wanyu/IteraTeR_v2 huggingface dataset:
Original:  This coefficient \sigma(H_1) is a minimal nonnegative real number such that, for every finitely generated subgroup H_2 of F, it is true that %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) \le \sigma(H_1) %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1) %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_2), where {\rm r} (H) :
Revised:  This coefficient \sigma(H_1) is a minimal nonnegative real number such that, for every finitely generated subgroup H_2 of F, it is true that %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1, H_2) \le \sigma(H_1) %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1) %DIFDELCMD < {\rm r}%%% \bar {\rm r (H_2), where {\rm r} (H) :
Edit intent: fluency
Original: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm   , H_2 \bar {\rm  \bar {\rm   .
Revised: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm r (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm , H_2 \bar {\rm \bar {\rm .
Edit intent: fluency
Original: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm   , H_2 \bar {\rm  \bar {\rm   .
Revised: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1, H_2) is the reduced rank of the generalized intersection of H_1 \bar {\rm , H_2 \bar {\rm \bar {\rm .
Edit intent: fluency
Original: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm   , H_2 \bar {\rm  \bar {\rm   .
Revised: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm r , H_2 \bar {\rm \bar {\rm .
Edit intent: fluency
Original: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm   , H_2 \bar {\rm  \bar {\rm   .
Revised: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm (H_1 , H_2 \bar {\rm \bar {\rm .
Edit intent: fluency
Original: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm   , H_2 \bar {\rm  \bar {\rm   .
Revised: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm , H_2 \bar {\rm r \bar {\rm .
Edit intent: fluency
Original: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm   , H_2 \bar {\rm  \bar {\rm   .
Revised: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm , H_2 \bar {\rm (H_1)\bar {\rm .
Edit intent: fluency
Original: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm  (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm   , H_2 \bar {\rm  \bar {\rm   .
Revised: = \max ( {\rm r} (H)-1,0) is the reduced rank of H, {\rm r} (H) is the rank of H, and %DIFDELCMD < {\rm r}%%% \bar {\rm (H_1, H_2) is the reduced rank of a generalized intersection of H_1 \bar {\rm , H_2 \bar {\rm \bar {\rm r .
Edit intent: fluency
Original:  Key to this computation is updating the posterior probability of all possible changepoint counts.
Revised:  Key to this computation is an update of the posterior probability of all possible changepoint counts.
Edit intent: fluency
Original:  We thus show how optimal observers accumulates evidence in changing environments, and map this computation to reduced models which perform inference using plausible neural mechanisms.
Revised:  We thus show how optimal observers accumulate evidence in changing environments, and map this computation to reduced models which perform inference using plausible neural mechanisms.
Edit intent: fluency
Original:  In order to represent the filtration of a simplicial complex, the entire filtration can be appended to any data structure that explicitly stores all the simplices of the complex such as the Hasse diagram or the recently introduced Simplex Tree by Boissonnat and Maria [Algorithmica '14].
Revised:  In order to represent the filtration of a simplicial complex, the entire filtration can be appended to any data structure that explicitly stores all the simplices of the complex such as the Hasse diagram or the recently introduced Simplex Tree [Algorithmica '14].
Edit intent: coherence
Original:  In this paper, we propose a new data structure called the Critical Simplex Diagram (CSD) which is a variant of the Simplex Array List (SAL) introduced by Boissonnat et al.
Revised:  In this paper, we propose a new data structure called the Critical Simplex Diagram (CSD) which is a variant of the Simplex Array List (SAL) 
Edit intent: coherence
Original:  Our data structure allows  to store in a compact way the filtration of a simplicial complex, and allows for the efficient implementation of a large range of basic operations.
Revised:  Our data structure allows one to store in a compact way the filtration of a simplicial complex, and allows for the efficient implementation of a large range of basic operations.
Edit intent: clarity
Original:  Next , we show that the CSD representation admits the following construction algorithms . \bullet A new edge-deletion algorithm for the fast construction of Flag complexes , which only depends on the number of critical simplices and the number of vertices.
Revised:  Finally , we show that the CSD representation admits the following construction algorithms . \bullet A new edge-deletion algorithm for the fast construction of Flag complexes , which only depends on the number of critical simplices and the number of vertices.
Edit intent: fluency
Original:  \bullet A new matrix-parsing algorithm to quickly construct the relaxed Delaunay complexes , depending only on the number of witnesses and the dimension of the complex .
Revised:  \bullet A new matrix-parsing algorithm to quickly construct the relaxed Delaunay complexes .
Edit intent: coherence
Original:  The measurements we consider are the degree distributions and the bipartite clustering coefficient, which we refer to as the metamorphosis coefficient .
Revised:  The characteristics we consider are the degree distributions and the bipartite clustering coefficient, which we refer to as the metamorphosis coefficient .
Edit intent: clarity
Original:  We define edge, node, and degreewise metamorphosis coefficients, enabling a more detailed understand of the bipartite community structure.
Revised:  We define edge, node, and degreewise metamorphosis coefficients, enabling a more detailed understanding of the bipartite community structure.
Edit intent: fluency
Original:  We explore the suitability of using automatically discovered topics from MOOC forums to measure students' academic abilities in a subject domain, under the Rasch model, which is the most common Item Response Theory (IRT) model.
Revised:  We explore the suitability of using automatically discovered topics from MOOC discussion forums for modelling students' academic abilities in a subject domain, under the Rasch model, which is the most common Item Response Theory (IRT) model.
Edit intent: clarity
Original:  The challenge is to discover topics that can fit the Rasch model as evidence of measuring educationally meaningful ability.
Revised:  The challenge is to discover meaningful topics that simultaneously achieve good statistical fit with the Rasch model as evidence of measuring educationally meaningful ability.
Edit intent: clarity
Original:  We demonstrate the suitability of our approach with both quantitative experiments on  three Coursera MOOCs, and with qualitative results of topic interpretability on a Discrete Optimisation MOOC.
Revised:  We demonstrate the suitability of our approach with quantitative experiments on three Coursera MOOCs, and with qualitative results of topic interpretability on a Discrete Optimisation MOOC.
Edit intent: clarity
Original:  We demonstrate the suitability of our approach with both quantitative experiments on  three Coursera MOOCs, and with qualitative results of topic interpretability on a Discrete Optimisation MOOC.
Revised:  We demonstrate the suitability of our approach with both quantitative experiments on data from three Coursera MOOCs, and with qualitative results of topic interpretability on a Discrete Optimisation MOOC.
Edit intent: clarity
Original:  We demonstrate the suitability of our approach with both quantitative experiments on  three Coursera MOOCs, and with qualitative results of topic interpretability on a Discrete Optimisation MOOC.
Revised:  We demonstrate the suitability of our approach with both quantitative experiments on three Coursera MOOCs, and with qualitative survey results on topic interpretability on a Discrete Optimisation MOOC.
Edit intent: clarity
Original:  Compared to the US Congress , a distinguishing feature of the Italian Chamber is the presence of a large number of political groups : the primary purpose of the analysis is thus to infer the pattern of collaborations between these groups .
Revised:  Compared to the US Congress , a distinguishing feature of the Chamber is the presence of a large number of political groups : the primary purpose of the analysis is thus to infer the pattern of collaborations between these groups .
Edit intent: clarity
Original:  Compared to the US Congress , a distinguishing feature of the Italian Chamber is the presence of a large number of political groups : the primary purpose of the analysis is thus to infer the pattern of collaborations between these groups .
Revised:  Compared to the US Congress , a distinguishing feature of the Italian Chamber is the presence of a large number of political groups . Our analysis aims to infer the pattern of collaborations between these groups .
Edit intent: coherence
Original:  We consider a stochastic blockmodel for edge-valued graphs that views bill cosponsorship as the result of a Poisson process, and derive measures of group relevance and preferential attachment between political parties.
Revised:  We consider a stochastic blockmodel for edge-valued graphs and derive measures of group relevance and preferential attachment between political parties.
Edit intent: clarity
Original:  We consider a stochastic blockmodel for edge-valued graphs that views bill cosponsorship as the result of a Poisson process, and derive measures of group relevance and preferential attachment between political parties.
Revised:  We consider a stochastic blockmodel for edge-valued graphs that views bill cosponsorship as the result of a Poisson process, and derive measures of group productivity and of collaboration between political parties.
Edit intent: clarity
Original:  As the number of model parameters increases quickly with the number of groups , we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph , which summarizes collaborations between political parties .
Revised:  As the proposed model encloses a large number of parameters , we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph , which summarizes collaborations between political parties .
Edit intent: clarity
Original:  As the number of model parameters increases quickly with the number of groups , we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph , which summarizes collaborations between political parties .
Revised:  As the number of model parameters increases quickly with the number of groups , we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph displaying collaborations between political parties .
Edit intent: clarity
Original:  In comparison to other parliaments, a distinguishing feature of the Chamber is the presence of a large number of political groups.
Revised:  In comparison with other parliaments, a distinguishing feature of the Chamber is the presence of a large number of political groups.
Edit intent: fluency
Original:  In comparison to other parliaments, a distinguishing feature of the Chamber is the presence of a large number of political groups.
Revised:  In comparison to other parliaments, a distinguishing feature of the Chamber is the large number of political groups.
Edit intent: clarity
Original:  We propose an extension of stochastic blockmodels for edge-valued graphs and derive measures of group productivity and of collaboration between political parties.
Revised:  We propose an extension of stochastic block models for edge-valued graphs and derive measures of group productivity and of collaboration between political parties.
Edit intent: fluency
Original:  As the proposed model encloses a large number of parameters, we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph displaying collaborations between political parties.
Revised:  As the model proposed encloses a large number of parameters, we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph displaying collaborations between political parties.
Edit intent: clarity
Original:  We also obtain formulae for the Estrada Gaussian index of Erdos-R\'enyi random graphs as well as for the Barab\'asi-Albert graphs.
Revised:  We also obtain formulas for the Estrada Gaussian index of Erdos-R\'enyi random graphs as well as for the Barab\'asi-Albert graphs.
Edit intent: fluency
Original:  In general, the Gaussian matrix function of the adjacency matrix of graphs characterizes important structural information not described in previously used matrix functions of graphs.
Revised:  In general, the Gaussian matrix function of the adjacency matrix of networks characterizes important structural information not described in previously used matrix functions of graphs.
Edit intent: clarity
Original:  To this end, we propose an effective general meta-path-based approach called \textit{Connector and Recursive Meta-Paths (CRMP).
Revised:  To this end, we propose an effective general meta-path-based approach called \textit{Connector and Recursive Meta-Paths (CRMP).
Edit intent: fluency
Original:  Modeling activity of  cortical circuitries in vivo, however, has been challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain.
Revised:  Modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain.
Edit intent: clarity
Original:  However, previous approaches modeling the dynamics of neural interactions suffer from computational cost;
Revised:  Previous approaches modeling the dynamics of neural interactions suffer from computational cost;
Edit intent: coherence
Original:  More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the  TAP mean-field or Bethe approximation to make the sequential Bayesian estimation of the model parameters possible.
Revised:  More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible.
Edit intent: clarity
Original: Recently, implementing Radio Access Network (RAN) functionality on cloud-based computing platform has become an emerging solution that leverages the many advantages of cloud infrastructure, such as shared computing resources and storage capacity, while lowering the operational cost.
Revised: Recently, implementing Radio Access Network (RAN) functionalities on cloud-based computing platform has become an emerging solution that leverages the many advantages of cloud infrastructure, such as shared computing resources and storage capacity, while lowering the operational cost.
Edit intent: clarity
Original:  In particular,  the cloud-cache in the cloud processing unit (CPU) presents a new layer in the RAN cache hierarchy, bridging the capacity-performance gap between the traditional edge-based and core-based caching schemes.
Revised:  In particular, we consider the cloud-cache in the cloud processing unit (CPU) presents a new layer in the RAN cache hierarchy, bridging the capacity-performance gap between the traditional edge-based and core-based caching schemes.
Edit intent: coherence
Original:  In particular,  the cloud-cache in the cloud processing unit (CPU) presents a new layer in the RAN cache hierarchy, bridging the capacity-performance gap between the traditional edge-based and core-based caching schemes.
Revised:  In particular, the cloud-cache in the cloud processing unit (CPU) as a new layer in the RAN cache hierarchy, bridging the capacity-performance gap between the traditional edge-based and core-based caching schemes.
Edit intent: clarity
Original:  The proposed method, "template-recursive iteration over tensors", is comparable to using  nested for loops in C and to vectorized code in Fortran, and it outperforms numpy, C-style tuple iteration, C-style integer reindexing, and boost::multi_array , and unlike some of those methods, it can be used when the dimension of the tensor is unknown at compile time  .
Revised:  The proposed method, "template-recursive iteration over tensors", is comparable to using nested for loops in C , Fortran, and it outperforms numpy, C-style tuple iteration, C-style integer reindexing, and boost::multi_array , and unlike some of those methods, it can be used when the dimension of the tensor is unknown at compile time .
Edit intent: clarity
Original:  The proposed method, "template-recursive iteration over tensors", is comparable to using  nested for loops in C and to vectorized code in Fortran, and it outperforms numpy, C-style tuple iteration, C-style integer reindexing, and boost::multi_array , and unlike some of those methods, it can be used when the dimension of the tensor is unknown at compile time  .
Revised:  The proposed method, "template-recursive iteration over tensors", is comparable to using nested for loops in C and to vectorized code in Fortran, and Go cannot be applied when the dimension of a tensor is unknown at compile time. Likewise, boost::multi_array , and unlike some of those methods, it can be used when the dimension of the tensor is unknown at compile time .
Edit intent: clarity
Original: This paper discusses about R package imputeTestbench , which provides a testbench to do comparison of methods used for missing data imputation.
Revised: This paper describes the R package imputeTestbench , which provides a testbench to do comparison of methods used for missing data imputation.
Edit intent: clarity
Original: This paper discusses about R package imputeTestbench , which provides a testbench to do comparison of methods used for missing data imputation.
Revised: This paper discusses about R package imputeTestbench that provides a testbench to do comparison of methods used for missing data imputation.
Edit intent: coherence
Original: This paper discusses about R package imputeTestbench , which provides a testbench to do comparison of methods used for missing data imputation.
Revised: This paper discusses about R package imputeTestbench , which provides a testbench for comparing imputation methods for missing data imputation.
Edit intent: clarity
Original:  The simplicity of the package usage and significant reduction in efforts and time consumption in state of art procedure, adds valuable advantage to it .
Revised:  The simplicity of use and significant reduction in efforts and time consumption in state of art procedure, adds valuable advantage to it .
Edit intent: clarity
Original:  This paper explains the use of all functions in imputeTestbench package with the demonstration of examples.
Revised:  This paper provides an overview of the core functions, including a demonstration with examples.
Edit intent: clarity
Original:  An adversarial perturbation modifies an input to change the prediction of a classifier without causing the input to appear substantially different to the human perceptual system.
Revised:  An adversarial perturbation modifies an input to change a classifier's prediction without causing the input to appear substantially different to the human perceptual system.
Edit intent: clarity
Original:  An adversarial perturbation modifies an input to change the prediction of a classifier without causing the input to appear substantially different to the human perceptual system.
Revised:  An adversarial perturbation modifies an input to change the prediction of a classifier without causing the input to seem substantially different to the human perceptual system.
Edit intent: fluency
Original: Stochastic Boolean networks  or more generally, stochastic discrete networks, are an important class of computational models for molecular interaction networks.
Revised: Stochastic Boolean networks , or more generally, stochastic discrete networks, are an important class of computational models for molecular interaction networks.
Edit intent: fluency
Original:  The standard updating schedules include the synchronous update, where all the nodes are updated at the same time, and the asynchronous update where a random node is updated at each time step.
Revised:  Standard updating schedules include the synchronous update, where all the nodes are updated at the same time, and the asynchronous update where a random node is updated at each time step.
Edit intent: clarity
Original:  The former gives a deterministic dynamics while the latter a stochastic dynamics.
Revised:  The former produces a deterministic dynamics while the latter a stochastic dynamics.
Edit intent: clarity
Original:  In this scheme, the 64 possible triplet codons are each indexed by a 6-bit label.
Revised:  In this scheme, the 64 triplet codons are each indexed by a 6-bit label.
Edit intent: clarity
Original:  The order of the bits reflects the hierarchical organization manifested by the DNA replication/repair and tRNA translation systems.
Revised:  The ordering of the bits reflects the hierarchical organization manifested by the DNA replication/repair and tRNA translation systems.
Edit intent: fluency
Original:  Transition and transversion mutations are naturally expressed as basic binary operations, and the severity of the different types is analyzed.
Revised:  In this system, transition and transversion mutations are naturally expressed as basic binary operations, and the severity of the different types is analyzed.
Edit intent: clarity
Original:  Transition and transversion mutations are naturally expressed as basic binary operations, and the severity of the different types is analyzed.
Revised:  Transition and transversion mutations are naturally expressed as binary operations, and the severity of the different types is analyzed.
Edit intent: clarity
Original:  Transition and transversion mutations are naturally expressed as basic binary operations, and the severity of the different types is analyzed.
Revised:  Transition and transversion mutations are naturally expressed as basic binary operations, and the severities of the different types is analyzed.
Edit intent: fluency