wanyu/IteraTeR_v2 huggingface dataset:
Original: We consider the problem of augmenting an n-vertex tree with one %DIFDELCMD < {\em %DIFDELCMD < %%% shortcut in order to minimize the diameter of the resulting graph.
Revised: We consider the problem of augmenting an n-vertex tree with one %DIFDELCMD < {\em %DIFDELCMD < %%% shortcut in order to minimize the diameter of the resulting graph.
Edit intent: fluency
Original:  The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of vertices u and v, reports the %DIFDELCMD < {\em %%% weight of the shortcut (u,v) in constant time.
Revised:  The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of vertices u and v, reports the %DIFDELCMD < {\em %%% weight of the shortcut (u,v) in constant time.
Edit intent: fluency
Original:  Previously, the problem was solved in O(n^2 \log^3 n) time (see~\mbox{ DBLP:conf/isaac/0001A16a ] { {\tt   and in O(n \log n) time for paths embedded in a metric space (see~\mbox{ DBLP:conf/wads/wang .
Revised:  Previously, the problem was solved in O(n^2 \log^3 n) time (see~\mbox{ DBLP:conf/isaac/0001A16a ] Gro{ {\tt and in O(n \log n) time for paths embedded in a metric space (see~\mbox{ DBLP:conf/wads/wang .
Edit intent: fluency
Original:  Previously, the problem was solved in O(n^2 \log^3 n) time (see~\mbox{ DBLP:conf/isaac/0001A16a ] { {\tt   and in O(n \log n) time for paths embedded in a metric space (see~\mbox{ DBLP:conf/wads/wang .
Revised:  Previously, the problem was solved in O(n^2 \log^3 n) time (see~\mbox{ DBLP:conf/isaac/0001A16a ] {\ss {\tt and in O(n \log n) time for paths embedded in a metric space (see~\mbox{ DBLP:conf/wads/wang .
Edit intent: clarity
Original:  Previously, the problem was solved in O(n^2 \log^3 n) time (see~\mbox{ DBLP:conf/isaac/0001A16a ] { {\tt   and in O(n \log n) time for paths embedded in a metric space (see~\mbox{ DBLP:conf/wads/wang .
Revised:  Previously, the problem was solved in O(n^2 \log^3 n) time (see~\mbox{ DBLP:conf/isaac/0001A16a ] { {\tt , and in O(n \log n) time for paths embedded in a metric space (see~\mbox{ DBLP:conf/wads/wang .
Edit intent: fluency
Original:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} }  } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Revised:  Furthermore, a (1+ \varepsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} } } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Edit intent: clarity
Original:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} }  } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Revised:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \varepsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} } } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Edit intent: fluency
Original:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} }  } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Revised:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d }\hspace{0pt} } } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Edit intent: coherence
Original:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} }  } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Revised:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} } Gro } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Edit intent: fluency
Original:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} }  } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Revised:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} } \ss} . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Edit intent: fluency
Original:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} }  } . The contribution of this paper is twofold: we solve the problem for trees (not only paths) and we also improve upon all known results.
Revised:  Furthermore, a (1+ \epsilon )-approximation algorithm running in O(n+1/ \epsilon ^{3}) has been designed for paths embedded in \mathbb{R}^d, for constant values of d , in~\mbox{ \cite{DBLP:conf/icalp/GrosseGKSS15}\hspace{0pt} } } . The contribution of this paper is twofold: we address the problem for trees (not only paths) and we also improve upon all known results.
Edit intent: clarity
Original:  More precisely, we design an {\em optimal } O(n^2) time algorithm .
Revised:  More precisely, we design a {\em optimal } O(n^2) time algorithm .
Edit intent: fluency
Original:  More precisely, we design an {\em optimal } O(n^2) time algorithm .
Revised:  More precisely, we design an {\em time-optimal } O(n^2) time algorithm .
Edit intent: clarity
Original:  Furthermore , for trees embedded in a metric space, we design (i) an exact O(n \log n) time algorithm and (ii) a (1+ \epsilon )-approximation algorithm that runs in O %DIFDELCMD < \left(%%% \big( n+ \frac{1{\epsilon}\log \frac{1}{\epsilon}}%DIFDELCMD < \right) %%% \log \varepsilon^{-1}}\big) time.
Revised:  Furthermore , for trees embedded in a metric space, we design (i) an exact O(n \log n) time algorithm and (ii) a (1+ \varepsilon )-approximation algorithm that runs in O %DIFDELCMD < \left(%%% \big( n+ \frac{1{\epsilon}\log \frac{1}{\epsilon}}%DIFDELCMD < \right) %%% \log \varepsilon^{-1}}\big) time.
Edit intent: fluency
Original:  Furthermore , for trees embedded in a metric space, we design (i) an exact O(n \log n) time algorithm and (ii) a (1+ \epsilon )-approximation algorithm that runs in O %DIFDELCMD < \left(%%% \big( n+ \frac{1{\epsilon}\log \frac{1}{\epsilon}}%DIFDELCMD < \right) %%% \log \varepsilon^{-1}}\big) time.
Revised:  Furthermore , for trees embedded in a metric space, we design (i) an exact O(n \log n) time algorithm and (ii) a (1+ \epsilon )-approximation algorithm that runs in O %DIFDELCMD < \left(%%% \big( n+ {\epsilon}\log \frac{1}{\epsilon}}%DIFDELCMD < \right) %%% \log \varepsilon^{-1}}\big) time.
Edit intent: fluency
Original:  Furthermore , for trees embedded in a metric space, we design (i) an exact O(n \log n) time algorithm and (ii) a (1+ \epsilon )-approximation algorithm that runs in O %DIFDELCMD < \left(%%% \big( n+ \frac{1{\epsilon}\log \frac{1}{\epsilon}}%DIFDELCMD < \right) %%% \log \varepsilon^{-1}}\big) time.
Revised:  Furthermore , for trees embedded in a metric space, we design (i) an exact O(n \log n) time algorithm and (ii) a (1+ \epsilon )-approximation algorithm that runs in O %DIFDELCMD < \left(%%% \big( n+ \frac{1{\epsilon}\log \frac{1}{\epsilon}}%DIFDELCMD < \right) %%% \varepsilon^{-1\log \varepsilon^{-1}}\big) time.
Edit intent: fluency
Original: We study the impact of the aggregation of nodes on the results for community detection over networks.
Edit intent: coherence
Original:  Many times the nodes  , whether deliberately or not, are aggregated for instance due to technical, ethical, legal limitations or privacy concerns, in which case the change of community structure may be seen as an unwanted distortion.
Revised:  Many times the nodes , whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy concerns, in which case the change of community structure may be seen as an unwanted distortion.
Edit intent: coherence
Original:  A common example is  geographic position: one may uncover communities in a network of places, or individuals identified to their typical geographical position, and then aggregate these places to larger entities, such as municipalities, thus obtaining another network with another, similar or dissimilar, community structure .
Revised:  A common example is the geographic position: one may uncover communities in a network of places, or individuals identified to their typical geographical position, and then aggregate these places to larger entities, such as municipalities, thus obtaining another network with another, similar or dissimilar, community structure .
Edit intent: fluency
Original:  A common example is  geographic position: one may uncover communities in a network of places, or individuals identified to their typical geographical position, and then aggregate these places to larger entities, such as municipalities, thus obtaining another network with another, similar or dissimilar, community structure .
Revised:  A common example is geographic position: one may uncover communities in a network of places, or of individuals identified with their typical geographical position, and then aggregate these places to larger entities, such as municipalities, thus obtaining another network with another, similar or dissimilar, community structure .
Edit intent: clarity
Original:  A common example is  geographic position: one may uncover communities in a network of places, or individuals identified to their typical geographical position, and then aggregate these places to larger entities, such as municipalities, thus obtaining another network with another, similar or dissimilar, community structure .
Revised:  A common example is geographic position: one may uncover communities in a network of places, or individuals identified to their typical geographical position, and then aggregate these places into larger entities, such as municipalities, thus obtaining another network with another, similar or dissimilar, community structure .
Edit intent: fluency
Original:  A common example is  geographic position: one may uncover communities in a network of places, or individuals identified to their typical geographical position, and then aggregate these places to larger entities, such as municipalities, thus obtaining another network with another, similar or dissimilar, community structure .
Revised:  A common example is geographic position: one may uncover communities in a network of places, or individuals identified to their typical geographical position, and then aggregate these places to larger entities, such as municipalities, thus obtaining another network .
Edit intent: clarity
Original:  The communities in the two networks may be similar or different .
Revised:  The communities found in the networks obtained at various levels of aggregation may exhibit various degrees of similarity, from full alignment to perfect independence .
Edit intent: clarity
Original:  This is akin to the problem of ecological fallacy in statistics, or to the Modified Area Unit Problem in geography.
Revised:  This is akin to the problem of ecological fallacy in statistics, or to the Modified Areal Unit Problem in geography.
Edit intent: fluency
Original:  We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure and illustrating its relevance on real-world examples (mobile phone and Twitter reply networks).
Revised:  We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure . We illustrate its relevance on real-world examples (mobile phone and Twitter reply networks).
Edit intent: coherence
Original:  We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure and illustrating its relevance on real-world examples (mobile phone and Twitter reply networks).
Revised:  We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure and illustrating its relevance on real-world examples (mobile phone and Twitter reply-to networks).
Edit intent: clarity
Original:  Our main message is that results computed on aggregated data may be interpreted with caution, as they may be strongly influenced by the level of the aggregation.
Revised:  Our main message is that any node-partitioning analysis performed on aggregated networks should be interpreted with caution, as they may be strongly influenced by the level of the aggregation.
Edit intent: clarity
Original:  Our main message is that results computed on aggregated data may be interpreted with caution, as they may be strongly influenced by the level of the aggregation.
Revised:  Our main message is that results computed on aggregated data may be interpreted with caution, as the outcome may be strongly influenced by the level of the aggregation.
Edit intent: clarity
Original: Multi-site studies are becoming important to increase statistical power, enhance generalizability, and to improve the likelihood of pooling relevant subgroups together activities which are otherwise limited by the availability of patients or funds at a single site .
Revised: Multi-site studies are becoming important to increase statistical power, enhance generalizability, and to improve the likelihood of pooling relevant subgroups together activities .
Edit intent: clarity
Original:  The aim of this study was to assess multi-site reproducibility in resting-state functional connectivity fingerprints, and to improve identifiability of obtained functional connectomes.
Revised:  The aim of this study was to assess multi-site reproducibility in resting-state functional connectivity fingerprints, and to improve identifiability of functional connectomes.
Edit intent: clarity
Original:  The individual fingerprinting of functional connectivity profiles is promising due to its potential as a robust neuroimaging biomarker with which to draw single-subject inferences .
Revised:  The individual fingerprinting of functional connectivity profiles is promising due to its potential as a robust neuroimaging biomarker .
Edit intent: clarity
Original:  Those principal components that maximized differential identifiability of a training dataset were used as an orthogonal connectivity basis to reconstruct the individual functional connectomes of training and validation sets.
Revised:  Those components that maximized differential identifiability of a training dataset were used as an orthogonal connectivity basis to reconstruct the individual functional connectomes of training and validation sets.
Edit intent: clarity
Original:  Those principal components that maximized differential identifiability of a training dataset were used as an orthogonal connectivity basis to reconstruct the individual functional connectomes of training and validation sets.
Revised:  Those principal components that maximized differential identifiability of a training dataset were used as an orthogonal connectivity basis to reconstruct the functional connectomes of training and validation sets.
Edit intent: clarity
Original:  The optimally reconstructed functional connectomes showed a substantial improvement in individual fingerprinting of the subjects within and across the two sites and test-retest visit pairs relative to the original data.
Revised:  The optimally reconstructed functional connectomes showed a substantial improvement in individual fingerprinting within and across the two sites and test-retest visit pairs relative to the original data.
Edit intent: clarity
Original:  The optimally reconstructed functional connectomes showed a substantial improvement in individual fingerprinting of the subjects within and across the two sites and test-retest visit pairs relative to the original data.
Revised:  The optimally reconstructed functional connectomes showed a substantial improvement in individual fingerprinting of the subjects within and across the two sites relative to the original data.
Edit intent: clarity
Original:  A notable increase in ICC values for functional edges and resting-state networks were also observedfor reconstructed functional connectomes .
Revised:  A notable increase in ICC values for functional edges and resting-state networks was also observed .
Edit intent: clarity
Original:  Improvements in identifiability were not found to be affected by the presence or absence of global signal regression.
Revised:  Improvements in identifiability were not found to be affected by global signal regression.
Edit intent: clarity
Original:  Result demonstrate that the data-driven method presented in this study can improve identifiability in resting-state functional connectomes in multi-site studies.
Revised:  Result demonstrate that the framework presented in this study can improve identifiability in resting-state functional connectomes in multi-site studies.
Edit intent: clarity
Original:  Result demonstrate that the data-driven method presented in this study can improve identifiability in resting-state functional connectomes in multi-site studies.
Revised:  Result demonstrate that the data-driven method presented in this study systematically improves identifiability in resting-state functional connectomes in multi-site studies.
Edit intent: clarity
Original: In this paper we suggest a new system-theoretic model order reduction method for quadratic-bilinear dynamical systems.
Revised: In this paper we suggest a moment matching method for quadratic-bilinear dynamical systems.
Edit intent: clarity
Original:  The obvious advantage is that moment matching then corresponds to one-dimensional , instead of mul- tidimensional interpolation as for the multivariate ones.
Revised:  The obvious advantage is that moment matching then corresponds to one-dimensional interpolation problem, not to multi-dimensional interpolation as for the multivariate ones.
Edit intent: clarity
Original:  However, they inherit a convenient tensor structure and can thus efficiently be tackled with low-rank tensor solvers as we will discuss .
Revised:  However, they inherit a convenient tensor structure and can thus efficiently be tackled with low-rank tensor structure, which enhances its efficiency .
Edit intent: coherence
Original:  In addition, our approach allows  the incorporation of more general input relations in the state equations - not only affine-linear ones as in former methods - in an elegant way  .
Revised:  In addition, our approach allows for the incorporation of more general input relations in the state equations - not only affine-linear ones as in former methods - in an elegant way .
Edit intent: fluency
Original:  In addition, our approach allows  the incorporation of more general input relations in the state equations - not only affine-linear ones as in former methods - in an elegant way  .
Revised:  In addition, our approach allows the incorporation of more general input relations in the state equations -- not only affine-linear ones as in former methods - in an elegant way .
Edit intent: fluency
Original:  In addition, our approach allows for the incorporation of more general input relations in the state equations -- not only affine-linear ones as in existing system-theoretic methods -- in an elegant way.
Revised:  In addition, our approach allows for the incorporation of more general input relations in the state equations - not only affine-linear ones as in existing system-theoretic methods -- in an elegant way.
Edit intent: fluency
Original:  In addition, our approach allows for the incorporation of more general input relations in the state equations -- not only affine-linear ones as in existing system-theoretic methods -- in an elegant way.
Revised:  In addition, our approach allows for the incorporation of more general input relations in the state equations -- not only affine-linear ones as in existing system-theoretic methods - in an elegant way.
Edit intent: fluency
Original:  In the part , we prove that the factorization of a rational word has a special form and that it can be computed in polynomial time from a rational expression describing the word.
Revised:  In the annex , we prove that the factorization of a rational word has a special form and that it can be computed in polynomial time from a rational expression describing the word.
Edit intent: coherence
Original:  In the part , we prove that the factorization of a rational word has a special form and that it can be computed in polynomial time from a rational expression describing the word.
Revised:  In the part , we prove that the factorization of a rational word has a special form and that it can be computed from a rational expression describing the word.
Edit intent: clarity
Original:  This is in contrast with the case k = 1, where the spectrum contains a half-line , but the initial part is not dense .
Revised:  This is in contrast with the case k = 1, where the spectrum contains a half-line .
Edit intent: coherence
Original:  In the context of classification in the PAC learning model, Kasiviswanathan et al. (2008) constructed an artificial class of functions that is PAC learnable with respect to a fixed distribution but cannot be learned by an efficient non-interactive (or one-round)SQ algorithm.
Revised:  In the context of classification in the PAC learning model, Kasiviswanathan et al. (2008) constructed an artificial class of functions with respect to a fixed distribution but cannot be learned by an efficient non-interactive (or one-round)SQ algorithm.
Edit intent: clarity
Original:  We complement this lower bound with a new efficient and label-non-adaptive SQ learning algorithm whose complexity is polynomial in the margin complexity .
Revised:  We complement this lower bound with a new efficient learning algorithm whose complexity is polynomial in the margin complexity .
Edit intent: coherence