wanyu/IteraTeR_v2 huggingface dataset:
Original: We develop the theory for monotone schemes of finite difference type for general nonlinear diffusion equations, \partial_t u-L^{\sigma,\mu}[\varphi(u)]=f (x,t)%DIFDELCMD < \qquad%%% \text{in}%DIFDELCMD < \qquad %DIFDELCMD < %%% \quad\quad}\quad\quad R^N\times(0,T), where L^{\sigma,\mu} is a general symmetric diffusion operator of L\'evy type and \varphi is merely continuous and non-decreasing.
Revised: We develop the theory for monotone schemes of finite difference type for general nonlinear diffusion equations, \partial_t u-L^{\sigma,\mu}[\varphi(u)]=f %DIFDELCMD < \qquad%%% \text{in}%DIFDELCMD < \qquad %DIFDELCMD < %%% \quad\quad}\quad\quad R^N\times(0,T), where L^{\sigma,\mu} is a general symmetric diffusion operator of L\'evy type and \varphi is merely continuous and non-decreasing.
Edit intent: coherence
Original: We develop the theory for monotone schemes of finite difference type for general nonlinear diffusion equations, \partial_t u-L^{\sigma,\mu}[\varphi(u)]=f (x,t)%DIFDELCMD < \qquad%%% \text{in}%DIFDELCMD < \qquad %DIFDELCMD < %%% \quad\quad}\quad\quad R^N\times(0,T), where L^{\sigma,\mu} is a general symmetric diffusion operator of L\'evy type and \varphi is merely continuous and non-decreasing.
Revised: We develop the theory for monotone schemes of finite difference type for general nonlinear diffusion equations, \partial_t u-L^{\sigma,\mu}[\varphi(u)]=f (x,t)%DIFDELCMD < \qquad%%% }%DIFDELCMD < \qquad %DIFDELCMD < %%% \quad\quad}\quad\quad R^N\times(0,T), where L^{\sigma,\mu} is a general symmetric diffusion operator of L\'evy type and \varphi is merely continuous and non-decreasing.
Edit intent: coherence
Original: We develop the theory for monotone schemes of finite difference type for general nonlinear diffusion equations, \partial_t u-L^{\sigma,\mu}[\varphi(u)]=f (x,t)%DIFDELCMD < \qquad%%% \text{in}%DIFDELCMD < \qquad %DIFDELCMD < %%% \quad\quad}\quad\quad R^N\times(0,T), where L^{\sigma,\mu} is a general symmetric diffusion operator of L\'evy type and \varphi is merely continuous and non-decreasing.
Revised: We develop the theory for monotone schemes of finite difference type for general nonlinear diffusion equations, \partial_t u-L^{\sigma,\mu}[\varphi(u)]=f (x,t)%DIFDELCMD < \qquad%%% \text{in}%DIFDELCMD < \qquad %DIFDELCMD < %%% \quad\quad\text{in}\quad\quad R^N\times(0,T), where L^{\sigma,\mu} is a general symmetric diffusion operator of L\'evy type and \varphi is merely continuous and non-decreasing.
Edit intent: fluency
Original:  This theory covers strongly degenerate Stefan problems and the full range of porous medium and fast diffusion equations.
Revised:  This theory covers strongly degenerate Stefan problems , the full range of porous medium and fast diffusion equations.
Edit intent: fluency
Original:  Examples of diffusion operators L^{\sigma,\mu} are the Laplacian \Delta, the fractionalLaplacian -(-\Delta)^{\frac\alpha2} , \alpha\in(0,2), discrete operators, and combinations of these .
Revised:  Examples of diffusion operators L^{\sigma,\mu} are the Laplacian \Delta, the fractionalLaplacian -(-\Delta)^{\frac\alpha2} for \alpha\in(0,2), discrete operators, and combinations of these .
Edit intent: clarity
Original:  Examples of diffusion operators L^{\sigma,\mu} are the Laplacian \Delta, the fractionalLaplacian -(-\Delta)^{\frac\alpha2} , \alpha\in(0,2), discrete operators, and combinations of these .
Revised:  Examples of diffusion operators L^{\sigma,\mu} are the Laplacian \Delta, the fractionalLaplacian -(-\Delta)^{\frac\alpha2} , \alpha\in(0,2), discrete operators, and combinations .
Edit intent: clarity
Original:  The observation that finite difference type operators are nonlocal L\'evy operators, allows us to give a unified , compact, and efficient nonlocal{\em  theory for both local and nonlocal, linear and nonlinear diffusion equations.
Revised:  The observation that finite difference type operators are nonlocal L\'evy operators, allows us to give a unified and compact{\em theory for both local and nonlocal, linear and nonlinear diffusion equations.
Edit intent: clarity
Original:  The theory includes well-posedness, stability, equicontinuity, compactness, and convergence of the methods under minimal assumptions  including assumptions that lead to very irregular solutions.
Revised:  The theory includes stability, compactness, and convergence of the methods under minimal assumptions including assumptions that lead to very irregular solutions.
Edit intent: clarity
Original:  The theory includes well-posedness, stability, equicontinuity, compactness, and convergence of the methods under minimal assumptions  including assumptions that lead to very irregular solutions.
Revised:  The theory includes well-posedness, stability, equicontinuity, compactness, and convergence of the methods under minimal assumptions -- including assumptions that lead to very irregular solutions.
Edit intent: fluency
Original:  As a byproduct of our numerical analysis, we obtain a new and general existence result for the original PDE, a result that was previously announced}\hspace{0pt} } . We also present some numerical tests, but extensive numerical testing is deferred to a companion paper }\hspace{0pt} } along with a more detailed discussion of the numerical methods included in our theory.
Revised:  As a byproduct , we prove the new and general existence result for the original PDE, a result that was previously announced}\hspace{0pt} } . We also present some numerical tests, but extensive numerical testing is deferred to a companion paper }\hspace{0pt} } along with a more detailed discussion of the numerical methods included in our theory.
Edit intent: clarity
Original:  As a byproduct of our numerical analysis, we obtain a new and general existence result for the original PDE, a result that was previously announced}\hspace{0pt} } . We also present some numerical tests, but extensive numerical testing is deferred to a companion paper }\hspace{0pt} } along with a more detailed discussion of the numerical methods included in our theory.
Revised:  As a byproduct of our numerical analysis, we obtain a new and general existence result for the original PDE, a result that was previously announced}\hspace{0pt} } . We also present some numerical tests, but extensive testing is deferred to a companion paper }\hspace{0pt} } along with a more detailed discussion of the numerical methods included in our theory.
Edit intent: fluency
Original:  However, previous research has largely focused on generating SMILES strings instead of molecular graphs.
Revised:  However, previous research has focused mainly on generating SMILES strings instead of molecular graphs.
Edit intent: clarity
Original:  It is shown that the graph-based model produces a higher fraction of valid output structures compared with SMILES-based methods .
Revised:  It is shown that the graph-based model outperforms SMILES based models in a variety of metrics, especially in the rate of valid outputs .
Edit intent: clarity
Original: Given a set S of n d-dimensional points  , the k-nearest neighbors ( KNN) is the problem of quickly finding k points in Sthat are nearest to a query point q.
Revised: Given a set S of n d-dimensional points and a d-dimensional query q , the k-nearest neighbors ( KNN) is the problem of quickly finding k points in Sthat are nearest to a query point q.
Edit intent: clarity
Original: As people increasingly use social media as a source for news consumption, its unmoderated nature enables the diffusion of hoaxes, which in turn jeopardises the credibility of information gathered from social media platforms.
Revised: The unmoderated nature of social media enables the diffusion of hoaxes, which in turn jeopardises the credibility of information gathered from social media platforms.
Edit intent: clarity
Original:  We introduce a semi-automated approach that leverages the Wikidata knowledge base to build large-scale datasets for veracity classification, which enables us to create a dataset with 4,007 reports including over 13 million tweets, 15\% of which are fake.
Revised:  We introduce a semi-automated method that leverages the Wikidata knowledge base to build large-scale datasets for veracity classification, which enables us to create a dataset with 4,007 reports including over 13 million tweets, 15\% of which are fake.
Edit intent: clarity
Original:  We describe a method for learning class-specific word representations using word embeddings , which we call multiw2v.
Revised:  Experiments using class-specific word representations using word embeddings , which we call multiw2v.
Edit intent: clarity
Original:  Our approach achieves competitive results with F1 scores over 72\% within 10 minutes of the first tweet being posted , outperforming other baselines .
Revised:  Our approach achieves competitive results with F1 scores nearing 72\% within 10 minutes of the first tweet being posted , outperforming other baselines .
Edit intent: clarity
Original:  Motivated within the context of statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and interpretable way to summarize the relative importance of predictor variables.
Revised:  Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and interpretable way to summarize the relative importance of predictor variables.
Edit intent: clarity
Original:  We focus on illustrating RATE through Bayesian Gaussian process regression ;
Revised:  We illustrate RATE through Bayesian Gaussian process regression ;
Edit intent: clarity
Original:  It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for outcomes generated by complex  architectures.
Revised:  It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for phenotypes generated by complex architectures.
Edit intent: clarity
Original:  Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel , interpretable, and computationally efficient way to summarize the relative importance of predictor variables.
Revised:  Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and interpretable way to summarize the relative importance of predictor variables.
Edit intent: coherence
Original:  Also we will further develop an idea from Schneider and Borchmann 5%DIFDELCMD < ] %%% to solve the previously open question of whether the entropy function is surjective .
Revised:  Also we will further develop an idea from Schneider and Borchmann %DIFDELCMD < ] %%% to solve the previously open question of whether the entropy function is surjective .
Edit intent: fluency
Original: We for the first time combine generated adversarial network (GAN) with wide-field light microscopy to achieve deep learning super-resolution under a large field of view (FOV).
Revised: We combine generative adversarial network (GAN) with wide-field light microscopy to achieve deep learning super-resolution under a large field of view (FOV).
Edit intent: clarity
Original: We for the first time combine generated adversarial network (GAN) with wide-field light microscopy to achieve deep learning super-resolution under a large field of view (FOV).
Revised: We for the first time combine generated adversarial network (GAN) with light microscopy to achieve deep learning super-resolution under a large field of view (FOV).
Edit intent: clarity
Original:  By appropriately adopting prior microscopy data in an adversarial training, the  network can recover a high-resolution, accurate image of new specimen from its single low-resolution measurement.
Revised:  By appropriately adopting prior microscopy data in an adversarial training, the neural network can recover a high-resolution, accurate image of new specimen from its single low-resolution measurement.
Edit intent: clarity
Original:  This capacity has been adequately demonstrated by imaging various types of samples, such as USAF resolution target, human pathological slides and fluorescence-labelled fibroblast cells .
Revised:  Its capacity has been adequately demonstrated by imaging various types of samples, such as USAF resolution target, human pathological slides and fluorescence-labelled fibroblast cells .
Edit intent: fluency
Original:  This capacity has been adequately demonstrated by imaging various types of samples, such as USAF resolution target, human pathological slides and fluorescence-labelled fibroblast cells .
Revised:  This capacity has been adequately demonstrated by imaging various types of samples, such as USAF resolution target, human pathological slides , fluorescence-labelled fibroblast cells .
Edit intent: fluency
Original:  Their gigapixel, multi-color reconstructions verify a successful GAN-based single image super-resolution procedure.
Revised:  Their gigapixel, multi-color reconstruction of these samples verifies a successful GAN-based single image super-resolution procedure.
Edit intent: clarity
Original:  However, conventional half-duplex (HD) transmission may not be sufficient to provide fast enough content delivery over D2D links and to meet strict latency targets of emerging D2D applications.
Revised:  However, conventional half-duplex (HD) transmission may not be sufficient to provide fast enough content delivery over D2D links in order to meet strict latency targets of emerging D2D applications.
Edit intent: clarity
Original:  We first carefully list all possible operating modes for an arbitrary device and use it to compute the number of devices that are actively transmitting at any given time.
Revised:  We first carefully list all possible operating modes for an arbitrary device using which we compute the number of devices that are actively transmitting at any given time.
Edit intent: clarity
Original:  Our analysis concretely demonstrates that the caching dictates the system performance in lower target SIR thresholds whereas interference dictates the performance at the higher target SIR thresholds.
Revised:  Our analysis concretely demonstrates that caching dictates the system performance in lower target SIR thresholds whereas interference dictates the performance at the higher target SIR thresholds.
Edit intent: fluency
Original:  In such studies, the data typically consists of a set of graphs  representing a system's state at different points in time or space .
Revised:  In such studies, the data typically consists of a set of graphs , each representing a system's state at different points in time or space .
Edit intent: clarity
Original:  In such studies, the data typically consists of a set of graphs  representing a system's state at different points in time or space .
Revised:  In such studies, the data typically consists of a set of graphs representing a system's state at different points in time .
Edit intent: clarity
Original:  However, these distances' sensitivity to perturbations in the network 's structure and their ability to identify important changes are crucial to the analysis, making the selection of an adequate metric a decisive -- yet delicate -- practical matter.
Revised:  However, these distances' sensitivity to perturbations in the network and detect important changes in graph dynamics. Thus the selection of an adequate metric a decisive -- yet delicate -- practical matter.
Edit intent: clarity
Original:  However, these distances' sensitivity to perturbations in the network 's structure and their ability to identify important changes are crucial to the analysis, making the selection of an adequate metric a decisive -- yet delicate -- practical matter.
Revised:  However, these distances' sensitivity to perturbations in the network 's structure and their ability to identify important changes are crucial to the analysis, making the selection of an adequate metric is a decisive --yet delicate--practical matter.
Edit intent: coherence
Original:  To see how this translates in real-life situations, we use as a guiding thread to our discussion the application of these distances to the analysis  a longitudinal microbiome study -- as well as on synthetic examples.
Revised:  We use as a guiding thread to our discussion the application of these distances to the analysis a longitudinal microbiome study -- as well as on synthetic examples.
Edit intent: coherence
Original:  To see how this translates in real-life situations, we use as a guiding thread to our discussion the application of these distances to the analysis  a longitudinal microbiome study -- as well as on synthetic examples.
Revised:  To see how this translates in real-life situations, we use as a guiding thread to our discussion the application of these distances to the analysis of both a longitudinal microbiome study -- as well as on synthetic examples.
Edit intent: clarity
Original:  conventional caching algorithms may crumble in effectiveness as their complexity increases with the number of SBSs . Furthermore,
Revised:  conventional caching algorithms are inapplicable as their complexity increases with the number of SBSs . Furthermore,
Edit intent: clarity
Original:  conventional caching algorithms may crumble in effectiveness as their complexity increases with the number of SBSs . Furthermore,
Revised:  conventional caching algorithms may crumble in effectiveness as their complexity increases with the number of small base stations (SBSs) . Furthermore,
Edit intent: clarity
Original:  the performance of a UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference , due to the large number of SBSs . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that specifies the content popularity changes within long-term and short-term periods .
Revised:  the performance of UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference , due to the large number of SBSs . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that specifies the content popularity changes within long-term and short-term periods .
Edit intent: fluency
Original:  the performance of a UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference , due to the large number of SBSs . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that specifies the content popularity changes within long-term and short-term periods .
Revised:  the performance of a UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that specifies the content popularity changes within long-term and short-term periods .
Edit intent: clarity
Original:  the performance of a UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference , due to the large number of SBSs . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that specifies the content popularity changes within long-term and short-term periods .
Revised:  the performance of a UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference , due to the large number of SBSs . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that characterizes the content popularity changes within long-term and short-term periods .
Edit intent: clarity
Original:  the performance of a UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference , due to the large number of SBSs . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that specifies the content popularity changes within long-term and short-term periods .
Revised:  the performance of a UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference , due to the large number of SBSs . To overcome such difficulties, we propose a distributed caching algorithm under a stochastic geometric network model, as well as a spatio-temporal user demand model that specifies the content popularity dynamics .
Edit intent: clarity
Original:  The performance of the proposed caching algorithm can easily be calculated using stochastic geometry (SG).
Edit intent: coherence
Original:  Numerical evaluations validate that the proposed caching algorithm reduces not only the long run average cost of the network but also the replicated caching data amount respectively by 24\% and 42\%, compared to a baseline caching algorithm.
Revised:  Numerical evaluations validate that the proposed caching algorithm reduces not only the long run average cost of the network but also the redundant cached data respectively by 24\% and 42\%, compared to a baseline caching algorithm.
Edit intent: clarity
Original:  The simulation results also show that the propose caching algorithm is robust to imperfect popularity information, while ensuring the low computational complexity.
Revised:  The simulation results also show that the proposed caching algorithm is robust to imperfect popularity information, while ensuring the low computational complexity.
Edit intent: fluency
Original:  The simulation results also show that the propose caching algorithm is robust to imperfect popularity information, while ensuring the low computational complexity.
Revised:  The simulation results also show that the propose caching algorithm is robust to imperfect popularity information, while ensuring a low computational complexity.
Edit intent: clarity
Original:  To avoid this loss, guarantee a minimum quality of service (QoS) and possibly increase the QoS, we add an aerial-BS to the network.
Revised:  To avoid this loss, guarantee a minimum quality-of-service (QoS) and possibly increase the QoS, we add an aerial-BS to the network.
Edit intent: fluency
Original:  For  fair comparison between the conventional terrestrial network and the aerial BS assisted one, we keep the total number of BSs similar in both networks.
Revised:  For a fair comparison between the conventional terrestrial network and the aerial BS assisted one, we keep the total number of BSs similar in both networks.
Edit intent: fluency
Original:  For  fair comparison between the conventional terrestrial network and the aerial BS assisted one, we keep the total number of BSs similar in both networks.
Revised:  For fair comparison between the conventional terrestrial network and the aerial-BS assisted one, we keep the total number of BSs similar in both networks.
Edit intent: fluency
Original:  For  fair comparison between the conventional terrestrial network and the aerial BS assisted one, we keep the total number of BSs similar in both networks.
Revised:  For fair comparison between the conventional terrestrial network and the aerial BS assisted one, we keep the total number of BSs identical in both networks.
Edit intent: clarity
Original:  Obtaining the max performance in such networks highly depends on the optimal ultimate placement of the aerial-BS.
Revised:  Obtaining the best performance in such networks highly depends on the optimal ultimate placement of the aerial-BS.
Edit intent: clarity
Original:  Obtaining the max performance in such networks highly depends on the optimal ultimate placement of the aerial-BS.
Revised:  Obtaining the max performance in such networks highly depends on the optimal placement of the aerial-BS.
Edit intent: clarity
Original:  To this end, we need an algorithm which can rely on more general and realistic assumptions and can decide where to go based on the past experiences  .
Revised:  To this end, an algorithm which can rely on more general and realistic assumptions and can decide where to go based on the past experiences .
Edit intent: coherence