wanyu/IteraTeR_v2 huggingface dataset:
Original:  This approach yields a time-varying reproduction number that is continuously adjusted based on infection information through a negative-feedback term that is equivalent to Holling type II functions in ecology and Hill functions in chemistry and molecular biology.
Revised:  This approach yields a time-varying reproduction number that depends on infection information through a negative-feedback term that is equivalent to Holling type II functions in ecology and Hill functions in chemistry and molecular biology.
Edit intent: clarity
Original:  We focus on the imposition of Dirichlet and mixed Dirichlet--Neumann conditions on the Helmholtz equation, and extend the analysis of the Laplace problem from the paper \emph{Boundary element methods with weakly imposed boundary conditions} to this case.
Revised:  We focus on the imposition of Dirichlet and mixed Dirichlet--Neumann conditions on the Helmholtz equation, and extend the analysis of the Laplace problem from \emph{Boundary element methods with weakly imposed boundary conditions} to this case.
Edit intent: coherence
Original:  We recently described a novel method to pharmacologically down-regulate the expression of target proteins at the post-translational level.
Revised:  A novel method has been recently described by some of the authors to pharmacologically downregulate the expression of target proteins at the post-translational level.
Edit intent: clarity
Original:  Here, we report the all-atom simulation of the entire sequence of events underlying the folding pathway of ACE2.
Revised:  Here, we report the all-atom simulations of the entire sequence of events underlying the folding pathway of ACE2.
Edit intent: fluency
Original:  Our data reveal the existence of a folding intermediate showing  druggable pockets hidden in the native conformation.
Revised:  Our data revealed the existence of a folding intermediate showing druggable pockets hidden in the native conformation.
Edit intent: fluency
Original:  Thus, the spike-ACE2 interaction represents a major target for vaccines and antiviral drugs.
Revised:  Thus, spike-ACE2 interaction represents a major target for vaccines and antiviral drugs.
Edit intent: fluency
Original:  Our results indicate that these drugs could act against SARS-CoV-2 by altering the folding pathway of its receptor ACE2.
Revised:  Importantly, the antiviral activity has been tested against live SARS-CoV-2 by altering the folding pathway of its receptor ACE2.
Edit intent: clarity
Original: Up to now, modern Machine Learning is  based on fitting high dimensional functions to enormous data sets, taking advantage of huge hardware resources.
Revised: Up to now, modern Machine Learning is mainly based on fitting high dimensional functions to enormous data sets, taking advantage of huge hardware resources.
Edit intent: coherence
Original: 5\\%DIF < . In Galicia, one of the regions where the effect has been the least, %DIF > . In Galicia, one of the regions where the effect has been the  the number of infections does not reach 2.5 \\%DIF < . Based on our findings, we %DIF > . Based on our  can: i) estimate the risk of a new outbreak before Autumn if we lift the quarantine;
Revised: 5\\%DIF < . In Galicia, one of the regions where the effect has been the least, %DIF > . In Galicia, one of the regions where the effect has been the least, the number of infections does not reach 2.5 \\%DIF < . Based on our findings, we %DIF > . Based on our can: i) estimate the risk of a new outbreak before Autumn if we lift the quarantine;
Edit intent: fluency
Original: 5\\%DIF < . In Galicia, one of the regions where the effect has been the least, %DIF > . In Galicia, one of the regions where the effect has been the  the number of infections does not reach 2.5 \\%DIF < . Based on our findings, we %DIF > . Based on our  can: i) estimate the risk of a new outbreak before Autumn if we lift the quarantine;
Revised: 5\\%DIF < . In Galicia, one of the regions where the effect has been the least, %DIF > . In Galicia, one of the regions where the effect has been the the number of infections does not reach 2.5 \\%DIF < . Based on our findings, we %DIF > . Based on our findings, we can: i) estimate the risk of a new outbreak before Autumn if we lift the quarantine;
Edit intent: fluency
Original:  We show how such expectations  can lead to  nonlinear BSM-like equations.
Revised:  We show how such expectations can lead to the nonlinear BSM-like equations.
Edit intent: fluency
Original:  Diversity of BSM-like equations with 2-5 or more dimensions emphasizes complexity of option pricing problem.
Revised:  Variety of the BSM-like equations with 2-5 or more dimensions emphasizes complexity of option pricing problem.
Edit intent: fluency
Original:  Such variety states the problem of reasonable balance between the accuracy of asset and option price description and the complexity of the equations under consideration.
Revised:  Such variety states the problem of reasonable balance between the accuracy and the complexity of the equations under consideration.
Edit intent: clarity
Original: Is face-voice association language independent?" and\textit{"Can a speaker be recognised irrespective of the spoken language?" . These two questions are very important to understand effectiveness and to boost development of multilingual biometric systems.
Revised: Is face-voice association language independent?" \textit{"Can a speaker be recognised irrespective of the spoken language?" . These two questions are very important to understand effectiveness and to boost development of multilingual biometric systems.
Edit intent: fluency
Original: Is face-voice association language independent?" and\textit{"Can a speaker be recognised irrespective of the spoken language?" . These two questions are very important to understand effectiveness and to boost development of multilingual biometric systems.
Revised: Is face-voice association language independent?" and\textit{"Is face-voice association language independent?" and "Can a speaker be recognised irrespective of the spoken language?" . These two questions are very important to understand effectiveness and to boost development of multilingual biometric systems.
Edit intent: coherence
Original:  The novel coronavirus (COVID-19) pandemic forced people to stay at home to reduce the spread of the virus by maintaining the social distancing.
Revised:  The novel coronavirus (COVID-19) pandemic forced people to stay at home to reduce the spread of the virus by maintaining social distancing.
Edit intent: clarity
Original:  Importantly, CLEAR uses a residual-based embedding learning framework, which focuses the embedding on the deep language structures and semantics that the lexical retrieval fails to capture.
Revised:  Importantly, CLEAR uses a residual-based embedding learning method, forcing the embedding to encode language structures and semantics that the lexical retrieval fails to capture.
Edit intent: clarity
Original:  Importantly, CLEAR uses a residual-based embedding learning framework, which focuses the embedding on the deep language structures and semantics that the lexical retrieval fails to capture.
Revised:  Importantly, CLEAR uses a residual-based embedding learning framework, which focuses the embedding on the deep language structures and semantics that lexical retrieval fails to capture.
Edit intent: fluency
Original:  Empirical evaluation demonstrates the advantages of CLEAR over classic bag-of-words retrieval models, recent BERT-enhanced lexical retrieval models , as well as a BERT-based embedding retrieval .
Revised:  Empirical evaluation demonstrates the advantages of CLEAR over classic bag-of-words retrieval models, recent BERT-enhanced lexical retrieval models and a BERT-based embedding retrieval .
Edit intent: coherence
Original:  By computing the thin QR factorizations of two certain matrices, the method implicitly solves the mathematically equivalent generalized eigenvalue problem of a certain cross-product matrix pair but does not explicitly form the cross-product matrices and thus avoids the  accuracy loss of the computed generalized singular values and generalized singular vectors.
Revised:  By computing the thin QR factorizations of two certain matrices, the method implicitly solves the mathematically equivalent generalized eigenvalue problem of a certain cross-product matrix pair but does not explicitly form the cross-product matrices and thus avoids the possible accuracy loss of the computed generalized singular values and generalized singular vectors.
Edit intent: clarity
Original:  A thick-restart CPF-JDGSVD algorithm with deflation is developed to compute several GSVD components, and some convergence results are established on inner and outer iterations, which are exploited to design practical stopping criteria for inner iterations.
Revised:  A thick-restart CPF-JDGSVD algorithm with deflation is developed to compute several GSVD components, and some convergence results are established for the inner and outer iterations, which are exploited to design practical stopping criteria for inner iterations.
Edit intent: clarity
Original:  A thick-restart CPF-JDGSVD algorithm with deflation is developed to compute several GSVD components, and some convergence results are established on inner and outer iterations, which are exploited to design practical stopping criteria for inner iterations.
Revised:  A thick-restart CPF-JDGSVD algorithm with deflation is developed to compute several GSVD components, and some convergence results are established on inner and outer iterations, based on some of which practical stopping criteria for inner iterations.
Edit intent: clarity
Original:  A thick-restart CPF-JDGSVD algorithm with deflation is developed to compute several GSVD components, and some convergence results are established on inner and outer iterations, which are exploited to design practical stopping criteria for inner iterations.
Revised:  A thick-restart CPF-JDGSVD algorithm with deflation is developed to compute several GSVD components, and some convergence results are established on inner and outer iterations, which are exploited to design practical stopping criteria are designed for the inner iterations.
Edit intent: clarity
Original:   Numerical experiments illustrate the effectiveness of the algorithm.
Revised:  Numerical experiments illustrate the efficiency of the algorithm.
Edit intent: clarity
Original: In this paper, we propose a finite-volume scheme for aggregation-diffusion equations that is based on a Scharfetter--Gummel approximation of the nonlinear , nonlocal flux term.
Revised: In this paper, we propose a finite-volume scheme for aggregation-diffusion equations based on a Scharfetter--Gummel approximation of the nonlinear , nonlocal flux term.
Edit intent: coherence
Original:  More specifically, it is shown that the discrete solutions satisfy a free-energy dissipation relation analogous to the continuous model , and, as a consequence, the numerical solutions converge in the large time limit to stationary solutions, for which we provide a thermodynamic characterization  .
Revised:  More specifically, it is shown that the discrete solutions satisfy a free-energy dissipation relation analogous to the continuous model . Consequently, the numerical solutions converge in the large time limit to stationary solutions, for which we provide a thermodynamic characterization .
Edit intent: coherence
Original:  Previous analyses of such methods have been performed  by Hemker et. al. for the Poisson problem focusing on optimizing the smoother .
Revised:  Previous analyses of such methods have been performed by Hemker et. al. for the Poisson problem .
Edit intent: clarity
Original:  Our main innovation is that we optimize the complete two-level process, and we obtain explicit formulas for the optimal relaxation parameter of the two-level method for the Poisson problem in 1D, and  closed form approximation formulas for the optimal choice in the reaction-diffusion case in all regimes.
Revised:  Our main innovation is that we obtain explicit formulas for the optimal relaxation parameter of the two-level method for the Poisson problem in 1D, and closed form approximation formulas for the optimal choice in the reaction-diffusion case in all regimes.
Edit intent: clarity
Original:  Our main innovation is that we optimize the complete two-level process, and we obtain explicit formulas for the optimal relaxation parameter of the two-level method for the Poisson problem in 1D, and  closed form approximation formulas for the optimal choice in the reaction-diffusion case in all regimes.
Revised:  Our main innovation is that we optimize the complete two-level process, and we obtain explicit formulas for the optimal relaxation parameter of the two-level method for the Poisson problem in 1D, and very accurate closed form approximation formulas for the optimal choice in the reaction-diffusion case in all regimes.
Edit intent: clarity
Original: For every constant c > 0, we show that there is a family \{P_{N, c\} }  of polynomials whose degree and algebraic circuit complexity are polynomially bounded in the number of variables, that satisfies the following properties:
Revised: For every constant c > 0, we show that there is a family \{P_{N, c\} } P_{N, c of polynomials whose degree and algebraic circuit complexity are polynomially bounded in the number of variables, that satisfies the following properties:
Edit intent: fluency
Original:  \bullet For every family \{f_n\ of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. \bullet There exists a family \{h_n\ of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Revised:  * For every family \{f_n\ of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. \bullet There exists a family \{h_n\ of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Edit intent: fluency
Original:  \bullet For every family \{f_n\ of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. \bullet There exists a family \{h_n\ of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Revised:  \bullet For every family f_n of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. \bullet There exists a family \{h_n\ of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Edit intent: fluency
Original:  \bullet For every family \{f_n\ of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. \bullet There exists a family \{h_n\ of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Revised:  \bullet For every family \{f_n\ of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. * There exists a family \{h_n\ of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Edit intent: fluency
Original:  \bullet For every family \{f_n\ of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. \bullet There exists a family \{h_n\ of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Revised:  \bullet For every family \{f_n\ of polynomials in VP, where f_n is an n variate polynomial of degree at most n^c with bounded integer coefficients and for N = n^c + n{n}, P_{N,c} vanishes on the coefficient vector of f_n. \bullet There exists a family h_n of polynomials where h_n is an n variate polynomial of degree at most n^c with bounded integer coefficients such that for N = n^c + n{n}, P_{N,c} does not vanish on the coefficient vector of h_n.
Edit intent: fluency
Original:  In other words, there are efficiently computable defining equations for polynomials in VP that have small integer coefficients.
Revised:  In other words, there are efficiently computable equations for polynomials in VP that have small integer coefficients.
Edit intent: clarity
Original:  Our proofs are elementary and rely on the existence of (non-explicit) hitting sets for VP (and VNP) to show that there are efficiently constructible, low degree defining equations for these classes and also extend to finite fields of small size.
Revised:  Our proofs are elementary and rely on the existence of (non-explicit) hitting sets for VP (and VNP) to show that there are efficiently constructible, low degree equations for these classes and also extend to finite fields of small size.
Edit intent: clarity
Original:  Our proofs are elementary and rely on the existence of (non-explicit) hitting sets for VP (and VNP) to show that there are efficiently constructible, low degree defining equations for these classes and also extend to finite fields of small size.
Revised:  Our proofs are elementary and rely on the existence of (non-explicit) hitting sets for VP (and VNP) to show that there are efficiently constructible, low degree defining equations for these classes . Our proofs also extend to finite fields of small size.
Edit intent: coherence
Original:  We leverage declarative knowledge expressed in both natural language and first-order logic  .
Revised:  Specifically, we leverage the declarative knowledge expressed in both natural language and first-order logic .
Edit intent: coherence
Original:  We leverage declarative knowledge expressed in both natural language and first-order logic  .
Revised:  We leverage declarative knowledge expressed in both first-order logic .
Edit intent: clarity
Original:  The latter refers to logical consistency between coarse- and fine- grained predictions, which is used to regularize the training process with propositional Boolean expressions.
Revised:  The latter refers to logical consistency between coarse- and fine-grained predictions, which is used to regularize the training process with propositional Boolean expressions.
Edit intent: fluency
Original:  Experiments show that our method achieves superior performance, demonstrating that injecting declarative knowledge expressed in both natural language and first-order logic can help the model to make more accurate predictions.
Revised:  Experiments show that our method achieves superior performance, demonstrating that leveraging declarative knowledge can help the model to make more accurate predictions.
Edit intent: clarity
Original:  We also find that the latency is further reduced to 68ms by pruning document representations, with virtually no difference in effectiveness 
Revised:  We also find that the latency is further reduced to 68ms by pruning document representations, with virtually no difference in effectiveness .
Edit intent: fluency
Original:  Specifically, we precompute part of the document term representations at indexing time  without a query  , and merge them with the query representation at query time to compute the final ranking score.
Revised:  Specifically, we precompute part of the document term representations at indexing time ( without a query , and merge them with the query representation at query time to compute the final ranking score.
Edit intent: fluency
Original:  Specifically, we precompute part of the document term representations at indexing time  without a query  , and merge them with the query representation at query time to compute the final ranking score.
Revised:  Specifically, we precompute part of the document term representations at indexing time without a query ) , and merge them with the query representation at query time to compute the final ranking score.
Edit intent: fluency
Original:  As the training process begins , our approach gradually shifts to weighting all samples equally, regardless of difficulty.
Revised:  As the training process progresses , our approach gradually shifts to weighting all samples equally, regardless of difficulty.
Edit intent: clarity
Original:  When applied to a BERT-based ranker, our method yields up to a 4\% improvement in MRR and a 9\% improvement in P@1 (compared to the model trained without a curriculum  .
Revised:  When applied to a BERT-based ranker, our method yields up to a 4\% improvement in MRR and a 9\% improvement in P@1 (compared to the model trained without a curriculum ) .
Edit intent: fluency
Original:  and finally when the online vertices are generated i.i.d. from a known distribution on the vertices of a known stochastic (type)graph .
Revised:  and finally when the online vertices are generated i.i.d. ) .
Edit intent: clarity
Original:  As an application, we obtain a new upper bound of O(n^{1.5 \sqrt{\log n}) on the approximate degree of the bipartite }  perfect matching function, improving the previous best known bound of \mathcal{O(n^{1.75}).
Revised:  \sqrt{\log n}) on the approximate degree of the bipartite } perfect matching function, improving the previous best known bound of \mathcal{O(n^{1.75}).
Edit intent: clarity
Original:  As an application, we obtain a new upper bound of O(n^{1.5 \sqrt{\log n}) on the approximate degree of the bipartite }  perfect matching function, improving the previous best known bound of \mathcal{O(n^{1.75}).
Revised:  As an application, we obtain a new upper bound of O(n^{1.5 \sqrt{\log n}) on the approximate degree of the bipartite } perfect matching function, (n^{1.75}).
Edit intent: clarity
Original:  In the absence of a vaccine or effective treatment for COVID-19, countries have adopted Non-Pharmaceutical Interventions (NPIs) such as social distancing and full lockdown.
Revised: Background In the absence of a vaccine or effective treatment for COVID-19, countries have adopted Non-Pharmaceutical Interventions (NPIs) such as social distancing and full lockdown.
Edit intent: coherence
Original:  An objective and quantitative means of monitoring the impact of, and compliance with, these interventions at a local level is urgently required.
Revised:  An objective and quantitative means of monitoring the impact and response of these interventions at a local level is urgently required.
Edit intent: clarity
Original:  Here we explore the utility of the recently developed open-source mobile health platform RADAR-base as a toolbox to test the effect and response to NPIs aimed at limiting the spread of COVID- 19.
Revised:  Here we explore the utility of the recently developed open-source mobile health platform RADAR-base as a toolbox to test the effect and response to NPIs aimed at limiting the spread of COVID-19. Methods
Edit intent: coherence
Original:  We included 1062 participants recruited in Italy, Spain, Denmark, the UK  and the Netherlands.
Revised:  We included 1062 participants recruited in Italy, Spain, Denmark, the UK , and the Netherlands.
Edit intent: fluency