wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper, we adopt a novelnode-based approach and propose aservice-balanced online scheduling algorithm, called NSB , which gives balanced scheduling opportunities to the nodes with heavy workload .
Revised:  In this paper, we adopt a novelnode-based approach service-balanced online scheduling algorithm, called NSB , which gives balanced scheduling opportunities to the nodes with heavy workload .
Edit intent: coherence
Original:  In this paper, we adopt a novelnode-based approach and propose aservice-balanced online scheduling algorithm, called NSB , which gives balanced scheduling opportunities to the nodes with heavy workload .
Revised:  In this paper, we adopt a novelnode-based approach and propose a scheduling algorithm, called NSB , which gives balanced scheduling opportunities to the nodes with heavy workload .
Edit intent: clarity
Original:  In this paper, we adopt a novelnode-based approach and propose aservice-balanced online scheduling algorithm, called NSB , which gives balanced scheduling opportunities to the nodes with heavy workload .
Revised:  In this paper, we adopt a novelnode-based approach and propose aservice-balanced online propose a novel Node-based Service-Balanced (NSB) online scheduling algorithm. NSB aims to give scheduling opportunities to the nodes with heavy workload .
Edit intent: clarity
Original:  It is based on an additive Schwarz method studied by J. Lottes and P.
Revised:  It extends the additive Schwarz method studied by J. Lottes and P.
Edit intent: clarity
Original:  We have analysed a model of cross-feeding , based on the replicator equation, with the aim of establishing criteria for coexistence in ecosystems containing three species .
Revised:  We have analysed a model of cross-feeding based on the replicator equation, with the aim of establishing criteria for coexistence in ecosystems containing three species .
Edit intent: fluency
Original:  The system is studied statistically and the probability of coexistence in the species triplet is computed for two models of the interactions between the species .
Revised:  The system is studied statistically and the probability of coexistence in the species triplet is computed for two models of species interactions .
Edit intent: clarity
Original: For k = 2,3 and a cubic graph G let \nu_k(G) denote the size of a maximum k-edge-colorable subgraph of G. Mkrtchyan, Petrosyan and Vardanyan proved that \nu_2(G)\geq 4{5}\cdot |V(G)|, \nu_3(G)\geq 7{6}\cdot |V(G)|  ~samvel:2010.
Revised: For k = 2,3 and a cubic graph G let \nu_k(G) denote the size of a maximum k-edge-colorable subgraph of G. Mkrtchyan, Petrosyan and Vardanyan proved that \nu_2(G)\geq 4{5}\cdot |V(G)|, \nu_3(G)\geq 7{6}\cdot |V(G)| for any cubic graph G ~samvel:2010.
Edit intent: clarity
Original:  In the  present work, we show that the last two inequalities imply the first two of them.
Revised:  In the first part of the present work, we show that the last two inequalities imply the first two of them.
Edit intent: clarity
Original:  Moreover, we show that \nu_2(G) \geq \alpha \cdot \frac{|V(G)| + 2\cdot \nu_3(G)}{4} , where \alpha=16{17}, if G is a cubic graph, \alpha=20{21}, if G is a cubic graph containing a perfect matching, \alpha=44{45}, if G is a bridgeless cubic graph. %DIFDELCMD < \\ %DIFDELCMD < %%% Finally, we investigate the parameters \nu_2(G) and \nu_3(G) in the class of claw-free cubic graphs.
Revised:  Moreover, we show that \nu_2(G) \geq \alpha \cdot \frac{|V(G)| + 2\cdot \nu_3(G)}{4} , where \alpha=16{17}, if G is a cubic graph, \alpha=20{21}, if G is a cubic graph containing a perfect matching, \alpha=44{45}, if G is a bridgeless cubic graph. %DIFDELCMD < \\ %DIFDELCMD < %%% We also investigate the parameters \nu_2(G) and \nu_3(G) in the class of claw-free cubic graphs.
Edit intent: coherence
Original:  We also show that \nu_2(G) \geq \frac{35{36} \cdot |V(G)| when n \geq 48. } On the basis of these inequalities we are able to improve the coefficient \alpha for bridgeless claw-free cubic (G)+\nu_{k+1}(G)}{2} for k\geq 2 and graphs G containing at most 1 cycle.
Revised:  {36} \cdot |V(G)| when n \geq 48. } On the basis of these inequalities we are able to improve the coefficient \alpha for bridgeless claw-free cubic (G)+\nu_{k+1}(G)}{2} for k\geq 2 and graphs G containing at most 1 cycle.
Edit intent: coherence
Original:  Many such queries contain common sub-expressions , either within a single query or among multiple queries submitted as a batch.
Revised:  Many such queries contain com- mon subexpressions , either within a single query or among multiple queries submitted as a batch.
Edit intent: clarity
Original:  Conventional query optimizers do not exploit these common sub-expressions and produce sub-optimal plans.
Revised:  Conventional query optimizers do not exploit these subexpressions and produce sub-optimal plans.
Edit intent: clarity
Original:  The problem of multi-query optimization (MQO) is to generate an optimal combined evaluation plan by computing common sub-expressions once and reusing them.
Revised:  The problem of multi-query optimization (MQO) is to generate an optimal combined evaluation plan by computing common sub-expressions once and reusing them.
Edit intent: fluency
Original:  The problem of multi-query optimization (MQO) is to generate an optimal combined evaluation plan by computing common sub-expressions once and reusing them.
Revised:  The problem of multi-query optimization (MQO) is to generate an optimal combined evaluation plan by computing common subexpressions once and reusing them.
Edit intent: fluency
Original:  Thus, this problem has primarily been tackled using various heuristic algorithms, without providing any theoretical guarantees on the quality of the solutionobtained .
Revised:  Thus, this problem has primarily been tackled using various heuristic algorithms, without providing any theoretical guarantees on the quality of their solution .
Edit intent: clarity
Original:  We propose a greedy algorithm for this transformed formulation of the problem, which under weak, intuitive assumptions, gives an approximation factor with respect to the optimal solution of this formulation.
Revised:  We propose a greedy algorithm for this transformed formulation of the problem, which under weak, intuitive assumptions, provides an approximation factor with respect to the optimal solution of this formulation.
Edit intent: clarity
Original:  We propose a greedy algorithm for this transformed formulation of the problem, which under weak, intuitive assumptions, gives an approximation factor with respect to the optimal solution of this formulation.
Revised:  We propose a greedy algorithm for this transformed formulation of the problem, which under weak, intuitive assumptions, gives an approximation factor guarantee for this formulation.
Edit intent: clarity
Original:  We go on to show that this factor is optimal, unless \mathsf{P = \mathsf{NP . Another noteworthy point about our algorithm is that it can be easily incorporated into existing transformation-based optimizers.
Revised:  We go on to show that this factor is optimal, unless P = \mathsf{NP . Another noteworthy point about our algorithm is that it can be easily incorporated into existing transformation-based optimizers.
Edit intent: fluency
Original:  We go on to show that this factor is optimal, unless \mathsf{P = \mathsf{NP . Another noteworthy point about our algorithm is that it can be easily incorporated into existing transformation-based optimizers.
Revised:  We go on to show that this factor is optimal, unless \mathsf{P = NP . Another noteworthy point about our algorithm is that it can be easily incorporated into existing transformation-based optimizers.
Edit intent: fluency
Original: A subspace bitrade of type T_q(t,k,v) is a pair (T_0,T_1) of two disjoint nonempty collections (trades) of k-dimensional subspaces of a v-dimensional space F^v over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T_0 and T_1.
Revised: A subspace bitrade of type T_q(t,k,v) is a pair (T_0,T_1) of two disjoint nonempty collections of k-dimensional subspaces of a v-dimensional space F^v over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T_0 and T_1.
Edit intent: clarity
Original: A subspace bitrade of type T_q(t,k,v) is a pair (T_0,T_1) of two disjoint nonempty collections (trades) of k-dimensional subspaces of a v-dimensional space F^v over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T_0 and T_1.
Revised: A subspace bitrade of type T_q(t,k,v) is a pair (T_0,T_1) of two disjoint nonempty collections (trades) of k-dimensional subspaces of a v-dimensional space V over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T_0 and T_1.
Edit intent: clarity
Original:  In a previous paper, the minimum cardinality of a subspace T_q(t,t+1,v) bitrade was establish .
Revised:  In a previous paper, the minimum cardinality of a subspace T_q(t,t+1,v) bitrade was established .
Edit intent: fluency
Original: A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplication , which greatly limits the benefits of so-called blocked algorithms.
Revised: A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplications , which greatly limits the benefits of so-called blocked algorithms.
Edit intent: fluency
Original: A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplication , which greatly limits the benefits of so-called blocked algorithms.
Revised: A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplication , which greatly limits the benefits that can be derived from so-called blocked algorithms.
Edit intent: clarity
Original: A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplication , which greatly limits the benefits of so-called blocked algorithms.
Revised: A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplication , which greatly limits the benefits of so-called blocking of algorithms.
Edit intent: clarity
Original:  It is demonstrated that the asymptotic flop count for the proposed method is 2mn^2 - (2/3)n^3 for an m\times n matrix with m \geq n , identical to that of the best classical  Householder QR factorization  (with or without pivoting).
Revised:  It is demonstrated that the asymptotic flop count for the proposed method is 2mn^2 - (2/3)n^3 for an m\times n matrix , identical to that of the best classical Householder QR factorization (with or without pivoting).
Edit intent: clarity
Original:  It is demonstrated that the asymptotic flop count for the proposed method is 2mn^2 - (2/3)n^3 for an m\times n matrix with m \geq n , identical to that of the best classical  Householder QR factorization  (with or without pivoting).
Revised:  It is demonstrated that the asymptotic flop count for the proposed method is 2mn^2 - (2/3)n^3 for an m\times n matrix with m \geq n , identical to that of the best classical Householder QR factorization algorithm (with or without pivoting).
Edit intent: clarity
Original:  Experiments demonstrate improvements in speed of substantial integer factors (between a factor of 3 and 5) relative to LAPACK's{\sc geqp3 implementation on a modern CPU  .
Revised:  Experiments demonstrate acceleration in speed of substantial integer factors (between a factor of 3 and 5) relative to LAPACK's{\sc geqp3 implementation on a modern CPU .
Edit intent: clarity
Original:  Relative entropy - that is, the Kullback--Leibler divergence, or various generalizations of this---provides a quantitative measure of how far from equilibrium the system is.
Revised:  Relative entropy - that is, the Kullback--Leibler divergence, or various generalizations of this - provides a quantitative measure of how far from equilibrium the system is.
Edit intent: fluency
Original:  This is mainly due to their efficient representation and the favorable computational complexity of important operations in high-dimensional spaces.
Revised:  This is mainly due to their efficient representation and their favorable computational complexity of important operations in high-dimensional spaces.
Edit intent: fluency
Original:  Besides those operations , zonotopes are also closed under Minkowski difference  .
Revised:  Unfortunately , zonotopes are also closed under Minkowski difference .
Edit intent: clarity
Original:  Besides those operations , zonotopes are also closed under Minkowski difference  .
Revised:  Besides those operations , zonotopes are not closed under Minkowski difference .
Edit intent: clarity
Original: We introduce a family of quantum walks on cycles parametrized by their liveliness, defined as the ability to execute a long-range move.
Revised: We introduce a family of quantum walks on cycles parametrized by their liveliness, defined by the ability to execute a long-range move.
Edit intent: fluency
Original:  We investigate the behavior of the probability distribution and time-averaged probability distribution.
Revised:  We investigate the behaviour of the probability distribution and time-averaged probability distribution.
Edit intent: fluency
Original:  We also show that the introduced model provides a simple recipe for improving the efficiency of the network exploration .
Revised:  We also show that the introduced model provides a method for network exploration which is robust against trapping .
Edit intent: clarity
Original:  Some studies have shown that the data published in these platforms may contain sensitive personal data and that external entities can gather and exploit this knowledge for their own benefit.
Revised:  Some studies have shown that the data published in these platforms may contain sensitive personal information and that external entities can gather and exploit this knowledge for their own benefit.
Edit intent: fluency
Original:  Even though some methods to preserve the privacy of the users of social networks have been proposed,
Revised:  Even though some methods to preserve the privacy of social networks users have been proposed,
Edit intent: fluency
Original:  they generally apply rigid access control measures to the protected content and, even worse, they do not enable the users to understand which contents are sensitive enough to require protection . Last but not least, most of them require the collaboration of social network operators or they fail to provide a practical solution capable of working with well-known and already deployed social platforms (e.g., Twitter).
Revised:  they generally apply rigid access control measures to the protected content and, even worse, they do not enable the users to understand which contents are sensitive . Last but not least, most of them require the collaboration of social network operators or they fail to provide a practical solution capable of working with well-known and already deployed social platforms (e.g., Twitter).
Edit intent: clarity
Original:  According to a set of privacy requirements intuitively defined by the users of a social network, the proposed scheme is able to: (i) automatically detect sensitive information in users' publications;
Revised:  According to a set of privacy requirements intuitively defined by the users of a social network, the proposed scheme is able to: (i) automatically detect sensitive data in users' publications;
Edit intent: fluency
Original:  and (iii) provide  transparent access to private contents and disclose more or less information (thus, achieving less or more privacy) to readers according to their credentials toward the owners of the publications.
Revised:  and (iii) provide transparent access to sensitive contents by disclosing more or less information (thus, achieving less or more privacy) to readers according to their credentials toward the owners of the publications.
Edit intent: clarity
Original:  and (iii) provide  transparent access to private contents and disclose more or less information (thus, achieving less or more privacy) to readers according to their credentials toward the owners of the publications.
Revised:  and (iii) provide transparent access to private contents and disclose more or less information to readers according to their credentials toward the owners of the publications.
Edit intent: clarity
Original:  and (iii) provide  transparent access to private contents and disclose more or less information (thus, achieving less or more privacy) to readers according to their credentials toward the owners of the publications.
Revised:  and (iii) provide transparent access to private contents and disclose more or less information (thus, achieving less or more privacy) to readers according to their credentials toward the owner of the publications.
Edit intent: fluency
Original:  Last but not least, most of them require the collaboration of social network operators or they fail to provide a practical solution capable of working with well-known and already deployed social platforms (e. g., Twitter).
Revised:  Last but not least, most of them require the collaboration of social network operators or they fail to provide a practical solution capable of working with well-known and already deployed social platforms .
Edit intent: coherence
Original:  We also study the applicability of the proposed system in general and illustrate its behavior in two well-known social networks (i.e., Twitter and PatientsLikeMe) .
Revised:  We also study the applicability of the proposed system in general and illustrate its behavior in two case studies .
Edit intent: clarity
Original:  Thus, analyses based on the average behavior of molecules valid at a macroscopic level (i.e., with a large-number limit) will not necessarily hold when considering a small size system containing a much smaller number of molecules  .
Revised:  Thus, analyses based on the average behavior of molecules valid at a macroscopic level (i.e., with a large number of molecules .
Edit intent: clarity
Original: This library manipulates ensembles of cycles (quadrics), which are interrelated through certain geometric relations (  to be orthogonal , to be tangent  , etc.) .
Revised: We propose to consider ensembles of cycles (quadrics), which are interrelated through certain geometric relations ( to be orthogonal , to be tangent , etc.) .
Edit intent: clarity
Original: This library manipulates ensembles of cycles (quadrics), which are interrelated through certain geometric relations (  to be orthogonal , to be tangent  , etc.) .
Revised: This library manipulates ensembles of cycles (quadrics), which are interrelated through certain geometric relations ( to be orthogonal ", " to be tangent , etc.) .
Edit intent: fluency
Original: This library manipulates ensembles of cycles (quadrics), which are interrelated through certain geometric relations (  to be orthogonal , to be tangent  , etc.) .
Revised: This library manipulates ensembles of cycles (quadrics), which are interrelated through certain geometric relations ( to be orthogonal , to be tangent " , etc.) .
Edit intent: fluency
Original:  In the two-dimensional case illustrations and animations can be produced  .
Revised:  Numeric calculations can be done in exact or approximate arithmetic. In the two- and three-dimensional cases illustrations and animations can be produced .
Edit intent: clarity
Original: We study the problem of finding a tour of n points in \mathbb{R which every edge is long.
Revised: We study the problem of finding a tour of n points in which every edge is long.
Edit intent: fluency
Original:  The problem is known as Maximum Scatter TSP, and it was introduced by Arkin et al. (SODA 1997), motivated by applications in manufacturing and medical imaging.
Revised:  The problem is known as Maximum Scatter TSP, and was introduced by Arkin et al. (SODA 1997), motivated by applications in manufacturing and medical imaging.
Edit intent: fluency
Original:  They raised the question of whether one can obtain a better approximation ratio in the planar Euclidean case .
Revised:  They raised the question of whether a better approximation ratio in the planar Euclidean case .
Edit intent: clarity
Original:  They raised the question of whether one can obtain a better approximation ratio in the planar Euclidean case .
Revised:  They raised the question of whether one can obtain a better approximation ratio can be obtained in the Euclidean plane .
Edit intent: clarity
Original:  It is reqired to find out, is there such an enumeration of the graphs vertices that the polynomials of the graphs are equal.
Revised:  It is required to find out, is there such an enumeration of the graphs vertices that the polynomials of the graphs are equal.
Edit intent: fluency
Original:  This being a popular public opinion, these notions have not been based on any rigorous scientific study or research.
Revised:  This being a popular public opinion, has not been based on any rigorous scientific study or research.
Edit intent: clarity
Original:  In this paper, we revisit the cultural divide among the Indian population from a purely social networks based approach.
Revised:  In this paper, we revisit the cultural divide among the Indian population from a purely social network based approach.
Edit intent: fluency
Original:  We study the distinct cluster formation that takes place in the Indian community , and find that this is largely due to the effect of caste-based homophily.
Revised:  We study the distinct cluster formation that takes place in the Indian community and find that this is largely due to the effect of caste-based homophily.
Edit intent: fluency
Original:  We study the changes that take place with regard to the average social distance of a cluster as well as network formation when a new link is established between the clusters which in its essence, is what the reservation system is accomplishing.
Revised:  We study the changes that take place with regard to the average social distance of a cluster when a new link is established between the clusters which in its essence, is what the reservation system is accomplishing.
Edit intent: clarity
Original:  Although the animosity towards the reservation system could be rooted due to historical influence, hero worship and herd mentality, our results make it clear that the system has had a considerable impact in the country's overall development by bridging the gap between the conflicting social groups  .
Revised:  Although the animosity towards the reservation system could be rooted due to historical influence, hero worship and herd mentality, our results make it clear that the system has had a considerable impact on the country's overall development by bridging the gap between the conflicting social groups .
Edit intent: fluency