wanyu/IteraTeR_v2 huggingface dataset:
Original:  As a result  initial complexity analyses of GP  focused on restricted settings such as evolving trees with given structures or estimating the quality of solutions using only a small polynomial number of input/output examples.
Revised:  As a result initial complexity analyses of GP have focused on restricted settings such as evolving trees with given structures or estimating the quality of solutions using only a small polynomial number of input/output examples.
Edit intent: fluency
Original:  As a result  initial complexity analyses of GP  focused on restricted settings such as evolving trees with given structures or estimating the quality of solutions using only a small polynomial number of input/output examples.
Revised:  As a result initial complexity analyses of GP focused on restricted settings such as the evolution of trees with given structures or estimating the quality of solutions using only a small polynomial number of input/output examples.
Edit intent: fluency
Original:  As a result  initial complexity analyses of GP  focused on restricted settings such as evolving trees with given structures or estimating the quality of solutions using only a small polynomial number of input/output examples.
Revised:  As a result initial complexity analyses of GP focused on restricted settings such as evolving trees with given structures or the estimation of solution quality using only a small polynomial number of input/output examples.
Edit intent: fluency
Original:  However, the first runtime analyses concerning GP applications for evolving proper functions with defined input/output behavior have recently appeared.
Revised:  However, the first computational complexity analyses of GP for evolving proper functions with defined input/output behavior have recently appeared.
Edit intent: clarity
Original:  In this chapter, we present an overview of the state-of-the-art .
Revised:  In this chapter, we present an overview of the state of the art .
Edit intent: fluency
Original: In this paper, we provide a rigorous analysis for exponential convergence of multivariate Gegenbauer approximations of analytic functions defined in the d-dimensional hypercube.
Revised: In this paper, we are concerned with multivariate Gegenbauer approximation of analytic functions defined in the d-dimensional hypercube.
Edit intent: clarity
Original:  We first derive two explicit and sharp bounds for the coefficients of multivariate Gegenbauer expansion  based on two different extensions of the Bernstein ellipse.
Revised:  Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion based on two different extensions of the Bernstein ellipse.
Edit intent: clarity
Original:  With the aid of these bounds, we further establish an explicit error bound for the multivariate Gegenbauer approximation associated with an \ell^q ball index set in the uniform norm.
Revised:  We then establish an explicit error bound for the multivariate Gegenbauer approximation associated with an \ell^q ball index set in the uniform norm.
Edit intent: clarity
Original: In this paper, we are concerned with multivariate Gegenbauer approximation of analytic functions defined in the d-dimensional hypercube.
Revised: In this paper, we are concerned with multivariate Gegenbauer approximation of functions defined in the d-dimensional hypercube.
Edit intent: clarity
Original: 3-D cross point phase change memory (PCM) is a promising emerging nonvolatile memoryin changing the current memory-storage hierarchy .
Revised: 3-D cross point phase change memory (PCM) is a promising emerging memory .
Edit intent: clarity
Original:  Among them, the high voltage variation of half-selected cells on the bit line is optimized by scheme design.
Edit intent: coherence
Original:  The maximum value of read current is 160.27 \mu%DIFDELCMD < }%%% A and reduced by 41.7\% compared to the conventional V/2 scheme.
Revised:  The \mu%DIFDELCMD < }%%% A and reduced by 41.7\% compared to the conventional V/2 scheme.
Edit intent: coherence
Original:  The maximum value of read current is 160.27 \mu%DIFDELCMD < }%%% A and reduced by 41.7\% compared to the conventional V/2 scheme.
Revised:  The maximum value of read current is 160.27 %DIFDELCMD < }%%% A and reduced by 41.7\% compared to the conventional V/2 scheme.
Edit intent: coherence
Original:  The chip shows zero read error in Monte Carlo simulations.
Edit intent: coherence
Original: The  proposed glymphatic system suggests a new mechanism for waste clearance from the brain, and has sparked new research on Alzheimer's disease where one of the defining features is that metabolic waste accumulate within the brain.
Revised: The proposed glymphatic system suggests a new mechanism for waste clearance from the brain, and as such may underlie the development of e.g. Alzheimer's disease where one of the defining features is that metabolic waste accumulate within the brain.
Edit intent: clarity
Original: Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the \v C ech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed.
Revised: Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the ech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed.
Edit intent: fluency
Original: Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the \v C ech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed.
Revised: Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. the \v C Cech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed.
Edit intent: fluency
Original:  2-WL corresponds to the original algorithm suggested by Weisfeiler and Leman  50 years ago. 1-WL is the classical color refinement routine.
Revised:  2-WL corresponds to the original algorithm suggested by Weisfeiler and Leman over 50 years ago. 1-WL is the classical color refinement routine.
Edit intent: clarity
Original:  Two graphs are indistinguishable by k-WL iff they are equivalent in (k+1)-variable first-order logic with counting quantifiers.
Revised:  Indistinguishability by k-WL iff they are equivalent in (k+1)-variable first-order logic with counting quantifiers.
Edit intent: clarity
Original:  Based on image analysis of tissue flow velocity and cell shape , we determine the tissue strain rate, cell deformation and cell rearrangement rate fields, which are spatially heterogeneous.
Revised:  Based on image analysis of tissue flow velocity and cell shape , we determine the tissue strain rate, cell deformation and rearrangement rate fields, which are spatially heterogeneous.
Edit intent: fluency
Original:  for example, mixtures of existing models can be estimated by adapting known expectation-maximization algorithms, and the significance of node features can be evaluated in a statistically rigorous manner  .
Revised:  for example, the significance of node features can be evaluated in a statistically rigorous manner .
Edit intent: clarity
Original:  for example, mixtures of existing models can be estimated by adapting known expectation-maximization algorithms, and the significance of node features can be evaluated in a statistically rigorous manner  .
Revised:  for example, mixtures of existing models can be estimated by adapting known expectation-maximization algorithms, and the significance of node features can be evaluated in a statistically rigorous manner , and mixtures of existing models can be estimated by adapting known expectation-maximization algorithms .
Edit intent: coherence
Original:  This shows that lower bounds obtained earlier by Carstensen (1983) and Mulmuley \& Shah (2000) for general graphs also hold for planar graphs.
Revised:  This shows that lower bounds obtained earlier by Carstensen (1983) and Mulmuley Shah (2000) for general graphs also hold for planar graphs.
Edit intent: fluency
Original:  Gusfield (1980) and Dean (2009) showed that the number of break points for an n-vertex graph is n^{\log n + O(1)} assuming linear edge weights;
Revised:  Gusfield (1980) and Dean (2009) showed that the number of break points for every n-vertex graph is n^{\log n + O(1)} assuming linear edge weights;
Edit intent: clarity
Original:  we show that if the edge weights are allowed to vary as a polynomial of degree at most d, then the number of break points is n^{\log n + \psi (  n)  ^d}, where \psi (n) \ll \log^* n is a slowly growing function arising from Davenport-Schinzel sequences.
Revised:  we show that if the edge weights are allowed to vary as a polynomial of degree at most d, then the number of break points is n^{\log n + ( n) ^d}, where \psi (n) \ll \log^* n is a slowly growing function arising from Davenport-Schinzel sequences.
Edit intent: fluency
Original: We construct a family of planar graphs (G_n: n\geq 4) , where G_n has n vertices including a source vertex s and a sink vertex t, and edge weights that change linearly with a parameter \lambda such that, as \lambda varies in (-\infty,+\infty), the piece-wise linear cost of the shortest path from s to t has n^{\Omega(\log n)} break points .
Revised: We construct a family of planar graphs (G_n: n\geq 4) , where G_n has n vertices including a source vertex s and a sink vertex t, and edge weights that change linearly with a parameter \lambda such that, as \lambda varies in (-\infty,+\infty), the piece-wise linear cost of the shortest path from s to t has n^{\Omega(\log n)} pieces .
Edit intent: clarity
Original:  our result refutes this conjecture . Gusfield (1980) and Dean (2009) showed that the number of break points for every n-vertex graph is n^{\log n + O(1) linear edge weights ;
Revised:  our result refutes this conjecture . Gusfield (1980) and Dean (2009) showed that the number of pieces for every n-vertex graph is n^{\log n + O(1) linear edge weights ;
Edit intent: clarity
Original:  our result refutes this conjecture . Gusfield (1980) and Dean (2009) showed that the number of break points for every n-vertex graph is n^{\log n + O(1) linear edge weights ;
Revised:  our result refutes this conjecture . Gusfield (1980) and Dean (2009) showed that the number of break points for every n-vertex graph with linear edge weights ;
Edit intent: clarity
Original:  we show that if the edge weights are allowed to vary as a polynomial of degree at most d, then the number of break points is n^{\log n + (\alpha(n)+O(1))^d}, where \alpha(n) is the slowly growing inverse Ackermann function.
Revised:  we show that if the edge weights vary as a polynomial of degree at most d, then the number of break points is n^{\log n + (\alpha(n)+O(1))^d}, where \alpha(n) is the slowly growing inverse Ackermann function.
Edit intent: clarity
Original:  we show that if the edge weights are allowed to vary as a polynomial of degree at most d, then the number of break points is n^{\log n + (\alpha(n)+O(1))^d}, where \alpha(n) is the slowly growing inverse Ackermann function.
Revised:  we show that if the edge weights are allowed to vary as a polynomial of degree at most d, then the number of pieces is n^{\log n + (\alpha(n)+O(1))^d}, where \alpha(n) is the slowly growing inverse Ackermann function.
Edit intent: clarity
Original:  we show that if the edge weights are allowed to vary as a polynomial of degree at most d, then the number of break points is n^{\log n + (\alpha(n)+O(1))^d}, where \alpha(n) is the slowly growing inverse Ackermann function.
Revised:  we show that if the edge weights are allowed to vary as a polynomial of degree at most d, then the number of break points is n^{\log n + (\alpha(n)+O(1))^d}, where \alpha(n) is the slow growing inverse Ackermann function.
Edit intent: fluency
Original: In Virtual Reality (VR) applications, understanding how users explore the visual content is important in order to optimize content creation and distribution, develop user-centric services, or even to detect disorders in medical applications.
Revised: In Virtual Reality (VR) applications, understanding how users explore the visual content is important to optimize content creation and distribution, develop user-centric services, or even to detect disorders in medical applications.
Edit intent: coherence
Original: In Virtual Reality (VR) applications, understanding how users explore the visual content is important in order to optimize content creation and distribution, develop user-centric services, or even to detect disorders in medical applications.
Revised: In Virtual Reality (VR) applications, understanding how users explore the visual content is important in order to optimize content creation , to develop user-centric services, or even to detect disorders in medical applications.
Edit intent: clarity
Original:  the proposed solution takes into account the spherical geometry of the content and correctly identifies clusters that group viewers who actually display the same portion of spherical content . Results, carried out by using a set of publicly available VR user navigation patterns , show that the proposed method identifies more meaningful clusters , i.e., clusters of users who are consistently attending the same portion of spherical content , with respect to other methods .
Revised:  the proposed solution takes into account the spherical geometry of the content and aims at clustering users based on the actual overlap of displayed content among users. Our method is tested on real VR user navigation patterns , show that the proposed method identifies more meaningful clusters , i.e., clusters of users who are consistently attending the same portion of spherical content , with respect to other methods .
Edit intent: clarity
Original:  the proposed solution takes into account the spherical geometry of the content and correctly identifies clusters that group viewers who actually display the same portion of spherical content . Results, carried out by using a set of publicly available VR user navigation patterns , show that the proposed method identifies more meaningful clusters , i.e., clusters of users who are consistently attending the same portion of spherical content , with respect to other methods .
Revised:  the proposed solution takes into account the spherical geometry of the content and correctly identifies clusters that group viewers who actually display the same portion of spherical content . Results, carried out by using a set of publicly available VR user navigation patterns . Results show that our solution leads to clusters in which at least 85\% of the content displayed by one user is shared among the other users belonging to the same cluster .
Edit intent: clarity
Original:  The hyperbolic character of these flows requires the introduction of another Eulerian field than the level set function.
Revised:  The hyperbolic character of these flows requires the introduction of another Eulerian field than the level-set function.
Edit intent: fluency
Original:  This Eulerian field represents the normal velocity of the interface, or equivalently in tissue growth, the surface density of tissue synthesising cells, anticipated at future locations of the interface.
Revised:  This additional field represents the normal velocity of the interface, or equivalently in tissue growth, the surface density of tissue synthesising cells, anticipated at future locations of the interface.
Edit intent: clarity
Original:  This Eulerian field represents the normal velocity of the interface, or equivalently in tissue growth, the surface density of tissue synthesising cells, anticipated at future locations of the interface.
Revised:  This Eulerian field represents the surface density of tissue synthesising cells, anticipated at future locations of the interface.
Edit intent: clarity
Original:  Examples that include tissue fragmentation and fusion during the evolution of complex tissue shapes under hyperbolic curvature flows are provided .
Revised:  Examples that include tissue fragmentation and fusion .
Edit intent: clarity
Original:  On the contrary, in the case of a finite length of the rod  the perturbations reach its boundary and are reflected from them .
Revised:  On the contrary, in the case of a finite length of the rod , the perturbations reach its boundary and are reflected from them .
Edit intent: fluency
Original:  On the contrary, in the case of a finite length of the rod  the perturbations reach its boundary and are reflected from them .
Revised:  On the contrary, in the case of a finite length of the rod the perturbations reach its boundary and are reflected from it .
Edit intent: clarity
Original: Long Range (LoRa) is a modem technology for wireless communication in  Internet of Things (IoT), which trades off low data-rate for low power consumption.
Revised: Long Range (LoRa) is a modem technology for wireless communication in the Internet of Things (IoT), which trades off low data-rate for low power consumption.
Edit intent: fluency
Original:  Long Range Wide Area Network (LoRaWAN) has an open specification that defines the Medium Access Control (MAC) protocol for LoRa networks.
Revised:  Long Range Wide Area Network (LoRaWAN) has an open specification that determines the Medium Access Control (MAC) protocol for LoRa networks.
Edit intent: clarity
Original:  The result shows the performance of LoRaWAN in a simulation environment and a large scale scenario, indicating the feature of flexible propagation range on physical layer, and limited channel capacity on  data-link layer.
Revised:  The result shows the performance of LoRaWAN in a simulation environment and a large scale scenario, indicating the feature of flexible propagation range on physical layer, and limited channel capacity on the data-link layer.
Edit intent: fluency
Original:  The result shows that Time on Air can be dramatically decreased.
Revised:  The result shows that Time on Air can be significantly decreased.
Edit intent: clarity
Original: We establish a general theory of  strong error estimation for numerical approximations of a second order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite dimensional Wiener process.
Revised: We establish a general theory of strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite dimensional Wiener process.
Edit intent: fluency
Original: We establish a general theory of  strong error estimation for numerical approximations of a second order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite dimensional Wiener process.
Revised: We establish a general theory of strong error estimation for numerical approximations of a second order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener process.
Edit intent: fluency
Original:  The equation is spatially discretized by Galerkin finite element method and temporally discretized by drift-implicit Euler or Milstein schemes.
Revised:  The equation is spatially discretized by Galerkin methods and temporally discretized by drift-implicit Euler or Milstein schemes.
Edit intent: clarity
Original:  The equation is spatially discretized by Galerkin finite element method and temporally discretized by drift-implicit Euler or Milstein schemes.
Revised:  The equation is spatially discretized by Galerkin finite element method and temporally discretized by drift-implicit Euler and Milstein schemes.
Edit intent: fluency
Original:  By the monotone assumption , we use both the variational and semigroup approaches to derive a spatial Sobolev regularity under the L_\omega^p L_t^\infty \dot H _x ^{1+\gamma}-norm and a temporal H\"older regularity under the L_\omega^p L_x^2-norm for the solution of the proposed equation with an \dot H _x ^{1+\gamma}-valued initial datum for \gamma\in [0,1].
Revised:  By the monotone assumption , we use both the variational and semigroup approaches to derive a spatial Sobolev regularity under the L_\omega^p L_t^\infty \dot H ^{1+\gamma}-norm and a temporal H\"older regularity under the L_\omega^p L_x^2-norm for the solution of the proposed equation with an \dot H _x ^{1+\gamma}-valued initial datum for \gamma\in [0,1].
Edit intent: fluency
Original:  By the monotone assumption , we use both the variational and semigroup approaches to derive a spatial Sobolev regularity under the L_\omega^p L_t^\infty \dot H _x ^{1+\gamma}-norm and a temporal H\"older regularity under the L_\omega^p L_x^2-norm for the solution of the proposed equation with an \dot H _x ^{1+\gamma}-valued initial datum for \gamma\in [0,1].
Revised:  By the monotone assumption , we use both the variational and semigroup approaches to derive a spatial Sobolev regularity under the L_\omega^p L_t^\infty \dot H _x ^{1+\gamma}-norm and a temporal H\"older regularity under the L_\omega^p L_x^2-norm for the solution of the proposed equation with an \dot H ^{1+\gamma}-valued initial datum for \gamma\in [0,1].
Edit intent: fluency
Original:  Finally, we make full use of the monotonicity of the equation and tools from stochastic calculus to derive the sharp strong convergence rates \mathcal O(h^{1+\gamma}+\tau^{1/2}) and \mathcal O(h^{1+\gamma}+\tau^{(1+\gamma)/2}) for the Galerkin-based Euler and Milstein schemes, respectively.
Revised:  Finally, we make full use of the monotonicity of the equation and tools from stochastic calculus to derive the sharp strong convergence rates O(h^{1+\gamma}+\tau^{1/2}) and \mathcal O(h^{1+\gamma}+\tau^{(1+\gamma)/2}) for the Galerkin-based Euler and Milstein schemes, respectively.
Edit intent: fluency
Original:  Finally, we make full use of the monotonicity of the equation and tools from stochastic calculus to derive the sharp strong convergence rates \mathcal O(h^{1+\gamma}+\tau^{1/2}) and \mathcal O(h^{1+\gamma}+\tau^{(1+\gamma)/2}) for the Galerkin-based Euler and Milstein schemes, respectively.
Revised:  Finally, we make full use of the monotonicity of the equation and tools from stochastic calculus to derive the sharp strong convergence rates \mathcal O(h^{1+\gamma}+\tau^{1/2}) and O(h^{1+\gamma}+\tau^{(1+\gamma)/2}) for the Galerkin-based Euler and Milstein schemes, respectively.
Edit intent: fluency
Original:  The generalized notion of symmetry can assume at every point in space a different direction , as long as it is possible to exhibit the unidirectional symmetry in some coordinate representation.
Revised:  A generalized notion of symmetry can assume at every point in space a different direction , as long as it is possible to exhibit the unidirectional symmetry in some coordinate representation.
Edit intent: fluency
Original:  The generalized notion of symmetry can assume at every point in space a different direction , as long as it is possible to exhibit the unidirectional symmetry in some coordinate representation.
Revised:  The generalized notion of symmetry can be defined with different directions at every point in space a different direction , as long as it is possible to exhibit the unidirectional symmetry in some coordinate representation.
Edit intent: clarity
Original:  The generalized notion of symmetry can assume at every point in space a different direction , as long as it is possible to exhibit the unidirectional symmetry in some coordinate representation.
Revised:  The generalized notion of symmetry can assume at every point in space , as long as it is possible to exhibit the unidirectional symmetry in some coordinate representation.
Edit intent: clarity