wanyu/IteraTeR_v2 huggingface dataset:
Original:  Each resulting iterate represents a periodic-like system, which could be further solved in parallel by using the diagonalization technique.
Revised:  Each resulting iteration represents a periodic-like system, which could be further solved in parallel by using the diagonalization technique.
Edit intent: fluency
Original:  Math., 143 (2019), pp. 489--527] to general BDF methods up to order 6.
Revised:  Math., 143 (2019), pp. 489--527] to general BDF methods up to order six.
Edit intent: fluency
Original:  The majority of prior literature adopted a `` snapshot" view of trust and typically evaluated trust through questionnaires administered at the end of an experiment.
Revised:  The majority of prior literature adopted a " snapshot" view of trust and typically evaluated trust through questionnaires administered at the end of an experiment.
Edit intent: fluency
Original:  According to the father of this research field, Philip Strong,  not only is the epidemic biological;
Revised:  According to Philip Strong, not only is the epidemic biological;
Edit intent: clarity
Original:  According to the father of this research field, Philip Strong,  not only is the epidemic biological;
Revised:  According to the father of this research field, Philip Strong, not only is an epidemic biological;
Edit intent: fluency
Original:  there is also the potential for three social epidemics: of fear, moralization, and action.
Revised:  there is also the potential for three psycho-social epidemics: of fear, moralization, and action.
Edit intent: clarity
Original:  This work is the first study to empirically test Strong's model at scale .
Revised:  This work empirically tests Strong's model at scale .
Edit intent: clarity
Original:  in the suspended reality phase (started after the announcement of the first death in the country), people' s fear translated into anger about the looming feeling that things were about to change ;
Revised:  in the suspended reality phase (started after the announcement of the first death in the country), users' fear translated into anger about the looming feeling that things were about to change ;
Edit intent: clarity
Original:  finally , in the acceptance phase (started after the authorities imposed physical-distancing measures ), people found a "new normal" for their daily activities.
Revised:  finally , in the acceptance phase , which began after the authorities imposed physical-distancing measures ), people found a "new normal" for their daily activities.
Edit intent: fluency
Original:  finally , in the acceptance phase (started after the authorities imposed physical-distancing measures ), people found a "new normal" for their daily activities.
Revised:  finally , in the acceptance phase (started after the authorities imposed physical-distancing measures , users settled into a "new normal" for their daily activities.
Edit intent: clarity
Original:   Our real-time operationalization of Strong's model  makes it possible to embed epidemic psychology in any real-time model (e.g., epidemiological and mobility models).
Revised:  Our real-time operationalization of Strong's model makes it possible to embed epidemic psychology into real-time model (e.g., epidemiological and mobility models).
Edit intent: clarity
Original:   Our real-time operationalization of Strong's model  makes it possible to embed epidemic psychology in any real-time model (e.g., epidemiological and mobility models).
Revised:  Our real-time operationalization of Strong's model makes it possible to embed epidemic psychology in any real-time models (e.g., epidemiological and mobility models).
Edit intent: fluency
Original:  In  numerical experiments from classification and surrogate modeling, GNvpro not only solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used optimization schemes .
Revised:  In numerical experiments from surrogate modeling, GNvpro not only solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used optimization schemes .
Edit intent: clarity
Original:  In  numerical experiments from classification and surrogate modeling, GNvpro not only solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used optimization schemes .
Revised:  In numerical experiments from classification and surrogate modeling, GNvpro not only solves the optimization problem more efficiently than commonly-used optimization schemes .
Edit intent: clarity
Original: We consider the cyclotomic identity testing  problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n}  a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Revised: We consider the cyclotomic identity testing (CIT) problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n} a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Edit intent: clarity
Original: We consider the cyclotomic identity testing  problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n}  a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Revised: We consider the cyclotomic identity testing problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, where \zeta_n = e^{2\pi i/n} a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Edit intent: clarity
Original: We consider the cyclotomic identity testing  problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n}  a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Revised: We consider the cyclotomic identity testing problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n} is a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Edit intent: fluency
Original: We consider the cyclotomic identity testing  problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n}  a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Revised: We consider the cyclotomic identity testing problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n} a primitive complex n-th root of unity and e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Edit intent: clarity
Original: We consider the cyclotomic identity testing  problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n}  a primitive complex n-th root of unity and integers e_1,\ldots,e_k . We assume that n and e_1,\ldots,e_k are represented in binary and consider several versions of the problem, according to the representation of f.
Revised: We consider the cyclotomic identity testing problem: given a polynomial f(x_1,\ldots,x_k), decide whether f(\zeta_n^{e_1},\ldots,\zeta_n^{e_k}) is zero, for \zeta_n = e^{2\pi i/n} a primitive complex n-th root of unity and integers e_1,\ldots,e_k are integers, represented in binary and consider several versions of the problem, according to the representation of f.
Edit intent: coherence
Original:  For the case that f is given by an algebraic circuit  we give a randomized polynomial-time algorithm with two-sided errors, showing that the problem lies in BPP.
Revised:  For the case that f is given by an algebraic circuit , we give a randomized polynomial-time algorithm with two-sided errors, showing that the problem lies in BPP.
Edit intent: fluency
Original:  In case f is given by a circuit of polynomially bounded syntactic degree,
Revised:  In case f is given by a circuit of polynomially bounded degree,
Edit intent: clarity
Original:  we give a randomized algorithm with two-sided errors that runs in poly-logarithmic parallel time, showing that the problem lies in BPNC . In case f is given by a depth-2 \Sigma\Pi circuit (or, equivalently, as a list of monomials), we show that the cyclotomic identity testing problem lies in NC. Under the generalised Riemann hypothesis, we are able to extend this approach to obtain a polynomial-time algorithm also for a very simple subclass of depth-3 \Sigma\Pi\Sigma circuits.
Revised:  we give a randomized NC algorithm . In case f is given by a depth-2 \Sigma\Pi circuit (or, equivalently, as a list of monomials), we show that the cyclotomic identity testing problem lies in NC. Under the generalised Riemann hypothesis, we are able to extend this approach to obtain a polynomial-time algorithm also for a very simple subclass of depth-3 \Sigma\Pi\Sigma circuits.
Edit intent: clarity
Original:  we give a randomized algorithm with two-sided errors that runs in poly-logarithmic parallel time, showing that the problem lies in BPNC . In case f is given by a depth-2 \Sigma\Pi circuit (or, equivalently, as a list of monomials), we show that the cyclotomic identity testing problem lies in NC. Under the generalised Riemann hypothesis, we are able to extend this approach to obtain a polynomial-time algorithm also for a very simple subclass of depth-3 \Sigma\Pi\Sigma circuits.
Revised:  we give a randomized algorithm with two-sided errors that runs in poly-logarithmic parallel time, showing that the problem lies in BPNC . In case f is given by a depth-2 \Sigma\Pi circuit (or, equivalently, as a list of monomials), we show that the problem lies in NC. Under the generalised Riemann hypothesis, we are able to extend this approach to obtain a polynomial-time algorithm also for a very simple subclass of depth-3 \Sigma\Pi\Sigma circuits.
Edit intent: coherence
Original:   Finally, we use cyclotomic identity testing to give a new proof that equality of compressed strings, i.e., strings presented using context-free grammars, can be decided in coRNC: randomized NCwith one-sided errors .
Revised:  Finally, we use our results to give a new proof that equality of compressed strings, i.e., strings presented using context-free grammars, can be decided in coRNC: randomized NCwith one-sided errors .
Edit intent: clarity
Original:   Finally, we use cyclotomic identity testing to give a new proof that equality of compressed strings, i.e., strings presented using context-free grammars, can be decided in coRNC: randomized NCwith one-sided errors .
Revised:  Finally, we use cyclotomic identity testing to give a new proof that equality of compressed strings, i.e., strings presented using context-free grammars, can be decided in randomized NC .
Edit intent: clarity
Original:  We propose the use of no-regret based econometrics for bid prediction, modelling players as no-regret learners with respect to a utility function, unknown to the analyst.
Revised:  We propose the use of no-regret based econometrics for bid prediction, modeling players as no-regret learners with respect to a utility function, unknown to the analyst.
Edit intent: fluency
Original:  We  apply these methods in a real-world dataset from the BingAds sponsored search auction marketplace and show that no-regret econometric methods perform comparable to state-of-the-art time-series machine learning methods when there is no co-variate shift, but significantly out-perform machine learning methods when there is a co-variate shift between the training and test periods.
Revised:  We apply these methods in a real-world dataset from the BingAds sponsored search auction marketplace . We show that the no-regret econometric methods perform comparable to state-of-the-art time-series machine learning methods when there is no co-variate shift, but significantly out-perform machine learning methods when there is a co-variate shift between the training and test periods.
Edit intent: coherence
Original:  We  apply these methods in a real-world dataset from the BingAds sponsored search auction marketplace and show that no-regret econometric methods perform comparable to state-of-the-art time-series machine learning methods when there is no co-variate shift, but significantly out-perform machine learning methods when there is a co-variate shift between the training and test periods.
Revised:  We apply these methods in a real-world dataset from the BingAds sponsored search auction marketplace and show that no-regret econometric methods perform comparable to state-of-the-art time-series machine learning methods when there is no co-variate shift, but significantly outperform machine learning methods when there is a co-variate shift between the training and test periods.
Edit intent: clarity
Original:  Moreover, we show that among structural econometric methods, approaches based on no-regret learning out-perform more traditional, equilibrium-based, econometric methods that assume that players continuously best-respond to competition  .
Revised:  Moreover, we show that among structural econometric methods, approaches based on no-regret learning outperform more traditional, equilibrium-based, econometric methods that assume that players continuously best-respond to competition .
Edit intent: clarity
Original:  This barrier corresponds to a distinct arrangement of transition probabilities, sometimes referred to as the %DIFDELCMD < {\em %%% pendulum arrangement .
Revised:  This barrier corresponds to a distinct arrangement of transition probabilities, sometimes referred to as the %DIFDELCMD < {\em %%% pendulum arrangement .
Edit intent: fluency
Original:  This implies a regularization phenomenon: an energy cascade from large singular values to small singular values acts as regularizer .
Revised:  This explains a (known) regularization phenomenon: an energy cascade from large singular values to small singular values acts as regularizer .
Edit intent: clarity
Original:  This implies a regularization phenomenon: an energy cascade from large singular values to small singular values acts as regularizer .
Revised:  This implies a regularization phenomenon: an energy cascade from large singular values to small singular values smoothes .
Edit intent: clarity
Original: There remains much uncertainty about the relative effectiveness of different nonpharmaceutical interventions (NPIs) against COVID-19 transmission.
Revised: To what extent are effectiveness estimates of nonpharmaceutical interventions (NPIs) against COVID-19 transmission.
Edit intent: clarity
Original:  Considering only the models that have good robustness , we find that results and policy-relevant conclusions are remarkably consistent across the structurally different models.
Revised:  Considering only the models that have good robustness , we find that previously published results are robust across these choices and across different models.
Edit intent: clarity
Original:  We mathematically show how to interpret effectiveness estimates when these assumptions are violated .
Revised:  We mathematically show how to interpret effectiveness estimates when certain common assumptions do not hold .
Edit intent: clarity
Original:  As such, they can be accurately evaluated everywhere in the complex plane---including at problematic points near and on the contour---by means of elementary quadrature rules.
Revised:  As such, they can be accurately evaluated everywhere in the complex plane -- including at problematic points near and on the contour---by means of elementary quadrature rules.
Edit intent: fluency
Original:  As such, they can be accurately evaluated everywhere in the complex plane---including at problematic points near and on the contour---by means of elementary quadrature rules.
Revised:  As such, they can be accurately evaluated everywhere in the complex plane---including at problematic points near and on the contour -- by means of elementary quadrature rules.
Edit intent: fluency
Original: The combination of deep reinforcement learning and search at both training and test time is a powerful paradigm that has led to a number of a successes in single-agent settings and perfect-information games, best exemplified by the success of AlphaZero.
Revised: The combination of deep reinforcement learning and search at both training and test time is a powerful paradigm that has led to a number of successes in single-agent settings and perfect-information games, best exemplified by the success of AlphaZero.
Edit intent: fluency
Original: The combination of deep reinforcement learning and search at both training and test time is a powerful paradigm that has led to a number of a successes in single-agent settings and perfect-information games, best exemplified by the success of AlphaZero.
Revised: The combination of deep reinforcement learning and search at both training and test time is a powerful paradigm that has led to a number of a successes in single-agent settings and perfect-information games, best exemplified by AlphaZero.
Edit intent: clarity
Original:  However,  algorithms of this form have been unable to cope with imperfect-information games.
Revised:  However, prior algorithms of this form have been unable to cope with imperfect-information games.
Edit intent: clarity
Original:  However,  algorithms of this form have been unable to cope with imperfect-information games.
Revised:  However, algorithms of this form cannot cope with imperfect-information games.
Edit intent: coherence
Original: In order to cope with the exponential growth in available data, the efficiency of data analysis and machine learning libraries have recently received increased attention.
Revised: To cope with the exponential growth in available data, the efficiency of data analysis and machine learning libraries have recently received increased attention.
Edit intent: coherence
Original: In order to cope with the exponential growth in available data, the efficiency of data analysis and machine learning libraries have recently received increased attention.
Revised: In order to cope with the rapid growth in available data, the efficiency of data analysis and machine learning libraries have recently received increased attention.
Edit intent: clarity
Original: In order to cope with the exponential growth in available data, the efficiency of data analysis and machine learning libraries have recently received increased attention.
Revised: In order to cope with the exponential growth in available data, the efficiency of data analysis and machine learning libraries has recently received increased attention.
Edit intent: fluency
Original:  Although corresponding array-based numerical kernels have been significantly improved , most are limited by the resources available on a single computational node.
Revised:  Although corresponding array-based computations , most are limited by the resources available on a single computational node.
Edit intent: clarity
Original:  Although corresponding array-based numerical kernels have been significantly improved , most are limited by the resources available on a single computational node.
Revised:  Although corresponding array-based numerical kernels have been significantly improved , most are limited by the resources available on a single computation node.
Edit intent: fluency
Original:  Consequently, kernels must exploit distributed resources, e.g. , distributed memory architectures.
Revised:  Consequently, novel approaches must be made to exploit distributed resources, e.g. , distributed memory architectures.
Edit intent: clarity
Original:  Consequently, kernels must exploit distributed resources, e.g. , distributed memory architectures.
Revised:  Consequently, kernels must exploit distributed resources, e.g. distributed memory architectures.
Edit intent: fluency
Original:  HeAT utilizes PyTorch as a node-local eager execution engine and distributes the workload via MPI on arbitrarily large high-performance computing systems  .
Revised:  HeAT utilizes PyTorch as a node-local eager execution engine and distributes the workload on arbitrarily large high-performance computing systems .
Edit intent: clarity
Original:  It provides both low-level array-based computations, as well as assorted higher-level algorithms.
Revised:  It provides both low-level array computations, as well as assorted higher-level algorithms.
Edit intent: clarity
Original:  Compared with applications written in similar frameworks, HeAT achieves speedups of up to two orders of magnitude.
Revised:  When compared to similar frameworks, HeAT achieves speedups of up to two orders of magnitude.
Edit intent: clarity
Original:  However, by the time they are to be inhaled, the diameters are most likely 5-6 times smaller with respect to their initial diameters.
Revised:  However, by the time they are inhaled, the diameters are most likely 5-6 times smaller with respect to their initial diameters.
Edit intent: fluency
Original:  Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector , extent of dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Revised:  Viral load, minimum infectious dose, sensitivity of the virus half-life to the phase of its vector and dilution of the respiratory jet/puff by the entraining air are the important factors that determine specific physical modes of transmission and the pandemic evolution .
Edit intent: clarity
Original: This paper explores the impact of the Covid-19 crisis at the level of individual information behavior, based on an online survey among 308 participants from  German-speaking countries  in April and May 2020, followed by semi-structured interviews of 10 survey participants by end of May and beginning of June 2020.
Revised: This paper explores the impact of the Covid-19 crisis at the level of individual information behavior, based on an online survey among 308 participants from the German-speaking countries in April and May 2020, followed by semi-structured interviews of 10 survey participants by end of May and beginning of June 2020.
Edit intent: fluency
Original: This paper explores the impact of the Covid-19 crisis at the level of individual information behavior, based on an online survey among 308 participants from  German-speaking countries  in April and May 2020, followed by semi-structured interviews of 10 survey participants by end of May and beginning of June 2020.
Revised: This paper explores the impact of the Covid-19 crisis at the level of individual information behavior, based on an online survey among 308 participants from German-speaking countries in April and May 2020.
Edit intent: coherence
Original:  The results show first , that the Covid-19 crisis has led to an increased demand for reliable information.
Revised:  The results show first that the Covid-19 crisis has led to an increased demand for reliable information.
Edit intent: fluency