wanyu/IteraTeR_v2 huggingface dataset:
Original:  The corresponding polynomial dynamical systems are often large , consisting of tens or even hundreds of ordinary differential equations , and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions).
Revised:  The corresponding polynomial dynamical systems are often large ( consisting of tens or even hundreds of ordinary differential equations , and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions).
Edit intent: fluency
Original:  The corresponding polynomial dynamical systems are often large , consisting of tens or even hundreds of ordinary differential equations , and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions).
Revised:  The corresponding polynomial dynamical systems are often large , consisting of tens or even hundreds of ordinary differential equations ) and poorly parametrized (due to noisy measurement data and a small number of data points and repetitions).
Edit intent: fluency
Original: Based on the stochastic model proposed by Patriarka-Kaski-Chakraborti that describes the exchange of wealth between n economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter \epsilon.
Revised: Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between n economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter \epsilon.
Edit intent: fluency
Original:  The relations among these subsets are shown using various visualization techniques.
Revised:  The relations among these subsets are explored using various visualization techniques.
Edit intent: clarity
Original:  However, this structure could not be retrieved using the ISI Subject Categories, including the 25 categories which are specific to the AHCI.
Revised:  However, we were not able to retrieve this structure using the ISI Subject Categories, including the 25 categories which are specific to the AHCI.
Edit intent: coherence
Original:  We discuss validation against the categories of the Humanities Indicators ( of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA ( as an example ) .
Revised:  We discuss options for validation such as against the categories of the Humanities Indicators ( of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA ( as an example ) .
Edit intent: clarity
Original:  We discuss validation against the categories of the Humanities Indicators ( of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA ( as an example ) .
Revised:  We discuss validation against the categories of the Humanities Indicators of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA ( as an example ) .
Edit intent: fluency
Original:  We discuss validation against the categories of the Humanities Indicators ( of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA ( as an example ) .
Revised:  We discuss validation against the categories of the Humanities Indicators ( of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA as an example ) .
Edit intent: fluency
Original:  We discuss validation against the categories of the Humanities Indicators ( of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA ( as an example ) .
Revised:  We discuss validation against the categories of the Humanities Indicators ( of the American Academy of Arts and Sciences ) and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA ( as an example of institutional organization .
Edit intent: clarity
Original: Using the Arts & Humanities Citation Index ( AHCI  ) 2008, we apply mapping techniques previously developed for mapping journal structures in the Science and Social Science Citation Indices.
Revised: Using the Arts & Humanities Citation Index ( A ) 2008, we apply mapping techniques previously developed for mapping journal structures in the Science and Social Science Citation Indices.
Edit intent: clarity
Original:  Can a cognitive structure be reconstructed from the aggregated citation patterns among these 1,157 journals containing 110, 718 records?
Revised:  Citation relations among the 110,718 records were aggregated at the level of 1,157 journals containing 110, 718 records?
Edit intent: clarity
Original:  including the 25 categories which are specific to the AHCI  . We discuss options for validation such as against the categories of the Humanities Indicators of the American Academy of Arts and Sciences, the panel structure of the European Reference Index for the Humanities (ERIH), and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA as an example of institutional organization.
Revised:  including the 25 categories which are specific to the A . We discuss options for validation such as against the categories of the Humanities Indicators of the American Academy of Arts and Sciences, the panel structure of the European Reference Index for the Humanities (ERIH), and compare our results with the curriculum organization of the Humanities Section of the College of Letters and Sciences of UCLA as an example of institutional organization.
Edit intent: clarity
Original: Motivated by the desire to cope with data imprecision \mbox{ Loeffler09 , we study methods for preprocessing a set of planar regions such that whenever we are given a set of points, each of which lies on a distinct region, we can compute a specified structure on these points more efficiently than in "standard settings" (that is, without preprocessing) .
Revised: Motivated by the desire to cope with \mbox{ Loeffler09 , we study methods for preprocessing a set of planar regions such that whenever we are given a set of points, each of which lies on a distinct region, we can compute a specified structure on these points more efficiently than in "standard settings" (that is, without preprocessing) .
Edit intent: clarity
Original: Motivated by the desire to cope with data imprecision \mbox{ Loeffler09 , we study methods for preprocessing a set of planar regions such that whenever we are given a set of points, each of which lies on a distinct region, we can compute a specified structure on these points more efficiently than in "standard settings" (that is, without preprocessing) .
Revised: Motivated by the desire to cope with data imprecision data imprecision , we study methods for preprocessing a set of planar regions such that whenever we are given a set of points, each of which lies on a distinct region, we can compute a specified structure on these points more efficiently than in "standard settings" (that is, without preprocessing) .
Edit intent: coherence
Original: Motivated by the desire to cope with data imprecision \mbox{ Loeffler09 , we study methods for preprocessing a set of planar regions such that whenever we are given a set of points, each of which lies on a distinct region, we can compute a specified structure on these points more efficiently than in "standard settings" (that is, without preprocessing) .
Revised: Motivated by the desire to cope with data imprecision \mbox{ Loeffler09 , we study methods for taking advantage of preliminary information about point sets in order to speed up the computation of certain structures associated with them .
Edit intent: clarity
Original:  We show that in quadratic time and space it is possible to construct a data structure on L that enables us to compute the convex hull of any such point set P in O(n \alpha (n) \log^* n) expected time.
Revised:  We show that in quadratic time and space it is possible to construct a data structure on L that enables us to compute the convex hull of any such point set P in O(n alpha (n) \log^* n) expected time.
Edit intent: fluency
Original:  We show that in quadratic time and space it is possible to construct a data structure on L that enables us to compute the convex hull of any such point set P in O(n \alpha (n) \log^* n) expected time.
Revised:  We show that in quadratic time and space it is possible to construct a data structure on L that enables us to compute the convex hull of any such point set P in O(n \alpha (n) log* n) expected time.
Edit intent: clarity
Original:  Here, we are given a planar n-point set P, and we wish to preprocess P such that given any set of lines L , each of which is incident to a distinct point of P, we can compute the (\leq k)-level of L efficiently.
Revised:  Here, we are given a planar n-point set P, and we wish to preprocess P such that given any set of lines L , each of which lies on a distinct point of P, we can compute the (\leq k)-level of L efficiently.
Edit intent: clarity
Original: In this document the optimal dimensional synthesis for planar mechanisms using differential evo- lution (DE) is shown.
Revised: The optimal dimensional synthesis for planar mechanisms using differential evo- lution (DE) is shown.
Edit intent: clarity
Original: In this document the optimal dimensional synthesis for planar mechanisms using differential evo- lution (DE) is shown.
Revised: In this document the optimal dimensional synthesis for planar mechanisms using differential evolution (DE) is shown.
Edit intent: fluency
Original:  Four study cases are presented : in the first case, the synthesis of a mechanism for hybrid-tasks, considering path generation, function generation, and motion generation, is car- ried out.
Revised:  Four study cases are presented : in the first case, the synthesis of a mechanism for hybrid-tasks, considering path generation, function generation, and motion generation, is carried out.
Edit intent: fluency
Original:  The second and third cases deal with path generation with and without prescribed timing.
Revised:  The second and third cases pertain to path generation, with and without prescribed timing.
Edit intent: clarity
Original:  The order defect problem is addressed by manipulating individuals instead of penalizing or discretizing the searching space for the parameters , as was proposed by other authors.
Revised:  The order defect problem is solved by manipulating individuals instead of penalizing or discretizing the searching space for the parameters , as was proposed by other authors.
Edit intent: clarity
Original:  The order defect problem is addressed by manipulating individuals instead of penalizing or discretizing the searching space for the parameters , as was proposed by other authors.
Revised:  The order defect problem is addressed by manipulating individuals instead of penalizing or discretizing the search space for the parameters , as was proposed by other authors.
Edit intent: fluency
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF, any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj . We generalise this result to sigma-symmetric matrices introduced by the author and Rao in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Edit intent: fluency
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices over\bF \bF a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj . We generalise this result to sigma-symmetric matrices introduced by the author and Rao in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Edit intent: clarity
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF-rank-width a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj . We generalise this result to sigma-symmetric matrices introduced by the author and Rao in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Edit intent: clarity
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF has a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj . We generalise this result to sigma-symmetric matrices introduced by the author and Rao in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Edit intent: clarity
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF a pair i< j, such that Mi is isomorphic to a principal submatrix of a . We generalise this result to sigma-symmetric matrices introduced by the author and Rao in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Edit intent: clarity
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mjprincipal pivot transform . We generalise this result to sigma-symmetric matrices introduced by the author and Rao in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Edit intent: fluency
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj . We generalise this result to sigma-symmetric matrices introduced by the author and Rao introduced by Rao and myself in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Edit intent: coherence
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF  a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj  . We generalise this result to sigma-symmetric matrices introduced by the author and Rao  in [The Rank-Width of Edge-Colored Graphs, arXiv:0709.1433v4].
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that for\bF any infinite sequence M1,M2 ,... of (skew) symmetric matrices of bounded rank-width there is\bF \bF a pair i< j, such that Mi is isomorphic to a principal sub-matrix of a principal pivot transform of Mj . We generalise this result to sigma-symmetric matrices introduced by the author and Rao in [The Rank-Width of Edge-Coloured Graphs, arXiv:0709.1433v4].
Edit intent: fluency
Original:  Sigma-symmetric matrices are generalisations of (skew ) symmetric matrices .
Revised:  (Skew ) symmetric matrices .
Edit intent: clarity
Original:  As a by-product, we obtain that for every infinite sequence G1,G2 ,... of edge-colored graphs of bounded rank-width there exists a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{ \emph{ .
Revised:  As a by-product, we obtain that for every infinite sequence G_1,G_2 ,... of edge-colored graphs of bounded rank-width there exists a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{ \emph{ .
Edit intent: fluency
Original:  As a by-product, we obtain that for every infinite sequence G1,G2 ,... of edge-colored graphs of bounded rank-width there exists a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{ \emph{ .
Revised:  As a by-product, we obtain that for every infinite sequence G1,G2 ,... of directed graphs of bounded rank-width there exists a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{ \emph{ .
Edit intent: clarity
Original:  As a by-product, we obtain that for every infinite sequence G1,G2 ,... of edge-colored graphs of bounded rank-width there exists a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{ \emph{ .
Revised:  As a by-product, we obtain that for every infinite sequence G1,G2 ,... of edge-colored graphs of bounded rank-width there exist a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{ \emph{ .
Edit intent: fluency
Original:  As a by-product, we obtain that for every infinite sequence G1,G2 ,... of edge-colored graphs of bounded rank-width there exists a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{ \emph{ .
Revised:  As a by-product, we obtain that for every infinite sequence G1,G2 ,... of edge-colored graphs of bounded rank-width there exists a pair i<j such that Gi is a pivot-minor of Gj . We also prove that non singular principal sub-matrices of a sigma-symmetric matrix forms a delta-matroid\emph{pivot-minor \emph{ .
Edit intent: fluency
Original: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that, for a fixed finite field %DIFDELCMD < \bF%%%  , any infinite sequence M_1,M_2,... of (skew) symmetric matrices over %DIFDELCMD < \bF %%% of bounded\emph{%DIFDELCMD < \bF%%% -
Revised: In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that, for a fixed finite field %DIFDELCMD < \bF%%% , any infinite sequence M_1,M_2,... of (skew) symmetric matrices over %DIFDELCMD < \bF %%% \emph{%DIFDELCMD < \bF%%% -
Edit intent: clarity
Original: rank-width has a pair i< j, such that M_i is isomorphic to a principal submatrix of a principal pivot transform of M_j. We generalise this result to \sigma-symmetric matrices introduced by Rao and myself in [The Rank-Width of Edge-Coloured Graphs, arXiv:0709.1433v4].
Revised: rank-width has a pair i< j, such that M_i is isomorphic to a principal submatrix of a principal pivot transform of M_j. We generalise this result to \sigma-symmetric matrices introduced by Rao and myself in [The Rank-Width of Edge-Coloured Graphs, arXiv:0709.1433v4].
Edit intent: fluency
Original:  As a by-product, we obtain that for every infinite sequence G_1,G_2,... of directed graphs of bounded rank-width there exist a pair i<j such that G_i is a pivot-minor of G_j. Another consequence is that non-singular principal submatrices of a \sigma-symmetric matrix form a delta-matroid .
Revised:  As a by-product, we obtain that for every infinite sequence G_1,G_2,... of directed graphs of bounded rank-width there exist a pair i<j such that G_i is a pivot-minor of G_j. Another consequence is that non-singular principal submatrices of a \sigma-symmetric matrix form a delta-matroid .
Edit intent: fluency