wanyu/IteraTeR_v2 huggingface dataset:
Original:  We propose a meta-algorithm called{\sc Iterative Local Voting for collective decision-making in this setting , in which voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm .
Revised:  We propose a algorithm called{\sc Iterative Local Voting for collective decision-making in this setting , in which voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm .
Edit intent: clarity
Original:  We propose a meta-algorithm called{\sc Iterative Local Voting for collective decision-making in this setting , in which voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm .
Revised:  We propose a meta-algorithm called{\sc Iterative Local Voting for collective decision-making in this setting . In this algorithm, voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm .
Edit intent: clarity
Original:  We study Shennon 's gate complexity function L(n, q) and depth function D(n, q) for a reversible circuit implementing a  transformation f\colon \mathbb Z_2^n \to \mathbb Z_2^n with 8n < q \lesssim n2^{n-o(n)} additional inputs.
Revised:  We study Shannon 's gate complexity function L(n, q) and depth function D(n, q) for a reversible circuit implementing a transformation f\colon \mathbb Z_2^n \to \mathbb Z_2^n with 8n < q \lesssim n2^{n-o(n)} additional inputs.
Edit intent: fluency
Original:  We prove general upper bounds L(n,q) \lesssim 2^n + 8n2^n \mathop / (\log_2 (q-4n) - \log_2 n - 2) and D(n,q) \lesssim 2^{n+1}(2,5 + \log_2 n - \log_2 (\log_2 (q - 4n) - \log_2 n - 2))  for this case.
Revised:  The general upper bounds L(n,q) \lesssim 2^n + 8n2^n \mathop / (\log_2 (q-4n) - \log_2 n - 2) and D(n,q) \lesssim 2^{n+1}(2,5 + \log_2 n - \log_2 (\log_2 (q - 4n) - \log_2 n - 2)) for this case.
Edit intent: coherence
Original:  We prove general upper bounds L(n,q) \lesssim 2^n + 8n2^n \mathop / (\log_2 (q-4n) - \log_2 n - 2) and D(n,q) \lesssim 2^{n+1}(2,5 + \log_2 n - \log_2 (\log_2 (q - 4n) - \log_2 n - 2))  for this case.
Revised:  We prove general upper bounds L(n,q) \lesssim 2^n + 8n2^n \mathop / (\log_2 (q-4n) - \log_2 n - 2) and D(n,q) \lesssim 2^{n+1}(2,5 + \log_2 n - \log_2 (\log_2 (q - 4n) - \log_2 n - 2)) are proved for this case.
Edit intent: coherence
Original:  In our model, users and base stations (BSs) are randomly located on a network formed by a two dimensional Poisson line process.
Revised:  In our model, users and base stations (BSs) are distributed according to a Poisson point process.
Edit intent: clarity
Original:  Our model is well suited for urban microcellular networks where the base stations are deployed at street level.
Revised:  Our model is well suited for urban microcellular networks where the BSs are deployed at street level.
Edit intent: clarity
Original:  Second, there is an ultradense regime where deploying (active ) BSs does not enhance coverage.
Revised:  Second, there is an ultra-dense regime where deploying (active ) BSs does not enhance coverage.
Edit intent: fluency
Original:  Second, there is an ultradense regime where deploying (active ) BSs does not enhance coverage.
Revised:  Second, there is an ultradense regime where deploying active BSs does not enhance coverage.
Edit intent: fluency
Original: Many machine learning models are reformulated as optimization problems.
Revised: Many machine learning models involve solving optimization problems.
Edit intent: clarity
Original:  Thus, it is important to solve a large-scale optimization problem in big data applications.
Revised:  Thus, it is important to deal with a large-scale optimization problem in big data applications.
Edit intent: clarity
Original:  Recently, subsampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high cost in each iteration while commanding a high convergence rate.
Revised:  Recently, subsampled Newton methods have emerged to attract much attention due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high cost in each iteration while commanding a high convergence rate.
Edit intent: clarity
Original:  Based on this framework, our theoretical analysis matches the performance in real applications  .
Revised:  Based on this framework, we present our theoretical results which match the performance in real applications .
Edit intent: clarity
Original: We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying (N - 1 )th order N tensors so that every fiber sums to one.
Revised: We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 )th order N tensors so that every fiber sums to one.
Edit intent: clarity
Original: We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying (N - 1 )th order N tensors so that every fiber sums to one.
Revised: We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying (N - 1 so that every fiber sums to one.
Edit intent: coherence
Original:  The key to our algorithm is that the gradient of the manifold, used as a Jacobian matrix in Newton's method, can be analytically obtained using the M\"obius inversion formula, the essential of combinatorial mathematics.
Revised:  The key to our algorithm is that the gradient of the manifold, used as a Jacobian matrix in Newton's method, can be analytically obtained using the Moebius inversion formula, the essential of combinatorial mathematics.
Edit intent: fluency
Original:  Our model is not limited to tensor balancing  but has a wide applicability as it includes various statistical and machine learning models such as weighted DAGs and Boltzmann machines.
Revised:  Our model is not limited to tensor balancing , but has a wide applicability as it includes various statistical and machine learning models such as weighted DAGs and Boltzmann machines.
Edit intent: fluency
Original: In this paper, we study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata.
Revised: We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata.
Edit intent: coherence
Original:  The framework allows editing , validating , visualizing the descriptors of services and components both textually and graphically .
Revised:  The framework allows editing and validating the descriptors of services and components both textually and graphically .
Edit intent: clarity
Original:  Then we have considered and integrated the modelling of components in a modular software router (Click), which goes beyond the traditional scope of NFV.
Revised:  Then we have considered the modelling of components in a modular software router (Click), which goes beyond the traditional scope of NFV.
Edit intent: clarity
Original: An astonishing fact was established by Lee A. Rubel in 81 : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with |y(t)-\phi(t)|<\epsilon(t) for all t. Rubel provided an explicit example of such a polynomial DAE.
Revised: An astonishing fact was established by Lee A. Rubel in 1981 : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with |y(t)-\phi(t)|<\epsilon(t) for all t. Rubel provided an explicit example of such a polynomial DAE.
Edit intent: fluency
Original: An astonishing fact was established by Lee A. Rubel in 1981  : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t.  Rubel provided an explicit example of such a polynomial DAE.
Revised: An astonishing fact was established by Lee A. Rubel ( 1981 : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t. Rubel provided an explicit example of such a polynomial DAE.
Edit intent: fluency
Original: An astonishing fact was established by Lee A. Rubel in 1981  : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t.  Rubel provided an explicit example of such a polynomial DAE.
Revised: An astonishing fact was established by Lee A. Rubel in 1981 ) : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t. Rubel provided an explicit example of such a polynomial DAE.
Edit intent: fluency
Original: An astonishing fact was established by Lee A. Rubel in 1981  : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t.  Rubel provided an explicit example of such a polynomial DAE.
Revised: An astonishing fact was established by Lee A. Rubel in 1981 : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function \varphi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t. Rubel provided an explicit example of such a polynomial DAE.
Edit intent: fluency
Original: An astonishing fact was established by Lee A. Rubel in 1981  : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t.  Rubel provided an explicit example of such a polynomial DAE.
Revised: An astonishing fact was established by Lee A. Rubel in 1981 : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \varphi (t) | < \epsilon(t) for all t. Rubel provided an explicit example of such a polynomial DAE.
Edit intent: fluency
Original: An astonishing fact was established by Lee A. Rubel in 1981  : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t.  Rubel provided an explicit example of such a polynomial DAE.
Revised: An astonishing fact was established by Lee A. Rubel in 1981 : there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any continuous function \phi on the reals, and for any positive continuous function \epsilon(t), it has a C^\infty solution with | y(t) - \phi (t) | < \epsilon(t) for all t. Lee A. Rubel provided an explicit example of such a polynomial DAE.
Edit intent: clarity
Original:   The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Revised:  The question whether one can require the solution that approximates \varphi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Edit intent: fluency
Original:   The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Revised:  The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Edit intent: fluency
Original:   The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Revised:  The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Edit intent: fluency
Original:   The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Revised:  The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Edit intent: coherence
Original:   The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 ) . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Revised:  The question whether one can require the solution that approximates \phi to be the unique solution for a given initial data is a well known open problem [ Rub81 ( page 2 ) , [ boshernitzan1986universal ( Conjecture 6.2 . In this article, we solve it and show that Rubel's statement holds for polynomial ordinary differential equations (ODEs), and since polynomial ODEs have a unique solution given an initial data, this positively answers Rubel's open problem.
Edit intent: fluency
Original:  More precisely, we show that there exists a \textbf{fixed} polynomial ODE such that for any \phi and \epsilon there exists some initial condition that yields a solution that is \epsilon-close to \phi at all times  .
Revised:  More precisely, we show that there exists a \textbf{fixed} polynomial ODE such that for any \phi and \epsilon there exists some initial condition that yields a solution that is \epsilon-close to \varphi at all times .
Edit intent: fluency
Original: In the context of tissue engineering, we recently proposed a lattice model for a bioactive porous tissue scaffold in order to understand the role of an active pore network in tissue growth [ Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold, preprint, 2017 ].
Revised: In the context of tissue engineering, we recently proposed a lattice model for a bioactive porous tissue scaffold [ Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold, preprint, 2017 ].
Edit intent: coherence
Original:  This model considered the scaffold as an evolving lattice of pores, with coupling between local cell growth in the pores, and fluid flow through the medium.
Revised:  This model considered the scaffold as a lattice of pores, with coupling between local cell growth in the pores, and fluid flow through the medium.
Edit intent: clarity
Original:  Depending on the size of the underlying network, we observe oscillations and steady states in cell density exhibited in both models.
Revised:  We find that long-time oscillations and steady states in cell density exhibited in both models.
Edit intent: clarity
Original:  Depending on the size of the underlying network, we observe oscillations and steady states in cell density exhibited in both models.
Revised:  Depending on the size of the underlying network, we observe oscillations and steady states in cell density are observed in both models.
Edit intent: clarity
Original:   Steady state behaviour can be described in large cell diffusion regimes via regular asymptotic expansions in the diffusion parameter.
Revised:  Steady state behaviour can be described in large cell diffusion regimes via asymptotic expansions in the diffusion parameter.
Edit intent: clarity
Original:  We numerically continue steady state solutions into intermediate diffusion regimes, where we observe symmetry-breaking bifurcations to both oscillatory and steady state behaviours that can be explained via local bifurcations, as well as symmetry-preserving oscillations that do not bifurcate from steady states.
Revised:  We numerically continue steady state solutions into intermediate diffusion regimes, where we observe symmetry-breaking bifurcations to both oscillatory and steady state behaviours that can be explained via local bifurcations, as well as symmetric oscillations that do not bifurcate from steady states.
Edit intent: clarity
Original:  The spatially continuous analogue of the model only exhibits  symmetric steady states and oscillatory solutions, and we conjecture that it is the finite lattice that gives rise to the more complicated symmetry-breaking dynamics .
Revised:  The spatially continuous analogue of the model only exhibits symmetric steady states and oscillatory solutions, and we conjecture that it is the finite lattice that gives rise to symmetry-breaking dynamics .
Edit intent: clarity
Original:  The spatially continuous analogue of the model only exhibits  symmetric steady states and oscillatory solutions, and we conjecture that it is the finite lattice that gives rise to the more complicated symmetry-breaking dynamics .
Revised:  The spatially continuous analogue of the model only exhibits symmetric steady states and oscillatory solutions, and we conjecture that it is the finite lattice that gives rise to the more complicated symmetry-breaking bifurcations .
Edit intent: clarity
Original:  Finally  we relate these results back to the original modelling question of how network topology influences tissue growth in a bioactive porous tissue scaffold.
Revised:  Finally , we relate these results back to the original modelling question of how network topology influences tissue growth in a bioactive porous tissue scaffold.
Edit intent: fluency
Original: In the context of tissue engineering, we recently proposed a lattice model for a bioactive porous tissue scaffold arXiv:1702.07711%DIFDELCMD < ]%%% . This model considered the scaffold as a lattice of pores, with coupling between local cell growth in the pores, and fluid flow through the scaffold.
Revised:  arXiv:1702.07711%DIFDELCMD < ]%%% . This model considered the scaffold as a lattice of pores, with coupling between local cell growth in the pores, and fluid flow through the scaffold.
Edit intent: clarity
Original: In the context of tissue engineering, we recently proposed a lattice model for a bioactive porous tissue scaffold arXiv:1702.07711%DIFDELCMD < ]%%% . This model considered the scaffold as a lattice of pores, with coupling between local cell growth in the pores, and fluid flow through the scaffold.
Revised: In the context of tissue engineering, we recently proposed a lattice model for a bioactive porous tissue scaffold %DIFDELCMD < ]%%% . This model considered the scaffold as a lattice of pores, with coupling between local cell growth in the pores, and fluid flow through the scaffold.
Edit intent: clarity
Original:  Characterisation of users into socio-demographic groups is crucial to improve these analyses.
Edit intent: coherence
Original:  We describe a methodology that relies on users' self-reported location to build  datasets for three territories -- Catalonia, the Basque Country and Scotland -- and we test language-independent classifiers using four types of features.
Revised:  We describe a methodology that relies on users' self-reported location to build large-scale datasets for three territories -- Catalonia, the Basque Country and Scotland -- and we test language-independent classifiers using four types of features.
Edit intent: clarity
Original:  \Re^{M} }\to  , we show that equivariance of \phi_W is linked to the symmetry group of network parameters W. We then propose a sparse parameter-sharing scheme to induce the desirable symmetry on W. Under some conditions on the action of G, our procedure for tying the parameters achieves G-equivariance and guarantee sensitivity to all other permutation groups outside G. We demonstrate the relation of our approach to recently-proposed "structured"
Revised:  \Re^{M} }\to , we show that \phi_{W the symmetry group of network parameters W. We then propose a sparse parameter-sharing scheme to induce the desirable symmetry on W. Under some conditions on the action of G, our procedure for tying the parameters achieves G-equivariance and guarantee sensitivity to all other permutation groups outside G. We demonstrate the relation of our approach to recently-proposed "structured"
Edit intent: clarity