wanyu/IteraTeR_v2 huggingface dataset:
Original:  Technical difficulties hindering  generalization of CNNs  are rooted in the lack of a canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.
Revised:  Technical difficulties hindering the generalization of CNNs are rooted in the lack of a canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.
Edit intent: fluency
Original:  Technical difficulties hindering  generalization of CNNs  are rooted in the lack of a canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.
Revised:  Technical difficulties hindering generalization of CNNs are rooted in the lacks of such key elements including the canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.
Edit intent: clarity
Original:  We also prove that a rotation of a convolution kernel equates to a  2 by 2 rotation matrix applied to Zernike polynomial coefficients, which can be critical in manifold domains.
Revised:  We also prove that a rotation of a convolution kernel equates to a 2 by 2 rotation matrices applied to Zernike polynomial coefficients, which can be critical in manifold domains.
Edit intent: fluency
Original: In many fields of science and engineering , geometric features play a key role in understanding certain quantity or phenomena.
Revised: In many fields of science and engineering , geometric features play a key role in understanding scientific phenomena. Thus, an ability to codify geometric features into a mathematical quantity can be critical.
Edit intent: clarity
Original:  Recently, convolutional neural networks (CNNs) have been shown to possess a promising capability of extracting and codifying features from visual information.
Revised:  Recently, convolutional neural networks (CNNs) have demonstrated the promising capability of extracting and codifying features from visual information.
Edit intent: clarity
Original:  However, the application of such capable CNNs has been quite limited to mostly computer vision problems where the visual information is inherently given on a grid-like structure.
Revised:  However, the progress has been concentrated in computer vision applications where there exists an inherent grid-like structure.
Edit intent: clarity
Original:  This, unfortunately, was not the case for the geometry processing community, where many visual recognition problems are defined on arbitrary surfaces(2D-manifolds).
Revised:  In contrast, many geometry processing problems are defined on arbitrary surfaces(2D-manifolds).
Edit intent: clarity
Original:  We also prove that a rotation of a convolution kernel equates to a set of 2 by 2 rotation matrices applied to Zernike polynomial coefficients, which can be critical in manifold domains .
Revised:  We also prove that a rotation of a convolution kernel equates to a set of 2 by 2 rotation matrices applied to the coefficients .
Edit intent: coherence
Original:  The transfer function is obtained by performing successive numeric-computational simulations and statistical regressions.
Revised:  The transfer relationship is obtained by performing successive numeric-computational simulations and statistical regressions.
Edit intent: clarity
Original:  Several interesting results are reported, including the identification  of linearity in the transfer functions , as well as the identification of regions in the parameter space characterized by sharper transfer functions  .
Revised:  Several interesting results are reported, including the identification and characterization of linearity in the transfer functions , as well as the identification of regions in the parameter space characterized by sharper transfer functions .
Edit intent: clarity
Original:  Several interesting results are reported, including the identification  of linearity in the transfer functions , as well as the identification of regions in the parameter space characterized by sharper transfer functions  .
Revised:  Several interesting results are reported, including the identification of linearity in the transfer relationship , as well as the identification of regions in the parameter space characterized by sharper transfer functions .
Edit intent: clarity
Original: In this paper, we analyze the sum of squares hierarchy (SOS) on the total ordering principle on n elements.
Revised: In this paper, we analyze the sum of squares hierarchy (SOS) on the ordering principle on n elements.
Edit intent: clarity
Original:  We show that degree (\sqrt{n ) SOS can prove the total ordering principleso in this setting SOS is considerably more powerful than resolution, polynomial calculus, and the Sherali-Adams hierarchy.
Revised:  We (\sqrt{n ) SOS can prove the total ordering principleso in this setting SOS is considerably more powerful than resolution, polynomial calculus, and the Sherali-Adams hierarchy.
Edit intent: coherence
Original: The number of triangles (  \Delta) is an important metric to analyze massive graphs.
Revised: The number of triangles ( hereafter denoted by \Delta) is an important metric to analyze massive graphs.
Edit intent: clarity
Original:  This paper proposes a new algorithm called PES (Priority Edge Sampling) to estimate  triangles in the streaming model where we need to minimize the memory window.
Revised:  This paper proposes a new algorithm called PES (Priority Edge Sampling) to estimate the number of triangles in the streaming model where we need to minimize the memory window.
Edit intent: clarity
Original:  This is especially important in the era of big data--while we can tolerate existing algorithms for smaller datasets, our method is indispensable in very large data sampling .
Revised:  This is especially important in the era of big data--while we can tolerate existing algorithms for smaller datasets, our method is indispensable when sampling very large data sampling .
Edit intent: clarity
Original:  This is especially important in the era of big data--while we can tolerate existing algorithms for smaller datasets, our method is indispensable in very large data sampling .
Revised:  This is especially important in the era of big data--while we can tolerate existing algorithms for smaller datasets, our method is indispensable in very large data .
Edit intent: clarity
Original: Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network is currently complete.
Revised: Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network currently being complete.
Edit intent: clarity
Original: The rapid evolution of deep neural networks is demanding deep learning (DL) frameworks not only to satisfy the traditional requirement of quickly executing large computations, but also to support straightforward programming models for quickly implementing and experimenting with complex network structures.
Revised: The rapid evolution of deep neural networks is demanding deep learning (DL) frameworks not only to satisfy the requirement of quickly executing large computations, but also to support straightforward programming models for quickly implementing and experimenting with complex network structures.
Edit intent: clarity
Original: One of the major issues in the theoretical modelling of epidemic spreading is the development of methods to control the transmission of an infectious agent.
Revised: One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent.
Edit intent: fluency
Original:  Unlike previous models, the information is propagated following a generalized Maki-Thompson rumour model.
Revised:  Unlike previous models, the information is propagated following a generalized Maki-Thompson rumor model.
Edit intent: fluency
Original:  Flexibility on the time scale between information and disease spreading is also included.
Revised:  Flexibility on the timescale between information and disease spreading is also included.
Edit intent: fluency
Original:  We use this characterization to prove that for an interval hypergraph  the conflict-free colouring number is the minimum partition of its intervals into sets such that each set has an exact hitting set (a hitting set in which each interval is hit exactly once).
Revised:  We use this characterization to prove that for an interval hypergraph , the conflict-free colouring number is the minimum partition of its intervals into sets such that each set has an exact hitting set (a hitting set in which each interval is hit exactly once).
Edit intent: fluency
Original:  Part of this problem is the sequencing problem, which focuses on ordering the patients.
Revised:  One aspect of this problem is the sequencing problem, which focuses on ordering the patients.
Edit intent: clarity
Original:  While it was known that SVF is not always optimal, many papers have found that it performs well in practice and simulation.
Revised:  While it was known that SVF is not always optimal, it has been widely observed that it performs well in practice and simulation.
Edit intent: clarity
Original:  We give theoretical justification for these observations by proving quantitative worst-case bounds on the ratio between the cost incurred by the SVF rule and the minimum attainable cost , in a number of settings .
Revised:  We provide a theoretical justification for these observations by proving quantitative worst-case bounds on the ratio between the cost incurred by the SVF rule and the minimum attainable cost , in a number of settings .
Edit intent: fluency
Original:  We give theoretical justification for these observations by proving quantitative worst-case bounds on the ratio between the cost incurred by the SVF rule and the minimum attainable cost , in a number of settings .
Revised:  We give theoretical justification for this observation by proving, in various settings, quantitative worst-case bounds on the ratio between the cost incurred by the SVF rule and the minimum attainable cost , in a number of settings .
Edit intent: clarity
Original:  We give theoretical justification for these observations by proving quantitative worst-case bounds on the ratio between the cost incurred by the SVF rule and the minimum attainable cost , in a number of settings .
Revised:  We give theoretical justification for these observations by proving quantitative worst-case bounds on the ratio between the cost incurred by the SVF rule and the minimum attainable cost .
Edit intent: clarity
Original:  We also show that under quite general conditions, this ratio approaches 1 as the number of patients grows large , showing that the SVF rule is asymptotically optimal.
Revised:  We also show that , in great generality, SVF is asymptotically optimal, i.e., the ratio approaches 1 as the number of patients grows large , showing that the SVF rule is asymptotically optimal.
Edit intent: clarity
Original: Given an undirected graph G(V, E, \tau) modeling a 'social network' \textit{ , where each node v is associated with a threshold value \tau(v), a set of vertices S \subseteq V(G) (called 'seed nodes' \textit{ ) is chosen initially.
Revised: Given an undirected graph G(V, E, \tau) modeling a \textit{ , where each node v is associated with a threshold value \tau(v), a set of vertices S \subseteq V(G) (called 'seed nodes' \textit{ ) is chosen initially.
Edit intent: clarity
Original: Given an undirected graph G(V, E, \tau) modeling a 'social network' \textit{ , where each node v is associated with a threshold value \tau(v), a set of vertices S \subseteq V(G) (called 'seed nodes' \textit{ ) is chosen initially.
Revised: Given an undirected graph G(V, E, \tau) modeling a 'social network' \textit{ , where each node v is associated with a threshold value \tau(v), a set of vertices S \subseteq V(G) (called \textit{ ) is chosen initially.
Edit intent: clarity
Original:  Now a 'social contagion process' is defined on G as follows.
Revised:  Now a social contagion process is defined on G as follows.
Edit intent: fluency
Original:  An 'un-influenced' node v will change its state to 'influenced' at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Revised:  An 'un-influenced' node v will change its state to influenced at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Edit intent: fluency
Original:  Based on this diffusion process, a well-studied problem in the literature is the 'Target Set Selection Problem (TSS Problem)' \textit{ , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Revised:  Based on this diffusion process, a well\mbox{- problem in the literature is the 'Target Set Selection Problem (TSS Problem)' \textit{ , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Edit intent: clarity
Original:  Based on this diffusion process, a well-studied problem in the literature is the 'Target Set Selection Problem (TSS Problem)' \textit{ , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Revised:  Based on this diffusion process, a well-studied problem in the literature is the \textit{ , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Edit intent: coherence
Original:  Based on this diffusion process, a well-studied problem in the literature is the 'Target Set Selection Problem (TSS Problem)' \textit{ , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Revised:  Based on this diffusion process, a well-studied problem in the literature is the 'Target Set Selection Problem (TSS Problem)' \textit{Target Set Selection Problem (TSS Problem) , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Edit intent: fluency
Original: Given an undirected graph \mathcal{G(V, E, \tau) modeling a }\textit{social network , where each node v is associated with a threshold value \tau(v) , a set of vertices S  \subseteq V( \mathcal{G)(called }\textit{seed nodes ) is chosen initially.
Revised: Given an undirected graph (V, E, \tau) modeling a }\textit{social network , where each node v is associated with a threshold value \tau(v) , a set of vertices S \subseteq V( \mathcal{G)(called }\textit{seed nodes ) is chosen initially.
Edit intent: fluency
Original: Given an undirected graph \mathcal{G(V, E, \tau) modeling a }\textit{social network , where each node v is associated with a threshold value \tau(v) , a set of vertices S  \subseteq V( \mathcal{G)(called }\textit{seed nodes ) is chosen initially.
Revised: Given an undirected graph \mathcal{G(V, E, \tau) modeling a }\textit{ , where each node v is associated with a threshold value \tau(v) , a set of vertices S \subseteq V( \mathcal{G)(called }\textit{seed nodes ) is chosen initially.
Edit intent: clarity
Original: Given an undirected graph \mathcal{G(V, E, \tau) modeling a }\textit{social network , where each node v is associated with a threshold value \tau(v) , a set of vertices S  \subseteq V( \mathcal{G)(called }\textit{seed nodes ) is chosen initially.
Revised: Given an undirected graph \mathcal{G(V, E, \tau) modeling a }\textit{social network , where each node v is associated with a threshold value \tau(v) , a set of vertices S \subseteq V( )(called }\textit{seed nodes ) is chosen initially.
Edit intent: coherence
Original: Given an undirected graph \mathcal{G(V, E, \tau) modeling a }\textit{social network , where each node v is associated with a threshold value \tau(v) , a set of vertices S  \subseteq V( \mathcal{G)(called }\textit{seed nodes ) is chosen initially.
Revised: Given an undirected graph \mathcal{G(V, E, \tau) modeling a }\textit{social network , where each node v is associated with a threshold value \tau(v) , a set of vertices S \subseteq V( \mathcal{G)(called }\textit{ ) is chosen initially.
Edit intent: clarity
Original:  Anun\mbox{-influenced node v will change its state toinfluenced at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Revised:  An node v will change its state toinfluenced at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Edit intent: clarity
Original:  Anun\mbox{-influenced node v will change its state toinfluenced at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Revised:  Anun\mbox{-influenced influenced at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Edit intent: clarity
Original:  Anun\mbox{-influenced node v will change its state toinfluenced at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Revised:  Anun\mbox{-influenced node v will change its state to at time step t if it has at least \tau(v) number of neighbors, which are influenced at time step t-1.
Edit intent: fluency
Original:  Based on this diffusion process , a well-studied problem in the literature is the\textit{Target Set Selection Problem (TSS Problem) , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Revised:  Based on this diffusion process , a well-studied problem in the literature is the\textit{ , where the goal is to influence all the nodes of the network by initially choosing the minimum number of seed nodes.
Edit intent: clarity
Original:  Further, by a self reduction from ]  the TSS Problem on general graphs to TSS Problem on bipartite graphs, we improve the inapproximability bound to \Omega ]  (2\SUPERSCRIPT{ \log^{1 - \epsilon \sqrt{n}}%DIFDELCMD < \MBLOCKRIGHTBRACE%%% ) , unless \mathcal{NP \subseteq DTIME(n\SUPERSCRIPT}%DIFDELCMD < {%%% polylog \ ( n )  } n\SUPERSCRIPT}{ )  , where n is the number of nodes present in the bipartite graph .
Revised:  Further, by a self reduction from ] the TSS Problem on general graphs to TSS Problem on bipartite graphs, we improve the inapproximability bound to \Omega ] (2\SUPERSCRIPT{ \log^{1 - \epsilon \sqrt{n}}%DIFDELCMD < \MBLOCKRIGHTBRACE%%% ) , unless \mathcal{NP \subseteq DTIME(n\SUPERSCRIPT}%DIFDELCMD < {%%% polylog \ ( n ) } n\SUPERSCRIPT}{ ) time , where n is the number of nodes present in the bipartite graph .
Edit intent: fluency
Original:  Further, by a self reduction from ]  the TSS Problem on general graphs to TSS Problem on bipartite graphs, we improve the inapproximability bound to \Omega ]  (2\SUPERSCRIPT{ \log^{1 - \epsilon \sqrt{n}}%DIFDELCMD < \MBLOCKRIGHTBRACE%%% ) , unless \mathcal{NP \subseteq DTIME(n\SUPERSCRIPT}%DIFDELCMD < {%%% polylog \ ( n )  } n\SUPERSCRIPT}{ )  , where n is the number of nodes present in the bipartite graph .
Revised:  Further, by a self reduction from ] the TSS Problem on general graphs to TSS Problem on bipartite graphs, we improve the inapproximability bound to \Omega ] (2\SUPERSCRIPT{ \log^{1 - \epsilon \sqrt{n}}%DIFDELCMD < \MBLOCKRIGHTBRACE%%% ) , unless \mathcal{NP \subseteq DTIME(n\SUPERSCRIPT}%DIFDELCMD < {%%% polylog \ ( n ) } n\SUPERSCRIPT}{ ) , where n denotes the number of nodes present in the bipartite graph .
Edit intent: clarity
Original:  Further, by a self reduction from ]  the TSS Problem on general graphs to TSS Problem on bipartite graphs, we improve the inapproximability bound to \Omega ]  (2\SUPERSCRIPT{ \log^{1 - \epsilon \sqrt{n}}%DIFDELCMD < \MBLOCKRIGHTBRACE%%% ) , unless \mathcal{NP \subseteq DTIME(n\SUPERSCRIPT}%DIFDELCMD < {%%% polylog \ ( n )  } n\SUPERSCRIPT}{ )  , where n is the number of nodes present in the bipartite graph .
Revised:  Further, by a self reduction from ] the TSS Problem on general graphs to TSS Problem on bipartite graphs, we improve the inapproximability bound to \Omega ] (2\SUPERSCRIPT{ \log^{1 - \epsilon \sqrt{n}}%DIFDELCMD < \MBLOCKRIGHTBRACE%%% ) , unless \mathcal{NP \subseteq DTIME(n\SUPERSCRIPT}%DIFDELCMD < {%%% polylog \ ( n ) } n\SUPERSCRIPT}{ ) , where n is the number of vertices of the graph under consideration .
Edit intent: clarity
Original: V(G) \rightarrow N, the Target Set Selection (TSS) Problem  is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G. Under the non-progressive diffusion model, we have the following results on the TSS Problem:
Revised: V(G) \rightarrow N, the Target Set Selection is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G. Under the non-progressive diffusion model, we have the following results on the TSS Problem:
Edit intent: clarity
Original:  We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% had shown an inapproximability result of \Omega(2^{\log^{1 - \epsilon was shown by Nichterlein et al.
Revised:  SIDMA, 2009%DIFDELCMD < ] %%% had shown an inapproximability result of \Omega(2^{\log^{1 - \epsilon was shown by Nichterlein et al.
Edit intent: coherence
Original: Given a simple, undirected graph G with a threshold function \tau:V(G) \rightarrow N, the Target Set Selection (TSS) Problem is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G.  We have the following results on the TSS Problem : -  It was shown by Nichterlein et al.
Revised: Given a simple, undirected graph G with a threshold function \tau:V(G) \rightarrow N, the Target Set Selection (TSS) problem is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G. We have the following results on the TSS Problem : - It was shown by Nichterlein et al.
Edit intent: fluency
Original: Given a simple, undirected graph G with a threshold function \tau:V(G) \rightarrow N, the Target Set Selection (TSS) Problem is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G.  We have the following results on the TSS Problem : -  It was shown by Nichterlein et al.
Revised: Given a simple, undirected graph G with a threshold function \tau:V(G) \rightarrow N, the Target Set Selection (TSS) Problem is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G. We have the following results on the TSS problem : - It was shown by Nichterlein et al.
Edit intent: fluency
Original: Given a simple, undirected graph G with a threshold function \tau:V(G) \rightarrow N, the Target Set Selection (TSS) Problem is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G.  We have the following results on the TSS Problem : -  It was shown by Nichterlein et al.
Revised: Given a simple, undirected graph G with a threshold function \tau:V(G) \rightarrow N, the Target Set Selection (TSS) Problem is about choosing a minimum cardinality set, say S \subseteq V(G), such that starting a diffusion process with S as its seed set will eventually result in activating all the nodes in G. We have the following results on the TSS Problem : - > It was shown by Nichterlein et al.
Edit intent: fluency