wanyu/IteraTeR_v2 huggingface dataset:
Original:  We also identify distinct generalizations of the notion of margin from hyperplanes to polytopes and investigate how they relate geometrically;
Revised:  We also identify distinct generalizations of the notion of margin from hyperplanes to polyhedra and investigate how they relate geometrically;
Edit intent: clarity
Original:  this result may be of interest beyond the learning setting.
Revised:  this result may have ramifications beyond the learning setting.
Edit intent: clarity
Original:  We address conjectures formulated in 2003 by Tuncel et al., involving certain interlacing properties of  eigenvalues of (A\otimes B + B\otimes A) for pairs of symmetric matrices Aand B.
Revised:  We address conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of eigenvalues of (A\otimes B + B\otimes A) for pairs of symmetric matrices Aand B.
Edit intent: clarity
Original:  We address conjectures formulated in 2003 by Tuncel et al., involving certain interlacing properties of  eigenvalues of (A\otimes B + B\otimes A) for pairs of symmetric matrices Aand B.
Revised:  We address conjectures formulated in 2003 by Tuncel et al., involving certain interlacing properties of the eigenvalues of (A\otimes B + B\otimes A) for pairs of symmetric matrices Aand B.
Edit intent: fluency
Original:  We address conjectures formulated in 2003 by Tuncel et al., involving certain interlacing properties of  eigenvalues of (A\otimes B + B\otimes A) for pairs of symmetric matrices Aand B.
Revised:  We address conjectures formulated in 2003 by Tuncel et al., involving certain interlacing properties of eigenvalues of (A\otimes B + B\otimes A) for pairs of n-by-n matrices A, B.
Edit intent: clarity
Original:  In particular, we prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of (A\otimes B + B\otimes A) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors). 
Revised:  In particular, we prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of (A\otimes B + B\otimes A) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors). 
Edit intent: fluency
Original: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of ( A\otimes B + B\otimes A ) for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of ( A\otimes B + B\otimes A ) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Revised: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of A\otimes B + B\otimes A ) for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of ( A\otimes B + B\otimes A ) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Edit intent: fluency
Original: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of ( A\otimes B + B\otimes A ) for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of ( A\otimes B + B\otimes A ) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Revised: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of ( A\otimes B + B\otimes A for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of ( A\otimes B + B\otimes A ) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Edit intent: fluency
Original: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of ( A\otimes B + B\otimes A ) for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of ( A\otimes B + B\otimes A ) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Revised: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of ( A\otimes B + B\otimes A ) for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of A\otimes B + B\otimes A ) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Edit intent: fluency
Original: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of ( A\otimes B + B\otimes A ) for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of ( A\otimes B + B\otimes A ) interlace its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Revised: Motivated by the conjectures formulated in 2003 by Tuncel et al., we study interlacing properties of the eigenvalues of ( A\otimes B + B\otimes A ) for pairs of n-by-n matrices A, B. We prove that for every pair of symmetric matrices (and skew-symmetric matrices) with one of them at most rank two, the odd spectrum (those eigenvalues determined by skew-symmetric eigenvectors) of ( A\otimes B + B\otimes A interlaces its even spectrum (those eigenvalues determined by symmetric eigenvectors).
Edit intent: fluency
Original:  Using this result, we also show that when n \leq 3, the odd spectrum of ( A\otimes B + B\otimes A ) interlace its even spectrum for every pair A, B. The interlacing results also specify the structure of the eigenvectors corresponding to the extreme eigenvalues.
Revised:  Using this result, we also show that when n \leq 3, the odd spectrum of A\otimes B + B\otimes A ) interlace its even spectrum for every pair A, B. The interlacing results also specify the structure of the eigenvectors corresponding to the extreme eigenvalues.
Edit intent: fluency
Original:  Using this result, we also show that when n \leq 3, the odd spectrum of ( A\otimes B + B\otimes A ) interlace its even spectrum for every pair A, B. The interlacing results also specify the structure of the eigenvectors corresponding to the extreme eigenvalues.
Revised:  Using this result, we also show that when n \leq 3, the odd spectrum of ( A\otimes B + B\otimes A interlaces its even spectrum for every pair A, B. The interlacing results also specify the structure of the eigenvectors corresponding to the extreme eigenvalues.
Edit intent: fluency
Original:  We settle the conjectures posed by by Tuncel et al. , and show they fail for some pairs of symmetric matrices A, B, when n\geq 4 and the ranks of A and B are at least 3.
Revised:  We settle the conjectures of Tuncel et al. , and show they fail for some pairs of symmetric matrices A, B, when n\geq 4 and the ranks of A and B are at least 3.
Edit intent: clarity
Original:  We settle the conjectures posed by by Tuncel et al. , and show they fail for some pairs of symmetric matrices A, B, when n\geq 4 and the ranks of A and B are at least 3.
Revised:  We settle the conjectures posed by by Tuncel et al. and show they fail for some pairs of symmetric matrices A, B, when n\geq 4 and the ranks of A and B are at least 3.
Edit intent: fluency
Original:  We have analyzed these globular proteins and have found that most of them are known to form amyloids more easily than many other globular proteins.
Revised:  We have analyzed these globular proteins and have found that many of them are known to form amyloids more easily than many other globular proteins.
Edit intent: clarity
Original:  Yet the complexity of these neural networks needs to be trimmed down both withinmodel and cross-model to fit in mobile storage and memory.
Revised:  Yet the complexity of these neural networks needs to be trimmed down both within-model and cross-model to fit in mobile storage and memory.
Edit intent: fluency
Original:  The number of iterations to retrain the combined network is at least 17.8 x lower than that of training a single VGG-16 network  .
Revised:  The number of iterations to retrain the combined network is at least 17.8 times lower than that of training a single VGG-16 network .
Edit intent: clarity
Original: Many real-world data sets, especially in biology, are produced by highly multivariate and nonlinear complex dynamical systems.
Revised: Many real-world data sets, especially in biology, are produced by complex nonlinear dynamical systems.
Edit intent: coherence
Original:  However, relatively little is known about how structural factors influence the spread of ideas, and specifically how where an idea originates can influence how it spreads.
Revised:  However, relatively little is known about how structural factors influence the spread of ideas, and specifically how where an idea originates might influence how it spreads.
Edit intent: clarity
Original:  Analyzing three popular research topics, we show empirically that faculty hiring plays a significant role in driving the spread of ideas across the community.
Revised:  Analyzing three popular research topics, we show empirically that faculty hiring can and does facilitate the spread of ideas across the community.
Edit intent: clarity
Original:  We then use epidemic models to simulate the generic spread of research ideas and quantify the consequences of where an idea originates on its longterm diffusion across the network.
Revised:  We then use epidemic models to simulate the generic spread of research ideas and quantify the impact of where an idea originates on its longterm diffusion across the network.
Edit intent: clarity
Original:  These results suggest a lower bound for epistemic inequality, identify a mechanism for the persistent epistemic advantage observed for elite institutions, and highlight limitations for meritocratic ideals .
Revised:  Our results establish faculty hiring as an underlying mechanism that drives the persistent epistemic advantage observed for elite institutions, and highlight limitations for meritocratic ideals .
Edit intent: clarity
Original: Few-shot learning aims to build a learner that quickly generalizes to novel classes even when a limited number of labeled examples (so-called low-data problem) are available.
Revised: The goal of few-shot learning is to learn a classifier that generalizes well even when trained with a limited number of labeled examples (so-called low-data problem) are available.
Edit intent: clarity
Original:  This framework gains a lot of attention to few-shot learning with impressive performance, though the low-data problem is not fully addressed .
Revised:  This framework gains a lot of attention to few-shot learning with impressive performance, though the low-data problem in the novel classification task still remains .
Edit intent: clarity
Original:  In this paper, we propose Transductive Propagation Network (TPN), a transductive method that classifies the entire test set at once to alleviate the low-data problem.
Revised:  In this paper, we propose Transductive Propagation Network (TPN), a novel meta-learning framework for transductive inference that classifies the entire test set at once to alleviate the low-data problem.
Edit intent: clarity
Original:  Specifically, our proposed network explicitly learns an underlying manifold space that is appropriate to propagate labels from few-shot examples, where all parameters of feature embedding , manifold structure, and label propagation are estimated in an end-to-end way on episodes.
Revised:  Specifically, we propose to learn to propagate labels from few-shot examples, where all parameters of feature embedding , manifold structure, and label propagation are estimated in an end-to-end way on episodes.
Edit intent: coherence
Original:  Specifically, our proposed network explicitly learns an underlying manifold space that is appropriate to propagate labels from few-shot examples, where all parameters of feature embedding , manifold structure, and label propagation are estimated in an end-to-end way on episodes.
Revised:  Specifically, our proposed network explicitly learns an underlying manifold space that is appropriate to propagate labels from few-shot examples, where all parameters of feature embedding and the graph construction in an end-to-end way on episodes.
Edit intent: clarity
Original:  We evaluate the proposed method on the commonly used miniImageNet and tieredImageNet benchmarks and achieve the state-of-the-art or promising resultson these datasets .
Revised:  We evaluate the proposed method on the commonly used miniImageNet and tieredImageNet benchmarks and achieve the state-of-the-art results .
Edit intent: clarity
Original:  However, two major limitations exist in state-of-the-art NE methods: structure preservation and uncertainty modeling.
Revised:  However, two major limitations exist in state-of-the-art NE methods: role preservation and uncertainty modeling.
Edit intent: clarity
Original:  Almost all previous methods represent a node into a point in space and focus on the local structural information, i.e., neighborhood information.
Revised:  Almost all previous methods represent a node into a point in space and focus on local structural information, i.e., neighborhood information.
Edit intent: fluency
Original:  However, neighborhood information does not capture the global structural information and point vector representation fails in modeling the uncertainty of node representations.
Revised:  However, neighborhood information does not capture global structural information and point vector representation fails in modeling the uncertainty of node representations.
Edit intent: coherence
Original:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering  task and provides more information on uncertainties of node representations.
Revised:  Experiments conducted on real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering task and provides more information on uncertainties of node representations.
Edit intent: clarity
Original:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering  task and provides more information on uncertainties of node representations.
Revised:  Experiments conducted on both synthetic and real-world networks demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering task and provides more information on uncertainties of node representations.
Edit intent: clarity
Original:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering  task and provides more information on uncertainties of node representations.
Revised:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering task and provides more information on uncertainties of node representations.
Edit intent: fluency
Original:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering  task and provides more information on uncertainties of node representations.
Revised:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fail to, outperforms other methods on the structure-based clustering task and provides more information on uncertainties of node representations.
Edit intent: fluency
Original:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering  task and provides more information on uncertainties of node representations.
Revised:  Experiments conducted on both synthetic and real-world data sets demonstrate that struc2gauss effectively captures the global structural information while state-of-the-art network embedding methods fails to, outperforms other methods on the structure-based clustering and classification task and provides more information on uncertainties of node representations.
Edit intent: clarity
Original: Representation learning of networks via embeddings has garnered popularity and has witnessed significant progress recently .
Revised: Representation learning of networks has witnessed significant progress recently .
Edit intent: clarity
Original: Representation learning of networks via embeddings has garnered popularity and has witnessed significant progress recently .
Revised: Representation learning of networks via embeddings has garnered popularity and has witnessed significant progress in recent times .
Edit intent: clarity
Original:  Such representations have been effectively used for classic network-based machine learning tasks like  link prediction, community detection, and network alignment.
Revised:  Such representations have been effectively used for classic network-based machine learning tasks like link prediction, and network alignment.
Edit intent: clarity
Original:  We present a modification of this method that uses a slope limiter to retain admissible solutions of the system, while providing high-order approximations in the physical and stochastic space.
Revised:  We apply a modification of this method that uses a slope limiter to retain admissible solutions of the system, while providing high-order approximations in the physical and stochastic space.
Edit intent: coherence
Original:  This is done using  spatial discontinuous Galerkin  and a Multi-Element stochastic Galerkin ansatz in the random space.
Revised:  This is done using a spatial discontinuous Galerkin and a Multi-Element stochastic Galerkin ansatz in the random space.
Edit intent: fluency
Original:  This is done using  spatial discontinuous Galerkin  and a Multi-Element stochastic Galerkin ansatz in the random space.
Revised:  This is done using spatial discontinuous Galerkin scheme and a Multi-Element stochastic Galerkin ansatz in the random space.
Edit intent: clarity
Original:  We analyze the convergence of the resulting scheme and apply it to the compressible Euler equations with different uncertain initial states .
Revised:  We analyze the convergence of the resulting scheme and apply it to the compressible Euler equations with various uncertain initial states .
Edit intent: fluency
Original:  The numerical results underline the strength of our method  if discontinuities are present in the uncertainty of the solution.
Revised:  The numerical results underline the strength of our method , especially if discontinuities are present in the uncertainty of the solution.
Edit intent: coherence
Original:  The embedded inference is fast and accurate while enforcing privacy by design, as no personal user data is ever ~ collected.
Revised:  The embedded inference is fast and accurate while enforcing privacy by design, as no personal user data is ever collected.
Edit intent: fluency
Original:  Here, we analyse the efficiency of a micro-macro acceleration method that couples short bursts of stochastic path simulation with extrapolation of spatial averages forward in time.
Revised:  This paper looks at the efficiency of a micro-macro acceleration method that couples short bursts of stochastic path simulation with extrapolation of spatial averages forward in time.
Edit intent: clarity
Original:  We make derivations and perform numerical experiments in the Gaussian setting, where only the evolution of mean and variance matters , and additionally analyse the asymptotics of non-Gaussian laws to indicate the scope of the method .
Revised:  We make derivations and perform numerical experiments in the Gaussian setting, where only the evolution of mean and variance matters .
Edit intent: clarity
Original: Computational multi-scale methods capitalize on large separation between different time scales in a model to efficiently simulate its slow dynamics over long time intervals.
Revised: Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate its slow dynamics over long time intervals.
Edit intent: clarity
Original: Computational multi-scale methods capitalize on large separation between different time scales in a model to efficiently simulate its slow dynamics over long time intervals.
Revised: Computational multi-scale methods capitalize on large separation between different time scales in a model to efficiently simulate slow dynamics over long time intervals.
Edit intent: clarity
Original:  For stochastic systems, the focus lies often on the statistics of the slowest dynamics and most methods rely on an approximate closed model for slow scale or a coupling strategy that alternates between the scales .
Revised:  For stochastic systems, one often aims at resolving the statistics of the slowest dynamics and most methods rely on an approximate closed model for slow scale or a coupling strategy that alternates between the scales .
Edit intent: clarity
Original:  For stochastic systems, the focus lies often on the statistics of the slowest dynamics and most methods rely on an approximate closed model for slow scale or a coupling strategy that alternates between the scales .
Revised:  For stochastic systems, the focus lies often on the statistics of the slowest dynamics .
Edit intent: coherence
Original:  To have explicit derivations, we first elicit an amenable linear model that can accommodate multiple time scales.
Revised:  To have explicit derivations, we elicit an amenable linear model that can accommodate multiple time scales.
Edit intent: coherence
Original:  To have explicit derivations, we first elicit an amenable linear model that can accommodate multiple time scales.
Revised:  To have explicit derivations, we first elicit an amenable linear test equation containing multiple time scales.
Edit intent: clarity