wanyu/IteraTeR_v2 huggingface dataset:
Original:  and M_2=(S, \mathcal{I {\cal  _2) on the same ground set S, and the goal is to determine the smallest number k such that given arbitrary lists L_s of k colours for s\in S, it is possible to choose a colour from each list so that every monochromatic set is independent in both M_1 and M_2. When both M_1 and M_2 are partition matroids, Galvin's celebrated list colouring theorem for bipartite graphs gives the answer.
Revised:  and M_2=(S, \mathcal{I {\cal _2) on the same ground set S, and the goal is to determine the smallest number k such that given arbitrary lists L_s of k colours for s\in S, it is possible to choose a color from each list so that every monochromatic set is independent in both M_1 and M_2. When both M_1 and M_2 are partition matroids, Galvin's celebrated list colouring theorem for bipartite graphs gives the answer.
Edit intent: fluency
Original:  and M_2=(S, \mathcal{I {\cal  _2) on the same ground set S, and the goal is to determine the smallest number k such that given arbitrary lists L_s of k colours for s\in S, it is possible to choose a colour from each list so that every monochromatic set is independent in both M_1 and M_2. When both M_1 and M_2 are partition matroids, Galvin's celebrated list colouring theorem for bipartite graphs gives the answer.
Revised:  and M_2=(S, \mathcal{I {\cal _2) on the same ground set S, and the goal is to determine the smallest number k such that given arbitrary lists L_s of k colours for s\in S, it is possible to choose a colour from each list so that every monochromatic set is independent in both M_1 and M_2. When both M_1 and M_2 are partition matroids, Galvin's list coloring theorem for bipartite graphs gives the answer.
Edit intent: clarity
Original:  One of the main open questions is to decide if there exists a constant c such that if the colouring number is k (i.e., the ground set can be partitioned into k  independent sets), then the list colouring number is at most c\cdot k.
Revised:  One of the main open questions is to decide if there exists a constant c such that if the coloring number is k (i.e., the ground set can be partitioned into k independent sets), then the list colouring number is at most c\cdot k.
Edit intent: fluency
Original:  One of the main open questions is to decide if there exists a constant c such that if the colouring number is k (i.e., the ground set can be partitioned into k  independent sets), then the list colouring number is at most c\cdot k.
Revised:  One of the main open questions is to decide if there exists a constant c such that if the colouring number is k (i.e., the ground set can be partitioned into k common independent sets), then the list colouring number is at most c\cdot k.
Edit intent: clarity
Original:  One of the main open questions is to decide if there exists a constant c such that if the colouring number is k (i.e., the ground set can be partitioned into k  independent sets), then the list colouring number is at most c\cdot k.
Revised:  One of the main open questions is to decide if there exists a constant c such that if the colouring number is k (i.e., the ground set can be partitioned into k independent sets), then the list coloring number is at most c\cdot k.
Edit intent: fluency
Original:  In the present paper, we consider matroid classes that appear naturally in combinatorial and graph optimization problems, namely graphic matroids, paving matroids and gammoids.
Revised:  We consider matroid classes that appear naturally in combinatorial and graph optimization problems, namely graphic matroids, paving matroids and gammoids.
Edit intent: coherence
Original:  In the present paper, we consider matroid classes that appear naturally in combinatorial and graph optimization problems, namely graphic matroids, paving matroids and gammoids.
Revised:  In the present paper, we consider matroid classes that appear naturally in combinatorial optimization problems, namely graphic matroids, paving matroids and gammoids.
Edit intent: coherence
Original:  We show that if both matroids are from these fundamental classes, then the list colouring number is at most twice the colouring number.
Revised:  We show that if both matroids are from these fundamental classes, then the list coloring number is at most twice the colouring number.
Edit intent: fluency
Original:  We show that if both matroids are from these fundamental classes, then the list colouring number is at most twice the colouring number.
Revised:  We show that if both matroids are from these fundamental classes, then the list colouring number is at most twice the coloring number.
Edit intent: fluency
Original:  The proof is based on a novel approach that reduces a matroid to a partition matroid  , and might be of independent combinatorial interest.
Revised:  The proof is based on a new approach that reduces a matroid to a partition matroid , and might be of independent combinatorial interest.
Edit intent: clarity
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal J {\cal in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: fluency
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal ) with{\cal in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: fluency
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal {\cal J in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: fluency
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal {\cal \subseteq{\cal I in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: fluency
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal {\cal in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% k independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: fluency
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal {\cal in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: fluency
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal {\cal in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil kr/(r-1)\rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: fluency
Original:  with \mathcal{J}\subseteq\mathcal{I} } {\cal  {\cal   in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%%  independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a transversal matroid , and (D) 2k-2 independent sets if M is a gammoid.
Revised:  with \mathcal{J}\subseteq\mathcal{I} } {\cal {\cal in which S can be partitioned into (A) %DIFDELCMD < \lceil %%% kr/(r-1)%DIFDELCMD < \rceil %%% independent sets if M is a paving matroidof rank r , (B) 2k-1 independent sets if M is a graphic matroid, (C) k \lceil \rceil independent sets if M is a paving matroid of rank r , and (D) 2k-2 independent sets if M is a gammoid.
Edit intent: clarity
Original: The Wiener index is a graph parameter originating from chemical graph theory.
Revised: The Wiener index is one of the most widely studied parameters in chemical graph theory.
Edit intent: clarity
Original:  In 1991, Solt\'es posed the following problem regarding the Wiener index . Find all graphs such that its Wiener index is preserved upon removal of any vertex.
Revised:  In 1991, Solt\'es posed the following problem regarding the Wiener index : Find all graphs such that its Wiener index is preserved upon removal of any vertex.
Edit intent: fluency
Original:  The problem is far from being solved and to this day, only one graph with such property is known --- the cycle graph on 11 vertices.
Revised:  The problem is far from being solved and to this day, only one graph with such property is known : the cycle graph on 11 vertices.
Edit intent: fluency
Original:  In this paper, we solve a relaxed version of the problem, proposed by Knor et al. in 2018.
Revised:  In this paper, we solve a relaxed version of the problem, proposed by Knor et al. 
Edit intent: coherence
Original:  While results of this work are promising in terms of delay bound quality and computational effort, there is little to no insight on why a prediction is made or if the trained machine can achieve similarly striking results in networks vastly differing from its training data.
Revised:  While results of this work were promising in terms of delay bound quality and computational effort, there is little to no insight on why a prediction is made or if the trained machine can achieve similarly striking results in networks vastly differing from its training data.
Edit intent: fluency
Original:  While results of this work are promising in terms of delay bound quality and computational effort, there is little to no insight on why a prediction is made or if the trained machine can achieve similarly striking results in networks vastly differing from its training data.
Revised:  While results of this work are promising in terms of delay bound quality and computational effort, there is little to no insight on when a prediction is made or if the trained machine can achieve similarly striking results in networks vastly differing from its training data.
Edit intent: clarity
Original:  While results of this work are promising in terms of delay bound quality and computational effort, there is little to no insight on why a prediction is made or if the trained machine can achieve similarly striking results in networks vastly differing from its training data.
Revised:  While results of this work are promising in terms of delay bound quality and computational effort, there is little to no insight on why a prediction is made or if the trained algorithm can achieve similarly striking results in networks vastly differing from its training data.
Edit intent: clarity
Original:  In this paper  we address these pending questions.
Revised:  In this paper , we address these pending questions.
Edit intent: fluency
Original:  The KKL theorem and the Friedgut junta theorem give a strong characterization of such functions whenever the bound on the total influence is o(\log n) , however, both results become useless when the total influence of the function is \omega(\log n).
Revised:  The KKL theorem and the Friedgut junta theorem give a strong characterization of such functions whenever the bound on the total influence is o(\log n) . However, both results become useless when the total influence of the function is \omega(\log n).
Edit intent: fluency
Original:  The only case in which this logarithmic barrier has been broken for an interesting class of function was proved by Bourgain and Kalai, who focused on functions that are symmetric under large enough subgroups of S_n. In this paper, we revisit the key ideas of the Bourgain-Kalai paper .
Revised:  The only case in which this logarithmic barrier has been broken for an interesting class of functions was proved by Bourgain and Kalai, who focused on functions that are symmetric under large enough subgroups of S_n. In this paper, we revisit the key ideas of the Bourgain-Kalai paper .
Edit intent: fluency
Original:  The only case in which this logarithmic barrier has been broken for an interesting class of function was proved by Bourgain and Kalai, who focused on functions that are symmetric under large enough subgroups of S_n. In this paper, we revisit the key ideas of the Bourgain-Kalai paper .
Revised:  The only case in which this logarithmic barrier has been broken for an interesting class of function was proved by Bourgain and Kalai, who focused on functions that are symmetric under large enough subgroups of S_n. In this paper, we build and improve on the techniques of the Bourgain-Kalai paper .
Edit intent: clarity
Original:  More precisely, we prove that the Fourier entropy of the low-degree part of f is at most O(I f%DIFDELCMD < ]%%% \log ^2 characters, improving an earlier result of Friedgut.
Revised:  More precisely, we prove that the Fourier f%DIFDELCMD < ]%%% \log ^2 characters, improving an earlier result of Friedgut.
Edit intent: clarity
Original:  More precisely, we prove that the Fourier entropy of the low-degree part of f is at most O(I f%DIFDELCMD < ]%%% \log ^2 characters, improving an earlier result of Friedgut.
Revised:  More precisely, we prove that the Fourier entropy of the low-degree part of f is at most O(I %DIFDELCMD < ]%%% \log ^2 characters, improving an earlier result of Friedgut.
Edit intent: clarity
Original:  Removing the \log } I[f] ), where I f%DIFDELCMD < ] %%% is the total influence of f.
Revised:  Removing the \log } I[f] f%DIFDELCMD < ] %%% is the total influence of f.
Edit intent: coherence
Original:  Removing the \log } I[f] ), where I f%DIFDELCMD < ] %%% is the total influence of f.
Revised:  Removing the \log } I[f] ), where I %DIFDELCMD < ] %%% is the total influence of f.
Edit intent: fluency
Original: Transgender individuals  show brain structural alterations that differ from their biological sex as well as their perceived gender.
Revised: Transgender individuals (TIs) show brain structural alterations that differ from their biological sex as well as their perceived gender.
Edit intent: clarity
Original:  To substantiate evidence that the brain structure of transgender individuals differs from male and female, we use a combined multivariate and univariate approach.
Revised:  To substantiate evidence that the brain structure of TIs differs from male and female, we use a combined multivariate and univariate approach.
Edit intent: clarity
Original:  The application of our biological sex classifier to the transgender sample resulted in a significantly lower true positive rate (  TPR-male = 56.0 \%).
Revised:  The application of our biological sex classifier to the transgender sample resulted in a significantly lower true positive rate ( TPR) ( TPR-male = 56.0 \%).
Edit intent: clarity
Original:  This finding substantiates evidence that transgender individuals show specific brain structural alterations leading to a different pattern of brain structure than CG individuals .
Revised:  This finding substantiates evidence that TIs show specific brain structural alterations leading to a different pattern of brain structure than CG individuals .
Edit intent: clarity
Original:  This finding substantiates evidence that transgender individuals show specific brain structural alterations leading to a different pattern of brain structure than CG individuals .
Revised:  This finding substantiates evidence that transgender individuals show specific brain structural alterations leading to a different pattern of brain structure than CG-individuals .
Edit intent: clarity
Original: Due to the rapid development of GANs , there has been significant progress in the field of human video motion transfer which has a wide range of applications in computer vision and graphics .
Revised: Due to the rapid development of GANs , there has been significant progress in the field .
Edit intent: clarity
Original:  Experimental results show that, when applied to motion transfer tasks involving a variety of human subjects, our proposed method achieves appearance-controllable synthesis with higher video quality than state-of-arts based on only one-time training .
Revised:  Experimental results show that, when applied to motion transfer tasks involving a variety of human subjects, our proposed method achieves appearance-controllable human video motion transfer but also achieve higher video quality than state-of-arts based on only one-time training .
Edit intent: clarity
Original:  Experimental results show that, when applied to motion transfer tasks involving a variety of human subjects, our proposed method achieves appearance-controllable synthesis with higher video quality than state-of-arts based on only one-time training .
Revised:  Experimental results show that, when applied to motion transfer tasks involving a variety of human subjects, our proposed method achieves appearance-controllable synthesis with higher video quality than state-of-art methods .
Edit intent: clarity
Original: Over the past two decades, topological data analysis has emerged as a young field of applied mathematics with new applications and algorithmic developments appearing rapidly.
Revised: Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly.
Edit intent: clarity
Original:  We find that while the total dissipation does not drastically change as the system undergoes a Hopf bifurcation, the EPF shows a dramatic change in the allocation of energy .
Revised:  The EPF quantifies the transition of dissipation from local to global coherent oscillations in space and time and integrating it gives a bound on the entropy production rate .
Edit intent: clarity
Original:  We introduce a novel measure of dissipation we term the entropy production factor (EPF) to quantify how time reversal symmetry is broken in field theories across scales.
Revised:  We introduce a novel measure of irreversibility we term the entropy production factor (EPF) to quantify how time reversal symmetry is broken in field theories across scales.
Edit intent: clarity
Original: In this paper  we address the problem of multichannel speech enhancement in the short-time Fourier transform (STFT) domain and in the framework of sequence-to-sequence deep learning .
Revised: In this paper , we address the problem of multichannel speech enhancement in the short-time Fourier transform (STFT) domain and in the framework of sequence-to-sequence deep learning .
Edit intent: fluency
Original: In this paper  we address the problem of multichannel speech enhancement in the short-time Fourier transform (STFT) domain and in the framework of sequence-to-sequence deep learning .
Revised: In this paper we address the problem of multichannel speech enhancement in the short-time Fourier transform (STFT) domain .
Edit intent: coherence
Original:  The network's output is a sequence of single-channel cleaned speech at the same frequency bin .
Revised:  The network's output is the corresponding sequence of single-channel cleaned speech at the same frequency bin .
Edit intent: clarity
Original:  The network's output is a sequence of single-channel cleaned speech at the same frequency bin .
Revised:  The network's output is a sequence of single-channel cleaned speech .
Edit intent: clarity
Original:  We propose several clean-speech network targets, namely, the magnitude ratio mask, the complex ideal ratio mask, the STFT coefficients and spatial filtering .
Revised:  We propose several clean-speech network targets, namely, the magnitude ratio mask, the complex STFT coefficients and spatial filtering .
Edit intent: clarity
Original:  The proposed deep filter is able to discriminate between speech and noise by exploiting their different temporal and spatial characteristics: speech is non-stationary and spatially coherent while noise is relatively stationary and weakly correlated across channels.
Revised:  The proposed deep filtering is able to discriminate between speech and noise by exploiting their different temporal and spatial characteristics: speech is non-stationary and spatially coherent while noise is relatively stationary and weakly correlated across channels.
Edit intent: fluency
Original: Let D be a directed graph cellularly embedded on a surface together with costs and capacities on its arcs.
Revised: Let D be a directed graph cellularly embedded in a surface together with costs and capacities on its arcs.
Edit intent: fluency
Original:  Given any integer circulation in D, we study the problem of finding a minimum-cost  integer circulation in D that is homologous ( over the integers ) to the given circulation and respects the capacities.
Revised:  Given any integer circulation in D, we study the problem of finding a minimum-cost integer circulation in D that is homologous over the integers ) to the given circulation and respects the capacities.
Edit intent: fluency