wanyu/IteraTeR_v2 huggingface dataset:
Original:  Based on previous research, this paper proposes a new quasi-best fast TT decomposition algorithm for large-scale sparse tensors with proven correctness and for which the upper bound of its complexity  derived.
Revised:  Based on previous research, this paper proposes a new quasi-best fast TT decomposition algorithm for large-scale sparse tensors with proven correctness and for which the upper bound of its complexity is derived.
Edit intent: clarity
Original: In this paper we present two versions of a parallel finger structure FS on p processors that supports searches, insertions and deletions, and has a fixed number of movable fingers .
Revised: In this paper we present two versions of a parallel finger structure FS on p processors that supports searches, insertions and deletions, and has a finger at each end .
Edit intent: clarity
Original:  These parameters are established by the base station (BS) for each block transmitted until reaching a target block error rate ( BLERt ).
Revised:  These parameters are established by the base station (BS) for each block transmitted until reaching a target block error rate ( BLER_t ).
Edit intent: clarity
Original:  To validate our proposal, we compare with alternative strategies using an open-source NB-IoT uplink simulator.
Revised:  To validate our proposal, we compare with alternative strategies using an open source NB-IoT uplink simulator.
Edit intent: fluency
Original: In this short note we show that every connected oriented cubic graph admits an  8-colouring.
Revised: In this note we show that every connected oriented cubic graph admits an 8-colouring.
Edit intent: clarity
Original: In this short note we show that every connected oriented cubic graph admits an  8-colouring.
Revised: In this short note we show every orientation of a connected cubic graph admits an 8-colouring.
Edit intent: clarity
Original:  This lowers the best known upper bound for the chromatic number of connected oriented cubic graphs ]  .
Revised:  This lowers the best-known upper bound for the chromatic number of connected oriented cubic graphs ] .
Edit intent: fluency
Original:  These results imply that either the chromatic number for the family of connected oriented cubic graphs equals the 2-dipath chromatic number or the long-standing conjecture of Sopena [Journal of Graph Theory 25:191-205 1997] regarding the chromatic number of orientations of connected cubic graphs is false.
Revised:  These results imply that either the chromatic number for the family of oriented connected cubic graphs equals the 2-dipath chromatic number or the long-standing conjecture of Sopena [Journal of Graph Theory 25:191-205 1997] regarding the chromatic number of orientations of connected cubic graphs is false.
Edit intent: fluency
Original: We propose a  sparse reconstruction framework for solving inverse problems  . Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transforms , we train an encoder-decoder network D \circ E with E acting as a nonlinear sparsifying transform.
Revised: We propose a sparse reconstruction framework for solving inverse problems . Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transformations , we train an encoder-decoder network D \circ E with E acting as a nonlinear sparsifying transform.
Edit intent: fluency
Original:  For this augmented sparse \ell^q-approach, we present a full convergence analysis , derive convergence rates and describe a training strategy .
Revised:  We present a full convergence analysis , derive convergence rates and describe a training strategy .
Edit intent: coherence
Original:  For this augmented sparse \ell^q-approach, we present a full convergence analysis , derive convergence rates and describe a training strategy .
Revised:  For this augmented sparse \ell^q-approach, we present a full convergence analysis and derive convergence rates and describe a training strategy .
Edit intent: fluency
Original:  Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transformations, we train an encoder-decoder network \mathbf{D \circ E to construct a regularizer formed by \ell^q-norm of }  the encoder coefficients enforcing sparsity and an additional term penalizing the distance to the data manifold.
Revised:  Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transformations, we train an encoder-decoder \circ E to construct a regularizer formed by \ell^q-norm of } the encoder coefficients enforcing sparsity and an additional term penalizing the distance to the data manifold.
Edit intent: clarity
Original:  Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transformations, we train an encoder-decoder network \mathbf{D \circ E to construct a regularizer formed by \ell^q-norm of }  the encoder coefficients enforcing sparsity and an additional term penalizing the distance to the data manifold.
Revised:  Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transformations, we train an encoder-decoder network \mathbf{D \circ E to construct a regularizer formed by \ell^q-norm of } the distance to the data manifold.
Edit intent: clarity
Original:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as  Amazon.com , Homes.mil or Wikipedia.org  . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Revised:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as " Amazon.com , Homes.mil or Wikipedia.org . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Edit intent: fluency
Original:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as  Amazon.com , Homes.mil or Wikipedia.org  . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Revised:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as Amazon.com ", " Homes.mil or Wikipedia.org . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Edit intent: fluency
Original:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as  Amazon.com , Homes.mil or Wikipedia.org  . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Revised:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as Amazon.com , Homes.mil " or " Wikipedia.org . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Edit intent: fluency
Original:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as  Amazon.com , Homes.mil or Wikipedia.org  . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Revised:  Utilizing this new approach, we construct the models for the volume of users, interacting through Internet platforms, such as Amazon.com , Homes.mil or Wikipedia.org " . Then, we perform qualitative analysis of the system's phase portrait and discuss the main characteristics of the platforms.
Edit intent: fluency
Original: 3D Compton scattering imaging is an upcoming concept focusing on exploiting the photons scattered, following on from the so-called Compton effect, by the atomic structure of an object under study.
Revised: 3D Compton scattering imaging is an upcoming concept exploiting the scattering of photons induced by the electronic structure of the object under study.
Edit intent: clarity
Original:  Therefore, the contours of the electron density are essentially encoded within the first-order scattering radiation and can be recovered from the full spectrum using a filtered backprojection kind inversion technique .
Revised:  Therefore, the contours of the electron density are essentially encoded within the first-order part. This opens the way to contour-based reconstruction techniques when using multiple scattered data .
Edit intent: clarity
Original:  (3) direct sums of an arbitrary collection of 2-dimensional convex sets defined as the epigraphs of univariate convex functions (including as special cases , geometric programming and entropy programming);
Revised:  (3) direct sums of an arbitrary collection of 2-dimensional convex sets defined as the epigraphs of univariate convex functions (including as special cases geometric programming and entropy programming);
Edit intent: fluency
Original:  (4) epigraph of a matrix norm (including as a special case , minimization of nuclear norm over a linear subspace);
Revised:  (4) epigraph of a matrix norm (including as a special case minimization of nuclear norm over a linear subspace);
Edit intent: fluency
Original:  and ( 6 ) constraints involving Hyperbolic polynomials.
Revised:  and ( 6 ) constraints involving hyperbolic polynomials.
Edit intent: fluency
Original:  This manuscript contains the installation method of DDS and the input format for different types of constraints .
Revised:  This manuscript contains the users' guide, as well as theoretical results needed for the implementation of the algorithms .
Edit intent: coherence
Original:  To help the users in using DDS, we include some examplesto illustrate the coding .
Revised:  To help the users , we included many examples .
Edit intent: clarity
Original:  We also discuss some implementation details and techniques we used to improve the efficiency  .
Revised:  We also discussed some implementation details and techniques we used to improve the efficiency .
Edit intent: fluency
Original: As semantically-enabled applications require high-quality ontologies, developing and maintaining  as correct and complete as possible ontologies is an important , although difficult task in ontology engineering.
Revised: As semantically-enabled applications require high-quality ontologies, developing and maintaining ontologies that are as correct and complete as possible ontologies is an important , although difficult task in ontology engineering.
Edit intent: clarity
Original: As semantically-enabled applications require high-quality ontologies, developing and maintaining  as correct and complete as possible ontologies is an important , although difficult task in ontology engineering.
Revised: As semantically-enabled applications require high-quality ontologies, developing and maintaining as correct and complete as possible is an important , although difficult task in ontology engineering.
Edit intent: fluency
Original: As semantically-enabled applications require high-quality ontologies, developing and maintaining  as correct and complete as possible ontologies is an important , although difficult task in ontology engineering.
Revised: As semantically-enabled applications require high-quality ontologies, developing and maintaining as correct and complete as possible ontologies is an important although difficult task in ontology engineering.
Edit intent: fluency
Original:  In this paper we formalize the repairing step as an abduction problem and situate the state of the art with respect to this framework.
Revised:  In this paper we discuss the state of the art regarding the repairing step. We do this by formalizing the repairing step as an abduction problem and situate the state of the art with respect to this framework.
Edit intent: clarity
Original:  In this paper we formalize the repairing step as an abduction problem and situate the state of the art with respect to this framework.
Revised:  In this paper we formalize the repairing step as an abduction problem and situating the state of the art with respect to this framework.
Edit intent: fluency
Original:  We show that there still are many open research problems and show opportunities for further work and advancing the field.
Revised:  We show that there are still many open research problems and show opportunities for further work and advancing the field.
Edit intent: fluency
Original: We formulate one methodology to put a value or price on knowledge , using well accepted techniques from finance.
Revised: We formulate one methodology to put a value or price on knowledge using well accepted techniques from finance.
Edit intent: fluency
Original:  Just because someone does not see a connection , does not mean that there is no connection.
Revised:  Just because someone does not see a connection does not mean that there is no connection.
Edit intent: fluency
Original:  But paradoxically, in many data-driven fields, the eureka moments are becoming more and more rare.
Revised:  But paradoxically, in many data-driven fields, the eureka moments are becoming increasingly rare.
Edit intent: clarity
Original:  Scientists , and the software tools they use, are struggling to keep pace with the explosion in the volume and complexity of scientific data.
Revised:  Scientists are struggling to keep pace with the explosion in the volume and complexity of scientific data.
Edit intent: clarity
Original:  We describe here , five architectural principles we believe are essential in order to create effective, robust, and flexible platforms that make us of the best of emerging technology  .
Revised:  We describe here , five architectural principles we believe are essential in order to create effective, robust, and flexible platforms that make the best use of emerging technology .
Edit intent: clarity
Original: A  lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes without any regularity assumptions .
Revised: A proof for the lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes without any regularity assumptions .
Edit intent: clarity
Original: A  lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes without any regularity assumptions .
Revised: A lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes .
Edit intent: clarity
Original:  The bound has the same form as the one by Graham and McLean [SIAM J. Numer.
Revised:  The bound has a similar form as the one by Graham and McLean [SIAM J. Numer.
Edit intent: fluency
Original:  Anal., 44 (2006), pp. 1487-1513 ] but doesn't require any mesh regularity assumptions, neither global nor local.
Revised:  Anal., 44 (2006), pp. 1487--1513 ] but doesn't require any mesh regularity assumptions, neither global nor local.
Edit intent: fluency
Original:  In two dimension , the bound depends on the number of degrees of freedom and a logarithmic term involving number of degrees of freedom and\lvert \lvert  }\rvert\rvert\lvert  }\rvert  the volume of the smallest patch  .
Revised:  In two dimensions , the bound depends on the number of degrees of freedom and a logarithmic term involving number of degrees of freedom and\lvert \lvert }\rvert\rvert\lvert }\rvert the volume of the smallest patch .
Edit intent: fluency
Original:  In two dimension , the bound depends on the number of degrees of freedom and a logarithmic term involving number of degrees of freedom and\lvert \lvert  }\rvert\rvert\lvert  }\rvert  the volume of the smallest patch  .
Revised:  In two dimension , the bound depends on the number of degrees of freedom and a logarithmic term involving number of degrees of freedom and\lvert \lvert }\rvert\rvert\lvert }\rvert denoting the volume of the smallest patch .
Edit intent: clarity
Original:  In the paper, we consider the case of finding the lowest cost replacement edge for each edge of the MST. A previous algorithm by Tarjan takes O(m \alpha( n, m )) time, where \alpha( n, m ) is the inverse Ackermann's function.
Revised:  In the paper, we consider the case of finding the lowest cost replacement edge for each edge of the MST. A previous algorithm by Tarjan takes O(m \alpha( m, n )) time, where \alpha( n, m ) is the inverse Ackermann's function.
Edit intent: fluency
Original:  In the paper, we consider the case of finding the lowest cost replacement edge for each edge of the MST. A previous algorithm by Tarjan takes O(m \alpha( n, m )) time, where \alpha( n, m ) is the inverse Ackermann's function.
Revised:  In the paper, we consider the case of finding the lowest cost replacement edge for each edge of the MST. A previous algorithm by Tarjan takes O(m \alpha( n, m )) time, where \alpha( m, n ) is the inverse Ackermann's function.
Edit intent: fluency
Original:  Our algorithm is the first that runs in O(  n + m ) time and O( n + m) space .
Revised:  Our algorithm is the first that runs in O( n ) time and O( n + m) space .
Edit intent: fluency
Original:  The most vital edge is the graph edge whose removal causes the largest increase in weight of the minimum spanning tree.
Revised:  Additionally, since the most vital edge is the graph edge whose removal causes the largest increase in weight of the minimum spanning tree.
Edit intent: coherence
Original:  The most vital edge is the graph edge whose removal causes the largest increase in weight of the minimum spanning tree.
Revised:  The most vital edge is the tree edge whose removal causes the largest increase in weight of the minimum spanning tree.
Edit intent: clarity
Original: We propose a new tetrahedral meshing technique , fTetWild, to convert triangle soups into high-quality tetrahedral meshes.
Revised: We propose a new tetrahedral meshing method , fTetWild, to convert triangle soups into high-quality tetrahedral meshes.
Edit intent: clarity
Original:  Our method builds upon the TetWild algorithm, inheriting its unconditional robustness, but dramatically reducing its computation cost and guaranteeing the generation of a valid tetrahedral mesh with floating point coordinates.
Revised:  Our method builds on the TetWild algorithm, inheriting its unconditional robustness, but dramatically reducing its computation cost and guaranteeing the generation of a valid tetrahedral mesh with floating point coordinates.
Edit intent: fluency
Original:  The theoretical analysis of our method is based on the asymptotic property in the operator norm from H^{1/2}( \mathbb S ^1) to H^{-1/2}( \mathbb S ^1) of the phaseless near-field operator defined in terms of the phaseless near-field data measured on \partial B_R with large enough R, where H^s( \mathbb S ^1) is a Sobolev space on the unit circle \mathbb S ^1 for real number s, together with the factorization of a modified far-field operator.
Revised:  The theoretical analysis of our method is based on the asymptotic property in the operator norm from H^{1/2}( \mathbb S ^1) to H^{-1/2}( \mathbb S ^1) of the phaseless total-field operator defined in terms of the phaseless near-field data measured on \partial B_R with large enough R, where H^s( \mathbb S ^1) is a Sobolev space on the unit circle \mathbb S ^1 for real number s, together with the factorization of a modified far-field operator.
Edit intent: clarity
Original:  The theoretical analysis of our method is based on the asymptotic property in the operator norm from H^{1/2}( \mathbb S ^1) to H^{-1/2}( \mathbb S ^1) of the phaseless near-field operator defined in terms of the phaseless near-field data measured on \partial B_R with large enough R, where H^s( \mathbb S ^1) is a Sobolev space on the unit circle \mathbb S ^1 for real number s, together with the factorization of a modified far-field operator.
Revised:  The theoretical analysis of our method is based on the asymptotic property in the operator norm from H^{1/2}( \mathbb S ^1) to H^{-1/2}( \mathbb S ^1) of the phaseless near-field operator defined in terms of the phaseless total-field data measured on \partial B_R with large enough R, where H^s( \mathbb S ^1) is a Sobolev space on the unit circle \mathbb S ^1 for real number s, together with the factorization of a modified far-field operator.
Edit intent: clarity
Original:  The theoretical analysis of our method is based on the asymptotic property in the operator norm from H^{1/2}( \mathbb S ^1) to H^{-1/2}( \mathbb S ^1) of the phaseless near-field operator defined in terms of the phaseless near-field data measured on \partial B_R with large enough R, where H^s( \mathbb S ^1) is a Sobolev space on the unit circle \mathbb S ^1 for real number s, together with the factorization of a modified far-field operator.
Revised:  The theoretical analysis of our method is based on the asymptotic property in the operator norm from H^{1/2}( \mathbb S ^1) to H^{-1/2}( \mathbb S ^1) of the phaseless near-field operator defined in terms of the phaseless near-field data measured on \partial B_R with large enough R, where H^s( \mathbb S ^1) is a Sobolev space on the unit circle \mathbb{S ^1 for real number s, together with the factorization of a modified far-field operator.
Edit intent: fluency
Original: Predicting the sale of an item is a critical problem in eCommerce search.
Revised: Surfacing a ranked list of items for a search query to help buyers discover inventory and make purchase decisions is a critical problem in eCommerce search.
Edit intent: clarity
Original:  Typically, items are independently predicted with a probability of sale for a given search query.
Revised:  Typically, items are independently predicted with a probability of sale with respect to a given search query.
Edit intent: clarity
Original:  The ranking model with proposed delta features result in 3-5\\%DIF < improvement in MRR over the baseline model.
Revised:  The ranking models with proposed delta features result in 3-5\\%DIF < improvement in MRR over the baseline model.
Edit intent: fluency
Original:  We also %DIF > improvement in MRR over the baseline  study impact of different sizes for neighborhood.
Revised:  We also %DIF > improvement in MRR over the baseline model. We also study impact of different sizes for neighborhood.
Edit intent: clarity
Original:  Under weak selection, meaning a small perturbation of the neutral model, we give a general first-order expansion of a mutant's fixation probability for an arbitrary initial configuration of mutant and resident types.
Revised:  Under weak selection, meaning the mutation's effect on the organism is small. We obtain a weak-selection perturbation expansion of a mutant's fixation probability for an arbitrary initial configuration of mutant and resident types.
Edit intent: clarity
Original:  Under weak selection, meaning a small perturbation of the neutral model, we give a general first-order expansion of a mutant's fixation probability for an arbitrary initial configuration of mutant and resident types.
Revised:  Under weak selection, meaning a small perturbation of the neutral model, we give a general first-order expansion of a mutant's fixation probability , from an arbitrary initial configuration of mutant and resident types.
Edit intent: clarity
Original:  This result reduces the problem of whether weak selection favors a trait from exponential to polynomial complexity in the population size .
Revised:  This result reduces the problem of whether selection favors a trait from exponential to polynomial complexity in the population size .
Edit intent: clarity
Original:  This result reduces the problem of whether weak selection favors a trait from exponential to polynomial complexity in the population size .
Revised:  This result reduces the problem of whether weak selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size .
Edit intent: clarity