wanyu/IteraTeR_v2 huggingface dataset:
Original:  Here with the help of game theory we show that minimalistic networks designed to maximise the navigation efficiency at minimal cost share basic structural properties of real networks.
Revised:  Here with the help of game theory we show that minimalistic networks designed to maximise the navigation efficiency at minimal cost share basic structural properties with real networks.
Edit intent: clarity
Original:  They are navigation skeletons that we show are present in the Internet, %DIFDELCMD < {\it %%% E. coli metabolicnetwork , English word network , US airport network, and the Hungarian road network .
Revised:  We show that these skeletons are present in the Internet, %DIFDELCMD < {\it %%% E. coli metabolicnetwork , English word network , US airport network, and the Hungarian road network .
Edit intent: clarity
Original:  They are navigation skeletons that we show are present in the Internet, %DIFDELCMD < {\it %%% E. coli metabolicnetwork , English word network , US airport network, and the Hungarian road network .
Revised:  They are navigation skeletons that we show are present in the Internet, %DIFDELCMD < {\it %%% E. coli metabolic , English word network , US airport network, and the Hungarian road network .
Edit intent: fluency
Original:  They are navigation skeletons that we show are present in the Internet, %DIFDELCMD < {\it %%% E. coli metabolicnetwork , English word network , US airport network, and the Hungarian road network .
Revised:  They are navigation skeletons that we show are present in the Internet, %DIFDELCMD < {\it %%% E. coli metabolicnetwork , English word , US airport network, and the Hungarian road network .
Edit intent: fluency
Original:  The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can dramatically improve or paralyse the navigation in the network.
Revised:  The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can efficiently improve or paralyse the navigation in the network.
Edit intent: clarity
Original:  The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can dramatically improve or paralyse the navigation in the network.
Revised:  The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can dramatically improve or paralyse navigation in the network.
Edit intent: fluency
Original:  The algorithm is applied to about 1,784 stocks listed on the first section of the Tokyo Stock Exchange leading up to totally _{1,784 1,590,436 pairs.
Revised:  The algorithm is applied to 1,784 stocks listed on the first section of the Tokyo Stock Exchange leading up to totally _{1,784 1,590,436 pairs.
Edit intent: clarity
Original:  The algorithm is applied to about 1,784 stocks listed on the first section of the Tokyo Stock Exchange leading up to totally _{1,784 1,590,436 pairs.
Revised:  The algorithm is applied to about 1,784 stocks listed on the first section of the Tokyo Stock Exchange leading up to totally 1,590,436 pairs.
Edit intent: fluency
Original:  In this work, we provide all the possible reasons behind occurrence of the zero degeneracy in the networks spectra.
Revised:  In this work, we provide possible reasons behind occurrence of the zero degeneracy in the networks spectra.
Edit intent: clarity
Original:  In this work, we provide all the possible reasons behind occurrence of the zero degeneracy in the networks spectra.
Revised:  In this work, we provide all the possible reasons behind occurrence of the zero degeneracy in various networks spectra.
Edit intent: clarity
Original:  In this study, we propose a  deep temporal convolutional neural network architecture  for brain decoding task in order to reduce dimensionality of feature space along with improved classification performance.
Revised:  In this study, we propose a deep temporal convolutional neural network architecture for brain decoding which aims to reduce dimensionality of feature space along with improved classification performance.
Edit intent: clarity
Original:  Temporal representations (filters) for each layer of the convolutional model are learned by leveraging unlabelled fMRI data in an unsupervised fashion by employing regularized autoencoders.
Revised:  Temporal representations (filters) for each layer of the convolutional model are learned by leveraging unlabelled fMRI data in an unsupervised fashion with regularized autoencoders.
Edit intent: clarity
Original:  Further  spatial pooling layers in the convolutional architecture reduce the dimensionality without losing excessive information.
Revised:  Further , spatial pooling layers in the convolutional architecture reduce the dimensionality without losing excessive information.
Edit intent: fluency
Original:  Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights W=(w1, ... \dots ,wn), W-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree \degW(X1^{\alpha1}, ... \dots ,Xn^{\alphan}) = \sum wi\alphai.
Revised:  Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights W=(w1, \dots ,wn), W-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree \degW(X1^{\alpha1}, ... \dots ,Xn^{\alphan}) = \sum wi\alphai.
Edit intent: fluency
Original:  Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights W=(w1, ... \dots ,wn), W-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree \degW(X1^{\alpha1}, ... \dots ,Xn^{\alphan}) = \sum wi\alphai.
Revised:  Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights W=(w1, ... \dots ,wn), W-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree \degW(X1^{\alpha1}, \dots ,Xn^{\alphan}) = \sum wi\alphai.
Edit intent: fluency
Original:  Gr \"o%DIFDELCMD < }%%% bner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case.
Revised:  \"o%DIFDELCMD < }%%% bner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case.
Edit intent: fluency
Original:  Gr \"o%DIFDELCMD < }%%% bner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case.
Revised:  Gr %DIFDELCMD < }%%% bner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case.
Edit intent: fluency
Original:  Gr \"o%DIFDELCMD < }%%% bner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case.
Revised:  Gr \"o%DIFDELCMD < }%%% Gr\"obner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case.
Edit intent: fluency
Original:  We show that in this case, the complexity estimate for Algorithm  \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  We show that in this case, the complexity estimate for Algorithm ~ \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Edit intent: fluency
Original:  We show that in this case, the complexity estimate for Algorithm  \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  We show that in this case, the complexity estimate for Algorithm \F5 \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Edit intent: fluency
Original:  We show that in this case, the complexity estimate for Algorithm  \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  We show that in this case, the complexity estimate for Algorithm \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Edit intent: fluency
Original:  We show that in this case, the complexity estimate for Algorithm  \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  We show that in this case, the complexity estimate for Algorithm \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor \left( \prod w\_{i} ) \right) ^{\omega}.
Edit intent: fluency
Original:  We show that in this case, the complexity estimate for Algorithm  \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  We show that in this case, the complexity estimate for Algorithm \F5 ( \left( \binom{n+\dmax-1}{\dmax}^{\omega} ) \right) can be divided by a factor ( \left( \prod w\_{i} \right) ^{\omega}.
Edit intent: fluency
Original:  For zero-dimensional systems, the complexity of Algorithm  \FGLM nD^{\omega} (where D is the number of solutions of the system) can be divided by the same factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  For zero-dimensional systems, the complexity of Algorithm ~ \FGLM nD^{\omega} (where D is the number of solutions of the system) can be divided by the same factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Edit intent: fluency
Original:  For zero-dimensional systems, the complexity of Algorithm  \FGLM nD^{\omega} (where D is the number of solutions of the system) can be divided by the same factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  For zero-dimensional systems, the complexity of Algorithm \FGLM nD^{\omega} (where D is the number of solutions of the system) can be divided by the same factor \left( \prod w\_{i} ) \right) ^{\omega}.
Edit intent: fluency
Original:  For zero-dimensional systems, the complexity of Algorithm  \FGLM nD^{\omega} (where D is the number of solutions of the system) can be divided by the same factor ( \left( \prod w\_{i} ) \right) ^{\omega}.
Revised:  For zero-dimensional systems, the complexity of Algorithm \FGLM nD^{\omega} (where D is the number of solutions of the system) can be divided by the same factor ( \left( \prod w\_{i} \right) ^{\omega}.
Edit intent: fluency
Original:  Under genericity assumptions, for zero-dimensional weighted homogeneous systems of W-degree (d\_{1}, ... \dots ,d\_{n}), these complexity estimates are polynomial in the weighted B \'e%DIFDELCMD < }%%% zout bound \prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}.
Revised:  Under genericity assumptions, for zero-dimensional weighted homogeneous systems of W-degree (d\_{1}, \dots ,d\_{n}), these complexity estimates are polynomial in the weighted B \'e%DIFDELCMD < }%%% zout bound \prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}.
Edit intent: fluency
Original:  Under genericity assumptions, for zero-dimensional weighted homogeneous systems of W-degree (d\_{1}, ... \dots ,d\_{n}), these complexity estimates are polynomial in the weighted B \'e%DIFDELCMD < }%%% zout bound \prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}.
Revised:  Under genericity assumptions, for zero-dimensional weighted homogeneous systems of W-degree (d\_{1}, ... \dots ,d\_{n}), these complexity estimates are polynomial in the weighted \'e%DIFDELCMD < }%%% zout bound \prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}.
Edit intent: clarity
Original:  Under genericity assumptions, for zero-dimensional weighted homogeneous systems of W-degree (d\_{1}, ... \dots ,d\_{n}), these complexity estimates are polynomial in the weighted B \'e%DIFDELCMD < }%%% zout bound \prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}.
Revised:  Under genericity assumptions, for zero-dimensional weighted homogeneous systems of W-degree (d\_{1}, ... \dots ,d\_{n}), these complexity estimates are polynomial in the weighted B %DIFDELCMD < }%%% zout bound \prod\_{i=1}^{n}d\_{i} / \prod\_{i=1}^{n}w\_{i}.
Edit intent: clarity
Original: In the context of large financial markets we formulate the notion of "no asymptotic free lunch with vanishing risk" \emph{ (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets.
Revised: In the context of large financial markets we formulate the notion of \emph{ (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets.
Edit intent: clarity
Original: In the context of large financial markets we formulate the notion of "no asymptotic free lunch with vanishing risk" \emph{ (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets.
Revised: In the context of large financial markets we formulate the notion of "no asymptotic free lunch with vanishing risk" \emph{no asymptotic free lunch with vanishing risk (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets.
Edit intent: fluency
Original: When a three-dimensional object moves through a scene, a corresponding change occurs on the  image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good  representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Revised: When a three-dimensional object moves relative to an observer, a change occurs on the image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Edit intent: clarity
Original: When a three-dimensional object moves through a scene, a corresponding change occurs on the  image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good  representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Revised: When a three-dimensional object moves through a scene, a corresponding change occurs on the observer's image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Edit intent: clarity
Original: When a three-dimensional object moves through a scene, a corresponding change occurs on the  image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good  representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Revised: When a three-dimensional object moves through a scene, a corresponding change occurs on the image plane and in the visual representation computed by a learned model . Starting with the idea that a good representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Edit intent: clarity
Original: When a three-dimensional object moves through a scene, a corresponding change occurs on the  image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good  representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Revised: When a three-dimensional object moves through a scene, a corresponding change occurs on the image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good visual representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Edit intent: fluency
Original: When a three-dimensional object moves through a scene, a corresponding change occurs on the  image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good  representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations.
Revised: When a three-dimensional object moves through a scene, a corresponding change occurs on the image plane and in the visual representation constructed by a learning algorithm . Starting with the idea that a good representation is one that transforms linearly under scene motions, we show, using the theory of group representations, that any such representation is equivalent to a combination of particularly simple irreducible representations.
Edit intent: clarity
Original: Allosteric communication in proteins is a central and yet not solved problem of structural biochemistry.
Revised: Allosteric communication in proteins is a central and yet unsolved problem of structural biochemistry.
Edit intent: clarity
Original:  Molecular communication in proteins requires the existence of allosteric pathways.
Edit intent: coherence
Original:  Previous findings, from computational biology (Ota and Agard, 2005), has proposed that heat diffuses in a protein through  allosteric pathways.
Revised:  Previous findings, from computational biology (Ota and Agard, 2005), have proposed that heat diffuses in a protein through allosteric pathways.
Edit intent: fluency
Original:  In this work we studied heat diffusion in the well know PDZ-2 protein .
Revised:  This work studied heat diffusion in the well know PDZ-2 protein .
Edit intent: clarity
Original:  In this work we studied heat diffusion in the well know PDZ-2 protein .
Revised:  In this work we studied heat diffusion in the well-known PDZ-2 protein .
Edit intent: fluency
Original:  This protein has two cognate allosteric pathways and we confirm that heat flows preferentially through them .
Revised:  This protein has two cognate allosteric pathways and that heat flows preferentially through them .
Edit intent: coherence
Original:  This protein has two cognate allosteric pathways and we confirm that heat flows preferentially through them .
Revised:  This protein has two cognate allosteric pathways and we confirm that heat flows preferentially through these .
Edit intent: fluency
Original:  Also, a new property is observed for protein structures : heat diffuses asymmetrically through them .
Revised:  Also, a new property was also observed for protein structures : heat diffuses asymmetrically through them .
Edit intent: clarity
Original:  Also, a new property is observed for protein structures : heat diffuses asymmetrically through them .
Revised:  Also, a new property is observed for protein structures - heat diffuses asymmetrically through them .
Edit intent: fluency
Original:  Also, a new property is observed for protein structures : heat diffuses asymmetrically through them .
Revised:  Also, a new property is observed for protein structures : heat diffuses asymmetrically through the structures .
Edit intent: clarity
Original:  The underling structure of this asymmetrical heat flow is the hydrogen bond of normal length (~2.85 {\AA}) , that can act as a thermal diode.
Revised:  The underling structure of this asymmetrical heat flow was a normal length hydrogen bond (~2.85 {\AA}) , that can act as a thermal diode.
Edit intent: clarity
Original:  The underling structure of this asymmetrical heat flow is the hydrogen bond of normal length (~2.85 {\AA}) , that can act as a thermal diode.
Revised:  The underling structure of this asymmetrical heat flow is the hydrogen bond of normal length (~2.85 {\AA}) that acted as a thermal diode.
Edit intent: clarity
Original:  Also asymmetrical heat diffusion is due, in } a higher scale, to local structural organization of residues  .
Revised:  Also asymmetrical heat diffusion is due, in \AA} a higher scale, to local structural organization of residues .
Edit intent: coherence
Original:  Also asymmetrical heat diffusion is due, in } a higher scale, to local structural organization of residues  .
Revised:  Also asymmetrical heat diffusion is due, in }), giving rise to symmetrical thermal diffusion. Asymmetrical heat diffusion was due, on a higher scale, to local structural organization of residues .
Edit intent: coherence
Original:  Also asymmetrical heat diffusion is due, in } a higher scale, to local structural organization of residues  .
Revised:  Also asymmetrical heat diffusion is due, in } a higher scale, to the local, structural organization of residues .
Edit intent: coherence
Original:  This asymmetrical  energy flow may be relevant for allosteric signal communication directionality in protein structures .
Revised:  This asymmetrical /symmetrical energy flow may be relevant for allosteric signal communication directionality in protein structures .
Edit intent: clarity
Original:  This scenario and the resulting pricing schemes can serve as an important step in migration to a future smart grid.
Revised:  This scenario for the coexistence of traditional and smart girds and the pricing schemes under this scenario can enable smooth migration to a future smart grid.
Edit intent: clarity
Original:  In this report we show that published deep network results on the MNIST handwritten digit dataset can straightforwardly be replicated (error rates below 1\%, without use of any distortions) with shallow 'Extreme Learning Machine' (ELM) networks, with a very rapid training time (~10 minutes).
Revised:  In this report we show that error rates below 1\% on the MNIST handwritten digit dataset can straightforwardly be replicated (error rates below 1\%, without use of any distortions) with shallow 'Extreme Learning Machine' (ELM) networks, with a very rapid training time (~10 minutes).
Edit intent: clarity
Original:  In this report we show that published deep network results on the MNIST handwritten digit dataset can straightforwardly be replicated (error rates below 1\%, without use of any distortions) with shallow 'Extreme Learning Machine' (ELM) networks, with a very rapid training time (~10 minutes).
Revised:  In this report we show that published deep network results on the MNIST handwritten digit dataset can straightforwardly be replicated (error rates below 1\%, without use of any distortions) with shallow 'Extreme Learning Machine' (ELM) approach, which also enables a very rapid training time (~10 minutes).
Edit intent: clarity