wanyu/IteraTeR_v2 huggingface dataset:
Original:  This scheme consists of two steps - starting from a state on the submanifold, we first update the state using a non-reversible stochastic differential equation which takes the state away from the submanifold, and in the second step we project the state back onto the manifold using the long-time limit of a ordinary differential equation.
Revised:  This scheme consists of two steps - starting from a state on the submanifold, we first update the state using a non-reversible stochastic differential equation which takes the state away from the submanifold, and in the second step we project the state back onto the manifold using the long-time limit of an ordinary differential equation.
Edit intent: fluency
Original:  This paperproposes a Chebyshev collocation method ( CCM ) based on domain decomposition  to solve this problem.
Revised:  This paperproposes a Chebyshev collocation method ( CCM ) based on domain decomposition is proposed to solve this problem.
Edit intent: clarity
Original:  A set of collocation points cannot penetrate two layers of media, thus necessitating domain decomposition and the use of two sets of collocation points.
Revised:  A set of collocation points cannot penetrate multiple layers of media, thus necessitating domain decomposition and the use of two sets of collocation points.
Edit intent: clarity
Original:  A set of collocation points cannot penetrate two layers of media, thus necessitating domain decomposition and the use of two sets of collocation points.
Revised:  A set of collocation points cannot penetrate two layers of media, thus necessitating domain decomposition and the use of multiple sets of collocation points.
Edit intent: clarity
Original:  thus, a dense matrix eigenvalue problem is formed, from which the solution for the horizontal wavenumbers and modes can be directly obtained.
Revised:  thus, a dense matrix eigenvalue system is formed, from which the solution for the horizontal wavenumbers and modes can be directly obtained.
Edit intent: clarity
Original:  A comparison with other methods shows that the CCM proposed in this article is slightly slower but more accurate than the FDM, while it offers roughly the same accuracy but a faster speed than other types of spectral methods.
Revised:  A comparison with other methods shows that the CCM proposed in this article is more accurate than the FDM, while it offers roughly the same accuracy but a faster speed than other types of spectral methods.
Edit intent: clarity
Original: The propagation of sound waves in a horizontally stratified environment, a classical problem in ocean acoustics, has traditionally been calculated using normal modes.
Revised: The propagation of sound waves in a horizontally stratified environment, a classic problem in ocean acoustics, has traditionally been calculated using normal modes.
Edit intent: fluency
Original:  A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM , while it offers roughly the same accuracy  but a faster  speed than other types of spectral methods.
Revised:  A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM and offers roughly the same accuracy but a faster speed than other types of spectral methods.
Edit intent: coherence
Original:  A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM , while it offers roughly the same accuracy  but a faster  speed than other types of spectral methods.
Revised:  A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM , while it offers roughly the same accuracy as but a faster speed than other types of spectral methods.
Edit intent: fluency
Original:  A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM , while it offers roughly the same accuracy  but a faster  speed than other types of spectral methods.
Revised:  A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM , while it offers roughly the same accuracy but a faster calculation speed than other types of spectral methods.
Edit intent: clarity
Original: We consider the problem of the detection of brain hemorrhages from three-dimensional (3D) electrical impedance tomography (EIT) measurements.
Revised: We consider the problem of the detection of brain hemorrhages from three dimensional (3D) electrical impedance tomography (EIT) measurements.
Edit intent: fluency
Original:  We consider changes in head anatomy and layers, electrode shape and position, measurement noise and conductivity values.
Revised:  We consider changes in head anatomy and layers, electrode position, measurement noise and conductivity values.
Edit intent: clarity
Original:  On most test datasets we achieved \geq 90\\%DIF < average accuracy with fully connected neural networks, %DIF > average accuracy with fully connected neural networks, while the convolutional ones had worse performances.
Revised:  On most test datasets we achieve \geq 90\\%DIF < average accuracy with fully connected neural networks, %DIF > average accuracy with fully connected neural networks, while the convolutional ones had worse performances.
Edit intent: fluency
Original:  On most test datasets we achieved \geq 90\\%DIF < average accuracy with fully connected neural networks, %DIF > average accuracy with fully connected neural networks, while the convolutional ones had worse performances.
Revised:  On most test datasets we achieved \geq 90\\%DIF < average accuracy %DIF > average accuracy with fully connected neural networks, while the convolutional ones had worse performances.
Edit intent: clarity
Original:  The so-far open issue that we close in this paper is regarding whether the \delta-partitions of \alpha can be computed without computing the partitions of \alpha in advance.
Revised:  We give a non-trivial algorithm that computes all \delta-partitions of \alpha can be computed without computing the partitions of \alpha in advance.
Edit intent: clarity
Original:  Numerical methods typically employ a uniform mesh fine enough the resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom.
Revised:  Numerical methods typically employ a uniform mesh fine enough to resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom.
Edit intent: fluency
Original: The numerical simulation of  nonlinear ultrasound is important in the treatment planning for high-intensity focused ultrasound ( HIFU) therapiesin the abdomen .
Revised: The numerical simulation of nonlinear ultrasound is important in treatment planning for high-intensity focused ultrasound ( HIFU) therapiesin the abdomen .
Edit intent: fluency
Original: The numerical simulation of  nonlinear ultrasound is important in the treatment planning for high-intensity focused ultrasound ( HIFU) therapiesin the abdomen .
Revised: The numerical simulation of nonlinear ultrasound is important in the treatment planning for focused ultrasound ( HIFU) therapiesin the abdomen .
Edit intent: fluency
Original:  This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to  wavelength of the harmonic.
Revised:  This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to the wavelength of the harmonic.
Edit intent: fluency
Original:  Numerical experiments are performed for HIFU transducers in homogeneous media in order to determine the size of the separate meshes required to accurately represent the harmonics.
Revised:  Numerical experiments are performed for HIFU transducers in homogeneous media in order to determine the size of the meshes required to accurately represent the harmonics.
Edit intent: clarity
Original:  In particular, a fast volume potential (VP) approach is proposed and employed to perform convergence experiments as the computation domain size is modified.
Revised:  In particular, a fast volume potential approach is proposed and employed to perform convergence experiments as the computation domain size is modified.
Edit intent: clarity
Original:  The VP approach allows each harmonic to be computed via the evaluation of an integral over the domain.
Revised:  This approach allows each harmonic to be computed via the evaluation of an integral over the domain.
Edit intent: coherence
Original:  As a consequence, VTC^0 can also prove the integer division axiom, and (by results of Je\v{r\'abek}  ) the RSUV-translation of induction and minimization for sharply bounded formulas.
Revised:  As a consequence, VTC^0 can also prove the integer division axiom, and (by \'abek} ) the RSUV-translation of induction and minimization for sharply bounded formulas.
Edit intent: clarity
Original: This paper studies a variant of the Art-gallery problem in which  "walls" can be replaced by reflecting-edges, which allows the guard to see further and thereby see a larger portion of the gallery.
Revised: This paper studies a variant of the Art Gallery problem in which "walls" can be replaced by reflecting-edges, which allows the guard to see further and thereby see a larger portion of the gallery.
Edit intent: fluency
Original: This paper studies a variant of the Art-gallery problem in which  "walls" can be replaced by reflecting-edges, which allows the guard to see further and thereby see a larger portion of the gallery.
Revised: This paper studies a variant of the Art-gallery problem in which the "walls" can be replaced by reflecting-edges, which allows the guard to see further and thereby see a larger portion of the gallery.
Edit intent: fluency
Original:  The art-gallery is a simple closed polygon P, a guard is a point p in P, and a guard sees another point q in P if the segment is contained in the interior of P.
Revised:  is contained in the interior of P.
Edit intent: coherence
Original:  Moreover, the number of times a ray can be reflected can be taken as a parameter.
Revised:  The number of times a ray can be reflected can be taken as a parameter.
Edit intent: coherence
Original:  Forvertex guarding polygons with k diffuse reflections, we establish an upper bound on the optimum solution.
Revised:  vertex guarding polygons with k diffuse reflections, we establish an upper bound on the optimum solution.
Edit intent: clarity
Original:  Forvertex guarding polygons with k diffuse reflections, we establish an upper bound on the optimum solution.
Revised:  For guarding polygons with k diffuse reflections, we establish an upper bound on the optimum solution.
Edit intent: clarity
Original: A self-governed community or society must have rules by which group decisions are made .
Revised: A self-governed society must have rules by which group decisions are made .
Edit intent: clarity
Original:  These rules are often codified by a written constitution that specifies not only the rules by which decisions are made, but also the means by which these rules can be changed, or amended .
Revised:  These rules are often codified in a written constitution that specifies not only the rules by which decisions are made, but also the means by which these rules can be changed, or amended .
Edit intent: fluency
Original:  These rules are often codified by a written constitution that specifies not only the rules by which decisions are made, but also the means by which these rules can be changed, or amended .
Revised:  These rules are often codified by a written constitution .
Edit intent: clarity
Original:  One of the defining characteristics of constitutions is entrenchment, or the difficulty of enacting changes.
Revised:  One of the defining features of a constitution is its degree of entrenchment, or the difficulty of enacting changes.
Edit intent: clarity
Original:  We take a stylized model of constitutions that use a fixed amendment rule to adjudicate amendments to a constitutionally designated decision rule to be used for decisions.
Revised:  We take a stylized model of constitutions that use reality-aware supermajority rules to make decisions.
Edit intent: clarity
Original:  Under this model we introduce desirable axioms for amendments, and design constitutions with amendment procedures based on these axioms to balance the degree of entrenchment, maintain stability, and avoid frustrating people .
Revised:  Under this model we introduce desirable axioms for amendments, and design constitutions with amendment procedures based on these principles .
Edit intent: clarity
Original:  The reuse of models produced by designers and the integration within geoinformation, necessary for many regulations, would make the process more effective .
Revised:  The reuse of models produced by designers would make the process more effective .
Edit intent: coherence
Original:  The reuse of models produced by designers and the integration within geoinformation, necessary for many regulations, would make the process more effective .
Revised:  The reuse of models produced by designers and the integration within geoinformation, necessary for many regulations, would make the process quicker and more objective .
Edit intent: clarity
Original:  However, a gap is left by most of studies and pilots adopting conceptual approaches .
Revised:  However, current studies and pilots often leave a gap with respect to the models as actually provided by architects, having varying quality and content .
Edit intent: clarity
Original:  In this paper , rather than taking a top-down approach, we departed from the data as available and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing a smooth automatic processing.
Revised:  In this study , rather than taking a top-down approach, we departed from the data as available and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing a smooth automatic processing.
Edit intent: clarity
Original:  In this paper , rather than taking a top-down approach, we departed from the data as available and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing a smooth automatic processing.
Revised:  In this paper , rather than taking a top down approach, we departed from the data as available and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing a smooth automatic processing.
Edit intent: fluency
Original:  In this paper , rather than taking a top-down approach, we departed from the data as available and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing a smooth automatic processing.
Revised:  In this paper , rather than taking a top-down approach, we started from the available data and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing a smooth automatic processing.
Edit intent: clarity
Original:  In this paper , rather than taking a top-down approach, we departed from the data as available and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing a smooth automatic processing.
Revised:  In this paper , rather than taking a top-down approach, we departed from the data as available and made the necessary inferences, which gave the opportunity to tackle basic and common issues often preventing smooth automatic processing.
Edit intent: fluency
Original:   While the case study is specific in location, regulations and input models, the type of issues encountered in data integration and extraction of incomplete and partially invalid data is exemplary for automated code compliance checking in general.
Revised:  While the case study is specific in location, regulations and input models, the type of issues encountered are a generally applicable example for automated code compliance checking in general.
Edit intent: clarity
Original:  Secondly, I show how a literature based analysis conducted with PubSqueezer results allows the describe of known facts about SARS-CoV-2.
Revised:  Secondly, I show how a literature based analysis conducted with PubSqueezer results allows to describe known facts about SARS-CoV-2.
Edit intent: fluency
Original:  While there has been extensive previous work on efficient quantum algorithms for linear differential equations, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics  . Despite this obstacle, we develop a quantum algorithm for initial value problems described by dissipative quadratic n-dimensional ordinary differential equations.
Revised:  While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum mechanics . Despite this obstacle, we develop a quantum algorithm for initial value problems described by dissipative quadratic n-dimensional ordinary differential equations.
Edit intent: clarity
Original:  While there has been extensive previous work on efficient quantum algorithms for linear differential equations, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics  . Despite this obstacle, we develop a quantum algorithm for initial value problems described by dissipative quadratic n-dimensional ordinary differential equations.
Revised:  While there has been extensive previous work on efficient quantum algorithms for linear differential equations, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics . Despite this obstacle, we develop a quantum algorithm for dissipative quadratic n-dimensional ordinary differential equations.
Edit intent: clarity
Original:  Assuming R < 1, where R is a parameter characterizing the ratio of the nonlinearity  to the linear dissipation, this algorithm has complexity T^2  poly(\log T, \log n, \log 1/\epsilon)/\epsilon, where T is the evolution time and \epsilon is the allowed error in the output quantum state .
Revised:  Assuming R < 1, where R is a parameter characterizing the ratio of the nonlinearity to the linear dissipation, this algorithm has complexity T^2 poly(\log T, \log n, \log 1/\epsilon)/\epsilon, where T is the evolution time , \epsilon is the allowed error in the output quantum state .
Edit intent: fluency
Original: We develop fast near-linear time approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem  and its generalization the Crossing Spanning Tree problem  .
Revised: We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem and its generalization the Crossing Spanning Tree problem .
Edit intent: clarity
Original: We develop fast near-linear time approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem  and its generalization the Crossing Spanning Tree problem  .
Revised: We develop fast near-linear time approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem .
Edit intent: clarity
Original:  We solve the underlying LP to within a (1+\epsilon) approximation factor in near-linear time via  multiplicative weight update (MWU) techniques.
Revised:  We solve the underlying LP to within a (1+\epsilon) approximation factor in near-linear time via the multiplicative weight update (MWU) techniques.
Edit intent: fluency
Original:  Together  these ideas lead to significantly faster approximation algorithms than known before  .
Revised:  Together , these ideas lead to significantly faster approximation algorithms than known before .
Edit intent: fluency
Original: Mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets.
Revised: The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets.
Edit intent: clarity
Original:  It has enjoyed great success in data science, from shape classification to cancer research and sports analytics.
Edit intent: coherence
Original:  Mapper Interactive makes the mapper algorithm accessible to nonspecialists and accelerates topological analysis workflows.
Revised:  Mapper Interactive makes the mapper algorithm accessible to nonspecialists and accelerates topological analytics workflows.
Edit intent: fluency
Original:  Nevertheless, in many specific scenarios involving the MPC methodology , accurate and effective system identification is a commonly encountered challenge  .
Revised:  Nevertheless, in many specific scenarios , accurate and effective system identification is a commonly encountered challenge .
Edit intent: clarity
Original:  As a consequence, the overall system performance could be significantly weakened in outcome when the traditional MPC algorithm is adopted under such circumstances .
Revised:  As a consequence, the overall system performance could be significantly degraded in outcome when the traditional MPC algorithm is adopted under such circumstances .
Edit intent: clarity
Original:  As a consequence, the overall system performance could be significantly weakened in outcome when the traditional MPC algorithm is adopted under such circumstances .
Revised:  As a consequence, the overall system performance could be significantly weakened in outcome when the traditional MPC algorithm is adopted under those circumstances when such accuracy is lacking .
Edit intent: clarity
Original:  To cater to this rather major shortcoming, this paper investigates  an alternate data-driven approach to solve the multi-agent decision-making problem .
Revised:  To cater to this rather major shortcoming, this paper investigates an alternate data-driven predictive control framework .
Edit intent: clarity
Original:  Utilizing an innovative modified methodology with suitable closed-loop input/output measurements that comply with the appropriate persistency of excitation condition, a non-parametric predictive model is suitably constructed .
Revised:  Utilizing an innovative methodology with closed-loop input/output measurements that comply with the appropriate persistency of excitation condition, a non-parametric predictive model is suitably constructed .
Edit intent: clarity
Original:  Utilizing an innovative modified methodology with suitable closed-loop input/output measurements that comply with the appropriate persistency of excitation condition, a non-parametric predictive model is suitably constructed .
Revised:  Utilizing an innovative modified methodology with suitable closed-loop input/output measurements that comply with the appropriate persistency of excitation condition, a non-parametric predictive model can be used for the determination of optimal control actions .
Edit intent: clarity
Original:  Finally, a multi-drone system is used to demonstrate the practical appeal and highly effective outcome of this promising development in achieving very good system performance .
Revised:  Finally, a multi-drone system is used to demonstrate the practical appeal and highly effective outcome of this promising development .
Edit intent: coherence
Original:  In this work, we measure the performance of a UAV user when it connects to an experimental two-tier cellular network in two different areas of Dublin city's Smart Docklands, which includes massive MIMO macrocells and wirelessly-backhauled small cells.
Revised:  In this work, we perform a novel measurement campaign of the performance of a UAV user when it connects to an experimental two-tier cellular network in two different areas of Dublin city's Smart Docklands, which includes massive MIMO macrocells and wirelessly-backhauled small cells.
Edit intent: clarity