wanyu/IteraTeR_v2 huggingface dataset:
Original:  Performance measurements on a broad range of datasets demonstate reductions in run-time of up to 60 times relative to the state of the art and the scalability of the algorithm to realistically-sized datasets up to several million records.
Revised:  Performance measurements on a broad range of datasets demonstrate substantial reductions in run-time of up to 60 times relative to the state of the art and the scalability of the algorithm to realistically-sized datasets up to several million records.
Edit intent: clarity
Original:  Performance measurements on a broad range of datasets demonstate reductions in run-time of up to 60 times relative to the state of the art and the scalability of the algorithm to realistically-sized datasets up to several million records.
Revised:  Performance measurements on a broad range of datasets demonstate reductions in run-time relative to the state of the art and the scalability of the algorithm to realistically-sized datasets up to several million records.
Edit intent: clarity
Original:  In this paper, we propose a new ensemble-based data assimilation method, named  "sampling filter" .
Revised:  In this paper, we propose a new ensemble-based data assimilation method, named the "sampling filter" .
Edit intent: fluency
Original:  The sampling strategy in the analysis phase of the filter follows a Hybrid Monte Carlo (HMC) approach that is, in principle, applicable in cases where Gaussian assumption is violated and also when observations are nonlinear.
Revised:  The sampling strategy is based on a Hybrid Monte Carlo (HMC) approach that is, in principle, applicable in cases where Gaussian assumption is violated and also when observations are nonlinear.
Edit intent: clarity
Original:  To address this  , we developed an open-source lipid bilayer amplifier, the OpenPicoAmp, which is appropriate for use in introductory courses in biophysics or neurosciences concerning the electrical properties of the cell membrane.
Revised:  To address this issue , we developed an open-source lipid bilayer amplifier, the OpenPicoAmp, which is appropriate for use in introductory courses in biophysics or neurosciences concerning the electrical properties of the cell membrane.
Edit intent: clarity
Original:  To address this  , we developed an open-source lipid bilayer amplifier, the OpenPicoAmp, which is appropriate for use in introductory courses in biophysics or neurosciences concerning the electrical properties of the cell membrane.
Revised:  To address this , we developed an open-source lipid bilayer amplifier, the OpenPicoAmp, which is appropriate for use in introductory courses in biophysics or neurosciences dealing with the electrical properties of the cell membrane.
Edit intent: clarity
Original:  This experimental setup can be used in simple experiments in which students monitor the bilayer formation by capacitance measurement and record unitary currents produced by ionophores like gramicidin A. Used in combination with a low-cost data acquisition board this system provides a complete solution for hands-on lessons, therefore improving the effectiveness in teaching basic neurosciences or biophysics.
Revised:  This experimental setup can be used in simple experiments in which students monitor the bilayer formation by capacitance measurement and record unitary currents produced by ionic channels like gramicidin A. Used in combination with a low-cost data acquisition board this system provides a complete solution for hands-on lessons, therefore improving the effectiveness in teaching basic neurosciences or biophysics.
Edit intent: clarity
Original: Given a non-decreasing sequence S=(s _1,s_2 , \ldots, s _k ) of positive integers, an {\em S-packing coloring} of a graph G is a mapping c from V(G) to \{s _1,s_2 , \ldots, s _k \} such that any two vertices with color s _i are at mutual distance greater than s _i , 1\le i\le k.
Revised: Given a non-decreasing sequence S=(s _1,s_2 , \ldots, s \_k ) of positive integers, an {\em S-packing coloring} of a graph G is a mapping c from V(G) to \{s _1,s_2 , \ldots, s _k \} such that any two vertices with color s _i are at mutual distance greater than s _i , 1\le i\le k.
Edit intent: clarity
Original: Given a non-decreasing sequence S=(s _1,s_2 , \ldots, s _k ) of positive integers, an {\em S-packing coloring} of a graph G is a mapping c from V(G) to \{s _1,s_2 , \ldots, s _k \} such that any two vertices with color s _i are at mutual distance greater than s _i , 1\le i\le k.
Revised: Given a non-decreasing sequence S=(s _1,s_2 , \ldots, s _k ) of positive integers, an {\em S-packing coloring} of a graph G is a mapping c from V(G) to \{s _1,s_2 , \ldots, s \_k \} such that any two vertices with color s _i are at mutual distance greater than s _i , 1\le i\le k.
Edit intent: clarity
Original:  Statistical analytics systems differ from conventional SQL-analytics in the amount and types of memory incoherence they can tolerate.
Edit intent: clarity
Original:  We conduct our study across five architectures using popular models including support vector machines , logistic regression, Gibbs sampling, and neural networks.
Revised:  We conduct our study across five architectures using popular models including SVMs , logistic regression, Gibbs sampling, and neural networks.
Edit intent: clarity
Original: We set the stage for studying some substitution subshifts defined on an infinite alphabet.
Revised: We set the stage for studying some substitution shifts defined on an infinite alphabet.
Edit intent: fluency
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Revised:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Edit intent: clarity
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Revised:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this shift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Edit intent: fluency
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Revised:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a shift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Edit intent: fluency
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Revised:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on \mathbb Z%DIFDELCMD < }%%% _p .
Edit intent: clarity
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Revised:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of %DIFDELCMD < }%%% _p .
Edit intent: fluency
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% _p .
Revised:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in \mathbb Z _p^{\mathbb N , we describe how this subshift is a letter-to-letter coding of a subshift generated by a constant-length substitution defined on a closed subset of \mathbb Z%DIFDELCMD < }%%% an uncountable alphabet .
Edit intent: clarity
Original:  We consider sequences of p-adic integers that project modulo p^\alpha to a p-automatic sequence for every \alpha \geq 0. Examples include algebraic sequences of integers,
Revised:  We consider sequences of p-adic integers project modulo p^\alpha to a p-automatic sequence for every \alpha \geq 0. Examples include algebraic sequences of integers,
Edit intent: clarity
Original:  We consider sequences of p-adic integers that project modulo p^\alpha to a p-automatic sequence for every \alpha \geq 0. Examples include algebraic sequences of integers,
Revised:  We consider sequences of p-adic integers that project modulo p^\alpha to p-automatic sequence for every \alpha \geq 0. Examples include algebraic sequences of integers,
Edit intent: fluency
Original:  We consider sequences of p-adic integers that project modulo p^\alpha to a p-automatic sequence for every \alpha \geq 0. Examples include algebraic sequences of integers,
Revised:  We consider sequences of p-adic integers that project modulo p^\alpha to a p-automatic sequences for every \alpha \geq 0. Examples include algebraic sequences of integers,
Edit intent: fluency
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in Z_p^N, we describe how this shift is a letter-to-letter coding of a shift generated by a constant-length substitution defined on an uncountable alphabet  .
Revised:  which satisfy this property for every prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in Z_p^N, we describe how this shift is a letter-to-letter coding of a shift generated by a constant-length substitution defined on an uncountable alphabet .
Edit intent: clarity
Original:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. By considering the shift-orbit closure of such a sequence in Z_p^N, we describe how this shift is a letter-to-letter coding of a shift generated by a constant-length substitution defined on an uncountable alphabet  .
Revised:  which satisfy this property for any prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. For such a sequence in Z_p^N, we describe how this shift is a letter-to-letter coding of a shift generated by a constant-length substitution defined on an uncountable alphabet .
Edit intent: clarity
Original:  The optimal policy is varying according to the primary and CR users arrival rates  as well as the channels connectivity.
Revised:  The optimal policy changes according to the primary and CR users arrival rates as well as the channels connectivity.
Edit intent: clarity
Original:  When n \gg d, one feasible approach to accelerating LSR is to randomly embed y and all columns of X into the subspace R^c where c\ll n ;
Revised:  When n \gg d, one feasible approach to speeding up LSR is to randomly embed y and all columns of X into the subspace R^c where c\ll n ;
Edit intent: clarity
Original:  When n \gg d, one feasible approach to accelerating LSR is to randomly embed y and all columns of X into the subspace R^c where c\ll n ;
Revised:  When n \gg d, one feasible approach to accelerating LSR is to randomly embed y and all columns of X into the subspace R^c ;
Edit intent: clarity
Original:  the induced LSR problem has the same number of columns but much fewer number of rows, and the induced problem can be solved in O(c d^2) time and O(c d) space.
Revised:  the induced LSR problem has the same number of columns but much fewer number of rows, and it can be solved in O(c d^2) time and O(c d) space.
Edit intent: clarity
Original:  The leverage scores based sampling is an effective subspace embedding method and can be applied to accelerate LSR . It was shown previously that c = O(d \epsilon^{-2} \log d) is sufficient for achieving 1+\epsilon accuracy .
Revised:  The leverage scores based sampling based LSR achieves 1+\epsilon accuracy when c \geq O(d \epsilon^{-2} \log d) is sufficient for achieving 1+\epsilon accuracy .
Edit intent: clarity
Original:  The leverage scores based sampling is an effective subspace embedding method and can be applied to accelerate LSR . It was shown previously that c = O(d \epsilon^{-2} \log d) is sufficient for achieving 1+\epsilon accuracy .
Revised:  The leverage scores based sampling is an effective subspace embedding method and can be applied to accelerate LSR . It was shown previously that c = O(d \epsilon^{-2} \log d) .
Edit intent: coherence
Original:  In this paper we sharpen this error bound, showing that c = O(d \log d + d \epsilon^{-1}) is enough for  1+\epsilon accuracy  \log d), the uniform sampling based LSR attains a 2+\epsilon bound with positive probability} .
Revised:  In this paper we sharpen this error bound, showing that c = O(d \log d + d \epsilon^{-1}) is enough for achieving 1+\epsilon accuracy \log d), the uniform sampling based LSR attains a 2+\epsilon bound with positive probability} .
Edit intent: clarity
Original: We analyze the unbiased black-box complexity of jump functions with large jump sizes . Among other results, we show that when the jump size is (1/2 - \varepsilon)n, that is, only a small constant fraction of the fitness values is visible, then the unbiased black-box complexities for arities 3 and higher are of the same order as those for the simple OneMax function.
Revised: We analyze the unbiased black-box complexity of jump functions with large jump sizes . Among other results, we show that when the jump size is (1/2 - \varepsilon)n, that is, only a small constant fraction of the fitness values is visible, then the unbiased black-box complexities for arities 3 and higher are of the same order as those for the simple OneMax function.
Edit intent: fluency
Original:  , EPJ B ( 84 ), 4 (2011) 535-540 ] we revisit the question whether the usage of large citation datasets allows for the quantitative assessment of social (by means of co-authorship of publications) influence on the progression of science.
Revised:  , EPJ B ( 84 ), 4 (2011) ] we revisit the question whether the usage of large citation datasets allows for the quantitative assessment of social (by means of co-authorship of publications) influence on the progression of science.
Edit intent: coherence
Original:  , EPJ B ( 84 ), 4 (2011) 535-540 ] we revisit the question whether the usage of large citation datasets allows for the quantitative assessment of social (by means of co-authorship of publications) influence on the progression of science.
Revised:  , EPJ B ( 84 ), 4 (2011) 535-540 ] we revisit the question whether the usage of large citation datasets allows for the quantitative assessment of social (by means of coauthorship of publications) influence on the progression of science.
Edit intent: fluency
Original:  Applying a more comprehensive and well-curated dataset containing the publications in the journals of the American Physical Society during the whole 20th century we find that the measure chosen in the original study, a score computed on small induced subgraphs, has to be used with caution, since the obtained results are highly sensitive against the exact implementation of the author disambiguation task.
Revised:  Applying a more comprehensive and well-curated dataset containing the publications in the journals of the American Physical Society during the whole 20th century we find that the measure chosen in the original study, a score based on small induced subgraphs, has to be used with caution, since the obtained results are highly sensitive against the exact implementation of the author disambiguation task.
Edit intent: clarity
Original:  Applying a more comprehensive and well-curated dataset containing the publications in the journals of the American Physical Society during the whole 20th century we find that the measure chosen in the original study, a score computed on small induced subgraphs, has to be used with caution, since the obtained results are highly sensitive against the exact implementation of the author disambiguation task.
Revised:  Applying a more comprehensive and well-curated dataset containing the publications in the journals of the American Physical Society during the whole 20th century we find that the measure chosen in the original study, a score computed on small induced subgraphs, has to be used with caution, since the obtained results are highly sensitive to the exact implementation of the author disambiguation task.
Edit intent: fluency
Original: We study generalized point-line configurations and their properties in the projective plane.
Revised: We study generalized point-line incidence structures and their properties in the projective plane.
Edit intent: clarity
Original:  These generalized configurations can serve as building blocks for (n_4) configurations .
Revised:  Our motivation is the problem of the existence of (n_4) configurations .
Edit intent: coherence
Original:  The existence problem of finding such configurations for the remaining cases (22_4), (23_4), and (26_4)  remains open.
Revised:  The existence problem of finding (22_4), (23_4), and (26_4) remains open.
Edit intent: clarity
Original:  The existence problem of finding such configurations for the remaining cases (22_4), (23_4), and (26_4)  remains open.
Revised:  The existence problem of finding such configurations for the remaining cases (22_4), (23_4), and (26_4) configurations remains open.
Edit intent: clarity
Original:  Given two input graphs G1;G2, a pair of vertex mappings induces an edge conservation if the vertex pairs are adjacent in their respective graphs.
Revised:  Given two input graphs G_1, G_2, a pair of vertex mappings induces an edge conservation if the vertex pairs are adjacent in their respective graphs.
Edit intent: clarity
Original:  Let m1 (m2 ) denote the number of G2-vertices (G1-vertices ) that each G1-vertex (G2-vertex ) is allowed to be mapped to.
Revised:  Let m_1 (m_2 ) denote the number of G2-vertices (G1-vertices ) that each G1-vertex (G2-vertex ) is allowed to be mapped to.
Edit intent: clarity
Original:  Let m1 (m2 ) denote the number of G2-vertices (G1-vertices ) that each G1-vertex (G2-vertex ) is allowed to be mapped to.
Revised:  Let m1 (m2 ) denote the number of G_2-vertices (G_1-vertices ) that each G1-vertex (G2-vertex ) is allowed to be mapped to.
Edit intent: fluency
Original:  Let m1 (m2 ) denote the number of G2-vertices (G1-vertices ) that each G1-vertex (G2-vertex ) is allowed to be mapped to.
Revised:  Let m1 (m2 ) denote the number of G2-vertices (G1-vertices ) that each G_1-vertex (G_2-vertex ) is allowed to be mapped to.
Edit intent: fluency
Original:  All problem versions considered herein assume m2 = 1. We provide a polynomial time solution for a special case where G1 is acyclic.
Revised:  All provided results assume m_2 = 1. We provide a polynomial time solution for a special case where G1 is acyclic.
Edit intent: clarity
Original:  All problem versions considered herein assume m2 = 1. We provide a polynomial time solution for a special case where G1 is acyclic.
Revised:  All problem versions considered herein assume m2 = 1. We provide a polynomial time solution for the special case where G1 is acyclic.
Edit intent: fluency
Original:  All problem versions considered herein assume m2 = 1. We provide a polynomial time solution for a special case where G1 is acyclic.
Revised:  All problem versions considered herein assume m2 = 1. We provide a polynomial time solution for a special case where G_1 is acyclic.
Edit intent: clarity
Original:  We show that the problem is NP-complete even under the setting m1 = 2. We provide several structural properties that lead to polynomial-time approximation algorithms under the same setting.
Revised:  We show that the problem is NP-complete even under the setting m1 = 2, we provide several structural properties that lead to polynomial-time approximation algorithms under the same setting.
Edit intent: coherence
Original:  Relaxing the constraint on m1, with further structural properties we provide several additional approximation algorithms for the problem .
Revised:  Relaxing the constraint on m1, with further structural properties for this setting which lead to several additional approximation algorithms for the problem .
Edit intent: clarity
Original: We consider the constrained graph alignment problem which has applications in biological network analysis studies . Given two input graphs G_1 , G_2, a pair of vertex mappings induces an edge conservation {\it  if the vertex pairs are adjacent in their respective graphs.
Revised: We consider the constrained graph alignment problem which has applications in biological network analysis . Given two input graphs G_1 , G_2, a pair of vertex mappings induces an edge conservation {\it if the vertex pairs are adjacent in their respective graphs.
Edit intent: clarity
Original: We consider the constrained graph alignment problem which has applications in biological network analysis studies . Given two input graphs G_1 , G_2, a pair of vertex mappings induces an edge conservation {\it  if the vertex pairs are adjacent in their respective graphs.
Revised: We consider the constrained graph alignment problem which has applications in biological network analysis studies . Given two input graphs G_1 , G_2, a pair of vertex mappings induces an {\it if the vertex pairs are adjacent in their respective graphs.
Edit intent: clarity
Original:   In general terms the goal is to provide a one-to-one mapping between the vertices of the input graphs such that edge conservationis maximized .
Revised:  \% In general terms the goal is to provide a one-to-one mapping between the vertices of the input graphs such that edge conservationis maximized .
Edit intent: coherence