wanyu/IteraTeR_v2 huggingface dataset:
Original:  A transposition to the continuous framework has recently been proposed in (Mui \~n%DIFDELCMD < }%%% o and Borgelt, 2014).
Revised:  A transposition to the continuous framework has recently been proposed in \~n%DIFDELCMD < }%%% o and Borgelt, 2014).
Edit intent: coherence
Original:  A transposition to the continuous framework has recently been proposed in (Mui \~n%DIFDELCMD < }%%% o and Borgelt, 2014).
Revised:  A transposition to the continuous framework has recently been proposed in (Mui %DIFDELCMD < }%%% o and Borgelt, 2014).
Edit intent: fluency
Original:  The extension of this study to more than two neurons has not been performed until the present work.
Revised:  The goal of the present paper is to extend this study to more than two neurons has not been performed until the present work.
Edit intent: clarity
Original:  We compare our new method and\hspace{0pt} . All the theoretical results are illustrated by a simulation study, and compared to } the UE method proposed in (Gr \"u%DIFDELCMD < }%%% n et al., 2002) over various simulations including changes in the underlying model}\hspace{0pt} } . Furthermore our method is applied on real data.
Revised:  We compare our new method and\hspace{0pt} . All the theoretical results are illustrated by a simulation study, and compared to } the UE method proposed in \"u%DIFDELCMD < }%%% n et al., 2002) over various simulations including changes in the underlying model}\hspace{0pt} } . Furthermore our method is applied on real data.
Edit intent: fluency
Original:  We compare our new method and\hspace{0pt} . All the theoretical results are illustrated by a simulation study, and compared to } the UE method proposed in (Gr \"u%DIFDELCMD < }%%% n et al., 2002) over various simulations including changes in the underlying model}\hspace{0pt} } . Furthermore our method is applied on real data.
Revised:  We compare our new method and\hspace{0pt} . All the theoretical results are illustrated by a simulation study, and compared to } the UE method proposed in (Gr %DIFDELCMD < }%%% n et al., 2002) over various simulations including changes in the underlying model}\hspace{0pt} } . Furthermore our method is applied on real data.
Edit intent: fluency
Original: We present a set of analyses aiming at quantifying the amount of information filtered by different hierarchical clustering methods on correlations between stock returns .
Revised: We quantify the amount of information filtered by different hierarchical clustering methods on correlations between stock returns .
Edit intent: clarity
Original:  In particular  by taking the industrial sector classification of stocks as a benchmark partition  we evaluate how the different methods retrieve this classification.
Revised:  In particular , by taking the industrial sector classification of stocks as a benchmark partition we evaluate how the different methods retrieve this classification.
Edit intent: fluency
Original:  In particular  by taking the industrial sector classification of stocks as a benchmark partition  we evaluate how the different methods retrieve this classification.
Revised:  In particular by taking the industrial sector classification of stocks as a benchmark partition , we evaluate how the different methods retrieve this classification.
Edit intent: fluency
Original:  The results show that the Directed Bubble Hierarchical Tree outperforms the other methods, being able to retrieve more information with fewer clusters.
Revised:  The results show that the Directed Bubble Hierarchical Tree can outperform other methods, being able to retrieve more information with fewer clusters.
Edit intent: clarity
Original:  The dynamical analysis  also reveals that the different methods show different degrees of sensitivity to financial events , like crises.
Revised:  The dynamical analysis also reveals that the different methods show different degrees of sensitivity to events affecting financial markets , like crises.
Edit intent: clarity
Original:  Here we demonstrate that the branching pattern of reconstructed genealogical trees contains information about the relative fitness of the sampled sequences and that this information can be used to infer the closest extant relative of future populations .
Revised:  Here we demonstrate that the branching patterns of reconstructed genealogical trees contains information about the relative fitness of the sampled sequences and that this information can be used to infer the closest extant relative of future populations .
Edit intent: fluency
Original:  Our approach is based on the assumption that evolution proceeds predominantly by accumulation of small effect mutations and does not require any species specific input .
Revised:  Our approach is based on the assumption that evolution proceeds by accumulation of small effect mutations and does not require any species specific input .
Edit intent: clarity
Original:  Our approach is based on the assumption that evolution proceeds predominantly by accumulation of small effect mutations and does not require any species specific input .
Revised:  Our approach is based on the assumption that evolution proceeds predominantly by accumulation of small effect mutations , does not require any species specific input .
Edit intent: coherence
Original:  Our approach is based on the assumption that evolution proceeds predominantly by accumulation of small effect mutations and does not require any species specific input .
Revised:  Our approach is based on the assumption that evolution proceeds predominantly by accumulation of small effect mutations and does not require species specific input .
Edit intent: clarity
Original:  We predict the progenitor lineage of the upcoming influenza season with near optimal performance in 30\% of cases and makes informative predictions in 16 out of 18 years.
Revised:  We predict the progenitor lineage of the upcoming influenza season with near optimal performance in 30\% of cases and make informative predictions in 16 out of 18 years.
Edit intent: fluency
Original:  Beyond providing a practical tool for prediction, our results suggest that continuous adaptation by small effect mutations is a major component of influenza virus evolution .
Revised:  Beyond providing a tool for prediction, our results suggest that continuous adaptation by small effect mutations is a major component of influenza virus evolution .
Edit intent: clarity
Original:  Beyond providing a practical tool for prediction, our results suggest that continuous adaptation by small effect mutations is a major component of influenza virus evolution .
Revised:  Beyond providing a practical tool for prediction, our ability to make informative predictions implies persistent fitness variation among circulating influenza A/H3N2 viruses .
Edit intent: clarity
Original: An efficient algorithm computing the rank of a group (that is , the size of a minimum generating subset) benefits mathematicians, who use numerical algebra systems for research, cryptographers, who rely on algebraic systems for proofs of security, and theoretical computer scientists, who seek to understand which problems can be solved in a particular model of computation.
Revised: The rank of a group (that is , the size of a minimum generating subset) benefits mathematicians, who use numerical algebra systems for research, cryptographers, who rely on algebraic systems for proofs of security, and theoretical computer scientists, who seek to understand which problems can be solved in a particular model of computation.
Edit intent: clarity
Original:  We reduced the best upper bound on the complexity of the group rank problem and provide a theoretically efficient algorithm for it .
Revised:  We reduced the best upper bounds on the complexity of the group rank problem and provide a theoretically efficient algorithm for it .
Edit intent: fluency
Original:  We reduced the best upper bound on the complexity of the group rank problem and provide a theoretically efficient algorithm for it .
Revised:  We reduced the best upper bound on the complexity of computing rank for quasigroups and for groups, and provide a theoretically efficient algorithm for it .
Edit intent: clarity
Original:  We reduced the best upper bound on the complexity of the group rank problem and provide a theoretically efficient algorithm for it .
Revised:  We reduced the best upper bound on the complexity of the group rank problem and provide a theoretically efficient algorithm for the latter .
Edit intent: clarity
Original:  This paper proves that with very short certificates of correctness, the group rank problem can be verified by highly restricted models of computation.
Revised:  This paper proves that with short certificates of correctness, the group rank problem can be verified by highly restricted models of computation.
Edit intent: clarity
Original:  We prove that the problem of deciding whether the rank of a finite group , given as a multiplication table, is smaller than a specified number is decidable not only by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits , but also by a Turing machine using O(\log n) space and O(\log^2 n) bits of nondeterminism.
Revised:  Specifically, we prove that the problem of deciding whether the rank of a finite group , given as a multiplication table, is smaller than a specified number is decidable not only by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits , but also by a Turing machine using O(\log n) space and O(\log^2 n) bits of nondeterminism.
Edit intent: coherence
Original:  We prove that the problem of deciding whether the rank of a finite group , given as a multiplication table, is smaller than a specified number is decidable not only by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits , but also by a Turing machine using O(\log n) space and O(\log^2 n) bits of nondeterminism.
Revised:  We prove that the problem of deciding whether the rank of a finite quasigroup , given as a multiplication table, is smaller than a specified number is decidable not only by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits , but also by a Turing machine using O(\log n) space and O(\log^2 n) bits of nondeterminism.
Edit intent: clarity
Original:  We prove that the problem of deciding whether the rank of a finite group , given as a multiplication table, is smaller than a specified number is decidable not only by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits , but also by a Turing machine using O(\log n) space and O(\log^2 n) bits of nondeterminism.
Revised:  We prove that the problem of deciding whether the rank of a finite group , given as a multiplication table, is smaller than a specified number is decidable by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits , but also by a Turing machine using O(\log n) space and O(\log^2 n) bits of nondeterminism.
Edit intent: coherence
Original:  These models of computation are extremely limited in computational power, and hence can be simulated by a deterministic Turing machine in polynomial time . Using limited nondeterminism and restrictive models of computation as verifiers may be useful in examining other algebraic problems .
Revised:  These are great improvements on the upper bounds for these problems, and for groups, this upper bound implies a deterministic polynomial time algorithm. The lens of limited nondeterminism provides an easy way to improve many simple algorithms, like the ones presented here, and we suspect it will be especially useful for other algebraic algorithms .
Edit intent: coherence
Original:  We reduce the best upper bounds on the complexity of computing rank for quasigroups and for groups , and provide a theoretically efficient algorithm for the latter .
Revised:  We reduce the best upper bounds on the complexity of computing rank for groups and for quasigroups .
Edit intent: clarity
Original:  This paper proves that with short certificates of correctness, the rank problem for these algebraic structures can be verified by highly restricted models of computation  . Specifically, we prove that the problem of deciding whether the rank of a finite quasigroup, given as a Cayley table, is smaller than a specified number is decidable by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits.
Revised:  This paper proves that the rank problem for these algebraic structures can be verified by highly restricted models of computation . Specifically, we prove that the problem of deciding whether the rank of a finite quasigroup, given as a Cayley table, is smaller than a specified number is decidable by a circuit of depth O(\log \log n) augmented with O(\log^2 n) nondeterministic bits.
Edit intent: clarity
Original:  We then present a stochastic counterpart for these algorithms and establish similar complexity bounds for solving a certain class of stochastic composite optimization problems.
Revised:  We then present a stochastic counterpart for these algorithms and establish similar complexity bounds for solving an important class of stochastic composite optimization problems.
Edit intent: clarity
Original:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal  {\cal   the situation where the smooth component is replaced by a certain structured nonsmooth one with a bi-linear saddle point structure.
Revised:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal O {\cal the situation where the smooth component is replaced by a certain structured nonsmooth one with a bi-linear saddle point structure.
Edit intent: fluency
Original:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal  {\cal   the situation where the smooth component is replaced by a certain structured nonsmooth one with a bi-linear saddle point structure.
Revised:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal {\cal O the situation where the smooth component is replaced by a certain structured nonsmooth one with a bi-linear saddle point structure.
Edit intent: fluency
Original:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal  {\cal   the situation where the smooth component is replaced by a certain structured nonsmooth one with a bi-linear saddle point structure.
Revised:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal {\cal the smooth component is replaced by a certain structured nonsmooth one with a bi-linear saddle point structure.
Edit intent: clarity
Original:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal  {\cal   the situation where the smooth component is replaced by a certain structured nonsmooth one with a bi-linear saddle point structure.
Revised:  Finally, we generalize these algorithms to the case when the smooth component is strongly convex, and discuss their applications to{\cal {\cal the situation where the smooth component is replaced by a nonsmooth one possessing a certain bi-linear saddle point structure.
Edit intent: clarity
Original: Let G be a finite abelian group acting faithfully on a finite set X. G-bent and G-perfect nonlinear functions on X are studied in [6,7] in terms of Fourier transforms of functions on ~ G. In this paper we further this research from a different approach.
Revised: Let G be a finite abelian group acting faithfully on a finite set X. G-bent and G-perfect nonlinearity of functions on X are studied in [6,7] in terms of Fourier transforms of functions on ~ G. In this paper we further this research from a different approach.
Edit intent: clarity
Original: Let G be a finite abelian group acting faithfully on a finite set X. G-bent and G-perfect nonlinear functions on X are studied in [6,7] in terms of Fourier transforms of functions on ~ G. In this paper we further this research from a different approach.
Revised: Let G be a finite abelian group acting faithfully on a finite set X. G-bent and G-perfect nonlinear functions on X are studied in [6,7] via Fourier transforms of functions on ~ G. In this paper we further this research from a different approach.
Edit intent: clarity
Original: Let G be a finite abelian group acting faithfully on a finite set X. G-bent and G-perfect nonlinear functions on X are studied in [6,7] in terms of Fourier transforms of functions on ~ G. In this paper we further this research from a different approach.
Revised: Let G be a finite abelian group acting faithfully on a finite set X. G-bent and G-perfect nonlinear functions on X are studied in [6,7] in terms of Fourier transforms of functions on G. In this paper we further this research from a different approach.
Edit intent: clarity
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: fluency
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C %DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: coherence
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: fluency
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C %DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: fluency
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: fluency
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: clarity
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X %DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: coherence
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: fluency
Original:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% X of%DIFDELCMD < {\Bbb %%% C ^X.
Revised:  Let%DIFDELCMD < {\Bbb %%% C be the complex field, and let%DIFDELCMD < {\Bbb %DIFDELCMD < %%% C ^X be the%DIFDELCMD < {\Bbb %%% C G-module of complex functions on X . By decomposing%DIFDELCMD < {\Bbb %%% C ^X into the direct sum of G-linear components, we obtain an orthogonal G-linear basis%DIFDELCMD < \widehat %%% %DIFDELCMD < {\Bbb %%% C ^X.
Edit intent: clarity