wanyu/IteraTeR_v2 huggingface dataset:
Original:  one in which the samples have a group structure and the other in which they have rank-one outer-product structure.
Revised:  one in which the samples have a group structure and an other in which they have rank-one outer-product structure.
Edit intent: fluency
Original:  As a consequence of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size n, constructs an Alon-Roichman expanding Cayley graph of logarithmic degree in  O(n^2 log^3 n) time.
Revised:  As a consequence of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size n, it constructs an expanding Cayley graph of logarithmic degree in O(n^2 log^3 n) time.
Edit intent: clarity
Original:  For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices (as defined in Sri10%DIFDELCMD < ]%%% ) which implies directly an improved deterministic algorithm for spectral graph sparsification for the case of dense graphs.
Revised:  For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices Sri10%DIFDELCMD < ]%%% ) which implies directly an improved deterministic algorithm for spectral graph sparsification for the case of dense graphs.
Edit intent: coherence
Original:  For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices (as defined in Sri10%DIFDELCMD < ]%%% ) which implies directly an improved deterministic algorithm for spectral graph sparsification for the case of dense graphs.
Revised:  For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices (as defined in Sri10%DIFDELCMD < ]%%% , which implies an improved deterministic algorithm for spectral graph sparsification for the case of dense graphs.
Edit intent: coherence
Original:  For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices (as defined in Sri10%DIFDELCMD < ]%%% ) which implies directly an improved deterministic algorithm for spectral graph sparsification for the case of dense graphs.
Revised:  For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices (as defined in Sri10%DIFDELCMD < ]%%% ) which implies directly an improved deterministic algorithm for spectral graph sparsification of dense graphs.
Edit intent: coherence
Original:  As a consequence, we obtain improved element-wise sparsification algorithms for self-adjoint and diagonally dominant-like matrices.
Revised:  As a consequence, we obtain improved element-wise sparsification algorithms for diagonally dominant-like matrices.
Edit intent: clarity
Original:  This paper proposes a third extension to support mutually recursive datatypes that is as powerful as Compos , as easy to use as Biplate, and more portable than both of them .
Revised:  This paper proposes a third extension to support mutually recursive data types that is as powerful as Compos , as easy to use as Biplate, and more portable than both of them .
Edit intent: fluency
Original:  This paper proposes a third extension to support mutually recursive datatypes that is as powerful as Compos , as easy to use as Biplate, and more portable than both of them .
Revised:  This paper proposes a third extension to support mutually recursive datatypes that is as powerful as Compos and as easy to use as Biplate, and more portable than both of them .
Edit intent: coherence
Original:  This paper proposes a third extension to support mutually recursive datatypes that is as powerful as Compos , as easy to use as Biplate, and more portable than both of them .
Revised:  This paper proposes a third extension to support mutually recursive datatypes that is as powerful as Compos , as easy to use as Uniplate .
Edit intent: clarity
Original:  We study the syntactic complexity of prefix-, suffix-, and bifix-free regular languages.
Revised:  We study the syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages.
Edit intent: clarity
Original: This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the Discretization of Exterior Calculus (DEC) . PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topological problems on abstract complexes.
Revised: This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus . PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topological problems on abstract complexes.
Edit intent: clarity
Original:  At physiological temperatures and superhelical densities, opening is strongly cooperative with average bubble sizes of %DIFDELCMD < {\cal %DIFDELCMD < %%% O (100-1000) bp.
Revised:  At physiological temperatures and superhelical densities, opening is strongly cooperative with average bubble sizes of %DIFDELCMD < {\cal %DIFDELCMD < %%% (100-1000) bp.
Edit intent: clarity
Original: In this paper we investigate the consistency across scales of the irreversible-thermodynamic structure of a continuous-state continuous-time stochastic dynamical system.
Revised: The consistency across scales of the irreversible-thermodynamic structure of a continuous-state continuous-time stochastic dynamical system.
Edit intent: clarity
Original:  We demonstrate that the thermodynamics derived from the continuous underlying detailed dynamics is exact in the Helmholtz free-energy representation.
Revised:  We demonstrate that the thermodynamics derived from the underlying detailed continuous dynamics is exact in the Helmholtz free-energy representation.
Edit intent: fluency
Original: The consistency across scales of a recently developed mathematical irreversible-thermodynamic structure, between a continuous stochastic nonlinear dynamical (Langevin-Fokker-Planck) system and its emergent discrete, inter-attractoral Markov jump process, is investigated.
Revised: The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical (Langevin-Fokker-Planck) system and its emergent discrete, inter-attractoral Markov jump process, is investigated.
Edit intent: clarity
Original:  We show that the thermodynamics derived from the underlying detailed continuous dynamics is exact in the Helmholtz free-energy representation.
Revised:  We show that the thermodynamics derived from the underlying detailed continuous dynamics is exact in the Helmholtz free-energy representation.
Edit intent: fluency
Original:  This result generalizes a fundamental idea from chemistry and the theory of Kramers to include thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described the law of mass action with rate constants, and Markov thermodynamics.
Revised:  This result generalizes a fundamental idea from chemistry and the theory of Kramers by including thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described the law of mass action with rate constants, and Markov thermodynamics.
Edit intent: coherence
Original:  This result generalizes a fundamental idea from chemistry and the theory of Kramers to include thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described the law of mass action with rate constants, and Markov thermodynamics.
Revised:  This result generalizes a fundamental idea from chemistry and the theory of Kramers to include thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described by the Law of Mass Action with rate constants, and Markov thermodynamics.
Edit intent: fluency
Original: In searching differentially expressed mRNAs / genes in a microarray experiment, the two commonly used measures are the fold change and the t-test statistic (or the t-test p-value) .
Revised: In searching differentially expressed mRNAs / standardized signal (e.g. t-statistic or -log10( p-value) .
Edit intent: clarity
Original: We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a  non-cooperative game whose strategy space corresponds to the users' distribution of transmission power over the network's channels.
Revised: We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a non-cooperative game whose strategy space represents the users' distribution of transmission power over the network's channels.
Edit intent: clarity
Original: We perform wavelet decomposition of high frequency financial time series into high and low-energy spectral sectors .
Revised: We perform wavelet decomposition of high frequency financial time series into large and small time scale components .
Edit intent: clarity
Original:  Our results indicate that the usual non-gaussian profiles of log-return distributions contain much more information than needed for option pricing, which is essentially dependent on hidden self-correlation properties of the underlying asset fluctuations .
Revised:  Our results indicate that the usual non-gaussian statistical structure of the original financial time series is essentially preserved for expiration times which are larger than just one trading day .
Edit intent: clarity
Original:  Our empirical study measures the extent and growth rate of globalisation in terms of the physical distance between co-authoring researchers.
Revised:  Our empirical study measures the extent and growth of scientific globalisation in terms of the physical distance between co-authoring researchers.
Edit intent: clarity
Original:  Our empirical study measures the extent and growth rate of globalisation in terms of the physical distance between co-authoring researchers.
Revised:  Our empirical study measures the extent and growth rate of globalisation in terms of physical distances between co-authoring researchers.
Edit intent: fluency
Original:  Our computations , drawing on 21 million research publications across all countries and fields of science, reveals that contemporary science has globalised at a fairly steady rate during recent decades.
Revised:  Our analysis , drawing on 21 million research publications across all countries and fields of science, reveals that contemporary science has globalised at a fairly steady rate during recent decades.
Edit intent: clarity
Original: This article concerns over-resolution methods for image reconstruction from data provided by a family of scanning instruments like the Herschel observatory.
Revised: We investigate super-resolution methods for image reconstruction from data provided by a family of scanning instruments like the Herschel observatory.
Edit intent: clarity
Original:  The work is centered on building a model of the instrument that faithfully reflects the physical reality, accurately taking the acquisition process into account so as to explain the data in a reliable manner.
Revised:  To do this, we constructed a model of the instrument that faithfully reflects the physical reality, accurately taking the acquisition process into account so as to explain the data in a reliable manner.
Edit intent: clarity
Original:  The work is centered on building a model of the instrument that faithfully reflects the physical reality, accurately taking the acquisition process into account so as to explain the data in a reliable manner.
Revised:  The work is centered on building a model of the instrument that faithfully reflects the physical reality, accurately taking the acquisition process into account to explain the data in a reliable manner.
Edit intent: coherence
Original:  The inversion, i.e. the image reconstruction process, is based on a linear approach resulting from a quadratic regularized criterion and numerical optimization tools.
Revised:  The inversion, ie the image reconstruction process, is based on a linear approach resulting from a quadratic regularized criterion and numerical optimization tools.
Edit intent: fluency
Original:  The proposed approach is also applied to real data with significant improvement in spatial resolution.
Revised:  The approach is also applied to real data with significant improvement in spatial resolution.
Edit intent: clarity
Original:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that if G is connected , has n vertices and maximum degree d  , then \M(G)\leq n-n{d}+O(1).
Revised:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that if a connected graph G has n vertices and maximum degree d , then \M(G)\leq n-n{d}+O(1).
Edit intent: clarity
Original:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Revised:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to constants, i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Edit intent: clarity
Original:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Revised:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Edit intent: fluency
Original:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Revised:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Edit intent: coherence
Original:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Revised:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta}n. Using the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Edit intent: fluency
Original:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Revised:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we give sharp estimates for the size of the minimum identifying code of size \Theta( \log d{d} )\cdot n.
Edit intent: clarity
Original:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Revised:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of random d-regular graphs, which is about \log d{d} )\cdot n.
Edit intent: clarity
Original:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} )\cdot n.
Revised:  Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds up to a constant factor ( i.e. \M(G)\leq n-n{\Theta(d)} ) . In the second part, we prove that in any graph G of minimum degree \delta and girth ~ 5, \M(G)\leq %DIFDELCMD < 3\log\delta{\delta}%%% n. Finally, using3\log\delta{2\delta} the former result, we also determine that almost all d-regular graphs have their minimum identifying code of size \Theta( \log d{d} n.
Edit intent: coherence
Original:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)}  up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth  5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Revised:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% %DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)} up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth 5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Edit intent: coherence
Original:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)}  up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth  5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Revised:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% n{\Theta(d)} up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth 5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Edit intent: coherence
Original:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)}  up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth  5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Revised:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)} up to constants ) for these classes of graphs. In the general case, we prove \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth 5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Edit intent: coherence
Original:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)}  up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth  5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Revised:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)} up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth 5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Edit intent: coherence