wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We list here the frequent complete subgraphs of the female and the male braingraphs of 414 subjects, each with 463 nodes, with a frequency threshold of 80\\%, and identify complete subgraphs, which are more frequent in male and female connectomes, respectively.abstract 
Revised:  We list here the frequent complete subgraphs of the female and the male braingraphs of 414 subjects, each with 463 nodes, with a frequency threshold of 80\\%, and identify complete subgraphs, which are more frequent in male and female connectomes, respectively.abstract \% of the graphs, then, most probably, it could not be an artifact of the measurement or the data processing workflow. We list here the frequent complete subgraphs of the human braingraphs of 414 subjects, each with 463 nodes, with a frequency threshold of 80\%, and identify 812 complete subgraphs, which are more frequent in male and 224 complete subgraphs, which are more frequent in female connectomes.
Edit intent: meaning-changed
Original: We derive a closed form solution for an optimal control of interbank lending subject to terminal probability constraints on the failure of  a bank. The solution can be applied to a network of banks providing a general solution when  aforementioned probability constraints are assumed for all the banks in the system .
Revised: We derive a closed form solution for an optimal control of interbank lending subject to terminal probability constraints on the failure of a general solution when aforementioned probability constraints are assumed for all the banks in the system .
Edit intent: clarity
Original: The k-means for lines is a set of k centers (points)  that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Revised: The input to the k-median for lines problem is a set of k centers (points) that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Edit intent: meaning-changed
Original: The k-means for lines is a set of k centers (points)  that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Revised: The k-means for lines is a set L of n lines in \mathbb{R k centers (points) that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Edit intent: meaning-changed
Original: The k-means for lines is a set of k centers (points)  that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Revised: The k-means for lines is a set of k centers (points) in \mathbb{R that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Edit intent: meaning-changed
Original: The k-means for lines is a set of k centers (points)  that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Revised: The k-means for lines is a set of k centers (points) that minimizes the sum of squared distances over every line in L and its nearest center . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Edit intent: meaning-changed
Original: The k-means for lines is a set of k centers (points)  that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Revised: The k-means for lines is a set of k centers (points) that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-median problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Edit intent: meaning-changed
Original: The k-means for lines is a set of k centers (points)  that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points . Related problems minimize sum of (non-squared) distances, other norms, m-estimators or ignore the t farthest points (outliers) from the k centers .
Revised: The k-means for lines is a set of k centers (points) that minimizes the sum of squared distances to a given set of n lines in R^d . This is a straightforward generalization of the k-means problem where the input is a set of n points instead of lines .
Edit intent: clarity
Original:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation  in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Revised:  We suggest the first PTAS that computes a (1+ epsilon )-approximation in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Edit intent: clarity
Original:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation  in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Revised:  We suggest the first provable PTAS algorithms for these problems that compute (1+ \epsilon )-approximation in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Edit intent: fluency
Original:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation  in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Revised:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation to this problem in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Edit intent: meaning-changed
Original:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation  in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Revised:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation in time O(n \log n) for any constant approximation error \epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Edit intent: meaning-changed
Original:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation  in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d , t \geq 1, including support for streaming and distributed input.
Revised:  We suggest the first provable PTAS algorithms for these problems that compute (1+ epsilon )-approximation in time O(n \log (n) /epsilon^2) for any given epsilon \in (0, 1), and constant integers k, d \geq 1. This is by proving that there is always a weighted subset (called coreset) of dk^{O(k)
Edit intent: meaning-changed
Original: We provide sufficient conditions under which any non-empty intersection of finitely many Euclidean balls intersected with a subset of \mathbb{Rech complex.
Revised: We derive conditions under which the reconstruction of a target space is topologically correct via the \v{C sufficient conditions under which any non-empty intersection of finitely many Euclidean balls intersected with a subset of \mathbb{Rech complex.
Edit intent: meaning-changed
Original:  Applying these results to the restricted Cech complex and using the interleaving relations with the Cech complex (or the Rips complex), we formulate conditions guaranteeing that the target space is homotopy equivalent to the Cech complex (or the Rips complex), in terms of the \mu-reach.
Revised:  Applying these results to the restricted Cech complex and using the interleaving relations with the Cech complex (or the Vietoris-Rips complex), we formulate conditions guaranteeing that the target space is homotopy equivalent to the Cech complex (or the Rips complex), in terms of the \mu-reach.
Edit intent: meaning-changed
Original:  Applying these results to the restricted Cech complex and using the interleaving relations with the Cech complex (or the Rips complex), we formulate conditions guaranteeing that the target space is homotopy equivalent to the Cech complex (or the Rips complex), in terms of the \mu-reach.
Revised:  Applying these results to the restricted Cech complex and using the interleaving relations with the Cech complex (or the Rips complex), we formulate conditions guaranteeing that the target space is homotopy equivalent to the Cech complex (or the Vietoris-Rips complex), in terms of the \mu-reach.
Edit intent: meaning-changed
Original:  This approach is based on a new computational characterisation of the singular points of the curve and on how this curve is located with respect to the projection of the considered quadrics (whose boundaries are the so called silhouette curves).
Revised:  This approach is based on a new computational characterisation of the singular points of the cutcurve and on how this curve is located with respect to the projection of the considered quadrics (whose boundaries are the so called silhouette curves).
Edit intent: clarity
Original: Given a planar straight-line graph G=(V,E) in R^2, a circumscribing polygon of G is a simple polygon P whose vertex set is V, and every edge in E is either an edge or an internal diagonal of P.
Revised: Given a planar straight-line graph G=(V,E) in R^2, a circumscribing polygon of G is a simple polygon P whose vertex set is V, and every edge in E is either an edge or an internal diagonal of P.
Edit intent: fluency
Original:  In particular, we show that in the case of constant branching  the eigenvalues are realized as the roots of a family of generalized Fibonacci polynomials and produce a limiting distribution for the eigenvalues as the tree depth goes to infinity.
Revised:  In particular, we show that in the case of constant branching , the eigenvalues are realized as the roots of a family of generalized Fibonacci polynomials and produce a limiting distribution for the eigenvalues as the tree depth goes to infinity.
Edit intent: fluency
Original: We develop from the ground up a new market-making model tailor-made for high-frequency trading under a limit order book (LOB), based on the well-known classification of order types in market microstructure.
Revised: We develop from the ground up a new market-making model , from the ground up, which is tailored towards high-frequency trading under a limit order book (LOB), based on the well-known classification of order types in market microstructure.
Edit intent: coherence
Original:  It also honors the consistency of price movements upon arrivals of different order types (e. g. price never goes down on buy market order) in additionto respecting the price-time priority of LOB.
Revised:  It also honors the consistency of price movements upon arrivals of different order types . For example, it is apparent that prices should never go down on buy market order) in additionto respecting the price-time priority of LOB.
Edit intent: meaning-changed
Original:  It also honors the consistency of price movements upon arrivals of different order types (e. g. price never goes down on buy market order) in additionto respecting the price-time priority of LOB.
Revised:  It also honors the consistency of price movements upon arrivals of different order types (e. g. price never goes down on buy market orders. In addition, it respects the price-time priority of LOB.
Edit intent: fluency
Original:  In contrast to the approach of regular control on diffusion as in the classical Avellaneda and Stoikov  market-making framework, we exploit the techniques of optimal switching and impulse control on marked point processes, which have proven to be very effective in modeling the order-book features.
Revised:  In contrast to the approach of regular control on diffusion as in the classical Avellaneda and Stoikov 1 market-making framework, we exploit the techniques of optimal switching and impulse control on marked point processes, which have proven to be very effective in modeling the order-book features.
Edit intent: meaning-changed
Original:  Here, we review the application of the homogenous rod( worm-like chain ) modelto the mechanics of the triple helix, including bend, twist, and stretch deformations  and the assumption of backbone linearity.
Revised:  Here, we review the treatment of the triple helix as a homogeneous flexible rod, including bend (standard worm-like chain ) modelto the mechanics of the triple helix, including bend, twist, and stretch deformations and the assumption of backbone linearity.
Edit intent: meaning-changed
Original:  Here, we review the application of the homogenous rod( worm-like chain ) modelto the mechanics of the triple helix, including bend, twist, and stretch deformations  and the assumption of backbone linearity.
Revised:  Here, we review the application of the homogenous rod( worm-like chain ) modelto the mechanics of the triple helix, including bend, twist, and stretch deformations , and the assumption of backbone linearity.
Edit intent: fluency
Original:  Thus, the highlighted areas can be interpreted as the 'positive evidence' used by the network for deciding whether an individual has AD. We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature.
Revised:  In particular, we show that (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature.
Edit intent: coherence
Original:  We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature.
Revised:  We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) the LRP method is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature.
Edit intent: clarity
Original:  We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature.
Revised:  We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little relevance for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature.
Edit intent: clarity
Original:  We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature.
Revised:  We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of relevance correlate well with what is known from literature.
Edit intent: clarity
Original:  To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. the 'evidence density ' or 'evidence gain' . Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala.
Revised:  To quantify the latter, we compute size-corrected metrics of the summed relevance per brain area, e.g. the 'evidence density ' or 'evidence gain' . Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala.
Edit intent: clarity
Original:  To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. the 'evidence density ' or 'evidence gain' . Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala.
Revised:  To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. , relevance density or relevance gain . Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala.
Edit intent: fluency
Original:  To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. the 'evidence density ' or 'evidence gain' . Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala.
Revised:  To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. the 'evidence density ' or 'evidence gain' . Although these metrics produce very individual "fingerprints" of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala.
Edit intent: fluency
Original:  To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. the 'evidence density ' or 'evidence gain' . Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala. We conclude that LRP provides a powerful tool for assisting clinicians in finding evidence for AD (and potentially other diseases) in structural MRI data.
Revised:  To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. the 'evidence density ' or 'evidence gain' . Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including the hippocampus. After discussing several limitations such as sensitivity toward the underlying model and computation parameters, we conclude that LRP provides a powerful tool for assisting clinicians in finding evidence for AD (and potentially other diseases) in structural MRI data.
Edit intent: meaning-changed
Original:  Here we tackle such questions proposing a novel experimental approach in which human subjects, instead of rating natural faces, are allowed to efficiently explore the face-space and "sculpt" their favorite variation of a reference facial image.
Revised:  Here we tackle such questions proposing a novel experimental approach in which human subjects, instead of rating natural faces, are allowed to efficiently explore the face-space and 'sculpt' their favorite variation of a reference facial image.
Edit intent: fluency
Original:  The temporal evolution of conflicts measured by these scaling variables display emergent symmetry, reflecting self-similarity in the trajectories of conflict avalanches. Taken together, our measurements describe a system that is distinct from prevailing explanations of conflict growth such as self-similar forest fire models.
Revised:  The temporal evolution of conflicts measured by these scaling variables display emergent symmetry, collapsing onto a universal dynamical profile over a range of scales. The measured exponents and dynamical profiles describe a system that is distinct from prevailing explanations of conflict growth such as self-similar forest fire models.
Edit intent: meaning-changed
Original:  The statistics of conflict show remarkable regularities like power law distributions of fatalities and duration , but lack a unifying framework. We explore a large, detailed data set of 10^5 armed conflict reports spanning 20 years across nearly 10^4 kilometers.
Revised:  The statistics of conflict show remarkable regularities like power law distributions of fatalities and duration over varying culture and geography. We systematically cluster conflict reports from a database of 10^5 armed conflict reports spanning 20 years across nearly 10^4 kilometers.
Edit intent: meaning-changed