wanyu/IteraTeR_full_sent huggingface dataset:
Original:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity.
Revised:  It is well known that the exponential utility function is connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity.
Edit intent: clarity
Original:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity.
Revised:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function through a limiting procedure : in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity.
Edit intent: clarity
Original:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity.
Revised:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure if the parameter of the HARA utility function is going to zero and in the second case to infinity.
Edit intent: clarity
Original:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to zero and in the second case to infinity. In our previous papers devoted to the optimization problem with a HARA and LOG utility functions we proved that also the corresponding analytical and Lie algebraic structures are connected with the same limiting procedure.
Revised:  It is well known that both the LOG and the EXPn utility functions are connected with the HARA utility function by means of a limiting procedure : in the first case the parameter of a HARA utility function is going to infinity. We show that the optimization problem with a HARA and LOG utility functions we proved that also the corresponding analytical and Lie algebraic structures are connected with the same limiting procedure.
Edit intent: coherence
Original:  In our previous papers devoted to the optimization problem with a HARA and LOG utility functions we proved that also the corresponding analytical and Lie algebraic structures are connected with the same limiting procedure. In this paper we show that the case of EXPn utility function differs from the case of the HARA utility and is not connected to the HARA case by the limiting procedure .
Revised:  In our previous papers devoted to the optimization problem with the exponential utility function is not connected to the HARA case by the limiting procedure .
Edit intent: meaning-changed
Original:  In this paper we show that the case of EXPn utility function differs from the case of the HARA utility and is not connected to the HARA case by the limiting procedure . We carry out the Lie group analysis of the PDEs for the cases EXPn and EXPp utility functions and proved that they are connected by a one-to-one analytical substitution and are identical from the economical, analytical or Lie algebraic point of view. The complete set of nonequivalent group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of sub algebras of the admitted Lie algebra.
Revised:  In this paper we show that the case of EXPn utility function differs from the case of the HARA utility and is not connected to the HARA case by the limiting procedure and we obtain essentially different results. For the main three dimensional PDE with the exponential utility function we obtain the complete set of nonequivalent group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of sub algebras of the admitted Lie algebra.
Edit intent: coherence
Original:  The complete set of nonequivalent group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of sub algebras of the admitted Lie algebra.
Revised:  The complete set of the nonequivalent Lie group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of sub algebras of the admitted Lie algebra.
Edit intent: fluency
Original:  The complete set of nonequivalent group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of sub algebras of the admitted Lie algebra.
Revised:  The complete set of nonequivalent group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of subalgebras of the admitted Lie algebra.
Edit intent: fluency
Original:  We prove this claim by showing that a special case of an intimately related decision problem SCMP - does there exist a measure with a non-mass-splitting transport cost and support size below prescribed bounds? - is NP-hard for all rational data.
Revised:  We prove this claim by showing that a special case of an intimately related decision problem SCMP -- does there exist a measure with a non-mass-splitting transport cost and support size below prescribed bounds? - is NP-hard for all rational data.
Edit intent: fluency
Original:  We prove this claim by showing that a special case of an intimately related decision problem SCMP - does there exist a measure with a non-mass-splitting transport cost and support size below prescribed bounds? - is NP-hard for all rational data.
Revised:  We prove this claim by showing that a special case of an intimately related decision problem SCMP - does there exist a measure with a non-mass-splitting transport cost and support size below prescribed bounds? -- is NP-hard for all rational data.
Edit intent: fluency
Original:  Our proof is based on a reduction from planar 3-dimensional matching and follows a strategy laid out by Spieksma and Woeginger  for a reduction to planar, minimum circumference 3-dimensional matching.
Revised:  Our proof is based on a reduction from planar 3-dimensional matching and follows a strategy laid out by Spieksma and Woeginger (1996) for a reduction to planar, minimum circumference 3-dimensional matching.
Edit intent: meaning-changed
Original:  Second, we prove thatgiven a rational measure, an optimal transport to a set of measures can be computed in polynomial time . However, the complexity of this task depends on the size of an encoding of this measure, not only on the input size to the underlying barycenter problem. We show that this distinction causes a simple proof that SCMP is in NP to fail; whether SCMP is in NP remains open .
Revised:  Second, we prove thatgiven a rational measure, an optimal transport to a set of measures can be computed in polynomial time in the size of a bit encoding of the measure. However, the encoding size of a barycenter may be exponential in the encoding size of the underlying measures .
Edit intent: clarity
Original: The mesoscopic Peyrard-Bishop DNA Hamiltonian describes the main molecular interactions with simple potentials , resulting in an efficient calculation of the melting of the duplex helix. It is based on a 2D model which can be simplified to calculate the classical partition function with the transfer-integral technique.
Revised: The mesoscopic Peyrard-Bishop DNA Hamiltonian describes the main molecular interactions with simple potentials which allow efficient calculations of melting temperatures. However, it is based on a 2D model which can be simplified to calculate the classical partition function with the transfer-integral technique.
Edit intent: clarity
Original:  It is based on a 2D model which can be simplified to calculate the classical partition function with the transfer-integral technique. At the heart of this approach are simplifications that leave only a single variable to integrate, but also make it impossible to apply the model to situations where a more detailed structural description is needed .
Revised:  It is based on a Hamiltonian that does not consider the helical twist or any other relevant molecular dimensions .
Edit intent: meaning-changed
Original:  Here, we start from a more realistic 3D description and work out several approximations to arrive at a form that can be handled by the transfer-integral technique. We show that this new approach naturally results very sharpopening transition .
Revised:  Here, we start from a more realistic 3D description and work out several approximations to arrive at a new non-linear 1D Hamiltonian with a twist angle dependence. Our approximations were numerically compared to full 3D calculations, and established its validity in the regime of small angles. For long DNA sequences we obtain sharp, first-order-like melting, transitions .
Edit intent: meaning-changed
Original:  Based on a monotonicity property afforded by such a geometric structure, we develop a bootstrap test thatis computationally convenient to implement. In particular , unlike many studies in similar nonstandard settings, the procedure dispenses with set estimation , and the critical values are obtained in a way as simple as computing the test statistic.
Revised:  Based on a monotonicity property afforded by such a geometric structure, we construct a bootstrap procedure that , unlike many studies in similar nonstandard settings, the procedure dispenses with set estimation , and the critical values are obtained in a way as simple as computing the test statistic.
Edit intent: clarity
Original:  Moreover, by appealing to the machinery of strong approximations, we accommodate nonparametric settings where estimators of the parameter of interest may not admit asymptotic distributions. We establish asymptotic uniform size control of our test, and characterize classes of alternatives against which it has nontrivial power.
Revised:  Moreover, by appealing to the machinery of strong approximations, our framework accommodates nonparametric regression models as well as distributional/density-related and structural settings.
Edit intent: meaning-changed
Original:  Nonetheless, there still exist BCI-illiterate subjects who struggle to use BCI systems, showing high intra-subject variabilities. Several methods have been proposed to enhance their performance via transfer learning. In such a case, high inter- and intrasubject variabilities are the points to be considered.
Revised:  Nonetheless, owing to high inter- and intrasubject variabilities are the points to be considered.
Edit intent: coherence
Original:  In such a case, high inter- and intrasubject variabilities are the points to be considered. Transfer learning , especially as a domain adaptation technique, has drawn increasing attention in various fields. However, the adaptation of approaches into BCI faces two challenging limitations. (i) Most domain adaptation  methods are designed for labeled source and unlabeled target domain whereas BCI tasks generally have multiple annotated domains.
Revised:  In such a case, high intra- and inter-subject variabilities, many studies on decoding EEG were designed in a subject-specific manner by using calibration samples, with no concern of its practical use, hampered by time-consuming steps and a large data requirement. To this end, recent studies adopted a transfer learning strategy, especially domain adaptation methods are designed for labeled source and unlabeled target domain whereas BCI tasks generally have multiple annotated domains.
Edit intent: meaning-changed
Original:  (i) Most domain adaptation  methods are designed for labeled source and unlabeled target domain whereas BCI tasks generally have multiple annotated domains.
Revised:  (i) Most domain adaptation techniques. Among those, to our knowledge, an adversarial learning has shown its potential in BCIs. In the meantime, it is known that adversarial learning-based domain adaptation methods are designed for labeled source and unlabeled target domain whereas BCI tasks generally have multiple annotated domains.
Edit intent: meaning-changed
Original:  (i) Most domain adaptation  methods are designed for labeled source and unlabeled target domain whereas BCI tasks generally have multiple annotated domains. (ii) Most of the existing methods do not consider a negative transfer to disrupt generalization ability.
Revised:  (i) Most domain adaptation methods are prone to negative transfer that disrupts learning generalized feature representations, applicable to diverse domains, e.g., subjects or sessions in BCIs.
Edit intent: clarity
Original:  In this paper, we propose a novel network architecture to tackle these limitations by estimating mutual information in high- and low-level representationsregardless of the domain that is considered as a subject in this paper. Specifically, our proposed method extracts subject-invariant and class-relevant features, thereby enhancing generalizability in overall classification.
Revised:  In this paper, we propose a novel network architecture to tackle these limitations by estimating mutual information in high- and subject-invariant and class-relevant features, thereby enhancing generalizability in overall classification.
Edit intent: clarity
Original:  Specifically, our proposed method extracts subject-invariant and class-relevant features, thereby enhancing generalizability in overall classification.
Revised:  Specifically, our proposed method extracts subject-invariant feature representations in an information-theoretic manner, without using adversarial learning. To be specific, we devise two operational components in a deep network that explicitly estimate mutual information between feature representations; (1) to decompose features in an intermediate layer into class-relevant features, thereby enhancing generalizability in overall classification.
Edit intent: meaning-changed
Original:  Specifically, our proposed method extracts subject-invariant and class-relevant features, thereby enhancing generalizability in overall classification. It is also noteworthy that our method can be applicable to a new subject with a small amount of data via fine-tuning, thus reducing calibration time for its practical uses. We validated our proposed method on two large motor imagery EEG datasets via comparisons with other competing methods .
Revised:  Specifically, our proposed method extracts subject-invariant and class-relevant and class-irrelevant ones, (2) to enrich class-discriminative feature representation. On two large EEG datasets, we validated the effectiveness of our proposed framework by comparing with several comparative methods in performance. Further, we conducted rigorous analyses by performing an ablation study in regard to the components in our network, explaining our model's decision on input EEG signals via layer-wise relevance propagation, and visualizing the distribution of learned features via t-SNE .
Edit intent: meaning-changed
Original: Accurate simulation of fluid flow in the presence of complex geometries with mesh-free  methods requires that the geometry surfaces be captured accurately with particles. The traditional ways to do this with particlesdo not result in an accurate representation of the geometry surfaces.
Revised: Accurate simulation of fluid flow in the presence of complex geometries with mesh-free methods requires that the geometry surfaces be captured accurately . Methods like weakly-compressible and incompressible smoothed particle hydrodynamics (SPH) perform better when the particle distribution is uniform. Moreover, SPH schemes typically require the mass or volume to be constant for all particles. For a uniform density, this necessitates a good initial particle distribution.
Edit intent: meaning-changed
Original:  In this paper we propose a simple SPH-based algorithm to produce homogeneous particle distributions that capture the geometry surfaces accurately in two and three dimensions.
Revised:  In this paper , various particle packing algorithms present in literature are implemented and compared with the intention of capturing the boundaries accurately while maintaining a uniform particle distribution of both the fictitious boundary and fluid particles. An improved SPH-based algorithm to produce homogeneous particle distributions that capture the geometry surfaces accurately in two and three dimensions.
Edit intent: meaning-changed
Original: Computer simulation of fluid flow in the presence of complex geometries with mesh-free particle methods requires that the geometry be captured accurately . Methods like weakly-compressible and incompressiblesmoothed particle hydrodynamics (SPH ) perform better when the particle distribution is uniform.
Revised: Computer simulation of fluid flow in the presence of complex geometries with mesh-free particle methods requires that the geometry be captured accurately in terms of particles. In the context of incompressible/ weakly-compressible and incompressiblesmoothed particle hydrodynamics (SPH ) perform better when the particle distribution is uniform.
Edit intent: meaning-changed
Original:  Moreover, SPH schemes typically require the mass or volume to be constant for all particles. For a uniform density, this necessitates a good initial particle distribution .
Revised:  Hence, for the time accurate simulation of flow in the presence of complex boundaries, one must have both an accurate boundary discretization as well as a uniform distribution of particles to initialize the simulation. This process of obtaining an initial uniform distribution of particles is called "particle packing" .
Edit intent: clarity
Original:  Through the Neuron Module, these neurons and components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons.
Revised:  Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons.
Edit intent: clarity
Original:  Through the Neuron Module, these neurons and components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package.
Revised:  Through the Neuron Module, these neurons and components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor .
Edit intent: coherence
Original:  To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated dMRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches,  include a comparison of the high b-value behavior between dendrite branches and whole neurons  .
Revised:  To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, include a comparison of the high b-value behavior between dendrite branches and whole neurons .
Edit intent: clarity
Original:  To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated dMRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches,  include a comparison of the high b-value behavior between dendrite branches and whole neurons  .
Revised:  To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated dMRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons .
Edit intent: coherence
Original:  To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated dMRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches,  include a comparison of the high b-value behavior between dendrite branches and whole neurons  .
Revised:  To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated dMRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, include a comparison of the high b-value behavior between dendrite branches and whole neurons . In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo. Finally, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches .
Edit intent: meaning-changed
Original: In this paper we consider a  velocity jump process with excluded-volume interactions in the context of cell chemotaxis, where  the size of each particle affects the motion . Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches.
Revised: In this paper we consider a biased velocity jump process with excluded-volume interactions in the context of cell chemotaxis, where the size of each particle affects the motion . Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches.
Edit intent: meaning-changed
Original: In this paper we consider a  velocity jump process with excluded-volume interactions in the context of cell chemotaxis, where  the size of each particle affects the motion . Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches.
Revised: In this paper we consider a velocity jump process with excluded-volume interactions for chemotaxis, where the size of each particle affects the motion . Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches.
Edit intent: clarity
Original: In this paper we consider a  velocity jump process with excluded-volume interactions in the context of cell chemotaxis, where  the size of each particle affects the motion . Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches.
Revised: In this paper we consider a velocity jump process with excluded-volume interactions in the context of cell chemotaxis, where we account for the size of each particle affects the motion . Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches.
Edit intent: clarity