wanyu/IteraTeR_v2 huggingface dataset:
Original:  Nevertheless , most genes should display topologically related phylogenies , and should group into one or more (for genetic hybrids) clustersin the "tree space.
Revised:  Nevertheless , most genes do display topologically related phylogenies , and should group into one or more (for genetic hybrids) clustersin the "tree space.
Edit intent: clarity
Original:  " In this paper we propose to apply the normalized-cut (Ncut) clustering algorithm to the set of gene trees with the geodesic distance between trees over the Billera-Holmes-Vogtmann (BHV) tree space.
Revised:  " In this paper we propose to apply the normalized-cut (Ncut) clustering algorithm to the set of gene trees based on the geodesic distance between trees over the Billera-Holmes-Vogtmann (BHV) tree space.
Edit intent: clarity
Original:  " In this paper we propose to apply the normalized-cut (Ncut) clustering algorithm to the set of gene trees with the geodesic distance between trees over the Billera-Holmes-Vogtmann (BHV) tree space.
Revised:  " In this paper we propose to apply the normalized-cut (Ncut) clustering algorithm to the set of gene trees with the geodesic distance between them over the Billera-Holmes-Vogtmann (BHV) tree space.
Edit intent: clarity
Original:  Based on general conditions in Kallsen and Shiryaev (2002), we derive explicit sufficient conditions for the true martingality of a wide class of exponentials of semimartingales.
Revised:  Based on general conditions in Kallsen and Shiryaev (2002), we derive explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales.
Edit intent: clarity
Original:  Suitably for applications, the conditions are expressed in terms of the semimartingale characteristics.
Revised:  We express the conditions in terms of the semimartingale characteristics.
Edit intent: clarity
Original:  Suitably for applications, the conditions are expressed in terms of the semimartingale characteristics.
Revised:  Suitably for applications, the conditions are expressed in terms of semimartingale characteristics.
Edit intent: fluency
Original:  However, many biofilm-forming bacteria tend to aggregate in the planktonic phase meaning it is possible that many natural and infectious biofilms originate wholly or partially from pre-formed cell aggregates.
Revised:  However, many biofilm-forming bacteria tend to aggregate in the planktonic phase so that it is possible that many natural and infectious biofilms originate wholly or partially from pre-formed cell aggregates.
Edit intent: coherence
Original:  Focusing on the role of aggregate shape , we find that the degree of spreading of an aggregate on a surface can play a key role in determining its eventual fate during biofilm development.
Revised:  Focusing on the initial shape the aggregate forms on the surface , we find that the degree of spreading of an aggregate on a surface can play a key role in determining its eventual fate during biofilm development.
Edit intent: clarity
Original:  Focusing on the role of aggregate shape , we find that the degree of spreading of an aggregate on a surface can play a key role in determining its eventual fate during biofilm development.
Revised:  Focusing on the role of aggregate shape , we find that the degree of spreading of an aggregate on a surface can play an important role in determining its eventual fate during biofilm development.
Edit intent: clarity
Original: To the knowledge of the author, this is the first time it has been shown that interest rates that are extremely high by modern standards  are necessary within a zero-sum monetary system  . Extreme interest rates persisted for long periods of time in many places . Prior to the invention of banking, most money was hard-money in the form of some type of coin .
Revised: To the knowledge of the author, this is the first time it has been shown that interest rates that are extremely high by modern standards are necessary within a zero-sum monetary system . Extreme interest rates that appeared in various places and times reinforce the idea that hard money may have contributed to high rates of interest .
Edit intent: clarity
Original:  Even with a 5\% advantage, an investor will not break even at 15\% interest.
Revised:  Even with a 5\% advantage, an investor won't break even at 15\% interest.
Edit intent: fluency
Original: We propose a label propagation approach to geolocation prediction based on Modified Absorption , with two enhancements:(1) the removal of "celebrity" nodes to increase location homophily and boost tractability;
Revised: We propose a label propagation approach to geolocation prediction based on Modified Adsorption , with two enhancements:(1) the removal of "celebrity" nodes to increase location homophily and boost tractability;
Edit intent: fluency
Original: We propose a label propagation approach to geolocation prediction based on Modified Adsorption, with two enhancements:(1) the removal of "celebrity" nodes to increase location homophily and boost tractability ;
Revised: We propose a label propagation approach to geolocation prediction based on Modified Adsorption, with two enhancements:(1) the removal of "celebrity" nodes to increase location homophily and boost tractability ,
Edit intent: fluency
Original:  In particular, we consider the case when H is either the set of 2-matching inequalities or the set of simple comb inequalities.
Revised:  In particular, we consider the case when H is either the set of 2-matching inequalities or the simple comb inequalities.
Edit intent: fluency
Original:  In addition we show that the extension complexity of the polytope formed by all comb inequalities is exponential.
Revised:  In addition we show that the extension complexity of polytope formed by all comb inequalities is exponential.
Edit intent: fluency
Original:  For our proofs, we introduce a subclass of comb inequalities, called (h,t)-uniform comb inequalities, which may be of independent interest in the study of the TSP .
Revised:  For our proofs, we introduce a subclass of comb inequalities, called (h,t)-uniform inequalities, which may be of independent interest in the study of the TSP .
Edit intent: fluency
Original:  For our proofs, we introduce a subclass of comb inequalities, called (h,t)-uniform comb inequalities, which may be of independent interest in the study of the TSP .
Revised:  For our proofs, we introduce a subclass of comb inequalities, called (h,t)-uniform comb inequalities, which may be of independent interest .
Edit intent: clarity
Original:  Video compression has been shown to have an adverse effect on feature matching performance.
Revised:  Video compression has been shown to have an adverse effect on feature-matching performance.
Edit intent: fluency
Original:  The negative impact of compression can be reduced by using the keypoints extracted from uncompressed video for descriptor calculation from the compressed video.
Revised:  The negative impact of compression can be reduced by using the keypoints extracted from the uncompressed video to calculate descriptors from the compressed video.
Edit intent: fluency
Original:  Based on this observation, we propose to signal the keypoints as side information to the server  and to extract only the descriptors from the compressed video.
Revised:  Based on this observation, we propose to provide these keypoints to the server and to extract only the descriptors from the compressed video.
Edit intent: clarity
Original:  First, we introduce four different frame types for keypoint encoding considering different types of changes in the video content.
Revised:  First, we introduce four different frame types for keypoint encoding to address different types of changes in the video content.
Edit intent: clarity
Original:  First, we introduce four different frame types for keypoint encoding considering different types of changes in the video content.
Revised:  First, we introduce four different frame types for keypoint encoding considering different types of changes in video content.
Edit intent: fluency
Original:  These frame types represent new scenes , the same scene, a slowly changing scene, and a fast moving scene , respectively, and are determined by comparing features between successive video frames.
Revised:  These frame types represent a new scene , the same scene, a slowly changing scene, and a fast moving scene , respectively, and are determined by comparing features between successive video frames.
Edit intent: fluency
Original:  These frame types represent new scenes , the same scene, a slowly changing scene, and a fast moving scene , respectively, and are determined by comparing features between successive video frames.
Revised:  These frame types represent new scenes , the same scene, a slowly changing scene, or a rapidly moving scene and are determined by comparing features between successive video frames.
Edit intent: clarity
Original:  Then, we propose Intra, P, and Skip modes to encode the keypoints for different frame types.
Revised:  Then, we propose Intra, Skip and Inter modes of encoding the keypoints for different frame types.
Edit intent: clarity
Original:  For example, keypoints for new scenes are encoded with Intra mode, and keypoints for unchanged scenes are skipped.
Revised:  For example, keypoints for new scenes are encoded using the Intra mode, and keypoints for unchanged scenes are skipped.
Edit intent: clarity
Original:  As a result, the bitrate of the side information for keypoint encoding is significantly reduced.
Revised:  As a result, the bitrate of the side information related to keypoint encoding is significantly reduced.
Edit intent: clarity
Original:  Finally, we perform pairwise matching and image retrieval  to evaluate the performance of the proposed approach using the Stanford mobile augmented reality dataset . Results show that the proposed approach significantly improves the feature matching performance at a given bitrate.
Revised:  Finally, we present pairwise matching and image retrieval to evaluate the performance of the proposed approach using the Stanford mobile augmented reality dataset . Results show that the proposed approach significantly improves the feature matching performance at a given bitrate.
Edit intent: clarity
Original:  Finally, we perform pairwise matching and image retrieval  to evaluate the performance of the proposed approach using the Stanford mobile augmented reality dataset . Results show that the proposed approach significantly improves the feature matching performance at a given bitrate.
Revised:  Finally, we perform pairwise matching and image retrieval experiments conducted to evaluate the performance of the proposed approach using the Stanford mobile augmented reality dataset . Results show that the proposed approach significantly improves the feature matching performance at a given bitrate.
Edit intent: clarity
Original:  Finally, we perform pairwise matching and image retrieval  to evaluate the performance of the proposed approach using the Stanford mobile augmented reality dataset . Results show that the proposed approach significantly improves the feature matching performance at a given bitrate.
Revised:  Finally, we perform pairwise matching and image retrieval to evaluate the performance of the proposed approach using the Stanford mobile augmented reality dataset . Results show that the proposed approach offers significantly improved feature matching and image retrieval performance at a given bitrate.
Edit intent: clarity
Original:  It has received great attention,  many community detection methods have been proposed in the last decade.
Revised:  It has received great attention, and many community detection methods have been proposed in the last decade.
Edit intent: coherence
Original:  In this paper, we propose a divisive spectral method for identifying communities from networks, which utilizes a sparsification operation to pre-process the networks first, and then uses a repeated bisection spectral algorithm to partition the networks into communities.
Revised:  In this paper, we propose a divisive spectral method for identifying community structures from networks, which utilizes a sparsification operation to pre-process the networks first, and then uses a repeated bisection spectral algorithm to partition the networks into communities.
Edit intent: clarity
Original:  The sparsification operation makes community structures of the networks being more clearly and sharply , so that the repeated spectral bisection algorithm extract high-quality community structures accurately from the sparsified networks.
Revised:  The sparsification operation makes the community boundaries more clearer and more sharper , so that the repeated spectral bisection algorithm extract high-quality community structures accurately from the sparsified networks.
Edit intent: clarity
Original:  Experiments show that the combination of network sparsification and spectral bisection algorithm is a high degree of success , the proposed method can be more effective in detecting community structures from networks than the others.
Revised:  Experiments show that the combination of network sparsification and spectral bisection algorithm is highly successful , the proposed method can be more effective in detecting community structures from networks than the others.
Edit intent: clarity
Original:  Experiments show that the combination of network sparsification and spectral bisection algorithm is a high degree of success , the proposed method can be more effective in detecting community structures from networks than the others.
Revised:  Experiments show that the combination of network sparsification and spectral bisection algorithm is a high degree of success , the proposed method is more effective in detecting community structures from networks than the others.
Edit intent: clarity
Original:  We prove efficient generalization bounds for our proposed method, with a polynomial sample complexity in the relevant parameters, such as input dimension and number of neurons.
Revised:  We prove efficient risk bounds for our proposed method, with a polynomial sample complexity in the relevant parameters, such as input dimension and number of neurons.
Edit intent: clarity
Original:  Thus, for the first time, we have a computationally efficient method with guaranteed generalization bounds for training neural networks  .
Revised:  Thus, we have a computationally efficient method with guaranteed generalization bounds for training neural networks .
Edit intent: clarity
Original:  While learning arbitrary target functions is NP-hard, we provide transparent conditions on the function and the input for generalizability .
Revised:  While learning arbitrary target functions is NP-hard, we provide transparent conditions on the function and the input for learnability .
Edit intent: clarity
Original:  Thus, we have a computationally efficient method with guaranteed risk bounds for training neural networks with general non-linear activations .
Revised:  Thus, we propose a computationally efficient method with guaranteed risk bounds for training neural networks with general non-linear activations .
Edit intent: clarity
Original:  For the kernelization and its analysis, we introduce the notion of `complete degree' of a vertex and also use the Sauer-Shelah Lemma J. of Comb.
Revised:  For the kernelization and its analysis, we introduce the notion of `complete degree' of a vertex J. of Comb.
Edit intent: coherence
Original:  Theory, Ser. A, 13:145--147, 1972 . We believe that these are of independent interest and the underlying ideas can be potentially applied to other problems.
Revised:  Theory, Ser. A, 13:145--147, 1972 . We believe that the underlying idea can be potentially applied to other problems.
Edit intent: coherence
Original:  A dynamic framework incorporates the sequence of the cash-flows involved in the waterfall of resources of the CCP .
Revised:  We introduce a dynamic framework that incorporates the sequence of the cash-flows involved in the waterfall of resources of the CCP .
Edit intent: clarity
Original:  A dynamic framework incorporates the sequence of the cash-flows involved in the waterfall of resources of the CCP .
Revised:  A dynamic framework incorporates the sequence of cash-flows involved in the waterfall of resources of the CCP .
Edit intent: fluency
Original:  A dynamic framework incorporates the sequence of the cash-flows involved in the waterfall of resources of the CCP .
Revised:  A dynamic framework incorporates the sequence of the cash-flows involved in the waterfall of resources of a clearing house .
Edit intent: clarity
Original:  We perform spectral clustering on =%DIFDELCMD < \left(%%% \frac{1{D_i D_j} A_{ij} }%DIFDELCMD < \right)%%% _{i,j=1 _i is the observed degree of node i.
Revised:  We =%DIFDELCMD < \left(%%% \frac{1{D_i D_j} A_{ij} }%DIFDELCMD < \right)%%% _{i,j=1 _i is the observed degree of node i.
Edit intent: clarity
Original:  We perform spectral clustering on =%DIFDELCMD < \left(%%% \frac{1{D_i D_j} A_{ij} }%DIFDELCMD < \right)%%% _{i,j=1 _i is the observed degree of node i.
Revised:  We perform spectral clustering on %DIFDELCMD < \left(%%% \frac{1{D_i D_j} A_{ij} }%DIFDELCMD < \right)%%% _{i,j=1 _i is the observed degree of node i.
Edit intent: fluency
Original:  We perform spectral clustering on =%DIFDELCMD < \left(%%% \frac{1{D_i D_j} A_{ij} }%DIFDELCMD < \right)%%% _{i,j=1 _i is the observed degree of node i.
Revised:  We perform spectral clustering on =%DIFDELCMD < \left(%%% {D_i D_j} A_{ij} }%DIFDELCMD < \right)%%% _{i,j=1 _i is the observed degree of node i.
Edit intent: clarity
Original:  We show that this leads to consistent recovery of the block-membership of all but a vanishing fraction of nodes, even when the lowest degree is of order log(n) . There turns out to be a natural connection between and random walks on instances of the random graph.
Revised:  We show that this algorithm consistently recovers the block-membership of all but a vanishing fraction of nodes, even when the lowest degree is of order log(n) . There turns out to be a natural connection between and random walks on instances of the random graph.
Edit intent: clarity
Original:  We show that this leads to consistent recovery of the block-membership of all but a vanishing fraction of nodes, even when the lowest degree is of order log(n) . There turns out to be a natural connection between and random walks on instances of the random graph.
Revised:  We show that this leads to consistent recovery of the block-membership of all but a vanishing fraction of nodes, in the regime where the lowest degree is of order log(n) . There turns out to be a natural connection between and random walks on instances of the random graph.
Edit intent: clarity
Original:  We show that this leads to consistent recovery of the block-membership of all but a vanishing fraction of nodes, even when the lowest degree is of order log(n) . There turns out to be a natural connection between and random walks on instances of the random graph.
Revised:  We show that this leads to consistent recovery of the block-membership of all but a vanishing fraction of nodes, even when the lowest degree is of order log(n) and random walks on instances of the random graph.
Edit intent: coherence
Original:  For infinite regular lattices in one  and two dimensions  , we find that initially the  innovation spreads linearly with the time t and diffusively in the long time limit , provided its introduction in the community is successful) in 1D and sub-diffusively (\sim t/\ln t) in 2D} . For finite lattices, the growth curves for the number of adopters are typically concave functions of t.
Revised:  For infinite regular lattices in one (1D) and two dimensions , we find that initially the innovation spreads linearly with the time t and diffusively in the long time limit , provided its introduction in the community is successful) in 1D and sub-diffusively (\sim t/\ln t) in 2D} . For finite lattices, the growth curves for the number of adopters are typically concave functions of t.
Edit intent: clarity
Original:  For infinite regular lattices in one  and two dimensions  , we find that initially the  innovation spreads linearly with the time t and diffusively in the long time limit , provided its introduction in the community is successful) in 1D and sub-diffusively (\sim t/\ln t) in 2D} . For finite lattices, the growth curves for the number of adopters are typically concave functions of t.
Revised:  For infinite regular lattices in one and two dimensions (2D) , we find that initially the innovation spreads linearly with the time t and diffusively in the long time limit , provided its introduction in the community is successful) in 1D and sub-diffusively (\sim t/\ln t) in 2D} . For finite lattices, the growth curves for the number of adopters are typically concave functions of t.
Edit intent: clarity
Original:  For infinite regular lattices in one  and two dimensions  , we find that initially the  innovation spreads linearly with the time t and diffusively in the long time limit , provided its introduction in the community is successful) in 1D and sub-diffusively (\sim t/\ln t) in 2D} . For finite lattices, the growth curves for the number of adopters are typically concave functions of t.
Revised:  For infinite regular lattices in one and two dimensions , we find that initially the successful innovation spreads linearly with the time t and diffusively in the long time limit , provided its introduction in the community is successful) in 1D and sub-diffusively (\sim t/\ln t) in 2D} . For finite lattices, the growth curves for the number of adopters are typically concave functions of t.
Edit intent: fluency
Original: For better comparison to fan broadband noise experiments the Random Particle Mesh (RPM) method  is extended to generalised turbulence spectra.
Revised: The Random Particle Mesh (RPM) method is extended to generalised turbulence spectra.
Edit intent: coherence
Original:  The RPM method synthesises turbulent fluctuations by filtering white noise with a Gaussian filter kernel , which in turn gives a Gaussian spectrum.
Revised:  With this method turbulent fluctuations are synthesised by filtering white noise with a Gaussian filter kernel , which in turn gives a Gaussian spectrum.
Edit intent: clarity
Original:  The RPM method synthesises turbulent fluctuations by filtering white noise with a Gaussian filter kernel , which in turn gives a Gaussian spectrum.
Revised:  The RPM method synthesises turbulent fluctuations by filtering white noise with a Gaussian filter kernel that in turn gives a Gaussian spectrum.
Edit intent: fluency
Original:  E.g. in turbo-machines , the von Karman , Liepmann, and modified von Karman spectra are the most relevant model spectra.
Revised:  E.g. in turbo-machines the von K\'arm\'an , Liepmann, and modified von Karman spectra are the most relevant model spectra.
Edit intent: fluency
Original:  E.g. in turbo-machines , the von Karman , Liepmann, and modified von Karman spectra are the most relevant model spectra.
Revised:  E.g. in turbo-machines , the von Karman , Liepmann, and modified von K\'arm\'an spectra are more realistic model spectra.
Edit intent: clarity
Original:  In the current paper we show how to analytically derive weighting functions to realise arbitrary spectra which are isotropic and solenoidal using a superposition of weighted Gaussian spectra of differing length scales.
Revised:  In this note we analytically derive weighting functions to realise arbitrary spectra which are isotropic and solenoidal using a superposition of weighted Gaussian spectra of differing length scales.
Edit intent: clarity
Original:  In the current paper we show how to analytically derive weighting functions to realise arbitrary spectra which are isotropic and solenoidal using a superposition of weighted Gaussian spectra of differing length scales.
Revised:  In the current paper we show how to analytically derive weighting functions to realise arbitrary isotropic solenoidal spectra using a superposition of weighted Gaussian spectra of differing length scales.
Edit intent: clarity