wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this article we review several important variants of MF, including: Basic MF, Non-negative MF, Orthogonal non-negative MF. As can be seen from their names, non-negative MF and orthogonal non-negative MF are variants of basic MF with non-negativity and/or orthogonality constraints.
Revised:  In this article we review several important variants of MF, including: Basic MF, Non-negative MF, Orthogonal non-negative MF. As can be told from their names, non-negative MF and orthogonal non-negative MF are variants of basic MF with non-negativity and/or orthogonality constraints.
Edit intent: clarity
Original:  We propose here a measure of such variability, namely an individual motor signature (IMS) able to capture the subtle differences in the way each of us moves.
Revised:  We propose here an index of such variability, namely an individual motor signature (IMS) able to capture the subtle differences in the way each of us moves.
Edit intent: clarity
Original:  We use our measure to confirm a key prediction of the theory of similarity that the level of coordination between two individuals performing a joint task is higher if their motions share similar kinematic features.
Revised:  We use our measure to confirm a key prediction of the theory of similarity that coordination between two individuals performing a joint task is higher if their motions share similar kinematic features.
Edit intent: clarity
Original:  We use our measure to confirm a key prediction of the theory of similarity that the level of coordination between two individuals performing a joint task is higher if their motions share similar kinematic features.
Revised:  We use our measure to confirm a key prediction of the theory of similarity that the level of coordination between two individuals performing a joint-action task is higher if their motions share similar kinematic features.
Edit intent: clarity
Original:  They have been used for many different purposes -- to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), to explore emerging phenomena, for forecasting, etc.
Revised:  They have been used for many different purposes -- to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), to explore emergent phenomena, for forecasting, etc.
Edit intent: fluency
Original:  In this essay, we sketch these historical developments, the role of mechanistic models in the social sciences and the influences from  natural and formal sciences.
Revised:  In this essay, we sketch these historical developments, the role of mechanistic models in the social sciences and the influences from the natural and formal sciences.
Edit intent: fluency
Original:  Computer simulations of social mechanisms have an over 60 years long history.
Revised:  Computer simulations of social mechanisms have a 60-year long history.
Edit intent: clarity
Original:  They have been used for many different purposes -- to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), to explore emergent phenomena, for forecasting , etc.
Revised:  They have been used for many different purposes -- to test scenarios, test the consistency of descriptive theories (proof-of-concept models), to explore emergent phenomena, for forecasting , etc.
Edit intent: fluency
Original:  They have been used for many different purposes -- to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), to explore emergent phenomena, for forecasting , etc.
Revised:  They have been used for many different purposes -- to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), explore emergent phenomena, for forecasting , etc.
Edit intent: fluency
Original:  They have been used for many different purposes -- to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), to explore emergent phenomena, for forecasting , etc.
Revised:  They have been used for many different purposes -- to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), to explore emergent phenomena, forecast , etc.
Edit intent: clarity
Original:  In this essay, we sketch these historical developments, the role of mechanistic models in the social sciences  and the influences from the natural and formal sciences.
Revised:  In this essay, we sketch these historical developments, the role of mechanistic models in the social sciences , and the influences from the natural and formal sciences.
Edit intent: fluency
Original:  We argue that mechanistic computational models form a natural common ground for social and natural sciences , and look forward to possible future information flow across the social-natural divide.
Revised:  We argue that mechanistic computational models form a common ground for social and natural sciences , and look forward to possible future information flow across the social-natural divide.
Edit intent: clarity
Original:  We argue that mechanistic computational models form a natural common ground for social and natural sciences , and look forward to possible future information flow across the social-natural divide.
Revised:  We argue that mechanistic computational models form a natural common ground for social and natural sciences and look forward to possible future information flow across the social-natural divide.
Edit intent: fluency
Original: We study the complexity of a group of distance-constrained graph labeling problems when parameterized by the neighborhood diversity (nd), which is a natural graph parameter between vertex cover and clique width.
Revised: We study computational complexity of the class of distance-constrained graph labeling problems when parameterized by the neighborhood diversity (nd), which is a natural graph parameter between vertex cover and clique width.
Edit intent: clarity
Original: We study the complexity of a group of distance-constrained graph labeling problems when parameterized by the neighborhood diversity (nd), which is a natural graph parameter between vertex cover and clique width.
Revised: We study the complexity of a group of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width.
Edit intent: clarity
Original:  Neighborhood diversity has been used to generalize and speed up algorithms previously parameterized by vertex cover, as is also demonstrated by our paper.
Revised:  algorithms previously parameterized by vertex cover, as is also demonstrated by our paper.
Edit intent: clarity
Original:  We show that the%DIFDELCMD < {\sc %%% Uniform Channel Assignment problem is fixed parameter tractable when parameterized by nd and the largest weight and that every%DIFDELCMD < {\sc %DIFDELCMD < %%%  L(p_1, p_2, \dots, p_k)-labeling problem is when parameterized by nd, maximum p_i and k.
Revised:  We show that the%DIFDELCMD < {\sc %%% problem is fixed parameter tractable when parameterized by nd and the largest weight and that every%DIFDELCMD < {\sc %DIFDELCMD < %%% L(p_1, p_2, \dots, p_k)-labeling problem is when parameterized by nd, maximum p_i and k.
Edit intent: coherence
Original:  We show that the%DIFDELCMD < {\sc %%% Uniform Channel Assignment problem is fixed parameter tractable when parameterized by nd and the largest weight and that every%DIFDELCMD < {\sc %DIFDELCMD < %%%  L(p_1, p_2, \dots, p_k)-labeling problem is when parameterized by nd, maximum p_i and k.
Revised:  We show that the%DIFDELCMD < {\sc %%% Uniform Channel Assignment problem is fixed parameter tractable when parameterized by %DIFDELCMD < {\sc %DIFDELCMD < %%% L(p_1, p_2, \dots, p_k)-labeling problem is when parameterized by nd, maximum p_i and k.
Edit intent: coherence
Original:  These results furthermore yield an algorithms for%DIFDELCMD < {\sc %%%  L(p_1, p_2, \dots, p_k)-labeling and%DIFDELCMD < {\sc %%% Channel Assignment problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Revised:  algorithms for%DIFDELCMD < {\sc %%% L(p_1, p_2, \dots, p_k)-labeling and%DIFDELCMD < {\sc %%% Channel Assignment problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Edit intent: clarity
Original:  These results furthermore yield an algorithms for%DIFDELCMD < {\sc %%%  L(p_1, p_2, \dots, p_k)-labeling and%DIFDELCMD < {\sc %%% Channel Assignment problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Revised:  These results furthermore yield an %DIFDELCMD < {\sc %%% L(p_1, p_2, \dots, p_k)-labeling and%DIFDELCMD < {\sc %%% Channel Assignment problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Edit intent: clarity
Original:  These results furthermore yield an algorithms for%DIFDELCMD < {\sc %%%  L(p_1, p_2, \dots, p_k)-labeling and%DIFDELCMD < {\sc %%% Channel Assignment problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Revised:  These results furthermore yield an algorithms for%DIFDELCMD < {\sc %%% L(p_1, p_2, \dots, p_k)-labeling %DIFDELCMD < {\sc %%% Channel Assignment problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Edit intent: fluency
Original:  These results furthermore yield an algorithms for%DIFDELCMD < {\sc %%%  L(p_1, p_2, \dots, p_k)-labeling and%DIFDELCMD < {\sc %%% Channel Assignment problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Revised:  These results furthermore yield an algorithms for%DIFDELCMD < {\sc %%% L(p_1, p_2, \dots, p_k)-labeling and%DIFDELCMD < {\sc %%% problems when parameterized by vertex cover size , answering an open question of Fiala et al.:
Edit intent: coherence
Original: In this paper we describe a novel method of exchanging data between Bluetooth smartphones on the Android platform without requiring any pairing of the devices.
Revised: In this paper we describe a novel method of exchanging data between Bluetooth smartphones on the Android platform without requiring pairing between devices.
Edit intent: clarity
Original: Fast algorithms for matrix multiplication, or those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest.
Revised: Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest.
Edit intent: clarity
Original:  Aside from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications.
Revised:  Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications.
Edit intent: fluency
Original:  While fast algorithms are known to be numerically stable,  their error bounds are slightly weaker than the classical algorithm  .
Revised:  Fast algorithms are known to be numerically stable, their error bounds are slightly weaker than the classical algorithm .
Edit intent: clarity
Original:  While fast algorithms are known to be numerically stable,  their error bounds are slightly weaker than the classical algorithm  .
Revised:  While fast algorithms are known to be numerically stable, but because their error bounds are slightly weaker than the classical algorithm .
Edit intent: coherence
Original:  We generalize and tighten previous error analyses of fast algorithms , compare the propertiesamong the class of known practical fast algorithms, and discuss algorithmic techniques for improving the error guarantees .
Revised:  We generalize and tighten previous error analyses of fast algorithms and compare their properties. We discuss algorithmic techniques for improving the error guarantees .
Edit intent: clarity
Original:  Finally, we include empirical results that test the various improvement techniques, in terms of both their numerical accuracyand their performance .
Revised:  Finally, we benchmark performance and demonstrate our improved numerical accuracy .
Edit intent: clarity
Original: Many of the systems that are traditionally analyzed as complex networks have natural interpretations as multiplex structures .
Revised: Many complex systems have natural representations as multi-layer networks .
Edit intent: clarity
Original:  We consider qubit Hamiltonians for which we have an upper bound on the number of terms in which each qubit participates, and find asymptotically optimal bounds for the operator norm and ground-state energy of such Hamiltonians under this constraint.
Revised:  We consider qubit Hamiltonians for which we have an upper bound on the number of terms in which each qubit participates, and find extensive bounds for the operator norm and ground-state energy of such Hamiltonians under this constraint.
Edit intent: clarity
Original: We consider the problem of how to assign treatment in a randomized experiment, when the correlation among the outcomes is informed by a network available pre-intervention.
Revised: We consider the problem of how to assign treatment in a randomized experiment, in which the correlation among the outcomes is informed by a network available pre-intervention.
Edit intent: clarity
Original:  Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes , and a strategy for allocating treatment optimally, for the goal of minimizing the integrated mean squared error of the estimated average treatment effect.
Revised:  Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes . Then we leverage these models to develop rerandomization strategies for allocating treatment optimally, for the goal of minimizing the integrated mean squared error of the estimated average treatment effect.
Edit intent: clarity
Original:  Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes , and a strategy for allocating treatment optimally, for the goal of minimizing the integrated mean squared error of the estimated average treatment effect.
Revised:  Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes , and a strategy for allocating treatment optimally, by minimizing the mean squared error of the estimated average treatment effect.
Edit intent: clarity
Original:  We provide insights into features of the optimal designs via an analytical decomposition of the mean squared error used for optimization .
Revised:  We provide insights into aspects of the optimal designs via an analytical decomposition of the mean squared error used for optimization .
Edit intent: clarity
Original:  We illustrate how the proposed treatment allocation strategy improves on allocations that ignore the network structure, with extensive simulations.
Revised:  We illustrate how the proposed treatment allocation strategies improve on allocations that ignore the network structure, with extensive simulations.
Edit intent: fluency
Original:  Then we leverage these models to develop rerandomization strategies for allocating treatment optimally, by minimizing the mean squared error of the estimated average treatment effect.
Revised:  Then we leverage these models to develop rerandomization strategies for allocating treatment optimally, by minimizing the mean square error of the estimated average treatment effect.
Edit intent: fluency
Original:  Analytical decompositions of the mean squared error, due both to the model and to the randomization distribution, provide insights into aspects of the optimal designs.
Revised:  Analytical decompositions of the mean square error, due both to the model and to the randomization distribution, provide insights into aspects of the optimal designs.
Edit intent: fluency
Original:  We propose a simple and very fast method for estimating the number of communities based on the spectral properties of certain graph operators, such as the non-backtracking matrix and the Bethe Hessian matrix.
Revised:  We study a simple and very fast method for estimating the number of communities based on the spectral properties of certain graph operators, such as the non-backtracking matrix and the Bethe Hessian matrix.
Edit intent: clarity
Original:  We compare the new method to several existing methods for estimating the number of communities and show that it is both more accurate and more computationally efficient.
Revised:  We compare this method to several existing methods for estimating the number of communities and show that it is both more accurate and more computationally efficient.
Edit intent: clarity
Original:  When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a computable threshold , then any cluster point of the sequence generated, if exists, will give a stationary point of the optimization problem.
Revised:  When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a threshold that is computable , then any cluster point of the sequence generated, if exists, will give a stationary point of the optimization problem.
Edit intent: clarity
Original:  The numerical tests show that our proposed method is faster than the Douglas-Rachford splitting method when applied to finding a sparse solution of a linear system, but with a slightly worse solution quality.
Revised:  The numerical tests show that our proposed method is faster than the Douglas-Rachford splitting method when applied to finding a sparse solution of a linear system, but with a slightly compromised solution quality.
Edit intent: clarity
Original:  We then discuss one way to split the objective so that the proposed method can be suitably applied to solving optimization problems whose objective is coercive, and is the sum of a (not necessarily strongly) convex Lipschitz differentiable function and a proper closed function;
Revised:  We then discuss one way to split the objective so that the proposed method can be suitably applied to solving optimization problems with a coercive objective that is the sum of a (not necessarily strongly) convex Lipschitz differentiable function and a proper closed function;
Edit intent: clarity
Original:  ] Mueller and Tribe [ 32 ] have shown that rescaled long-range voter models in one-dimension converge to a Wright-Fisher SPDE , also known as a stochastic Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) wave.
Revised:  25] Mueller and Tribe [ 32 ] have shown that rescaled long-range voter models in one-dimension converge to a Wright-Fisher SPDE , also known as a stochastic Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) wave.
Edit intent: fluency
Original: Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects are represented and on the distribution assumed on these representations: here we assume , as is often done, that they are represented by tuples of reduced words (generators of a subgroup) or of cyclically reduced words (relators).
Revised: Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects are represented and on the distribution assumed on these representations: here we assume that they are represented by tuples of reduced words (generators of a subgroup) or of cyclically reduced words (relators).
Edit intent: coherence
Original: Our first results rely on a relatively mild prefix-heaviness hypothesis on the distributions, which states essentially that the probability of a word decreases exponentially faster than its length . Under this hypothesis, we generalize the classical resultson the free basis property ( generically a randomly chosen tuple is a basis of the subgroup it generates ), on malnormality or on small cancellation properties.
Revised: Our first results rely on a relatively mild prefix-heaviness hypothesis on the distributions, which states essentially that the probability of a word decreases exponentially fast as its length grows . Under this hypothesis, we generalize the classical resultson the free basis property ( generically a randomly chosen tuple is a basis of the subgroup it generates ), on malnormality or on small cancellation properties.
Edit intent: clarity
Original: Our first results rely on a relatively mild prefix-heaviness hypothesis on the distributions, which states essentially that the probability of a word decreases exponentially faster than its length . Under this hypothesis, we generalize the classical resultson the free basis property ( generically a randomly chosen tuple is a basis of the subgroup it generates ), on malnormality or on small cancellation properties.
Revised: Our first results rely on a relatively mild prefix-heaviness hypothesis on the distributions, which states essentially that the probability of a word decreases exponentially faster than its length . Under this hypothesis, we generalize several classical results: exponentially generically a randomly chosen tuple is a basis of the subgroup it generates ), on malnormality or on small cancellation properties.
Edit intent: clarity
Original: Computations with integro-differential operators are often carried out in an associative algebra with unit  and they are essentially non-commutative computations.
Revised: Computations with integro-differential operators are often carried out in an associative algebra with unit , and they are essentially non-commutative computations.
Edit intent: fluency
Original:  That gives an adequate framework for a computer-algebra implementation via monoidal factorization, (pure) transcendence bases and Poincar\'e-Birkhoff-Witt bases.
Revised:  That gives an adequate framework for a computer-algebra implementation via monoidal factorization, (pure) transcendence bases and Poincar\'e--Birkhoff--Witt bases.
Edit intent: fluency
Original:  The paper ends by the combinatorial setting of systems of local systems of coordinates on the group of group-like series . * The present work is part of a series of papers devoted to the study of the renormalization of divergent polyzetas (at positive and at non-positive indices) via the factorization of the non commutative generating series of polylogarithms and of harmonic sums and via the effective construction of pairs of dual bases in duality in \phi-deformed shuffle algebras.
Revised:  The paper ends by the combinatorial setting of local systems of coordinates on the group of group-like series . * The present work is part of a series of papers devoted to the study of the renormalization of divergent polyzetas (at positive and at non-positive indices) via the factorization of the non commutative generating series of polylogarithms and of harmonic sums and via the effective construction of pairs of dual bases in duality in \phi-deformed shuffle algebras.
Edit intent: fluency
Original:  It is a sequel to 3%DIFDELCMD < ] %%% and its content was presented in several seminars and meetings, including the 74th S\'eminaire Lotharingien de Combinatoire .
Revised:  It is a sequel to %DIFDELCMD < ] %%% and its content was presented in several seminars and meetings, including the 74th S\'eminaire Lotharingien de Combinatoire .
Edit intent: clarity
Original:  It is a sequel to 3%DIFDELCMD < ] %%% and its content was presented in several seminars and meetings, including the 74th S\'eminaire Lotharingien de Combinatoire .
Revised:  It is a sequel to 3%DIFDELCMD < ] %%% .
Edit intent: coherence