wanyu/IteraTeR_v2 huggingface dataset:
Original:  In 1987, Ghosh presented approximation algorithms for vertex guards and edge guards that achieved a ratio of O(\log n), which was improved up to O(\log\log OPT) by King and Kirkpatrick in 2011.
Revised:  In 1987, Ghosh presented approximation algorithms for vertex guards and edge guards that achieved a ratio of O(\log n), which was improved upto O(\log\log OPT) by King and Kirkpatrick in 2011.
Edit intent: fluency
Original:  On the other hand, when holesare allowed, we show that the problem of vertex guarding a weak visibility polygon is APX-hard by constructing a reduction from the Set Cover problem  \ln n for any \epsilon > 0, unless NP \subseteq TIME(n^{O(\log\log n)})} .
Revised:  On the other hand, for weak visibility polygons with holes, we present a reduction from the Set Cover problem \ln n for any \epsilon > 0, unless NP \subseteq TIME(n^{O(\log\log n)})} .
Edit intent: clarity
Original:  Finally, we consider the point guard problem and show that it is NP-hard in the case of polygons weakly visible from an edge.
Revised:  Finally, we consider the Point Guard problem and show that it is NP-hard in the case of polygons weakly visible from an edge.
Edit intent: fluency
Original: This paper introduces a  methodology that applies to solve graph edge-coloring problems and in particular to prove that the Ramsey number R(4,3,3) =30.
Revised: This paper introduces a general methodology that applies to solve graph edge-coloring problems and in particular to prove that the Ramsey number R(4,3,3) =30.
Edit intent: clarity
Original:  Yet, it has been sought after for more than 50 years.
Revised:  Yet, its precise value has remained unknown for more than 50 years.
Edit intent: clarity
Original:  We illustrate  two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings  } .
Revised:  We illustrate the approach via two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings } .
Edit intent: clarity
Original:  We illustrate  two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings  } .
Revised:  We illustrate two applications: proving that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings } .
Edit intent: fluency
Original:  We illustrate  two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings  } .
Revised:  We illustrate two applications: to prove that R(4,3,3)=30 and computing the previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings } .
Edit intent: fluency
Original:  We illustrate  two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings  } .
Revised:  We illustrate two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 %DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings } .
Edit intent: fluency
Original:  We illustrate  two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings  } .
Revised:  We illustrate two applications: to prove that R(4,3,3)=30 and to compute the , previously unknown number , 78 ,%DIFDELCMD < }%%% 892, of (3,3,3;13) Ramsey colorings ,} .
Edit intent: fluency
Original:  The proposed technique is based on two well-studied concepts,abstraction andsymmetry .
Revised:  abstraction andsymmetry .
Edit intent: clarity
Original:  The proposed technique is based on two well-studied concepts,abstraction andsymmetry .
Revised:  The proposed technique is based on two well-studied concepts, andsymmetry .
Edit intent: fluency
Original:  The proposed technique is based on two well-studied concepts,abstraction andsymmetry .
Revised:  The proposed technique is based on two well-studied concepts,abstraction symmetry .
Edit intent: fluency
Original:  The proposed technique is based on two well-studied concepts,abstraction andsymmetry .
Revised:  The proposed technique is based on two well-studied concepts,abstraction and .
Edit intent: clarity
Original:  First,we introduce an abstraction on graph colorings } , degree matrices ,that specify the degree of each vertex in each color.
Revised:  First,we introduce an abstraction on graph colorings ,} , degree matrices ,that specify the degree of each vertex in each color.
Edit intent: fluency
Original:  First,we introduce an abstraction on graph colorings } , degree matrices ,that specify the degree of each vertex in each color.
Revised:  First,we introduce an abstraction on graph colorings } , ,that specify the degree of each vertex in each color.
Edit intent: clarity
Original:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% 892).
Revised:  We illustrate the approach via two applications: proving that R (4,3,3 ; 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% 892).
Edit intent: coherence
Original:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% 892).
Revised:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 ) Ramsey coloring exists implying that R(4 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% 892).
Edit intent: clarity
Original:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% 892).
Revised:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ,%DIFDELCMD < }%%% 892).
Edit intent: coherence
Original:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% 892).
Revised:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 %DIFDELCMD < }%%% 892).
Edit intent: fluency
Original:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% 892).
Revised:  We illustrate the approach via two applications: proving that R (4,3,3 )= 30 and computing the previously unknown number of (3 ,3,3 ;13)Ramsey colorings (78 ,%DIFDELCMD < }%%% )=30.
Edit intent: clarity
Original:  Applications in coding theory are briefly discussed .
Revised:  Several communication scenarios are described for which the obtained results, and codes in A_n lattices in general, are relevant .
Edit intent: clarity
Original: This paper presents a geometric/coding theoretic interpretation of planar difference sets and the corresponding reformulations of two important conjectures in the field .
Revised: The paper presents a geometric/coding theoretic interpretation of planar difference sets and the corresponding reformulations of two important conjectures in the field .
Edit intent: fluency
Original: This paper presents a geometric/coding theoretic interpretation of planar difference sets and the corresponding reformulations of two important conjectures in the field .
Revised: This paper presents a geometric/coding theoretic interpretation of difference sets and the corresponding reformulations of two important conjectures in the field .
Edit intent: clarity
Original:  It is shown that such sets of order n exist if and only if the A_n lattice admits a lattice tiling by balls of radius 2 under \ell_1 metric ( i.e., a linear 2 -perfect code ).
Revised:  It is shown that such sets of order n exist if and only if the A_n lattice admits a lattice tiling by balls of radius 1 , i.e., a linear 2 -perfect code ).
Edit intent: clarity
Original:  More general difference sets and perfect codes of larger radius are also studied.
Revised:  More general difference sets and perfect codes of radius r is also studied.
Edit intent: clarity
Original:  Several communication scenarios are described for which the obtained results , and codes in A_n lattices in general, are relevant.
Revised:  Several communication scenarios are described for which the obtained results are relevant.
Edit intent: coherence
Original:  It is shown that an Abelian planar difference set with n + 1 elements exists if and only if the A_n lattice admits a lattice tiling by balls of radius 1 , i.e., a linear 1 -perfect code .
Revised:  It is shown that the A_n lattice admits a lattice tiling by balls of radius 1 , i.e., a linear 1 -perfect code .
Edit intent: clarity
Original:  It is shown that an Abelian planar difference set with n + 1 elements exists if and only if the A_n lattice admits a lattice tiling by balls of radius 1 , i.e., a linear 1 -perfect code .
Revised:  It is shown that an Abelian planar difference set with n + 1 elements exists if and only if the A_n lattice admits a linear perfect code of radius 1 , i.e., a linear 1 -perfect code .
Edit intent: clarity
Original:  It is shown that an Abelian planar difference set with n + 1 elements exists if and only if the A_n lattice admits a lattice tiling by balls of radius 1 , i.e., a linear 1 -perfect code .
Revised:  It is shown that an Abelian planar difference set with n + 1 elements exists if and only if the A_n lattice admits a lattice tiling by balls of radius 1 , i.e., a linear 1 .
Edit intent: clarity
Original:  Similarly, B_{2r linear codes of radius r in the A_n lattice  .
Revised:  Similarly, B_{2r linear codes of radius r in the A_n lattice and B_{2r .
Edit intent: coherence
Original:  B_{2r+1} sequences are also represented geometrically in a slightly different way.
Revised:  B_{2r+1} sets are also represented geometrically in a slightly different way.
Edit intent: clarity
Original: Motivated by several communication scenarios, such as the permutation channel, the 0 -insertion/deletion channel, and q -ary asymmetric channels, we investigate properties of (linear) codes in A_n lattices  .
Revised: This chapter investigates the properties of (linear) codes in A_n lattices .
Edit intent: clarity
Original:  In particular, we demonstrate a connection between such codes and notions of difference sets and B_h sets in Abelian groups  .
Revised:  In particular, a connection between such codes and notions of difference sets and B_h sets in Abelian groups .
Edit intent: clarity
Original:  In particular, we demonstrate a connection between such codes and notions of difference sets and B_h sets in Abelian groups  .
Revised:  In particular, we demonstrate a connection between these codes and notions of difference sets and B_h sets in Abelian groups .
Edit intent: clarity
Original:  It is shown that the A_n lattice admits a linear perfect code of radius 1 if and only if there exists an Abelian planar difference set of cardinality n + 1 . Similarly, a direct link is given between linear codes of radius r in the A_n lattice and B_{2r cardinality n + 1 . B_{2r+1 are also represented geometrically in a slightly different way.
Revised:  It is shown that the A_n lattice admits a linear perfect code of radius 1 if and only if there exists an Abelian planar difference set of cardinality n + 1 . Similarly, a direct link is given between linear codes of radius r in the A_n lattice and B_{2r cardinality n + 1 . B_{2r+1 are also represented geometrically in a similar way.
Edit intent: coherence
Original:  Apart from providing a geometric intuition about B_h sets, this interpretation enables simple derivations of bounds on their parameters, which are either equivalent to, or improve upon the known bounds.
Revised:  Apart from providing geometric intuition about B_h sets, this interpretation enables simple derivations of bounds on their parameters, which are either equivalent to, or improve upon the known bounds.
Edit intent: fluency
Original:  Using combinatorial arguments, we give a full classification of the complexity of multiplicatively approximating the norm of the partition function for complex edge interactions.
Revised:  Using combinatorial arguments, we give the first full classification of the complexity of multiplicatively approximating the norm of the partition function for complex edge interactions.
Edit intent: clarity
Original:  We also classify the complexity of additively approximating the argument of the partition function (and of approximating the partition function according to a natural complex metric) .
Revised:  We also classify the complexity of additively approximating the argument of the partition function .
Edit intent: clarity
Original:  We give a complete dichotomy for the case in which the parameters are roots of unity.
Revised:  We give a complete dichotomy for the case where the parameters are roots of unity.
Edit intent: clarity
Original:  Previous results were known just for a few such points, and we strengthen these results from BQP-hardness to #P-hardness.
Revised:  Previous results were known just for a few such points, and we strengthen them from BQP-hardness to #P-hardness.
Edit intent: coherence
Original: We study the complexity of approximating the Ising and Tutte partition functions with complex parameters.
Revised: We study the complexity of approximately evaluating the Ising and Tutte partition functions with complex parameters.
Edit intent: clarity
Original:  The main motivation for this paper is to go the other way around . Partition functions are combinatorial in nature and classifying the difficulty of approximating these partition functions does not require a detailed understanding of quantum computation.
Revised:  The main motivation for this paper is to go the other way around . Partition functions are combinatorial in nature and quantifying their approximation complexity does not require a detailed understanding of quantum computation.
Edit intent: clarity
Original:  We give a complete dichotomy for the case where the parameters are roots of unity.
Revised:  We give a complete dichotomy when the parameters are roots of unity.
Edit intent: clarity
Original:  Previous results were known just for a few such points, and we strengthen them from BQP-hardness to #P-hardness  .
Revised:  Previous results were known just for a few such points, and we strengthen these results from BQP-hardness to #P-hardness .
Edit intent: clarity
Original:  This is mainly because one can measure the expression profiles for thousands of genes at the same time and that makes this technology a good option for some studies focused on systems biology.
Revised:  This is mainly because one can measure the expression profiles for thousands of genes simultaneously, what makes this technology a good option for some studies focused on systems biology.
Edit intent: coherence
Original:  One of the main problems is that the experimental procedureis complex and the data has several sources of variance, that makes the statistical modelingmore difficult .
Revised:  One of its main problem is complexity of experimental procedure, presenting several sources of variance, that makes the statistical modelingmore difficult .
Edit intent: clarity
Original:  One of the main problems is that the experimental procedureis complex and the data has several sources of variance, that makes the statistical modelingmore difficult .
Revised:  One of the main problems is that the experimental procedureis complex and the data has several sources of variability, hindering statistical modeling .
Edit intent: clarity
Original:  So far, there is no standard protocol for the generation and evaluation of microarray data.
Revised:  So far, there is no standard protocol for generation and evaluation of microarray data.
Edit intent: fluency
Original:  Besides that, it makes the analysis more robust, reliable and reproducible.
Revised:  Besides that, it makes data analysis process more robust, reliable and reproducible.
Edit intent: clarity
Original:  The package aggregates several data analysis procedures reported in the literature, for instance: cluster analysis, differential expression, supervised classifiers, relevance networks and functional classification of gene groups or gene networks.
Revised:  The package aggregates several data analysis procedures reported in literature, for instance: cluster analysis, differential expression, supervised classifiers, relevance networks and functional classification of gene groups or gene networks.
Edit intent: fluency
Original:  We characterize the scientific fitness of each nation-that is, the competitiveness of its research system-and the complexity of each scientific domain by means of a non-linear iterative algorithm able to assess quantitatively the advantage of scientific diversification.
Revised:  We characterize the scientific fitness of each nation (that is, the competitiveness of its research system-and the complexity of each scientific domain by means of a non-linear iterative algorithm able to assess quantitatively the advantage of scientific diversification.
Edit intent: fluency
Original:  We characterize the scientific fitness of each nation-that is, the competitiveness of its research system-and the complexity of each scientific domain by means of a non-linear iterative algorithm able to assess quantitatively the advantage of scientific diversification.
Revised:  We characterize the scientific fitness of each nation-that is, the competitiveness of its research system) and the complexity of each scientific domain by means of a non-linear iterative algorithm able to assess quantitatively the advantage of scientific diversification.
Edit intent: fluency
Original:  In this paper, we propose the tree-based convolutional neural network (TBCNN) to model programming languages, which contain rich and explicit tree structural information.
Revised:  In this paper, we propose a novel tree-based convolutional neural network (TBCNN) to model programming languages, which contain rich and explicit tree structural information.
Edit intent: clarity
Original:  Using five different similarity measures we show that our model significantly improves the classification accuracy over the current best composition-based model , when predicting the taxonomic lineage for both short viral sequence fragments (reads in the 100bp - 500bp range) and complete viral sequences.
Revised:  Using five different similarity measures we show that our model significantly improves the classification accuracy over the current best composition-based model , when predicting the taxonomic lineage for both short viral sequence fragments and complete viral sequences.
Edit intent: clarity
Original: This research considers the problem of base station association in a small cell environment.
Revised: This work considers the problem of base station association in a small cell environment.
Edit intent: clarity
Original:  The paper considers two optimization problems , maximizing the set of associated users  and maximizing the set of weighted associated users by the FBSs, subject to signal-to-interference-plus-noise ratio (SINR) requirements as well as the quality of service (QoS) of the macrocell user . Both problems are formulated as linear integer programs.
Revised:  The paper considers two optimization problems , maximizing the set of associated users and maximizing the set of weighted associated users by the FBSs, subject to signal-to-interference-plus-noise ratio (SINR) model . Both problems are formulated as linear integer programs.
Edit intent: clarity
Original:  This work develops two heuristic polynomial time algorithms to solve both problems.
Revised:  This work develops two heuristic polynomial-time algorithms to solve both problems.
Edit intent: fluency
Original:  The results demonstrate the efficiency of the proposed algorithms in terms of complexity and sub-optimality .
Revised:  The results demonstrate the close to optimal performance of the proposed algorithms in terms of complexity and sub-optimality .
Edit intent: clarity
Original:  The results demonstrate the efficiency of the proposed algorithms in terms of complexity and sub-optimality .
Revised:  The results demonstrate the efficiency of the proposed algorithms .
Edit intent: clarity
Original:  They also show that the weighted problem can be solved to provide solutions that are fair between the users and load balance among femtocells .
Revised:  They also show that the weighted problem can be solved to provide solutions that are fair between users or to balance the load among SBSs .
Edit intent: clarity
Original: This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small cell network (HetSNet).
Revised: This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small-cell network (HetSNet).
Edit intent: fluency
Original:  Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under the signal-to-interference-plus-noise ratio (SINR) model . Both problems are formulated as linear integer programs.
Revised:  Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under signal-to-interference-plus-noise ratio (SINR) model . Both problems are formulated as linear integer programs.
Edit intent: fluency
Original:  Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under the signal-to-interference-plus-noise ratio (SINR) model . Both problems are formulated as linear integer programs.
Revised:  Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under the signal-to-interference-plus-noise ratio (SINR) constraints . Both problems are formulated as linear integer programs.
Edit intent: clarity
Original:  The weighted problem is known to be NP-hard and  in this paper, the unweighted problem is proved to be NP-hard as well.
Revised:  The weighted problem is known to be NP-hard and , in this paper, the unweighted problem is proved to be NP-hard as well.
Edit intent: fluency
Original:  Moreover, the paper benchmarks the performance of the proposed algorithms against the BF algorithm, the branch-and-bound (B  B) algorithm and an industry standard algorithm , through numerical simulations.
Revised:  Moreover, the paper benchmarks the performance of the proposed algorithms against the BF algorithm, the branch-and-bound (B B) algorithm and standard algorithms , through numerical simulations.
Edit intent: clarity
Original:  The results demonstrate the close to optimal performance of the proposed algorithms.
Revised:  The results demonstrate the close-to-optimal performance of the proposed algorithms.
Edit intent: fluency
Original:  To test the model prediction we inhibited Apelin signaling in our model and in an in vitro model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting.
Revised:  To test the model prediction we inhibited Apelin signaling in our model and in an in vitro model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting.
Edit intent: fluency