wanyu/IteraTeR_v2 huggingface dataset:
Original:  Suppose that errors \|u- \|_{H^1_0 and \|u-}%DIFDELCMD < u%%% \|_{L^{\infty between an exact solution u and a numerically computed approximate solution u . We estimate the number of sign-changes of the solution u (the number of nodal domains) and  the location of zero level-sets of u (the location of the nodal line).
Revised:  Suppose that errors \|u- \|_{H^1_0 and \|u-}%DIFDELCMD < u%%% \|_{L^{\infty between an exact solution u and a numerically computed approximate solution u , we evaluate the number of sign-changes of the solution u (the number of nodal domains) and the location of zero level-sets of u (the location of the nodal line).
Edit intent: clarity
Original:  Suppose that errors \|u- \|_{H^1_0 and \|u-}%DIFDELCMD < u%%% \|_{L^{\infty between an exact solution u and a numerically computed approximate solution u . We estimate the number of sign-changes of the solution u (the number of nodal domains) and  the location of zero level-sets of u (the location of the nodal line).
Revised:  Suppose that errors \|u- \|_{H^1_0 and \|u-}%DIFDELCMD < u%%% \|_{L^{\infty between an exact solution u and a numerically computed approximate solution u . We estimate the number of sign-changes of u (the number of nodal domains) and the location of zero level-sets of u (the location of the nodal line).
Edit intent: fluency
Original:  Suppose that errors \|u- \|_{H^1_0 and \|u-}%DIFDELCMD < u%%% \|_{L^{\infty between an exact solution u and a numerically computed approximate solution u . We estimate the number of sign-changes of the solution u (the number of nodal domains) and  the location of zero level-sets of u (the location of the nodal line).
Revised:  Suppose that errors \|u- \|_{H^1_0 and \|u-}%DIFDELCMD < u%%% \|_{L^{\infty between an exact solution u and a numerically computed approximate solution u . We estimate the number of sign-changes of the solution u (the number of nodal domains) and determine the location of zero level-sets of u (the location of the nodal line).
Edit intent: clarity
Original: This paper proposes a method for rigorously analyzing the sign-change structure of solutions to elliptic problems subject to one of the three types of homogeneous boundary conditions: Dirichlet, Neumann, and mixed.
Revised: This paper proposes a method for rigorously analyzing the sign-change structure of solutions of elliptic partial differential equations subject to one of the three types of homogeneous boundary conditions: Dirichlet, Neumann, and mixed.
Edit intent: clarity
Original:  The nodal line of solutions to this equation represents the interface between two coexisting phases.
Revised:  The nodal line of solutions of this equation represents the interface between two coexisting phases.
Edit intent: clarity
Original:  We further provide an upper-bound for the RID of multi-dimensional random measures that are obtained by Lipschitz functions of component-wise independent discrete-continuous random variables ( \mathbf{x ).
Revised:  We further provide an upper-bound for the RID of multi-dimensional random measures that are obtained by Lipschitz functions of component-wise independent discrete-continuous random variables ( x ).
Edit intent: coherence
Original:  The upper-bound is shown to be achievable when the Lipschitz function is A x , where A satisfies %DIFDELCMD < \spark%%% ( A ) = %DIFDELCMD < \rank %%% ( A )+1 (e.g., Vandermonde matrices).
Revised:  The upper-bound is shown to be achievable when the Lipschitz function is A x , where A satisfies %DIFDELCMD < \spark%%% A ) = %DIFDELCMD < \rank %%% ( A )+1 (e.g., Vandermonde matrices).
Edit intent: fluency
Original:  The upper-bound is shown to be achievable when the Lipschitz function is A x , where A satisfies %DIFDELCMD < \spark%%% ( A ) = %DIFDELCMD < \rank %%% ( A )+1 (e.g., Vandermonde matrices).
Revised:  The upper-bound is shown to be achievable when the Lipschitz function is A x , where A satisfies %DIFDELCMD < \spark%%% ( A ) = %DIFDELCMD < \rank %%% A )+1 (e.g., Vandermonde matrices).
Edit intent: fluency
Original:  they include the general rate-distortion curve, as well as more specific notions such as Renyi information dimension (RID), and dimensional-rate bias (DRB).
Revised:  they include general approaches, such as using the rate-distortion curve, as well as more specific notions such as Renyi information dimension (RID), and dimensional-rate bias (DRB).
Edit intent: clarity
Original:  they include the general rate-distortion curve, as well as more specific notions such as Renyi information dimension (RID), and dimensional-rate bias (DRB).
Revised:  they include the general rate-distortion curve, as well as more specific notions , such as the Renyi information dimension (RID), and dimensional-rate bias (DRB).
Edit intent: fluency
Original:  These cases are of interest when working with linear transformation of component-wise independent discrete-continuous random variables.
Revised:  This class of distributions naturally arises when considering linear transformation of component-wise independent discrete-continuous random variables.
Edit intent: clarity
Original:  We further provide an upper-bound for the RID of multi-dimensional random measures that are obtained by Lipschitz functions of component-wise independent discrete-continuous random variables ( x ).
Revised:  We further provide an upper-bound for the RID of multi-dimensional random measures that are obtained by Lipschitz functions of component-wise independent discrete-continuous random variables ( X ).
Edit intent: fluency
Original:  The upper-bound is shown to be achievable when the Lipschitz function is Ax , where A satisfies SPARK(A) = rank(A) + 1 (e.g., Vandermonde matrices).
Revised:  The upper-bound is shown to be achievable when the Lipschitz function is AX , where A satisfies SPARK(A) = rank(A) + 1 (e.g., Vandermonde matrices).
Edit intent: fluency
Original:  The above results in the case of discrete-domain moving-average processes with non-Gaussian excitation noise  allow us to evaluate the block-average RID and to find a relationship between this parameter and other existing compressibility measures.
Revised:  When considering discrete-domain moving-average processes with non-Gaussian excitation noise allow us to evaluate the block-average RID and to find a relationship between this parameter and other existing compressibility measures.
Edit intent: clarity
Original:  The above results in the case of discrete-domain moving-average processes with non-Gaussian excitation noise  allow us to evaluate the block-average RID and to find a relationship between this parameter and other existing compressibility measures.
Revised:  The above results in the case of discrete-domain moving-average processes with non-Gaussian excitation noise , the above results allow us to evaluate the block-average RID and to find a relationship between this parameter and other existing compressibility measures.
Edit intent: coherence
Original:  The above results in the case of discrete-domain moving-average processes with non-Gaussian excitation noise  allow us to evaluate the block-average RID and to find a relationship between this parameter and other existing compressibility measures.
Revised:  The above results in the case of discrete-domain moving-average processes with non-Gaussian excitation noise allow us to evaluate the block-average RID and to find a relationship between these parameters and other existing compressibility measures.
Edit intent: fluency
Original:  The upper-bound is shown to be achievable when the Lipschitz function is AX , where A satisfies SPARK(A {\changed\spark  ) = rank(A) +1 (e.g., Vandermonde matrices).
Revised:  The upper-bound is shown to be achievable when the Lipschitz function is AX , where A satisfies {\changed\spark ) = rank(A) +1 (e.g., Vandermonde matrices).
Edit intent: coherence
Original:  The upper-bound is shown to be achievable when the Lipschitz function is AX , where A satisfies SPARK(A {\changed\spark  ) = rank(A) +1 (e.g., Vandermonde matrices).
Revised:  The upper-bound is shown to be achievable when the Lipschitz function is AX , where A satisfies SPARK(A {\changed\spark( ) = rank(A) +1 (e.g., Vandermonde matrices).
Edit intent: fluency
Original:  In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory --- finite or infinite --- is almost always required.
Revised:  In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory -- finite or infinite --- is almost always required.
Edit intent: fluency
Original:  In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory --- finite or infinite --- is almost always required.
Revised:  In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory --- finite or infinite -- is almost always required.
Edit intent: fluency
Original:  We also prove an equivalent to their celebrated corollary of utmost practical interest: if both players have optimal (arena-independent-)finite-memory strategies in all one-player games, then it is also the case in all two-player games.
Revised:  We also prove an equivalent to their celebrated corollary of great practical interest: if both players have optimal (arena-independent-)finite-memory strategies in all one-player games, then it is also the case in all two-player games.
Edit intent: clarity
Original: This paper introduces  `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'.
Revised: This paper introduces the notion of `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'.
Edit intent: clarity
Original: This paper introduces  `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'.
Revised: This paper introduces `commonly knowing whether', a non-standard version of standard common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'.
Edit intent: clarity
Original: This paper introduces  `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'.
Revised: This paper introduces `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of standard `knowing that'.
Edit intent: fluency
Original:  After giving five possible definitions of this concept , we explore the logical relations among them both in the multi-agent case and in the single-agent case.
Revised:  After giving five possible definitions of this notion , we explore the logical relations among them both in the multi-agent case and in the single-agent case.
Edit intent: fluency
Original:  After giving five possible definitions of this concept , we explore the logical relations among them both in the multi-agent case and in the single-agent case.
Revised:  After giving five possible definitions of this concept , we explore the logical relations among them in the single-agent case.
Edit intent: clarity
Original: This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity , including the correction of stratigraphic boundaries, given new mesh surfaces.
Revised: This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity given new mesh surfaces.
Edit intent: clarity
Original:  Using surfaces that represent geological boundaries, the objectives are to identify areas where refinement is needed, increase spatial resolution to minimise surface approximation error, reduce redundancy to increase the compactness of the model , and identify the geological domain on a block-by-block basis.
Revised:  Using surfaces that represent geological boundaries, the objectives are to identify areas where refinement is needed, increase spatial resolution to minimize surface approximation error, reduce redundancy to increase the compactness of the model , and identify the geological domain on a block-by-block basis.
Edit intent: coherence
Original:  Using surfaces that represent geological boundaries, the objectives are to identify areas where refinement is needed, increase spatial resolution to minimise surface approximation error, reduce redundancy to increase the compactness of the model , and identify the geological domain on a block-by-block basis.
Revised:  Using surfaces that represent geological boundaries, the objectives are to identify areas where refinement is needed, increase spatial resolution to minimise surface approximation error, reduce redundancy to increase the compactness of the model and identify the geological domain on a block-by-block basis.
Edit intent: fluency
Original:  The main contributions are a coordinate-ascent merging algorithm and a flexible architecture for updating the spatial structure of a block model when given multiple surfaces, which emphasises the ability to selectively retain or modify previously assigned block labels.
Revised:  The main contributions are a coordinate-ascent merging algorithm and a flexible architecture for updating the spatial structure of a block model when given multiple surfaces, which emphasizes the ability to selectively retain or modify previously assigned block labels.
Edit intent: fluency
Original:  To demonstrate the robustness and applicability of the block merging technique to a wider class of problem, the core approach is extended to reduce fragmentation in a block model where surfaces are not directly involved.
Revised:  To demonstrate the robustness and applicability of the proposed block merging strategy in a more narrow setting, it is used to reduce block fragmentation in an existing model where surfaces are not directly involved.
Edit intent: clarity
Original:  The overall framework is applicable to orebody modelling given mineralisation or stratigraphic boundaries, and 3D segmentation more generally, where there is a need to delineate spatial regions using mesh surfaces within a block model.
Revised:  The overall framework is applicable to orebody modelling given geological boundaries, and 3D segmentation more generally, where there is a need to delineate spatial regions using mesh surfaces within a block model.
Edit intent: clarity
Original: This project describes an approach to analyze public sentiments with social media data and provides an example of the Twitter discourse during the 2019 Chinese National Day.
Revised: This project describes an approach to analyze online public sentiments using social media data and provides an example of the Twitter discourse during the 2019 Chinese National Day.
Edit intent: clarity
Original: This project describes an approach to analyze public sentiments with social media data and provides an example of the Twitter discourse during the 2019 Chinese National Day.
Revised: This project describes an approach to analyze public sentiments with social media data and provides an example of Twitter discourse during the 2019 Chinese National Day.
Edit intent: fluency
Original: We study the dynamics of a droplet placing on an inclined rough surface , which can be described by gradient flows on a Hilbert manifold.
Revised: We study the dynamics of a droplet moving on an inclined rough surface , which can be described by gradient flows on a Hilbert manifold.
Edit intent: clarity
Original:  We propose unconditionally stable first/second order numeric schemes to simulate the geometric motion of the droplet  described using motion by mean curvature  with moving contact lines.
Revised:  We propose unconditionally stable first/second order numerical schemes to simulate the geometric motion of the droplet described using motion by mean curvature with moving contact lines.
Edit intent: fluency
Original:  We propose unconditionally stable first/second order numeric schemes to simulate the geometric motion of the droplet  described using motion by mean curvature  with moving contact lines.
Revised:  We propose unconditionally stable first/second order numeric schemes to simulate this geometric motion of the droplet described using motion by mean curvature with moving contact lines.
Edit intent: clarity
Original:  We propose unconditionally stable first/second order numeric schemes to simulate the geometric motion of the droplet  described using motion by mean curvature  with moving contact lines.
Revised:  We propose unconditionally stable first/second order numeric schemes to simulate the geometric motion of the droplet , which is described using motion by mean curvature with moving contact lines.
Edit intent: coherence
Original:  We propose unconditionally stable first/second order numeric schemes to simulate the geometric motion of the droplet  described using motion by mean curvature  with moving contact lines.
Revised:  We propose unconditionally stable first/second order numeric schemes to simulate the geometric motion of the droplet described using motion by mean curvature coupled with moving contact lines.
Edit intent: clarity
Original:  The schemes base on (i) explicit moving boundaries, which decouple the dynamics of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with an inexact nonlinear elliptic solver  .
Revised:  The schemes are based on (i) explicit moving boundaries, which decouple the dynamics of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with an inexact nonlinear elliptic solver .
Edit intent: fluency
Original:  The schemes base on (i) explicit moving boundaries, which decouple the dynamics of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with an inexact nonlinear elliptic solver  .
Revised:  The schemes base on (i) explicit moving boundaries, which decouple the dynamic updates of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with an inexact nonlinear elliptic solver .
Edit intent: clarity
Original:  The schemes base on (i) explicit moving boundaries, which decouple the dynamics of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with an inexact nonlinear elliptic solver  .
Revised:  The schemes base on (i) explicit moving boundaries, which decouple the dynamics of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with a nonlinear elliptic solver .
Edit intent: clarity
Original:  Inspired by biological snakes, our control architecture is composed of two key modules: A deep reinforcement learning (RL) module for achieving adaptive goal-reaching behaviors with changing goals, and a central pattern generator (CPG) system with Matsuoka oscillators for generating stable and diverse behavior patterns.
Revised:  Inspired by biological snakes, our control architecture is composed of two key modules: A deep reinforcement learning (RL) module for achieving adaptive goal-tracking behaviors with changing goals, and a central pattern generator (CPG) system with Matsuoka oscillators for generating stable and diverse behavior patterns.
Edit intent: clarity
Original:  Inspired by biological snakes, our control architecture is composed of two key modules: A deep reinforcement learning (RL) module for achieving adaptive goal-reaching behaviors with changing goals, and a central pattern generator (CPG) system with Matsuoka oscillators for generating stable and diverse behavior patterns.
Revised:  Inspired by biological snakes, our control architecture is composed of two key modules: A deep reinforcement learning (RL) module for achieving adaptive goal-reaching behaviors with changing goals, and a central pattern generator (CPG) system with Matsuoka oscillators for generating stable and diverse locomotion patterns.
Edit intent: clarity
Original:  The two modules are interconnected into a closed-loop system: The RL module, acting as the "brain" , regulates the input of the CPG system based on state feedback from the robot.
Revised:  The two modules are interconnected into a closed-loop system: The RL module, acting as the "brain" , regulates the input to the CPG system based on state feedback from the robot.
Edit intent: clarity
Original:  The two modules are interconnected into a closed-loop system: The RL module, acting as the "brain" , regulates the input of the CPG system based on state feedback from the robot.
Revised:  The two modules are interconnected into a closed-loop system: The RL module, acting as the "brain" , regulates the input of the CPG system given state feedback from the robot.
Edit intent: clarity
Original:  The output of the CPG system is then translated into pressure inputs to pneumatic actuators of a soft snake robot.
Revised:  The output of the CPG system is then translated into pressure inputs to pneumatic actuators of the soft snake robot.
Edit intent: fluency
Original:  Since the oscillation frequency and wave amplitude of the Matsuoka oscillator can be independently controlled under different time scales, we  adapt the option-critic framework to improve the learning performance measured by optimality and data efficiency.
Revised:  Based on the fact that the oscillation frequency and wave amplitude of the Matsuoka oscillator can be independently controlled under different time scales, we adapt the option-critic framework to improve the learning performance measured by optimality and data efficiency.
Edit intent: coherence
Original:  Since the oscillation frequency and wave amplitude of the Matsuoka oscillator can be independently controlled under different time scales, we  adapt the option-critic framework to improve the learning performance measured by optimality and data efficiency.
Revised:  Since the oscillation frequency and wave amplitude of the Matsuoka oscillator can be independently controlled under different time scales, we further adapt the option-critic framework to improve the learning performance measured by optimality and data efficiency.
Edit intent: clarity
Original:  We verify the performance of the proposed control method in experiments with both simulated and real  snake robots.
Revised:  The performance of the proposed control method in experiments with both simulated and real snake robots.
Edit intent: clarity
Original:  We verify the performance of the proposed control method in experiments with both simulated and real  snake robots.
Revised:  We verify the performance of the proposed controller is experimentally validated with both simulated and real snake robots.
Edit intent: clarity
Original: The radio access network (RAN) is regarded as one of the potential proposals for massive Internet of Things (mIoT)  , where the random access channel (RACH) procedure should be exploited for IoT devices to access to the RAN . However, modelling of the dynamic process of RACH of mIoT devices is challenging.
Revised: Future wireless networks are envisioned to serve massive Internet of Things (mIoT) , where the random access channel (RACH) procedure should be exploited for IoT devices to access to the RAN . However, modelling of the dynamic process of RACH of mIoT devices is challenging.
Edit intent: clarity