity
Original:  It has been demonstrated that empirical interpolation can become unstable if the samples from the nonlinear terms are perturbed due to, e.g., noise, turbulence, and numerical inaccuracies.
Revised:  It has been demonstrated that empirical interpolation can become unstable if the samples are perturbed due to, e.g., noise, turbulence, and numerical inaccuracies.
Edit intent: clarity
Original:  We demonstrate with a probabilistic analysis that randomized oversampling stabilizes empirical interpolation in the presence of noise.
Revised:  The main contribution of this work is a probabilistic analysis that randomized oversampling stabilizes empirical interpolation in the presence of noise.
Edit intent: clarity
Original:  To prevent future outbreaks  , knowledge about the arrival time and location of dengue infected travellers is crucial.
Revised:  To prevent future outbreaks , knowledge about the arrival time and location of infected travellers is crucial.
Edit intent: clarity
Original:  We propose a network model that predicts the monthly number of dengue infected air passengers arriving at any given airport , considering international air travel volumes,  incidence rates and temporal infection dynamics.
Revised:  We propose a network model that predicts the monthly number of dengue infected air passengers arriving at any given airport . We consider international air travel volumes, incidence rates and temporal infection dynamics.
Edit intent: fluency
Original:  We propose a network model that predicts the monthly number of dengue infected air passengers arriving at any given airport , considering international air travel volumes,  incidence rates and temporal infection dynamics.
Revised:  We propose a network model that predicts the monthly number of dengue infected air passengers arriving at any given airport , considering international air travel volumes, monthly dengue incidence rates and temporal infection dynamics.
Edit intent: clarity
Original:  We verify the model's output with dengue notification data from Australia and Europe.
Edit intent: coherence
Original:  Our findings shed light onto dengue importation routes and further reveal country-specific reporting rates that are likely attributable to differences in awareness and notification policies .
Revised:  Our findings shed light onto dengue importation routes and reveal country-specific reporting rates that are likely attributable to differences in awareness and notification policies .
Edit intent: clarity
Original:  Our findings shed light onto dengue importation routes and further reveal country-specific reporting rates that are likely attributable to differences in awareness and notification policies .
Revised:  Our findings shed light onto dengue importation routes and further reveal country-specific reporting rates that have been until now largely unknown .
Edit intent: clarity
Original:  We propose a network model that predicts the monthly number of dengue infected air passengers arriving at any given airport.
Revised:  We propose a network model that predicts the monthly number of dengue-infected air passengers arriving at any given airport.
Edit intent: fluency
Original: We propose a novel hp-Multilevel Monte Carlo method for the quantification of uncertainties in compressible flows using the Discontinuous Galerkin method as deterministic solver.
Revised: We propose a novel hp-multilevel Monte Carlo method for the quantification of uncertainties in compressible flows using the Discontinuous Galerkin method as deterministic solver.
Edit intent: fluency
Original:  The multilevel approach exploits hierarchies of uniformly refined meshes jointly with an increasing polynomial degree for the ansatz space.
Revised:  The multilevel approach exploits hierarchies of uniformly refined meshes while simultaneously increasing the polynomial degree of the ansatz space.
Edit intent: clarity
Original:  We prove that the overall complexity of the hp-Multilevel Monte Carlo method to compute the mean field with prescribed accuracy is  of quadratic order with respect to the accuracy.
Revised:  We prove that the overall complexity of the hp-multilevel Monte Carlo method to compute the mean field with prescribed accuracy is of quadratic order with respect to the accuracy.
Edit intent: fluency
Original:  We also propose a novel and simple approach to estimate a lower confidence bound for the optimal number of samples per level, which helps to prevent overshooting the optimal number of samples .
Revised:  We also propose a novel and simple approach to estimate a lower confidence bound for the optimal number of samples per level, which helps to prevent overestimating these quantities .
Edit intent: clarity
Original:  The method is in particular adapted to the needs of high-performance computing .
Revised:  The method is in particular designed for application on queue-based computing systems, where it is desirable to compute a large number of samples during one iteration, without overestimating the optimal number of samples .
Edit intent: clarity
Original:  Our theoretical results are verified by numerical experiments for the two dimensional compressible Navier-Stokes equations.
Revised:  Our theoretical results are verified by numerical experiments for the two-dimensional compressible Navier-Stokes equations.
Edit intent: fluency
Original: How can we reduce the size of a graph without significantly altering its basic properties?
Revised: Can one reduce the size of a graph without significantly altering its basic properties?
Edit intent: clarity
Original:  We approach the graph reduction problem  from the perspective of restricted similarity , a modification of a well-known measure for graph approximation.
Revised:  The graph reduction problem from the perspective of restricted similarity , a modification of a well-known measure for graph approximation.
Edit intent: clarity
Original:  Our choice is motivated by the observation that restricted similarity implies strong spectral guarantees and can be used to prove statements about certain unsupervised learning problems  .
Revised:  Our choice is motivated by the observation that restricted approximation carries strong spectral and cut guarantees, and that it implies approximation results for unsupervised learning problems .
Edit intent: clarity
Original:  We derive sufficient conditions for a small graph to approximate a larger one in the sense of restricted similarity.
Revised:  Sufficient conditions are derived for a small graph to approximate a larger one in the sense of restricted similarity.
Edit intent: clarity
Original:  Our theoretical findings give rise to a novel quasi-linear algorithm.
Revised:  These findings give rise to a novel quasi-linear algorithm.
Edit intent: clarity
Original:  Compared to both standard and advanced graph reduction methods, the proposed algorithm finds coarse graphs of improved quality -often by a large margin- without sacrificing speed.
Revised:  Compared to both standard and advanced graph reduction methods, find coarse graphs of improved quality -often by a large margin- without sacrificing speed.
Edit intent: clarity
Original:  Compared to both standard and advanced graph reduction methods, the proposed algorithm finds coarse graphs of improved quality -often by a large margin- without sacrificing speed.
Revised:  Compared to both standard and advanced graph reduction methods, the proposed algorithm finds coarse graphs of improved quality , often by a large margin- without sacrificing speed.
Edit intent: fluency
Original:  Compared to both standard and advanced graph reduction methods, the proposed algorithm finds coarse graphs of improved quality -often by a large margin- without sacrificing speed.
Revised:  Compared to both standard and advanced graph reduction methods, the proposed algorithm finds coarse graphs of improved quality -often by a large margin, without sacrificing speed.
Edit intent: fluency
Original:  Resistive crossbar systems have emerged as promising candidates due to their ability to compactly and efficiently realize the primitive DNN operation , viz., vector-matrix multiplication.
Revised:  Resistive crossbar systems have emerged as promising building blocks for realizing DNNs due to their ability to compactly and efficiently realize the primitive DNN operation , viz., vector-matrix multiplication.
Edit intent: clarity
Original:  Resistive crossbar systems have emerged as promising candidates due to their ability to compactly and efficiently realize the primitive DNN operation , viz., vector-matrix multiplication.
Revised:  Resistive crossbar systems have emerged as promising candidates due to their ability to compactly and efficiently realize the dominant DNN computational kernel , viz., vector-matrix multiplication.
Edit intent: clarity
Original:  However, in practice, the functionality of resistive crossbars may deviate considerably from the ideal abstraction due to the device and circuit level non-idealities such as driver resistance, sensing resistance , sneak paths, and interconnect parasitics.
Revised:  However, a key challenge with resistive crossbars is that they suffer from a range of device and circuit level non-idealities such as driver resistance, sensing resistance , sneak paths, and interconnect parasitics.
Edit intent: clarity
Original:  However, in practice, the functionality of resistive crossbars may deviate considerably from the ideal abstraction due to the device and circuit level non-idealities such as driver resistance, sensing resistance , sneak paths, and interconnect parasitics.
Revised:  However, in practice, the functionality of resistive crossbars may deviate considerably from the ideal abstraction due to the device and circuit level non-idealities such as interconnect parasitics, peripheral circuits , sneak paths, and interconnect parasitics.
Edit intent: clarity
Original:  Unfortunately, device and circuit-level models are not feasible to use in the context of large-scale DNNs with 2.6-15.5 billion synaptic connections .
Revised:  Unfortunately, device and circuit-level models are not feasible to use in application-level evaluation .
Edit intent: clarity
Original:  We  propose a Fast Crossbar Model (FCM) that accurately captures the errors arising due to  non-idealities while being five orders of magnitude faster than circuit simulation.
Revised:  We propose a Fast Crossbar Model (FCM) to accurately capture the errors arising due to non-idealities while being five orders of magnitude faster than circuit simulation.
Edit intent: fluency
Original:  We use Rx-Caffe to evaluate large-scale image recognition DNNs designed for the ImageNet dataset .
Revised:  We use Rx-Caffe to evaluate large-scale DNNs developed for the ImageNet dataset .
Edit intent: clarity
Original:  Our experiments reveal that  crossbar non-idealities can significantly degrade DNN accuracy by 9.6\%-32\%  .
Revised:  Our experiments reveal that crossbar non-idealities can lead to significant accuracy degradations ( 9.6\%-32\% .
Edit intent: clarity
Original:  To the best of our knowledge, this work is the first  evaluation of the accuracy for large-scale DNNs on resistive crossbars and highlights the need for further efforts to address the impact of non-idealities .
Revised:  To the best of our knowledge, this work is the first quantitative evaluation of the accuracy for large-scale DNNs on resistive crossbars and highlights the need for further efforts to address the impact of non-idealities .
Edit intent: clarity
Original:  To the best of our knowledge, this work is the first  evaluation of the accuracy for large-scale DNNs on resistive crossbars and highlights the need for further efforts to address the impact of non-idealities .
Revised:  To the best of our knowledge, this work is the first evaluation of the accuracy of large-scale DNNs on resistive crossbars and highlights the need for further efforts to address the impact of non-idealities .
Edit intent: clarity
Original:  To the best of our knowledge, this work is the first  evaluation of the accuracy for large-scale DNNs on resistive crossbars and highlights the need for further efforts to address the impact of non-idealities .
Revised:  To the best of our knowledge, this work is the first evaluation of the accuracy for large-scale DNNs on resistive crossbar based hardware .
Edit intent: clarity
Original: Resistive crossbars  have emerged as promising building blocks for realizing DNNs due to their ability to compactly and efficiently realize the dominant DNN computational kernel , viz. , vector-matrix multiplication.
Revised: Resistive crossbars have emerged as promising building blocks for Deep Neural Network (DNN) hardware, due to their ability to compactly and efficiently realize the dominant DNN computational kernel , viz. , vector-matrix multiplication.
Edit intent: clarity
Original: Resistive crossbars  have emerged as promising building blocks for realizing DNNs due to their ability to compactly and efficiently realize the dominant DNN computational kernel , viz. , vector-matrix multiplication.
Revised: Resistive crossbars have emerged as promising building blocks for realizing DNNs due to their ability to compactly and efficiently realize vector-matrix multiplication.
Edit intent: clarity
Original:  These non-idealities can lead to errors in vector-matrix multiplication that eventually degrade the DNN's accuracy.
Revised:  These non-idealities can lead to errors in VMMs, eventually degrading the DNN's accuracy.
Edit intent: clarity
Original:  There has been no study of the impact of  non-idealities on the accuracy of large-scale DNNs , in part because existing device and circuit models are infeasible to use in application-level evaluation.
Revised:  It is therefore critical to study the impact of non-idealities on the accuracy of large-scale DNNs , in part because existing device and circuit models are infeasible to use in application-level evaluation.
Edit intent: clarity
Original:  There has been no study of the impact of  non-idealities on the accuracy of large-scale DNNs , in part because existing device and circuit models are infeasible to use in application-level evaluation.
Revised:  There has been no study of the impact of non-idealities on the accuracy of large-scale DNNs . However, this is challenging because existing device and circuit models are infeasible to use in application-level evaluation.
Edit intent: coherence
Original:  There has been no study of the impact of  non-idealities on the accuracy of large-scale DNNs , in part because existing device and circuit models are infeasible to use in application-level evaluation.
Revised:  There has been no study of the impact of non-idealities on the accuracy of large-scale DNNs , in part because existing device and circuit models are too slow to use in application-level evaluation.
Edit intent: clarity