wanyu/IteraTeR_v2 huggingface dataset:
Original:  In addition , we show that the problem is fixed-parameter tractable when parameterized by  clique-width, which implies polynomial time solvability for many interesting graph classes of such as distance-hereditary graphs and outerplanar graphs.
Revised:  In addition , we show that the problem is fixed-parameter tractable when parameterized by the clique-width, which implies polynomial time solvability for many interesting graph classes of such as distance-hereditary graphs and outerplanar graphs.
Edit intent: fluency
Original:  In addition , we show that the problem is fixed-parameter tractable when parameterized by  clique-width, which implies polynomial time solvability for many interesting graph classes of such as distance-hereditary graphs and outerplanar graphs.
Revised:  In addition , we show that the problem is fixed-parameter tractable when parameterized by clique-width, which implies polynomial-time solution for many interesting graph classes of such as distance-hereditary graphs and outerplanar graphs.
Edit intent: clarity
Original:  In addition , we show that the problem is fixed-parameter tractable when parameterized by  clique-width, which implies polynomial time solvability for many interesting graph classes of such as distance-hereditary graphs and outerplanar graphs.
Revised:  In addition , we show that the problem is fixed-parameter tractable when parameterized by clique-width, which implies polynomial time solvability for many interesting graph classes , such as distance-hereditary graphs and outerplanar graphs.
Edit intent: fluency
Original:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where  vc(G) and  nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Revised:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where vc(G) and nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Edit intent: clarity
Original:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where  vc(G) and  nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Revised:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel of at most~ 2\cdot nd(G) vertices are presented, where vc(G) and nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Edit intent: clarity
Original:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where  vc(G) and  nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Revised:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where ~ vc(G) and nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Edit intent: fluency
Original:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where  vc(G) and  nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Revised:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where vc(G) and ~ nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Edit intent: fluency
Original:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where  vc(G) and  nd(G) are the vertex cover number and the neighborhood diversity of the input graph , respectively.
Revised:  Finally, a\left( 2^{ \left( vc(G) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% \cdot nalgorithm, \right)} \right) and a kernel having at most 2\cdot nd(G) vertices are presented, where vc(G) and nd(G) are the vertex cover number and the neighborhood diversity of ~G , respectively.
Edit intent: clarity
Original: As the demand for mobile connectivity continues to grow, there is a strong need to quantify the performance of Mobile Broadband (MBB) networks.
Revised: As the demand for mobile connectivity continues to grow, there is a strong need to evaluate the performance of Mobile Broadband (MBB) networks.
Edit intent: clarity
Original:  In the last years, mobile speed gained popularity as the most commonly accepted metric to describe  performance.
Revised:  In the last years, mobile speed gained popularity as the widely accepted metric to describe performance.
Edit intent: clarity
Original:  In the last years, mobile speed gained popularity as the most commonly accepted metric to describe  performance.
Revised:  In the last years, mobile speed gained popularity as the most commonly accepted metric to describe their performance.
Edit intent: clarity
Original:  However, there is no consensus on how exactly to measure mobile speed .
Revised:  However, there is a lack of consensus on how exactly to measure mobile speed .
Edit intent: clarity
Original:  However, there is no consensus on how exactly to measure mobile speed .
Revised:  However, there is no consensus on how mobile speed should be measured .
Edit intent: clarity
Original: Non-normality can underlie pulse dynamics in  engineering contexts.
Revised: Non-normality can underlie pulse dynamics in many engineering contexts.
Edit intent: clarity
Original:  However, its role in pulses generated in biological contexts is generally unclear.
Revised:  However, its role in pulses generated in biomolecular contexts is generally unclear.
Edit intent: clarity
Original:  Here, we address this issue using  tools of linear algebra and control systems theory on simple computational models of biomolecular circuits.
Revised:  Here, we address this issue using the mathematical tools of linear algebra and control systems theory on simple computational models of biomolecular circuits.
Edit intent: clarity
Original:  Here, we address this issue using  tools of linear algebra and control systems theory on simple computational models of biomolecular circuits.
Revised:  Here, we address this issue using tools of linear algebra and systems theory on simple computational models of biomolecular circuits.
Edit intent: clarity
Original:  We used a generalized framework and pseudosepctrum analysis to identify non-normality in larger biomolecular circuit models, finding that it correlates well with pulsing dynamics.
Revised:  We used a generalized framework and pseudospectrum analysis to identify non-normality in larger biomolecular circuit models, finding that it correlates well with pulsing dynamics.
Edit intent: fluency
Original:  In this paper, we apply the recent massively parallelizable Bayesian uncertainty quantification framework %DIFDELCMD < \Pi4U %DIFDELCMD < %%% to a model of a disease spreading on a network of communities , showing that the method can accurately and tractably recover system parameters and select optimal models in this setting .
Revised:  In this paper, we apply the recent massively parallelizable Bayesian uncertainty quantification framework %DIFDELCMD < \Pi4U %DIFDELCMD < %%% to infer model parameters for a disease spreading on a network of communities , showing that the method can accurately and tractably recover system parameters and select optimal models in this setting .
Edit intent: clarity
Original:  We translated our model to a biased random walk on percolation lattice and explored the effect of mentioned topic on population dynamics .
Revised:  We translated our model to a biased random walk on percolation lattice . Then we explored the effect of mentioned topic on population dynamics .
Edit intent: coherence
Original:  For metastasis, our model predicts tat the interplay between the structure of metastatic niche and interactions between metastatic cells arrived from different colons determines that which kind of seeds, polyclonal or monoclonal, can successfully metastasized there.
Revised:  For metastasis, our model predicts that the interplay between the structure of metastatic niche and interactions between metastatic cells arrived from different colons determines that which kind of seeds, polyclonal or monoclonal, can successfully metastasized there.
Edit intent: fluency
Original:  Using spectral statistics and Shannon entropy, we visualize the asymmetric information in market impacts.
Revised:  Using spectral statistics and Shannon entropy, we visualize the asymmetric information in price impacts.
Edit intent: clarity
Original:  We show that the useful information is encoded in the impacts corresponding to the small entropy.
Revised:  We show that the useful information is encoded in the impacts corresponding to small entropy.
Edit intent: fluency
Original:  We present an approach to estimate periodic, time-varying parameters using nonlinear Bayesian filtering.
Revised:  We present an approach to estimating periodic, time-varying parameters using nonlinear Bayesian filtering.
Edit intent: fluency
Original:  The proposed technique imposes periodic structure by treating the time-varying parameter as a piecewise function with unknown coefficients , estimated using the ensemble Kalman filter (EnKF) .
Revised:  The proposed technique imposes periodic structure by treating the time-varying parameter as a piecewise function with unknown coefficients .
Edit intent: clarity
Original: Mathematical models of the circulation continue to be an essential tool to study how the cardiovascular (CV) system maintains homeostasis.
Revised: Mathematical models are essential tools to study how the cardiovascular (CV) system maintains homeostasis.
Edit intent: clarity
Original: Mathematical models of the circulation continue to be an essential tool to study how the cardiovascular (CV) system maintains homeostasis.
Revised: Mathematical models of the circulation continue to be an essential tool to study how the cardiovascular system maintains homeostasis.
Edit intent: clarity
Original:  The utility of these models is ultimately limited by how much we can trust the accuracy of their predictions .
Revised:  The utility of such models is limited by the accuracy of their predictions .
Edit intent: clarity
Original:  A challenge in implementing UQ procedures is that many published methods require that the model be identifiable .
Revised:  A challenge associated with the use of UQ is that many published methods require that the model be identifiable .
Edit intent: clarity
Original:  An identifiable model is one with a one-to-one mapping  from the parameter space to the model output  .
Revised:  An identifiable model is one with a one-to-one mapping exists from the parameter space to the model output .
Edit intent: clarity
Original:  An identifiable model is one with a one-to-one mapping  from the parameter space to the model output  .
Revised:  An identifiable model is one with a one-to-one mapping from the parameter space to the model output ) .
Edit intent: fluency
Original:  and (4) both frequentist and Bayesian UQ methods to assess the predictive capability of the model  .
Revised:  and (4) frequentist and Bayesian UQ methods to assess the predictive capability of the model .
Edit intent: clarity
Original:  and (4) both frequentist and Bayesian UQ methods to assess the predictive capability of the model  .
Revised:  and (4) both frequentist and Bayesian UQ calculations to assess the predictive capability of the model .
Edit intent: clarity
Original:  However, the study of source space synchronization is still a tedious task , as the high computational cost of the algorithm escalates with the square of the number of signals evaluated  .
Revised:  However, the study of source space synchronization is still a tedious task . The high computational cost of the algorithm escalates with the square of the number of signals evaluated .
Edit intent: coherence
Original:  However, the study of source space synchronization is still a tedious task , as the high computational cost of the algorithm escalates with the square of the number of signals evaluated  .
Revised:  However, the study of source space synchronization is still a tedious task , as the high computational cost of the algorithms escalates with the square of the number of signals evaluated .
Edit intent: fluency
Original:  In this work , we take the original implementation of Phase Locking Value (PLV) and re-formulate it in a highly computational efficient way.
Revised:  In this work , we take the original implementation of Phase Locking Value (PLV) and re-formulated it in a highly computational efficient way.
Edit intent: fluency
Original:  We used this symmetry to introduce two new derived metrics insensitive to zero lag synchronization, the imaginary part of PLV (iPLV) and corrected imaginary part of PLV (ciPLV).
Revised:  We used this symmetry to introduce two new metrics insensitive to zero lag synchronization, the imaginary part of PLV (iPLV) and corrected imaginary part of PLV (ciPLV).
Edit intent: clarity
Original:  We used this symmetry to introduce two new derived metrics insensitive to zero lag synchronization, the imaginary part of PLV (iPLV) and corrected imaginary part of PLV (ciPLV).
Revised:  We used this symmetry to introduce two new derived metrics insensitive to zero lag synchronization, the imaginary part of PLV (iPLV) and its corrected counterpart (ciPLV).
Edit intent: clarity
Original:  Our simulations prove that these metrics, especially ciPLV, are highly robust in the presence of volume conduction. ciPLV, in particular, proves capable of ignoring zero-lag connectivity, while correctly estimating nonzero-lag connectivity.
Revised:  Our simulations prove that these metrics, especially ciPLV, are highly robust in the presence of volume conduction. ciPLV, in particular, proved capable of ignoring zero-lag connectivity, while correctly estimating nonzero-lag connectivity.
Edit intent: fluency
Original:  We present the first deterministic 1-local O(1)-memory routing algorithm that is guaranteed to find a path between two vertices in the visibility graph of P with respect to a set of constraints S.
Revised:  We present the first deterministic 1-local O(1)-memory routing algorithm that is guaranteed to find a path between two vertices in the visibility graph of P with respect to a set of constraints S.
Edit intent: fluency
Original:  The arithmetic complexity of our probabilistic algorithm is in O \mathcal{O} (N^{\omega+1}), where N is the bound on the degree of a representation of the first integral and \omega \in [2;3] is the exponent of linear algebra.
Revised:  The arithmetic complexity of our probabilistic algorithm is in \mathcal{O} (N^{\omega+1}), where N is the bound on the degree of a representation of the first integral and \omega \in [2;3] is the exponent of linear algebra.
Edit intent: clarity
Original:  We extend these ideas to rigid frameworks in three dimensions and we derive similar lower bounds, by exploiting data from extensive Gr\"obner basis computations.
Revised:  We extend these ideas to rigid graphs in three dimensions and we derive similar lower bounds, by exploiting data from extensive Gr\"obner basis computations.
Edit intent: clarity
Original: Nauticle is a general-purpose numerical solver pursuing the easy adoption and application of arbitrary particle-based numerical schemes.
Revised: Nauticle is a general-purpose simulation tool for the flexible and highly configurable application of particle-based numerical schemes.
Edit intent: clarity
Original:  Consolidating multiple VNFs in a smaller number of locations would allow to decrease capital expenditures.
Revised:  Consolidating multiple VNFs in a smaller number of locations would allow decreasing capital expenditures.
Edit intent: fluency
Original:  However, excessive consolidation of VNFs might cause additional latency penalties due to processing-resource sharing, and this is undesirable, as SCs are bounded by service-specific latency requirements.
Revised:  However, excessive consolidation of VNFs might cause additional latency penalties due to processing-resource sharing, and this is undesirable, as SFCs are bounded by service-specific latency requirements.
Edit intent: clarity
Original:  These costs affect how the chained VNFs are placed in the network to meet the performance requirement of the SCs . We evaluate their impact while considering SCs with different bandwidth and latency requirements in a scenario of VNF consolidation.
Revised:  These costs affect how the chained VNFs are placed in the network to meet the performance requirement of the SCs . We evaluate their impact while considering SFCs with different bandwidth and latency requirements in a scenario of VNF consolidation.
Edit intent: clarity
Original:  Given Jaccard index \delta, using k buckets of size O(\log(l) + \log\log(|A \cup B|)) (in practice, typically 2 bytes) per set, HyperMinHash streams over A and B and generates an estimate of the Jaccard index \delta with error O( 1 /l + \sqrt{k/\delta\left( }\left( { t \epsilon} }\right)\right)  MinHash, which requires the same number of storage units (buckets), but using O(\log(|A \cup B|)) bit per bucket.
Revised:  For a multiplicative approximation error 1 /l + \sqrt{k/\delta\left( }\left( { t \epsilon} }\right)\right) MinHash, which requires the same number of storage units (buckets), but using O(\log(|A \cup B|)) bit per bucket.
Edit intent: clarity
Original:  Given Jaccard index \delta, using k buckets of size O(\log(l) + \log\log(|A \cup B|)) (in practice, typically 2 bytes) per set, HyperMinHash streams over A and B and generates an estimate of the Jaccard index \delta with error O( 1 /l + \sqrt{k/\delta\left( }\left( { t \epsilon} }\right)\right)  MinHash, which requires the same number of storage units (buckets), but using O(\log(|A \cup B|)) bit per bucket.
Revised:  Given Jaccard index \delta, using k buckets of size O(\log(l) + \log\log(|A \cup B|)) (in practice, typically 2 bytes) per set, HyperMinHash streams over A and B and generates an estimate of the Jaccard index \delta with error O( 1 + \sqrt{k/\delta\left( }\left( { t \epsilon} }\right)\right) MinHash, which requires the same number of storage units (buckets), but using O(\log(|A \cup B|)) bit per bucket.
Edit intent: clarity
Original:  the previous state-of-the-art MinHash can only estimate Jaccard indices for cardinalities of 10^{10} with the same memory consumption.
Revised:  MinHash can only estimate Jaccard indices for cardinalities of 10^{10} with the same memory consumption.
Edit intent: coherence
Original:  Our new algorithm allows estimating Jaccard indices of 0.01 for set cardinalities on the order of 10^{19} with relative error of around 10\\%DIF < using 64KiB of %DIF > using 64KiB of memory;
Revised:  Our new algorithm allows estimating Jaccard indices of 0.01 for set cardinalities on the order of 10^{19} with relative error of around 10\\%DIF < %DIF > using 64KiB of memory;
Edit intent: clarity
Original:  There is a large literature on \emph{graph sampling , where the goal is to estimate properties (especially the degree distribution) of a large graph through a small, random sample.
Revised:  There is a large literature on \emph{graph sampling , where the goal is to estimate properties (especially the degree distribution) of a large graph through a small, random sample.
Edit intent: fluency
Original:  We design a new algorithm, SADDLES, for this problem, using recent mathematical techniques from the field of sublinear algorithms .
Revised:  We design a new algorithm, SADDLES, for this problem, using recent mathematical techniques from the field of sublinear algorithms .
Edit intent: fluency
Original:  For the analysis, we define two fatness measures of the degree distribution, called the h-index and thez-index .
Revised:  For the analysis, we define two fatness measures of the degree distribution, called the and thez-index .
Edit intent: clarity
Original:  For the analysis, we define two fatness measures of the degree distribution, called the h-index and thez-index .
Revised:  For the analysis, we define two fatness measures of the degree distribution, called the h-index z-index .
Edit intent: clarity
Original:  For the analysis, we define two fatness measures of the degree distribution, called the h-index and thez-index .
Revised:  For the analysis, we define two fatness measures of the degree distribution, called the h-index and theh-index and the z-index .
Edit intent: coherence
Original:  On the other hand, the average of the attachment exponents in the citation network is 0.3 , which suggests the rich get richer phenomenon in the citation network is weaker than in the co-authorship network .
Revised:  On the other hand, the average of the attachment exponents in the citation network , which suggests the rich get richer phenomenon in the citation network is weaker than in the co-authorship network .
Edit intent: coherence
Original:  On the other hand, the average of the attachment exponents in the citation network is 0.3 , which suggests the rich get richer phenomenon in the citation network is weaker than in the co-authorship network .
Revised:  On the other hand, the average of the attachment exponents in the citation network is 0.3 , which suggests the rich get richer phenomenon is similarly weak in both networks .
Edit intent: clarity
Original:  This implies that the intrinsic scientific quality of each author is more important in getting new citations than co-authorship . Furthermore, author fitness in both co-authorship and citation networks are found to be consistent with the history of the strategic management scientific community.
Revised:  This implies that the intrinsic scientific quality of each author is important in both getting new citations than co-authorship . Furthermore, author fitness in both co-authorship and citation networks are found to be consistent with the history of the strategic management scientific community.
Edit intent: clarity
Original:  This implies that the intrinsic scientific quality of each author is more important in getting new citations than co-authorship . Furthermore, author fitness in both co-authorship and citation networks are found to be consistent with the history of the strategic management scientific community.
Revised:  This implies that the intrinsic scientific quality of each author is more important in getting new citations and new co-authorships . Furthermore, author fitness in both co-authorship and citation networks are found to be consistent with the history of the strategic management scientific community.
Edit intent: clarity
Original:  These are often described as the rich get richer and the fit get richer phenomena.
Edit intent: coherence
Original:  The average of the attachment exponents of four time periods in the co-author network is 0.3 while it is 0.29 in the citation network, which suggests the rich get richer phenomenon is similarly weak in both networks.
Revised:  The average of the attachment exponents in the co-author network is 0.3 while it is 0.29 in the citation network, which suggests the rich get richer phenomenon is similarly weak in both networks.
Edit intent: clarity
Original:  This implies that the intrinsic scientific quality of each author is important in both getting new citations and new co-authorships.
Revised:  This implies that the intrinsic scientific quality of each author plays a crucial role in getting new citations and new co-authorships.
Edit intent: clarity