wanyu/IteraTeR_v2 huggingface dataset:
Original:  The main result of the paper is the explicit construction of a systematic MDS code for d = n-1 >= 2k-1 termed the MISER code, that makes use of interference alignment to achieve the cut-set bound on the repair bandwidth for systematic nodes.
Revised:  The main result of the paper is the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that makes use of interference alignment to achieve the cut-set bound on the repair bandwidth for systematic nodes.
Edit intent: clarity
Original:  The main result of the paper is the explicit construction of a systematic MDS code for d = n-1 >= 2k-1 termed the MISER code, that makes use of interference alignment to achieve the cut-set bound on the repair bandwidth for systematic nodes.
Revised:  The main result of the paper is the explicit construction of a systematic MDS code for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for systematic nodes.
Edit intent: clarity
Original:  It is also proven that it is impossible to construct a code with these properties for d < 2k-3 . A second major result of the paper is the construction, also explicit, of a minimum-storage regenerating code for d = k+1.
Revised:  It is also proven that it is impossible to construct a code with these properties for d < 2k-3 . A second major result of the paper is the construction, also explicit, of MSR codes for d = k+1.
Edit intent: clarity
Original:  To our knowledge, the constructions presented in this paper are the first  explicit constructions of regenerating codes that achieve the cut set bound.
Revised:  To our knowledge, the constructions presented in this paper are the first , explicit constructions of regenerating codes that achieve the cut set bound.
Edit intent: fluency
Original:  To our knowledge, the constructions presented in this paper are the first  explicit constructions of regenerating codes that achieve the cut set bound.
Revised:  To our knowledge, the constructions presented in this paper are the first explicit constructions of regenerating codes that achieve the cut-set bound.
Edit intent: fluency
Original:  We also approximate this significance level by observing that asymptotically the distribution of the distance under the null hypothesis of no clustering is a functional of a suitable Gaussian process indexed by the reference phylogenetic tree.
Revised:  We also approximate this significance level by observing that asymptotically the distribution of the distance under the null hypothesis of no clustering is a functional of a Gaussian process indexed by the reference phylogenetic tree.
Edit intent: clarity
Original: Metagenomics attempts to sample and study all the genetic material present in a community of microorganisms in a given environment.
Revised: Using modern technology, it is now common to survey microbial communities by sequencing DNA or RNA extracted in bulk from a given environment.
Edit intent: clarity
Original:  A key problem in this new field is the development of comparative methods that indicate the extent to which two communities differ .%DIFDELCMD < {\em %%% UniFrac , a method constructed from a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses.
Revised:  Comparative methods are needed that indicate the extent to which two communities differ .%DIFDELCMD < {\em %%% UniFrac , a method constructed from a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses.
Edit intent: clarity
Original:  A key problem in this new field is the development of comparative methods that indicate the extent to which two communities differ .%DIFDELCMD < {\em %%% UniFrac , a method constructed from a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses.
Revised:  A key problem in this new field is the development of comparative methods that indicate the extent to which two communities differ %DIFDELCMD < {\em %%% UniFrac , a method constructed from a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses.
Edit intent: fluency
Original:  A key problem in this new field is the development of comparative methods that indicate the extent to which two communities differ .%DIFDELCMD < {\em %%% UniFrac , a method constructed from a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses.
Revised:  A key problem in this new field is the development of comparative methods that indicate the extent to which two communities differ .%DIFDELCMD < {\em %%% UniFrac , a method built around a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses.
Edit intent: fluency
Original:  We provide a foundation for such methods by establishing that  the %DIFDELCMD < {\em %%% weighted UniFrac distance is a special case of the classical Kantorovich-Rubinstein (KR) metric applied to probability distributions representing the metagenomic samples on a reference phylogenetic tree .
Revised:  We provide a foundation for such methods by establishing that the %DIFDELCMD < {\em %%% weighted UniFrac classical Kantorovich-Rubinstein (KR) metric applied to probability distributions representing the metagenomic samples on a reference phylogenetic tree .
Edit intent: clarity
Original:  We provide a foundation for such methods by establishing that  the %DIFDELCMD < {\em %%% weighted UniFrac distance is a special case of the classical Kantorovich-Rubinstein (KR) metric applied to probability distributions representing the metagenomic samples on a reference phylogenetic tree .
Revised:  We provide a foundation for such methods by establishing that the %DIFDELCMD < {\em %%% weighted UniFrac distance is a special case of the classical Kantorovich-Rubinstein (KR) distance between the corresponding empirical distributions .
Edit intent: clarity
Original:  We demonstrate that in this case the KR distance can be written as an integral over the tree,  develop L^p Zolotarev-type generalizations of the metric, and  show how the p-value of the  natural permutation test of the null hypothesis "no difference between the two communities" can be approximated using a functional of a Gaussian process indexed by the tree.
Revised:  We demonstrate that in this case the KR distance can be written as an integral over the tree, we develop L^p Zolotarev-type generalizations of the metric, and show how the p-value of the natural permutation test of the null hypothesis "no difference between the two communities" can be approximated using a functional of a Gaussian process indexed by the tree.
Edit intent: fluency
Original:  We demonstrate that in this case the KR distance can be written as an integral over the tree,  develop L^p Zolotarev-type generalizations of the metric, and  show how the p-value of the  natural permutation test of the null hypothesis "no difference between the two communities" can be approximated using a functional of a Gaussian process indexed by the tree.
Revised:  We demonstrate that in this case the KR distance can be written as an integral over the tree, develop L^p Zolotarev-type generalizations of the metric, and we show how the p-value of the natural permutation test of the null hypothesis "no difference between the two communities" can be approximated using a functional of a Gaussian process indexed by the tree.
Edit intent: fluency
Original: The underlying reality of a succession of interbreeding populations is a vastly complicated network N. Since Darwin, species trees have been used as a simplified description of the relationships which summarize the overly complicated network N  . Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate.
Revised:  Since Darwin, species trees have been used as a simplified description of the relationships which summarize the overly complicated network N . Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate.
Edit intent: clarity
Original: The underlying reality of a succession of interbreeding populations is a vastly complicated network N. Since Darwin, species trees have been used as a simplified description of the relationships which summarize the overly complicated network N  . Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate.
Revised: The underlying reality of a succession of interbreeding populations is a vastly complicated network N. Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network N . Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate.
Edit intent: clarity
Original: The underlying reality of a succession of interbreeding populations is a vastly complicated network N. Since Darwin, species trees have been used as a simplified description of the relationships which summarize the overly complicated network N  . Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate.
Revised: The underlying reality of a succession of interbreeding populations is a vastly complicated network N. Since Darwin, species trees have been used as a simplified description of the relationships which summarize the overly complicated network N of reality . Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate.
Edit intent: clarity
Original:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M which either collapses an arc to a single point or takes an arc to an arc, which is surjective, and such that the inverse image of a point is always connected.
Revised:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M such that every arc is either collapsed to a single point or takes an arc to an arc, which is surjective, and such that the inverse image of a point is always connected.
Edit intent: clarity
Original:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M which either collapses an arc to a single point or takes an arc to an arc, which is surjective, and such that the inverse image of a point is always connected.
Revised:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M which either collapses an arc to a single vertex or is taken to an arc, which is surjective, and such that the inverse image of a point is always connected.
Edit intent: clarity
Original:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M which either collapses an arc to a single point or takes an arc to an arc, which is surjective, and such that the inverse image of a point is always connected.
Revised:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M which either collapses an arc to a single point or takes an arc to an arc, such that f is surjective, and such that the inverse image of a point is always connected.
Edit intent: coherence
Original:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M which either collapses an arc to a single point or takes an arc to an arc, which is surjective, and such that the inverse image of a point is always connected.
Revised:  Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M which either collapses an arc to a single point or takes an arc to an arc, which is surjective, and such that the inverse image of a vertex is always connected.
Edit intent: clarity
Original:  If there is such a CSD map, the network M is shown to arise naturally as a quotient structure from N.
Edit intent: coherence
Original:  It is proved that if there is a CSD map from N to M, then there is in a way to lift an undirected version of M into N, possibly with added resolution.
Revised:  It is proved that if there is a CSD map from N to M, then there is a way to lift an undirected version of M into N, possibly with added resolution.
Edit intent: clarity
Original:  It is proved that if there is a CSD map from N to M, then there is in a way to lift an undirected version of M into N, possibly with added resolution.
Revised:  It is proved that if there is a CSD map from N to M, then there is in a way to lift an undirected version of M into N, often with added resolution.
Edit intent: clarity
Original: In the study of complex networks almost all theoretical models are infinite growth, but the size of actual networks is finite.
Revised: In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite.
Edit intent: clarity
Original:  Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, we propose a finite network model with the bulk growth.
Revised:  Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with the bulk growth.
Edit intent: clarity
Original:  Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, we propose a finite network model with the bulk growth.
Revised:  Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, we propose a finite network model with a bulk growth.
Edit intent: fluency
Original:  The model is called S-curve network.
Revised:  The model is said to be an S-curve network.
Edit intent: clarity
Original:  We develop a new method to predict the growth dynamics of the individual nodes, and use this to calculate analytically the connectivity distribution and the scaling exponents.
Revised:  It develops an approximate method to predict the growth dynamics of the individual nodes, and use this to calculate analytically the connectivity distribution and the scaling exponents.
Edit intent: clarity
Original: The problem of finding "small" sets that meet every straight-line which intersects a given unit square was initiated by Mazurkiewicz in 1916.
Revised: The problem of finding ``small'' sets that meet every straight-line which intersects a given unit square was initiated by Mazurkiewicz in 1916.
Edit intent: fluency
Original:  We call such a set  {\em opaque  } or a {\em barrier} for the square.
Revised:  We call such a set an {\em opaque } or a {\em barrier} for the square.
Edit intent: fluency
Original:  We present a simple O(n) time approximation algorithm with ratio 1/2 + \frac{2 +2}{\pi}=1.5867 ....
Revised:  We present a simple O(n) time approximation algorithm with ratio \frac{1 + \frac{2 +2}{\pi}=1.5867 ....
Edit intent: clarity
Original: The problem of finding ``small'' sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916.
Revised: The problem of finding "small" sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916.
Edit intent: fluency
Original:   For general barriers, we present a simple O(n) time approximation algorithm with ratio 1{2}+ \frac{2 +2}{\pi}=1.5867\ldots.
Revised:  For general barriers, we present a O(n) time approximation algorithm with ratio 1{2}+ \frac{2 +2}{\pi}=1.5867\ldots.
Edit intent: clarity
Original:  For single-arc barriers, we propose an algorithm which we conjecture finds an optimal barrier, running in O(n) time.
Edit intent: coherence
Original:  We also show that for the connected and single-arc cases, the problem is polynomially solvable if the barrier is restricted to the interior and the boundary of the input polygon  .
Revised:  We also show that if the barrier is restricted to the interior and the boundary of the input polygon .
Edit intent: coherence
Original:  For general barriers, we present a O(n) time approximation algorithm with ratio \frac{1 + \frac{2 +2}{\pi}=1.5867 \ldots.
Revised:  For general barriers, we present an approximation algorithm with ratio \frac{1 + \frac{2 +2}{\pi}=1.5867 \ldots.
Edit intent: clarity
Original:  For general barriers, we present a O(n) time approximation algorithm with ratio \frac{1 + \frac{2 +2}{\pi}=1.5867 \ldots.
Revised:  For general barriers, we present a O(n) time approximation algorithm with ratio \frac{1 + \frac{2 +2}{\pi}=1.5867 ....
Edit intent: coherence
Original:  We also show that if the barrier is restricted to the  interior and the boundary of the  input polygon, then the problem admits a fully polynomial-time approximation scheme for the connected case and a quadratic-time exact algorithm for the single-arc case.
Revised:  We also show that if the barrier is restricted to the ( interior and the boundary of the input polygon, then the problem admits a fully polynomial-time approximation scheme for the connected case and a quadratic-time exact algorithm for the single-arc case.
Edit intent: fluency
Original:  We also show that if the barrier is restricted to the  interior and the boundary of the  input polygon, then the problem admits a fully polynomial-time approximation scheme for the connected case and a quadratic-time exact algorithm for the single-arc case.
Revised:  We also show that if the barrier is restricted to the interior and the boundary of the ) input polygon, then the problem admits a fully polynomial-time approximation scheme for the connected case and a quadratic-time exact algorithm for the single-arc case.
Edit intent: fluency
Original:  Via Pontryagin duality, the indices of vertices spanning constituent n-cubes within this set form a finite group, and its representation theory is a product of discrete Fourier transforms over the finite subgroup structures supported by X.
Revised:  Via Pontryagin duality, the indices of vertices spanning constituent n-cubes within this set form a finite group, and its representation theory is a product of discrete Fourier transforms over the finite subgroup presentations supported by X.
Edit intent: clarity
Original:  Higher-order set membership at deeper logical depths is discussed, and invariants of depth complexity are defined.
Revised:  Higher-order set membership at deeper logical depths is discussed, and measures of depth complexity are defined.
Edit intent: clarity
Original: The irreducible topological, algebraic, and logical content of a finite binary sequence is classified using the universal covering topology of circuits which generate the sequence.
Revised: The irreducible topological, algebraic, and logical content of a finite binary sequence is classified using the universal covering topology of circuits that generate the sequence.
Edit intent: fluency
Original:  Via Pontryagin duality, the indices of vertices spanning constituent n-cubes within this set form a finite group, and its representation theory is a product of discrete Fourier transforms over the finite subgroup presentations supported by X . The upper bounds in this spectrum form the universal covering group of X , and its corresponding Cayley graph classifies the topology of algorithms enumerating the indices of X.
Revised:  Via Pontryagin duality, the indices of vertices spanning constituent n-cubes within this set form a finite group, and its representation theory is a product of discrete Fourier transforms over the finite subgroup presentations supported by X . The upper bounds in this spectrum form the universal covering group of X , and its corresponding Cayley graph classifies the topology of circuits or directed graphs enumerating X.
Edit intent: clarity
Original:  This measure of logical complexity generates finite proofs of the redundancy (reducibility ) or randomness (irreducibility ) of binary sequences with regard to first-order set membership . Higher-order set membership at deeper logical depths is discussed, and measures of depth complexity are defined .
Revised:  This measure of logical complexity generates finite proofs of the redundancy (reducibility ) of binary sequences with regard to first-order set membership . Higher-order set membership at deeper logical depths is discussed, and measures of depth complexity are defined .
Edit intent: clarity
Original:  This measure of logical complexity generates finite proofs of the redundancy (reducibility ) or randomness (irreducibility ) of binary sequences with regard to first-order set membership . Higher-order set membership at deeper logical depths is discussed, and measures of depth complexity are defined .
Revised:  This measure of logical complexity generates finite proofs of the redundancy (reducibility ) or randomness (irreducibility ) of binary sequences with regard to first-order set membership .
Edit intent: clarity
Original:  This covering group is a minimal  automorphism group of X and its Cayley graph classifies the topology of circuits or directed graphs enumerating X.
Revised:  This covering group is a minimal presentation of the automorphism group of X and its Cayley graph classifies the topology of circuits or directed graphs enumerating X.
Edit intent: clarity
Original: The irreducible topological, algebraic, and logical content of a finite binary sequence is classified using the universal covering topology of circuits that generate the sequence.
Revised: The irreducible information content of finite strings are considered with regard to universal representations. First, finite binary sequences are classified using the universal covering topology of circuits that generate the sequence.
Edit intent: clarity
Original:  This machine-independent measure of first-order logical complexity may be used to test the reducibility (regularity) or irreducibility (quasi-randomness) of binary sequences with regard to first-order set membership. 
Revised:  This machine-independent measure of first order logic may be used to test the reducibility (regularity) or irreducibility (quasi-randomness) of binary sequences with regard to first-order set membership. 
Edit intent: clarity
Original:  This machine-independent measure of first-order logical complexity may be used to test the reducibility (regularity) or irreducibility (quasi-randomness) of binary sequences with regard to first-order set membership. 
Revised:  This machine-independent measure of first-order logical complexity may be used to test the reducibility of binary sequences with regard to first-order set membership. 
Edit intent: clarity