wanyu/IteraTeR_v2 huggingface dataset:
Original:  The practical success has elicited the theoretical analysis of the function rank in this paper, which is an upper bound of the matrix rank.
Revised:  Their practical success motivates our analysis of the function rank in this paper, which is an upper bound of the matrix rank.
Edit intent: clarity
Original:  The practical success has elicited the theoretical analysis of the function rank in this paper, which is an upper bound of the matrix rank.
Revised:  The practical success has elicited the theoretical analysis of the function rank , an upper bound of the matrix rank.
Edit intent: coherence
Original:  We consider radial basis functions (RBF) in particular, and approximate the RBF kernel with a low-rank representation that is a finite sum of separate products , and provide explicit upper bounds on the function rank and the L_\infty error for such approximation .
Revised:  We consider radial basis functions (RBF) , approximate the RBF kernel with a low-rank representation that is a finite sum of separate products , and provide explicit upper bounds on the function rank and the L_\infty error for such approximation .
Edit intent: coherence
Original:  We consider radial basis functions (RBF) in particular, and approximate the RBF kernel with a low-rank representation that is a finite sum of separate products , and provide explicit upper bounds on the function rank and the L_\infty error for such approximation .
Revised:  We consider radial basis functions (RBF) in particular, and approximate the RBF kernel with a low-rank representation that is a finite sum of separate products and provide explicit upper bounds on the function rank and the L_\infty error for such approximation .
Edit intent: fluency
Original:  We consider radial basis functions (RBF) in particular, and approximate the RBF kernel with a low-rank representation that is a finite sum of separate products , and provide explicit upper bounds on the function rank and the L_\infty error for such approximation .
Revised:  We consider radial basis functions (RBF) in particular, and approximate the RBF kernel with a low-rank representation that is a finite sum of separate products , and provide explicit upper bounds on the function rank and the L_\infty error for such approximations .
Edit intent: clarity
Original:  And last , a group pattern in the magnitude of singular values for RBF kernel matrices is observed and analyzed, and is explained by a grouping of the expansion terms in the kernel's low-rank representation.
Revised:  Finally , a group pattern in the magnitude of singular values for RBF kernel matrices is observed and analyzed, and is explained by a grouping of the expansion terms in the kernel's low-rank representation.
Edit intent: coherence
Original:  We fully characterize these variants of TRVB as polynomially solvable or NP-complete.
Edit intent: coherence
Original: Traditional methods for image compressive sensing (CS) reconstruction solve a well-defined inverse problem that is based on a predefined CS model, which defines the underlying structure of the problem and is generally solved by employing convergent iterative solvers.
Revised: With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction solve a well-defined inverse problem that is based on a predefined CS model, which defines the underlying structure of the problem and is generally solved by employing convergent iterative solvers.
Edit intent: clarity
Original:  We propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general l _1 norm CS reconstruction model.
Revised:  Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general l _1 norm CS reconstruction model.
Edit intent: coherence
Original:  We propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general l _1 norm CS reconstruction model.
Revised:  We propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general \ell _1 norm CS reconstruction model.
Edit intent: fluency
Original:   ISTA-Net essentially implements a truncated form of ISTA , where all ISTA-Net parameters\eg  are learned end-to-end to minimize a reconstruction error in training.
Revised:  ISTA-Net (\eg are learned end-to-end to minimize a reconstruction error in training.
Edit intent: clarity
Original:  Interestingly, this acceleration naturally leads to skip connections in the underlying network design } . Extensive CS experiments demonstrate that the proposed ISTA-Net and FISTA-Net outperform existing optimization-based and network-based CS methods by large margins, while maintaining a fast runtime.
Revised:  Interestingly, this acceleration naturally leads to skip connections in the underlying network design ISTA-Net} . Extensive CS experiments demonstrate that the proposed ISTA-Net and FISTA-Net outperform existing optimization-based and network-based CS methods by large margins, while maintaining a fast runtime.
Edit intent: fluency
Original:  Interestingly, this acceleration naturally leads to skip connections in the underlying network design } . Extensive CS experiments demonstrate that the proposed ISTA-Net and FISTA-Net outperform existing optimization-based and network-based CS methods by large margins, while maintaining a fast runtime.
Revised:  Interestingly, this acceleration naturally leads to skip connections in the underlying network design } . Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining a fast runtime.
Edit intent: clarity
Original:  However, apart from the fact that Connected Vertex Cover is NP-complete for line graphs (and thus for claw-free graphs) not much is known when the input is restricted to H-free graphs  .
Revised:  However, apart from the fact that Connected Vertex Cover is NP-complete even for H-free graphs .
Edit intent: clarity
Original: Counting the number of interior disjoint empty convex polygons in a point set is a typical Erdos-Szekeres-type problem.
Revised: Counting interior-disjoint empty convex polygons in a point set is a typical Erdos-Szekeres-type problem.
Edit intent: clarity
Original:  A subset Q of P  with four points  is called a 4-hole in P if the convex hull of Q is a quadrilateral and does not contain any point of P in its interior.
Revised:  A subset Q of P , with four points is called a 4-hole in P if the convex hull of Q is a quadrilateral and does not contain any point of P in its interior.
Edit intent: fluency
Original:  A subset Q of P  with four points  is called a 4-hole in P if the convex hull of Q is a quadrilateral and does not contain any point of P in its interior.
Revised:  A subset Q of P with four points , is called a 4-hole in P if the convex hull of Q is a quadrilateral and does not contain any point of P in its interior.
Edit intent: fluency
Original:  The original model was simplified due to the experimental constraint .
Revised:  The original model was simplified due to experimental constraints .
Edit intent: fluency
Original:  Here we calibrated the simplified model with experimental data using  multiple objective genetic algorithm.
Revised:  Here we calibrated the simplified model with experimental data using a multiple objective genetic algorithm.
Edit intent: fluency
Original:  As a corollary of this fact, we obtain a relatively short proof of a major conjecture of Goldstein and Reingold (1995), which was recently proved through other means (Kinnersley, 2015)  .
Revised:  As a corollary of this fact, we obtain a relatively short proof of a major conjecture of Goldstein and Reingold (1995), which was recently proved through other means by the author ( 2015) .
Edit intent: clarity
Original:  The species that inhabit the patches interact with each other through a  network of feeding interactions , a foodweb.
Revised:  The species that inhabit the patches interact with each other through a foodweb, the network of feeding interactions , a foodweb.
Edit intent: fluency
Original:  Previous work on meta-food-webs has focussed on landscape networks that do not have an explicit spatial embedding, but in real landscapes the patches are usually distributed in space.
Revised:  Previous work on meta-foodwebs has focussed on landscape networks that do not have an explicit spatial embedding, but in real landscapes the patches are usually distributed in space.
Edit intent: fluency
Original:  Here we compare the dispersal of a meta-food-web on \ER networks, that do not have a spatial embedding, and random geometric networks, that do have a spatial embedding.
Revised:  Here we compare the dispersal of a meta-foodweb on \ER networks, that do not have a spatial embedding, and random geometric networks, that do have a spatial embedding.
Edit intent: fluency
Original:  In particular  we found that spatial separations makes coexistence of competing species more likely.
Revised:  In particular , we found that spatial separations makes coexistence of competing species more likely.
Edit intent: fluency
Original:  In particular  we found that spatial separations makes coexistence of competing species more likely.
Revised:  In particular we found that spatial separations make the coexistence of competing species more likely.
Edit intent: fluency
Original:  Our results highlight the effects of spatial embeddings for meta-food-web models, and the need for new analytical approaches to them.
Revised:  Our results highlight the effects of spatial embeddings for meta-foodweb models, and the need for new analytical approaches to them.
Edit intent: fluency
Original: This paper presents a margin-based multiclass generalization bound for neural networks which scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight matrices, times a certain correction factor.
Revised: This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight matrices, times a certain correction factor.
Edit intent: fluency
Original:  We present an online software that allows fast and visual simulation of several types  hedonic games. 
Revised:  We present an online software that allows fast and visual simulation of several types of hedonic games. 
Edit intent: fluency
Original:  We present an online software that allows fast and visual simulation of several types  hedonic games. 
Revised:  We present an online software that allows fast and visual simulation of several types hedonic games. URL
Edit intent: coherence
Original:  We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [ 5, 13  ] in the so-called G-framework.
Revised:  We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [ 13 ] in the so-called G-framework.
Edit intent: coherence
Original:  We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [ 5, 13  ] in the so-called G-framework.
Revised:  We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [ 5, 13 ] in the so--called G-framework.
Edit intent: fluency
Original: This paper studies the assortment optimization problem under the General Luce Model (GLM ), a discrete choice  introduced by Echenique and Saito ( 2015 ) that generalizes the standard multinomial logit model (MNL).
Revised: This paper studies the assortment optimization problem under the General Luce Model (GLM ), a discrete choice model introduced by Echenique and Saito ( 2015 ) that generalizes the standard multinomial logit model (MNL).
Edit intent: fluency
Original: This paper studies the assortment optimization problem under the General Luce Model (GLM ), a discrete choice  introduced by Echenique and Saito ( 2015 ) that generalizes the standard multinomial logit model (MNL).
Revised: This paper studies the assortment optimization problem under the General Luce Model (GLM ), a discrete choice introduced by Echenique and Saito ( 2015 ) that generalizes the multinomial logit model (MNL).
Edit intent: clarity
Original:  Given a proposed assortment S, consumers first discard all dominated products in S before using a MNL model on the remaining products .
Revised:  When consumers are offered an assortmentS , they first discard all dominated products in S before using a MNL model on the remaining products .
Edit intent: clarity
Original:  Given a proposed assortment S, consumers first discard all dominated products in S before using a MNL model on the remaining products .
Revised:  Given a proposed assortment S, consumers first discard all dominated products in S and then select one of the remaining products .
Edit intent: clarity
Original:  The General Luce Model may violate the traditional regularity condition, which states that the probability of choosing a product cannot increase if the offer set is enlarged.
Revised:  The General Luce Model may violate the regularity condition, which states that the probability of choosing a product cannot increase if the offer set is enlarged.
Edit intent: clarity
Original:  As a result, the model can model behaviour that cannot be captured by any discrete choice model based on random utilities.
Revised:  Therefore, the 2SLM falls outside the large family of discrete choice models based on random utilities.
Edit intent: clarity
Original:  Moreover, it proves that the capacitated assortment optimization problem under the General Luce Model (GLM) is NP-hard and presents polynomial-time algorithms for the  cases where (1) the dominance relation is utility-correlated and (2) its transitive reduction  is a forest.
Revised:  Moreover, we show that the capacitated assortment optimization problem under the General Luce Model (GLM) is NP-hard and presents polynomial-time algorithms for the cases where (1) the dominance relation is utility-correlated and (2) its transitive reduction is a forest.
Edit intent: coherence
Original:  Moreover, it proves that the capacitated assortment optimization problem under the General Luce Model (GLM) is NP-hard and presents polynomial-time algorithms for the  cases where (1) the dominance relation is utility-correlated and (2) its transitive reduction  is a forest.
Revised:  Moreover, it proves that the capacitated assortment optimization problem is NP-hard and presents polynomial-time algorithms for the cases where (1) the dominance relation is utility-correlated and (2) its transitive reduction is a forest.
Edit intent: clarity
Original:  We specifically present a tight lower-bound on the decay rate of the number of nodes infected by a susceptible-infected-susceptible (SIS) stochastic spreading process.
Revised:  We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible-infected-susceptible (SIS) stochastic spreading process.
Edit intent: clarity
Original:  However, existing lower-bounds on the decay rate based on first-order mean field approximations are often accompanied by a large error resulting in inefficient containment strategies.
Revised:  However, existing lower-bounds on the decay rate based on first-order mean-field approximations are often accompanied by a large error resulting in inefficient containment strategies.
Edit intent: fluency
Original:  To overcome this deficiency, we derive a novel and tight lower-bound based on a second-order moment-closure of the stochastic SIS processes.
Revised:  To overcome this deficiency, we derive a lower-bound based on a second-order moment-closure of the stochastic SIS processes.
Edit intent: clarity
Original:  Despite their importance, functional responses are generally considered with a phenomenological approach, without clear mechanistic justifications from individual traits and behaviours .
Revised:  Despite their importance, functional responses are generally considered with a phenomenological approach, without clear mechanistic justifications from individual traits and behaviors .
Edit intent: fluency
Original:  Here, we develop a bottom-up stochastic framework grounded in the renewal theory showing how functional responses emerge from the level of the individuals through the decomposition of interactions into different activities.
Revised:  Here, we develop a bottom-up stochastic framework grounded in Renewal Theory showing how functional responses emerge from the level of the individuals through the decomposition of interactions into different activities.
Edit intent: fluency
Original:  First, we show how the mean and variance of classical functional responses are obtained with explicit ecological assumptions, for instance regarding foraging behaviours . Second, we give examples in specific ecological contexts, such as in nuptial-feeding species or size dependent handling times.
Revised:  First, we show how the mean and variance of classical functional responses are obtained with explicit ecological assumptions, for instance regarding foraging behaviors . Second, we give examples in specific ecological contexts, such as in nuptial-feeding species or size dependent handling times.
Edit intent: fluency
Original:  Finally, we demonstrate how to analyse data with our framework, especially highlighting that observed variability in the number of interactions can be used to infer parameters and compare functional response models.
Revised:  Finally, we demonstrate how to analyze data with our framework, especially highlighting that observed variability in the number of interactions can be used to infer parameters and compare functional response models.
Edit intent: fluency
Original: Characterization of host responses associated with severe malaria through an integrative approach is necessary to understand how Plasmodium cynolmogi infectionis controlled  .
Revised: Characterization of host responses associated with severe malaria through an integrative approach is necessary to understand the dynamics of a .
Edit intent: clarity
Original:  In this study, we conducted temporal immune profiling, cytokine profiling and transcriptomic analysis of five Macaca mulatta infected with P. cynomolgi.
Revised:  In this study, we conducted temporal immune profiling, cytokine profiling and transcriptomic analysis of five Macaca mulatta
Edit intent: clarity
Original:   This experiment resulted in one death, two severe infections, and two mild infections.
Revised:  infected with This experiment resulted in one death, two severe infections, and two mild infections.
Edit intent: clarity
Original:   This experiment resulted in one death, two severe infections, and two mild infections.
Revised:  . This experiment resulted in one death, two severe infections, and two mild infections.
Edit intent: fluency
Original:   This experiment resulted in one death, two severe infections, and two mild infections.
Revised:  This experiment resulted in two severe infections, and two mild infections.
Edit intent: clarity
Original:  The combined data provide a molecular and cellular basis for the development of severe malaria during P. cynolmogi infection.
Revised:  The combined data provide a molecular and cellular basis for the development of severe malaria during P. cynomolgi infection.
Edit intent: fluency
Original:  As the number of weakened people increases, they eventually can become infected in a rapid cascading process and a pandemic outbreak occurs.
Revised:  As the number of weakened people increases, they eventually can become infected in a short time period and a pandemic outbreak occurs.
Edit intent: clarity
Original:   Here we find that there exist two types of golden times in the two-step contagion model, which scale as O(N^{1/3}) and O(N^{ 1/4 }) with the system size N on Erd\"os-R\'enyi networks.s-R\'enyi networks, where the measured \zeta is slightly larger than 1/4. } They are distinguished by the initial number of infected nodes, o(N) and O(N), respectively.
Revised:  Here we find that there exist two types of golden times in the two-step contagion model, which scale as O(N^{1/3}) and O(N^{ \zeta }) with the system size N on Erd\"os-R\'enyi networks.s-R\'enyi networks, where the measured \zeta is slightly larger than 1/4. } They are distinguished by the initial number of infected nodes, o(N) and O(N), respectively.
Edit intent: fluency
Original:   Here we find that there exist two types of golden times in the two-step contagion model, which scale as O(N^{1/3}) and O(N^{ 1/4 }) with the system size N on Erd\"os-R\'enyi networks.s-R\'enyi networks, where the measured \zeta is slightly larger than 1/4. } They are distinguished by the initial number of infected nodes, o(N) and O(N), respectively.
Revised:  Here we find that there exist two types of golden times in the two-step contagion model, which scale as O(N^{1/3}) and O(N^{ 1/4 }) with the system size N on Erd\H{os-R\'enyi networks, where the measured \zeta is slightly larger than 1/4. } They are distinguished by the initial number of infected nodes, o(N) and O(N), respectively.
Edit intent: clarity
Original:  To this end, each sender constantly measures the bottleneck bandwidth and round-trip propagation time of the network pipe, and uses the  results to govern its behavior .
Revised:  To this end, each sender constantly measures the bottleneck bandwidth and round-trip delay of the network pipe, and uses the results to govern its behavior .
Edit intent: clarity
Original:  To this end, each sender constantly measures the bottleneck bandwidth and round-trip propagation time of the network pipe, and uses the  results to govern its behavior .
Revised:  To this end, each sender constantly measures the bottleneck bandwidth and round-trip propagation time of the network pipe, and uses the measured results to govern its behavior .
Edit intent: clarity
Original:  However, our deployment in geo-distributed cloud servers reveals an unexpected RTT fairness problem: unlike conventional loss-based congestion control, BBR has an opposite bias towards long RTT flows.
Revised:  However, our deployment in geo-distributed cloud servers reveals a severe RTT fairness problem: unlike conventional loss-based congestion control, BBR has an opposite bias towards long RTT flows.
Edit intent: clarity
Original:  Based on this observation, we design a simple, yet effective algorithm, BBQ, with better RTT fairness while retaining BBR 's promising performance advantages .
Revised:  Based on this observation, we design a derivative of BBR that achieves guaranteed flow fairness, at the meantime without losing any merits .
Edit intent: clarity
Original:  Moreover, SCSG is never worse than the state of the art methods based on variance reduction and it significantly outperforms them when the target accuracy is low.
Revised:  Moreover, SCSG is never worse than the state-of-the-art methods based on variance reduction and it significantly outperforms them when the target accuracy is low.
Edit intent: fluency
Original: Identifying the factors which influence academic performance is an essential part of educational research.
Revised: Identifying the factors that influence academic performance is an essential part of educational research.
Edit intent: fluency
Original:  However, because most of these analyses were based on a single behavioral aspect and/or small sample sizes, we lack a quantification of the interplay of these factors.
Revised:  Because most of these analyses were based on a single behavioral aspect and/or small sample sizes, we lack a quantification of the interplay of these factors.
Edit intent: coherence