wanyu/IteraTeR_v2 huggingface dataset:
Original:  We expect  this improvement in detection to help efforts to realize the full potential of gene expression profiling, especially in analyses of cellular processes involving complex modulations of gene expression.
Revised:  We expect that this improvement in detection to help efforts to realize the full potential of gene expression profiling, especially in analyses of cellular processes involving complex modulations of gene expression.
Edit intent: fluency
Original:  We expect  this improvement in detection to help efforts to realize the full potential of gene expression profiling, especially in analyses of cellular processes involving complex modulations of gene expression.
Revised:  We expect this improvement in detection will help efforts to realize the full potential of gene expression profiling, especially in analyses of cellular processes involving complex modulations of gene expression.
Edit intent: fluency
Original: The problem of finding low rank m \times m matrices\ge  in a real affine subspace of dimension n has many applications in information and systems theory, where low rank is synonymous of structure and parcimony .
Revised: The problem of finding low rank m \times m matrices\ge in a real affine subspace of dimension n has many applications in information and systems theory, where low rank is synonymous of structure and parsimony .
Edit intent: fluency
Original:  We design a symbolic computation algorithm to solve this problem efficiently , exactly and rigorously : the input are the rational coefficients of the matrices spanning the affine subspace as well as the expected maximum rank, and the output is a rational parametrization encoding a finite set of points that intersects each connected component of the low rank real algebraic set.
Revised:  We design computer algebra algorithms to solve this problem efficiently , exactly and rigorously : the input are the rational coefficients of the matrices spanning the affine subspace as well as the expected maximum rank, and the output is a rational parametrization encoding a finite set of points that intersects each connected component of the low rank real algebraic set.
Edit intent: clarity
Original:  We design a symbolic computation algorithm to solve this problem efficiently , exactly and rigorously : the input are the rational coefficients of the matrices spanning the affine subspace as well as the expected maximum rank, and the output is a rational parametrization encoding a finite set of points that intersects each connected component of the low rank real algebraic set.
Revised:  We design a symbolic computation algorithm to solve this problem efficiently and exactly : the input are the rational coefficients of the matrices spanning the affine subspace as well as the expected maximum rank, and the output is a rational parametrization encoding a finite set of points that intersects each connected component of the low rank real algebraic set.
Edit intent: clarity
Original:  It is essentially polynomial in binomial( n+m( m--r) ,n) where r is the expected maximum rank ;
Revised:  It is essentially polynomial in n+m( m--r) ,n) where r is the expected maximum rank ;
Edit intent: clarity
Original: The problem of finding m \times s matrices (with m %DIFDELCMD < \ge %%% s) of rank r in a real affine subspace of dimension n has many applications in information and systems theory, where low rank is synonymous of structure and parsimony.
Revised: We consider m \times s matrices (with m %DIFDELCMD < \ge %%% s) of rank r in a real affine subspace of dimension n has many applications in information and systems theory, where low rank is synonymous of structure and parsimony.
Edit intent: clarity
Original: The problem of finding m \times s matrices (with m %DIFDELCMD < \ge %%% s) of rank r in a real affine subspace of dimension n has many applications in information and systems theory, where low rank is synonymous of structure and parsimony.
Revised: The problem of finding m \times s matrices (with m %DIFDELCMD < \ge %%% \geq s) in a real affine subspace of dimension n has many applications in information and systems theory, where low rank is synonymous of structure and parsimony.
Edit intent: clarity
Original:  it  improves on the state-of-the-art in the field .
Revised:  it . It improves on the state-of-the-art in the field .
Edit intent: coherence
Original:  The growing enormity of available data on the networks becomes a computational challenge for the conventional alignment algorithms.
Revised:  However, the growing enormity of available data on the networks becomes a computational challenge for the conventional alignment algorithms.
Edit intent: coherence
Original:  Quantum algorithms generally provide  efficiency over their classical counterparts in solving various problems.
Revised:  Quantum algorithms generally provide greater efficiency over their classical counterparts in solving various problems.
Edit intent: clarity
Original:  In the present paper, we obtain closed-form solutions for the inter-layer degree distribution of heterogeneously growing multilayer networks with arbitrary number of layers in the steady state.
Revised:  In the present paper, we obtain closed-form solutions for the inter-layer degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state.
Edit intent: clarity
Original:  Here, we take a system wide view and investigate the timing of school attacks and the dynamical feedback with social media.
Revised:  Here, we take a system-wide view and investigate the timing of school attacks and the dynamical feedback with social media.
Edit intent: fluency
Original: In ~\mbox{ Tal94 , Talagrand showed a generalization of the celebrated KKL theorem.
Revised: In 1994 , Talagrand showed a generalization of the celebrated KKL theorem.
Edit intent: fluency
Original: We give asymptotically tight estimate of tangent space variation on a Riemannian submanifold of Euclidean space with respect to the local feature size of the submanifold .
Revised: We give asymptotically tight estimates of tangent space variation on a Riemannian submanifold of Euclidean space with respect to the local feature size of the submanifold .
Edit intent: fluency
Original: We give asymptotically tight estimate of tangent space variation on a Riemannian submanifold of Euclidean space with respect to the local feature size of the submanifold .
Revised: We give asymptotically tight estimate of tangent space variation on Riemannian submanifolds of Euclidean space with respect to the local feature size of the submanifold .
Edit intent: fluency
Original: We give asymptotically tight estimate of tangent space variation on a Riemannian submanifold of Euclidean space with respect to the local feature size of the submanifold .
Revised: We give asymptotically tight estimate of tangent space variation on a Riemannian submanifold of Euclidean space with respect to the local feature size of the submanifolds .
Edit intent: fluency
Original:  We show that the result is a consequence of structural properties of local feature size function of the Riemannian submanifold   .
Revised:  We show that the result is a consequence of structural properties of local feature size of the Riemannian submanifold .
Edit intent: clarity
Original:  The algorithm provides the best polynomial time approximation of TSP on simple cubic graphs known at present.
Edit intent: coherence
Original:  Inspired by the recent Neural Turing Machines 8%DIFDELCMD < ]%%% , we store the intermediate representations in stacked layers of memories, and use read-write operations on the memories to realize the nonlinear transformations of those representations.
Revised:  Inspired by the 8%DIFDELCMD < ]%%% , we store the intermediate representations in stacked layers of memories, and use read-write operations on the memories to realize the nonlinear transformations of those representations.
Edit intent: coherence
Original:  Inspired by the recent Neural Turing Machines 8%DIFDELCMD < ]%%% , we store the intermediate representations in stacked layers of memories, and use read-write operations on the memories to realize the nonlinear transformations of those representations.
Revised:  Inspired by the recent Neural Turing Machines %DIFDELCMD < ]%%% , we store the intermediate representations in stacked layers of memories, and use read-write operations on the memories to realize the nonlinear transformations of those representations.
Edit intent: fluency
Original:  Through layer-by-layer transformations, NTram can model complicated relations  necessary for applications such as machine translation between distant languages.
Revised:  Through layer-by-layer transformations, NTram can model complicated relations between sequences necessary for applications such as machine translation between distant languages.
Edit intent: clarity
Original:  The architecture can be trained with normal back-propagation on parallel texts , and the learning can be easily scaled up to a large corpus.
Revised:  The architecture can be trained with normal back-propagation on sequence-to-sequence data , and the learning can be easily scaled up to a large corpus.
Edit intent: clarity
Original:  Remarkably, NTram , being purely neural network-based, can achieve performance comparable to the traditional phrase-based machine translation system (Moses ) with a small vocabulary and a modest parameter size.
Revised:  Remarkably, NTram , being purely neural network-based, can achieve performance comparable to the traditional phrase-based machine translation system Moses with a small vocabulary and a modest parameter size.
Edit intent: clarity
Original:  The architecture can be trained with normal back-propagation on sequence-to-sequence data, and the learning can be easily scaled up to a large corpus.
Revised:  The architecture can be trained with normal back-propagation on sequenceto-sequence data, and the learning can be easily scaled up to a large corpus.
Edit intent: fluency
Original:  DEEPMEMORY is broad enough to subsume the state-of-the-art neural translation model in (Bahdanau et al., 2015) as its special case, while significantly improves upon the model with its deeper architecture.
Revised:  DEEPMEMORY is broad enough to subsume the state-of-the-art neural translation model in (Bahdanau et al., 2015) as its special case, while significantly improving upon the model with its deeper architecture.
Edit intent: fluency
Original:  *BEAST, a fully Bayesian implementation of the multispecies coalescent, is popular but computationally intensive, so the advent of large phylogenomic data sets is both a computational challenge and an opportunity for better systematics.
Revised:  *BEAST, a fully Bayesian implementation of the multispecies coalescent, is popular but computationally intensive, so the increasing size of phylogenetic data sets is both a computational challenge and an opportunity for better systematics.
Edit intent: clarity
Original:  Using simulation studies, we characterise the scaling behaviour of *BEAST, and enable quantitative prediction of the impact increasing the number of loci has on both computational performance and statistical accuracy.
Revised:  Using simulation studies, we characterize the scaling behaviour of *BEAST, and enable quantitative prediction of the impact increasing the number of loci has on both computational performance and statistical accuracy.
Edit intent: fluency
Original:  Our results provide insight into the practicalities of Bayesian species tree estimation, the number of genes required to obtain a given level of accuracy and the situations in which supermatrix or summary methods will be outperformed by the fully Bayesian multispecies coalescent.
Revised:  Our results provide insight into the practicalities of Bayesian species tree estimation, the number of loci required to obtain a given level of accuracy and the situations in which supermatrix or summary methods will be outperformed by the fully Bayesian multispecies coalescent.
Edit intent: clarity
Original: Under the multispecies coalescent model of molecular evolution gene trees evolve within a species tree, and follow predicted distributions of topologies and coalescent times .
Revised: Under the multispecies coalescent model of molecular evolution , gene trees have independent evolutionary histories within a shared species tree .
Edit intent: clarity
Original:  In comparison, supermatrix concatenation methods assume that gene trees share a common history and equate gene coalescence with species divergence.
Revised:  In comparison, supermatrix concatenation methods assume that gene trees share a single common genealogical history, thereby equating gene coalescence with species divergence.
Edit intent: clarity
Original:  A systematic framework for studying the space of local learning rules must first define the nature of the local variables, and then the functional form that ties them together into each learning rule.
Revised:  A systematic framework for studying the space of local learning rules is obtained by first specifying the nature of the local variables, and then the functional form that ties them together into each learning rule.
Edit intent: clarity
Original:  As a byproduct, this framework enables also the  discovery of new learning rules as well as important relationships between learning rules and group symmetries.
Revised:  As a byproduct, this framework enables also the discovery of new learning rules and exploration of relationships between learning rules and group symmetries.
Edit intent: clarity
Original:  Learning complex input-output functions requires local deep learning where target information is propagated to the deep layers through a backward  channel.
Revised:  Learning complex input-output functions requires local deep learning where target information is communicated to the deep layers through a backward channel.
Edit intent: clarity
Original:  Learning complex input-output functions requires local deep learning where target information is propagated to the deep layers through a backward  channel.
Revised:  Learning complex input-output functions requires local deep learning where target information is propagated to the deep layers through a backward learning channel.
Edit intent: clarity
Original:  The nature of the propagated information about the targets , and the backward channel through which this information is propagated, partition the space of learning algorithms.
Revised:  The nature of the communicated information about the targets , and the backward channel through which this information is propagated, partition the space of learning algorithms.
Edit intent: clarity
Original:  The nature of the propagated information about the targets , and the backward channel through which this information is propagated, partition the space of learning algorithms.
Revised:  The nature of the propagated information about the targets and the structure of the learning channel partition the space of learning algorithms.
Edit intent: clarity
Original:  For any learning algorithm, the capacity of the backward channel can be defined as the number of bits provided about the gradient per weight, divided by the number of required operations per weight.
Edit intent: coherence
Original:  We estimate the  capacity associated with several learning algorithms and show that backpropagation outperforms them and achieves the maximum possible capacity .
Revised:  We estimate the capacity associated with several algorithms and show that backpropagation outperforms them and achieves the maximum possible capacity .
Edit intent: clarity
Original:  In 1975, Babai characterized which of these abstract groups can be realized as  automorphism groups of planar graphs.
Revised:  In 1975, Babai characterized which of these abstract groups can be realized as the automorphism groups of planar graphs.
Edit intent: fluency
Original:  Second, the automorphism group of a connected planar graph is obtained as semidirect product of a direct product of these stabilizers with a spherical group.
Revised:  The automorphism group of a connected planar graph is obtained as semidirect product of a direct product of these stabilizers with a spherical group.
Edit intent: coherence
Original:  Our approach connects automorphism groups with geometry of planar graphs and it is based on a reduction to 3-connected components , described by Fiala et al.
Revised:  Our approach is based on a reduction to 3-connected components , described by Fiala et al.
Edit intent: coherence
Original:  Our approach connects automorphism groups with geometry of planar graphs and it is based on a reduction to 3-connected components , described by Fiala et al.
Revised:  Our approach connects automorphism groups with geometry of planar graphs and it is based on the decomposition to 3-connected components , described by Fiala et al.
Edit intent: clarity
Original:  Our approach connects automorphism groups with geometry of planar graphs and it is based on a reduction to 3-connected components , described by Fiala et al.
Revised:  Our approach connects automorphism groups with geometry of planar graphs and it is based on a reduction to 3-connected components 
Edit intent: coherence
Original: By Frucht's Theorem, every abstract finite group is isomorphic to the automorphism group of some graph.
Edit intent: coherence
Original:  In 1975, Babai characterized which of these abstract groups can be realized as the automorphism groups of planar graphs.
Revised:  In 1975, Babai characterized which abstract groups can be realized as the automorphism groups of planar graphs.
Edit intent: clarity
Original:  The automorphism group of a connected planar graph is obtained as semidirect product of a direct product of these stabilizers with a spherical group.
Revised:  The automorphism group of a connected planar graph is then obtained as a semidirect product of a direct product of these stabilizers with a spherical group.
Edit intent: coherence
Original: In 1975, Babai characterized which abstract groups can be realized as the automorphism groups of planar graphs.
Revised: We investigate automorphism groups of planar graphs.
Edit intent: clarity
Original: A new aperiodic tile set containing 11 Wang tiles on 4 colors is presented.
Revised: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors is presented.
Edit intent: coherence
Original: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and  show that this tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic.
Revised: We present a new aperiodic tileset containing 11 Wang tiles on 4 colors, and show that this tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic.
Edit intent: fluency
Original: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and  show that this tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic.
Revised: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and we show that this tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic.
Edit intent: fluency
Original: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and  show that this tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic.
Revised: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and show that this tileset is minimal, in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic.
Edit intent: fluency
Original: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and  show that this tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic.
Revised: We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and show that this tile set is minimal in the sense that no Wang set with less than 11 tiles or fewer than 4 colors is aperiodic.
Edit intent: clarity
Original:  This gives a final answer to a problem raised by a question asked by Wang in 1961.
Revised:  This gives a definitive answer to the problem raised by Wang in 1961.
Edit intent: clarity
Original:  We study  probabilistic aspects by considering the synchronization of Bernoulli sequences of letters, under the light of Bernoulli  measures recently introduced for trace monoids.
Revised:  We study the probabilistic aspects by considering the synchronization of Bernoulli sequences of letters, under the light of Bernoulli measures recently introduced for trace monoids.
Edit intent: fluency
Original:  However, even if single cells do not chemotaxsignificantly , small clusters may still follow a gradient ;
Revised:  However, experiments have shown that even under conditions when single cells cannot chemotax , small clusters may still follow a gradient ;
Edit intent: clarity
Original:  We show collective chemotaxis can exist without single-cell chemotaxis if contact inhibition of locomotion (CIL), where cells polarize away from cell-cell contact, is regulated by the chemoattractant.
Revised:  Our approach posits that the contact inhibition of locomotion (CIL), where cells polarize away from cell-cell contact, is regulated by the chemoattractant.
Edit intent: clarity
Original:  Pairs of cells will have velocities that are strongly dependent on the cell pair's orientation : this provides a simple test for the presence of collective guidance in neural crest cells and other systems.
Revised:  The presence of strong orientation effects provides a simple test for the presence of collective guidance in neural crest cells and other systems.
Edit intent: clarity
Original:  Pairs of cells will have velocities that are strongly dependent on the cell pair's orientation : this provides a simple test for the presence of collective guidance in neural crest cells and other systems.
Revised:  Pairs of cells will have velocities that are strongly dependent on the cell pair's orientation : this provides a simple test for our theory of collective guidance in neural crest cells and other systems.
Edit intent: clarity
Original: Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours wake-sleep cycle.
Revised: Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours sleep-wake cycle.
Edit intent: fluency
Original:  However, activity fluctuations also appear over a wide range of temporal scales, from days to  few seconds, resulting from the concatenation of  myriad of individual smaller motor events.
Revised:  However, activity fluctuations also appear over a wide range of temporal scales, from days to a few seconds, resulting from the concatenation of myriad of individual smaller motor events.
Edit intent: fluency
Original:  However, activity fluctuations also appear over a wide range of temporal scales, from days to  few seconds, resulting from the concatenation of  myriad of individual smaller motor events.
Revised:  However, activity fluctuations also appear over a wide range of temporal scales, from days to few seconds, resulting from the concatenation of a myriad of individual smaller motor events.
Edit intent: fluency
Original:  Are activity fluctuations across temporal scales intrinsically different, or is there an universal description encompassing them?
Revised:  Are activity fluctuations across temporal scales intrinsically different, or is there a universal description encompassing them?
Edit intent: fluency