wanyu/IteraTeR_v2 huggingface dataset:
Original:  In his book `The Art of Computer Programming Vol. 4A' Knuth raised a stronger form of this conjecture (Problem 56 in  Section 2.1.3 , Chapter 7 ), which requires that the sequence of positions with which the first bit is swapped in each step of such an ordering has 2n+1 blocks of the same length, and each block is obtained by adding s=1 (modulo 2n+1) to the previous block.
Revised:  In his book `The Art of Computer Programming Vol. 4A' Knuth raised a stronger form of this conjecture (Problem 56 in Section 2.1.3 ), which requires that the sequence of positions with which the first bit is swapped in each step of such an ordering has 2n+1 blocks of the same length, and each block is obtained by adding s=1 (modulo 2n+1) to the previous block.
Edit intent: clarity
Original:  Finally, we demonstrate that CIR data-structures can identify Generative Adversarial Network (GAN) ``blind spots'' : areas where GANs fail to properly model the true data distribution.
Revised:  Finally, we demonstrate that CIR data-structures can identify Generative Adversarial Network (GAN) "blind spots" : areas where GANs fail to properly model the true data distribution.
Edit intent: fluency
Original:  Finally, we demonstrate that  CIR data-structures can identify Generative Adversarial Network (GAN) "blind spots" : areas where GANs fail to properly model the true data distribution.
Revised:  Finally, we demonstrate that our CIR data-structures can identify Generative Adversarial Network (GAN) "blind spots" : areas where GANs fail to properly model the true data distribution.
Edit intent: fluency
Original:  Finally, we demonstrate that  CIR data-structures can identify Generative Adversarial Network (GAN) "blind spots" : areas where GANs fail to properly model the true data distribution.
Revised:  Finally, we demonstrate that CIR data-structures can identify "blind spots" : areas where GANs fail to properly model the true data distribution.
Edit intent: clarity
Original:  Finally, we demonstrate that  CIR data-structures can identify Generative Adversarial Network (GAN) "blind spots" : areas where GANs fail to properly model the true data distribution.
Revised:  Finally, we demonstrate that CIR data-structures can identify Generative Adversarial Network (GAN) "blind spots" in Generative Adversarial Networks (GAN) where they fail to properly model the true data distribution.
Edit intent: clarity
Original:  Previous approaches are mostly based on a two-step procedure: first learn an inner-product model  and then use maximum inner product search (MIPS) algorithms to search top candidates, leading to potential loss of retrieval accuracy .
Revised:  Previous approaches are mostly based on a two-step procedure: first learn an inner-product model , and then use maximum inner product search (MIPS) algorithms to search top candidates, leading to potential loss of retrieval accuracy .
Edit intent: fluency
Original:  Those latent codes for the candidates are model parameters and to be learnt together with other neural network parameters to maximize the same objective function.
Revised:  Those latent codes for the candidates are model parameters and learnt together with other neural network parameters to maximize the same objective function.
Edit intent: coherence
Original:  With the model learnt, a beam search over the latent codes is performed to retrieve the top candidates  . Empirically, we showed that DR, with sub-linear computational complexity, can achieve almost the same accuracy as the brute-force baseline  .
Revised:  With the model learnt, a beam search over the structure is performed to retrieve the top candidates . Empirically, we showed that DR, with sub-linear computational complexity, can achieve almost the same accuracy as the brute-force baseline .
Edit intent: clarity
Original:  With the model learnt, a beam search over the latent codes is performed to retrieve the top candidates  . Empirically, we showed that DR, with sub-linear computational complexity, can achieve almost the same accuracy as the brute-force baseline  .
Revised:  With the model learnt, a beam search over the latent codes is performed to retrieve the top candidates . Empirically, we first demonstrate that DR, with sub-linear computational complexity, can achieve almost the same accuracy as the brute-force baseline .
Edit intent: clarity
Original:  of a minimum link visibility path (tour) is Opt for a simple polygon P with n vertices, we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1))Opt (or (\gamma+a_l/k)Opt), where k is a parameter dependent on P, a_l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the geometric traveling salesman problem (path or tour version).
Revised:  of a minimum link visibility path (tour) is Opt for a simple polygon P with n vertices, we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1))Opt (or (\gamma+a_l/k)Opt), where k is a parameter dependent on P, a_l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the graphic traveling salesman problem (path or tour version).
Edit intent: clarity
Original:  We present a complete characterization of uniallpass FDNs, i.e., FDNs, which are allpass for an arbitrary choice of delays.
Revised:  We present a characterization of uniallpass FDNs, i.e., FDNs, which are allpass for an arbitrary choice of delays.
Edit intent: clarity
Original: Mathematical disease modeling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population.
Revised: Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population.
Edit intent: fluency
Original:  This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modeling community to focus on the complexity of other factors such as population structure and interventions.
Revised:  This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions.
Edit intent: fluency
Original:  More generally, our model illustrates the richness of behaviors that are possible even in well-mixed host populations once we consider strain diversity and go beyond the "one disease equals one pathogen" paradigm.
Revised:  More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the "one disease equals one pathogen" paradigm.
Edit intent: fluency
Original:  However, the mechanisms are unknown for many of these mechanisms .
Revised:  However, the mechanisms are unknown for many of these motifs .
Edit intent: clarity
Original: The study of motifs in networks can help researchers uncover links between  structure and function of networks in biology, the sociology, economics, and many other areas.
Revised: The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, the sociology, economics, and many other areas.
Edit intent: fluency
Original: The study of motifs in networks can help researchers uncover links between  structure and function of networks in biology, the sociology, economics, and many other areas.
Revised: The study of motifs in networks can help researchers uncover links between structure and function of networks in biology, sociology, economics, and many other areas.
Edit intent: fluency
Original:  However, the mechanisms are unknown for many of these motifs.
Revised:  However, these mechanisms are unknown for many of these motifs.
Edit intent: fluency
Original: We study the domain reduction problem of eliminating dependence on n from the complexity of property testing and learning algorithms on domain n%DIFDELCMD < ]%%% ^d, and the related problem of establishing testing and learning results for product distributions over R^d.
Revised: We study the domain reduction problem of eliminating dependence on n from the complexity of property testing and learning n%DIFDELCMD < ]%%% ^d, and the related problem of establishing testing and learning results for product distributions over R^d.
Edit intent: clarity
Original: We study the domain reduction problem of eliminating dependence on n from the complexity of property testing and learning algorithms on domain n%DIFDELCMD < ]%%% ^d, and the related problem of establishing testing and learning results for product distributions over R^d.
Revised: We study the domain reduction problem of eliminating dependence on n from the complexity of property testing and learning algorithms on domain %DIFDELCMD < ]%%% ^d, and the related problem of establishing testing and learning results for product distributions over R^d.
Edit intent: fluency
Original:  Our method, which we call downsampling, gives conceptually simple proofs for several results : 1. A 1-page proof of the recent o(d)-query monotonicity tester for the hypergrid ( ]\to  Black, Chakrabarty  & Seshadhri, SODA 2020 ), and an improvement from O(d^7) to \widetilde O(d ^4)in the sample complexity of their distribution-free monotonicity tester for product distributions over R^d;
Revised:  Our method, which we call downsampling, gives conceptually simple proofs for several results : 1. A 1-page proof of the recent o(d)-query monotonicity tester for the hypergrid ( n]\to Black, Chakrabarty & Seshadhri, SODA 2020 ), and an improvement from O(d^7) to \widetilde O(d ^4)in the sample complexity of their distribution-free monotonicity tester for product distributions over R^d;
Edit intent: clarity
Original:  Our method, which we call downsampling, gives conceptually simple proofs for several results : 1. A 1-page proof of the recent o(d)-query monotonicity tester for the hypergrid ( ]\to  Black, Chakrabarty  & Seshadhri, SODA 2020 ), and an improvement from O(d^7) to \widetilde O(d ^4)in the sample complexity of their distribution-free monotonicity tester for product distributions over R^d;
Revised:  Our method, which we call downsampling, gives conceptually simple proofs for several results : 1. A 1-page proof of the recent o(d)-query monotonicity tester for the hypergrid ( ]^d\to Black, Chakrabarty & Seshadhri, SODA 2020 ), and an improvement from O(d^7) to \widetilde O(d ^4)in the sample complexity of their distribution-free monotonicity tester for product distributions over R^d;
Edit intent: fluency
Original:  Our method, which we call downsampling, gives conceptually simple proofs for several results : 1. A 1-page proof of the recent o(d)-query monotonicity tester for the hypergrid ( ]\to  Black, Chakrabarty  & Seshadhri, SODA 2020 ), and an improvement from O(d^7) to \widetilde O(d ^4)in the sample complexity of their distribution-free monotonicity tester for product distributions over R^d;
Revised:  Our method, which we call downsampling, gives conceptually simple proofs for several results : 1. A 1-page proof of the recent o(d)-query monotonicity tester for the hypergrid ( ]\to Black, Chakrabarty , & Seshadhri, SODA 2020 ), and an improvement from O(d^7) to \widetilde O(d ^4)in the sample complexity of their distribution-free monotonicity tester for product distributions over R^d;
Edit intent: fluency
Original:  Though intuitive , easy-to-implement, and widely-used, the sample complexity of model-based MARL algorithms has not been fully investigated.
Revised:  Though intuitive and widely-used, the sample complexity of model-based MARL algorithms has not been fully investigated.
Edit intent: clarity
Original:  We also consider the original conjecture from a subtree intersection model point of view, showing that a recent result of Abuieda et al is nearly best possible.
Revised:  We also consider the original conjecture from a subtree intersection model point of view, showing that a result of Abuieda et al is nearly best possible.
Edit intent: clarity
Original:  Since it is common practice to compare network properties between patients and controls, it is crucial for inferred network models to reflect key underlying structural properties.
Revised:  Interpreting their properties requires inferred network models to reflect key underlying structural properties.
Edit intent: clarity
Original:  Mutual information , bivariate transfer entropy, and multivariate transfer entropy are respectively used for inferring functional, directed-functional, and effective networks .
Revised:  Mutual information , bivariate transfer entropy, and multivariate transfer entropy .
Edit intent: clarity
Original:   We find that multivariate transfer entropy captures key properties of all network structures for longer time series.
Revised:  We find that multivariate transfer entropy captures key properties of all networks for longer time series.
Edit intent: clarity
Original:  however, as available data increases, they are unable to control false positives (lower specificity)  .
Revised:  however, as available data increases, they are unable to control false positives (lower specificity) as available data increases .
Edit intent: fluency
Original: Membrane tubulation is an ubiquitous process that occurs  at the plasma membrane and at the intracellular organelle membranes .
Revised: Membrane tubulation is a ubiquitous process that occurs at the plasma membrane and at the intracellular organelle membranes .
Edit intent: fluency
Original: Membrane tubulation is an ubiquitous process that occurs  at the plasma membrane and at the intracellular organelle membranes .
Revised: Membrane tubulation is an ubiquitous process that occurs both at the plasma membrane and at the intracellular organelle membranes .
Edit intent: clarity
Original: Membrane tubulation is an ubiquitous process that occurs  at the plasma membrane and at the intracellular organelle membranes .
Revised: Membrane tubulation is an ubiquitous process that occurs at the plasma membrane and on the membranes of intracellular organelles .
Edit intent: clarity
Original:  These tubulation events are known to be mediated by the forces applied on the membrane by motor proteinsand due to the interactions between membrane proteins binding onto the membrane.
Revised:  These tubulation events are known to be mediated by forces applied on the membrane by motor proteinsand due to the interactions between membrane proteins binding onto the membrane.
Edit intent: fluency
Original:  These experimental observations have been amply supported by mathematical modeling of  membrane mechanics and have provided insights into the force-displacement relationships for tubulation.
Revised:  The numerous experimental observations of tube formation have been amply supported by mathematical modeling of membrane mechanics and have provided insights into the force-displacement relationships for tubulation.
Edit intent: clarity
Original:  The advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple  physics that occur simultaneously.
Revised:  The advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously.
Edit intent: clarity
Original:  Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements to enable us to expand our understanding of the tubulation processes in cells.
Revised:  Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our understanding of the tubulation processes in cells.
Edit intent: clarity
Original:  Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements to enable us to expand our understanding of the tubulation processes in cells.
Revised:  Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements to enable us to expand our mechanistic understanding of tubulation processes in cells.
Edit intent: clarity
Original:  We present numerical tests to show the properties of the algorithm.
Revised:  We present numerical tests to show the performance of the algorithm.
Edit intent: clarity
Original:  The variables are discretized as discrete differential forms fitting in a de Rham complex.
Revised:  The variables are discretized as discrete differential forms in a de Rham complex.
Edit intent: clarity
Original:  CYSEC uses assessment questions and recommendations to communicate cybersecurity knowledge to the end user SMBs and encourage self-motivated change.
Revised:  CYSEC uses assessment questions and recommendations to communicate cybersecurity knowledge to the end-user SMBs and encourage self-motivated change.
Edit intent: fluency
Original:  First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to improve its convergence.
Revised:  First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to speed up its convergence.
Edit intent: clarity
Original:  Audio declipping is the task of estimating the original audio signal  given its clipped measurements  and has attracted a lot of interest in recent years.
Revised:  The task of audio declipping is estimating the original audio signal given its clipped measurements and has attracted a lot of interest in recent years.
Edit intent: fluency
Original:  Audio declipping is the task of estimating the original audio signal  given its clipped measurements  and has attracted a lot of interest in recent years.
Revised:  Audio declipping is the task of estimating the original audio signal , given its clipped measurements and has attracted a lot of interest in recent years.
Edit intent: fluency
Original:  Audio declipping is the task of estimating the original audio signal  given its clipped measurements  and has attracted a lot of interest in recent years.
Revised:  Audio declipping is the task of estimating the original audio signal given its clipped measurements , and has attracted a lot of interest in recent years.
Edit intent: fluency
Original:  Audio declipping is the task of estimating the original audio signal  given its clipped measurements  and has attracted a lot of interest in recent years.
Revised:  Audio declipping is the task of estimating the original audio signal given its clipped measurements and has attracted much interest in recent years.
Edit intent: clarity
Original:  Audio declipping algorithms often make assumptions about the underlying signal, such as sparsity or low-rankness, as well as the measurement system.
Revised:  Audio declipping algorithms often make assumptions about the underlying signal, such as sparsity or low-rankness, and about the measurement system.
Edit intent: coherence
Original:  For each algorithm, we present the assumptions being made about the audio signal, the modeling domain, as well as the optimization algorithm.
Revised:  For each algorithm, we present assumptions that are made about the audio signal, the modeling domain, as well as the optimization algorithm.
Edit intent: fluency
Original:  For each algorithm, we present the assumptions being made about the audio signal, the modeling domain, as well as the optimization algorithm.
Revised:  For each algorithm, we present the assumptions being made about the audio signal, the modeling domain, and the optimization algorithm.
Edit intent: coherence
Original:  We evaluate each algorithm in terms of the Signal-to-Distortion Ratio, as well as using perceptual metrics of sound quality.
Revised:  We evaluate each algorithm in terms of the Signal-to-Distortion Ratio, and also using perceptual metrics of sound quality.
Edit intent: coherence
Original:  The article is accompanied with the repository containing the evaluated methods.
Revised:  The article is accompanied by a repository containing the evaluated methods.
Edit intent: fluency
Original:  Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-conserving time-discrete schemes  .
Revised:  Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-preserving time-discrete schemes .
Edit intent: fluency
Original:  The main difficulty of the challenge exists in the large degree of varying phonetic overlap between the optionally cross-lingual trials, along with the limited availability of in-domain DeepMine Farsi training data.
Revised:  The main difficulty of the challenge exists in the large degree of varying phonetic overlap between the potentially cross-lingual trials, along with the limited availability of in-domain DeepMine Farsi training data.
Edit intent: fluency
Original:  We propose a decomposition-based algorithm to deal with the computationally challenging representation of the two-stage CVaR model.
Edit intent: coherence
Original:  An independent set in a hypergraph G is a subset of vertices covering no hyperedge, and its independence number \alpha(G) is the size of its largest independent set.
Edit intent: coherence
Original:   By combining our designs with a recent explicit construction of a leakage-resilient extractor that works for low-entropy (Chattopadhyay et al., FOCS 2020), we obtain simple and significantly improved low-error explicit extractors for adversarial and small-space sources.
Revised:  2. Extractors for adversarial sources: By combining our designs with a recent explicit construction of a leakage-resilient extractor that works for low-entropy (Chattopadhyay et al., FOCS 2020), we obtain simple and significantly improved low-error explicit extractors for adversarial and small-space sources.
Edit intent: coherence
Original:   By combining our designs with a recent explicit construction of a leakage-resilient extractor that works for low-entropy (Chattopadhyay et al., FOCS 2020), we obtain simple and significantly improved low-error explicit extractors for adversarial and small-space sources.
Revised:  By combining our designs with leakage-resilient extractor that works for low-entropy (Chattopadhyay et al., FOCS 2020), we obtain simple and significantly improved low-error explicit extractors for adversarial and small-space sources.
Edit intent: clarity
Original:   By combining our designs with a recent explicit construction of a leakage-resilient extractor that works for low-entropy (Chattopadhyay et al., FOCS 2020), we obtain simple and significantly improved low-error explicit extractors for adversarial and small-space sources.
Revised:  By combining our designs with a recent explicit construction of a leakage-resilient extractors (Chattopadhyay et al., FOCS 2020), we obtain simple and significantly improved low-error explicit extractors for adversarial and small-space sources.
Edit intent: clarity
Original:  As a result, we get extractors for small-space  sources over n bits with entropy requirement k\geq n^{1/2+\delta}  , whereas the previous best result (Chattopadhyay et al., STOC 2020) required k\geq n^{2/3+\delta} .
Revised:  3. Extractors for small-space sources over n bits with entropy requirement k\geq n^{1/2+\delta} , whereas the previous best result (Chattopadhyay et al., STOC 2020) required k\geq n^{2/3+\delta} .
Edit intent: coherence