wanyu/IteraTeR_v2 huggingface dataset:
Original:  We apply the same technique to modular composition: fix a square-free G \in \mathbb{K}[x] and generic R \in \mathbb{K available for precomputation, we then input f \in \mathbb{K}[x,y] and output f(x, R (x)) ~\mathrm{rem~ G \in \mathbb{K}[x] } \operatorname{rem}  in quasi-linear time in the size of f, G, R .
Revised:  We apply the same technique to modular composition: fix a square-free G \in \mathbb{K}[x] and generic R \in \mathbb{K available for precomputation, we then input f \in \mathbb{K}[x,y] and output f(x, R (x)) ~\mathrm{rem~ G \in \mathbb{K}[x] } \operatorname{rem} in quasi-linear time .
Edit intent: clarity
Original: Somitogenesis , the process of body segmentation during embryonic development, exhibits a key set of features that is conserved across all vertebrate species despite differences in the detailed mechanisms.
Revised: Somitogenesis , the process of body segmentation during embryonic development, that is invariant across all vertebrate species despite differences in the detailed mechanisms.
Edit intent: clarity
Original:  In this paper we have proposed a unified mechanism that reproduces the sequence of dynamical transitions observed during somitogenesis by combining the local interactions mediated via Notch-Delta intercellular coupling with global spatial heterogeneity introduced through a morphogen gradient that is known to occur along the anteroposterior axis of the growing PSM.
Revised:  In this paper we have proposed a unified mechanism that reproduces the sequence of dynamical transitions observed during somitogenesis by combining the local interactions mediated via Notch-Delta intercellular coupling with global spatial heterogeneity introduced through a morphogen gradient known to occur along the anteroposterior axis of the growing PSM.
Edit intent: fluency
Original: In this paper , we provide a holistic analysis of the primal-dual dynamics associated to linear equality-constrained optimization problems and aimed at computing saddle-points of the associated Lagrangian using contraction analysis.
Revised: In this paper , we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems and aimed at computing saddle-points of the associated Lagrangian using contraction analysis.
Edit intent: clarity
Original: In this paper , we provide a holistic analysis of the primal-dual dynamics associated to linear equality-constrained optimization problems and aimed at computing saddle-points of the associated Lagrangian using contraction analysis.
Revised: In this paper , we provide a holistic analysis of the primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis.
Edit intent: coherence
Original:  We analyze the well-known standard version of the problem: we establish convergence results for convex objective functions and further characterize its convergence rate under strong convexity.
Revised:  For the well-known standard version of the problem: we establish convergence results for convex objective functions and further characterize its convergence rate under strong convexity.
Edit intent: coherence
Original:  Then, we consider a popular implementation of a distributed optimization problem and, using weaker notations of contraction theory, we establish the global exponential convergence of its associated distributed primal-dual dynamics.
Revised:  Then, for a canonical distributed optimization problem and, using weaker notations of contraction theory, we establish the global exponential convergence of its associated distributed primal-dual dynamics.
Edit intent: clarity
Original:  Then, we consider a popular implementation of a distributed optimization problem and, using weaker notations of contraction theory, we establish the global exponential convergence of its associated distributed primal-dual dynamics.
Revised:  Then, we consider a popular implementation of a distributed optimization problem and, using weaker notations of contraction theory, we establish the global exponential convergence of its primal-dual dynamics.
Edit intent: clarity
Original:  Moreover, based on this analysis, we propose a new distributed solver for the least-squares problem with global exponential convergence guarantees.
Revised:  Moreover, based on this analysis, we propose a new distributed solver for the least-squares problem with the same convergence guarantees.
Edit intent: clarity
Original:  Finally, we consider time-varying versions of the centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Revised:  Finally, for time-varying versions of the centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Edit intent: coherence
Original:  Finally, we consider time-varying versions of the centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Revised:  Finally, we consider time-varying versions of both centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Edit intent: clarity
Original:  Finally, we consider time-varying versions of the centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Revised:  Finally, we consider time-varying versions of the centralized and distributed primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Edit intent: clarity
Original:  Finally, we consider time-varying versions of the centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Revised:  Finally, we consider time-varying versions of the centralized and distributed implementations of primal-dual dynamics , we exploit their contractive nature to establish asymptotic bounds on their tracking error.
Edit intent: fluency
Original:  Finally, we consider time-varying versions of the centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish asymptotic bounds on their tracking error.
Revised:  Finally, we consider time-varying versions of the centralized and distributed implementations of primal-dual dynamics and exploit their contractive nature to establish bounds on their tracking error.
Edit intent: clarity
Original:  To support our convergence analyses, we introduce novel results on contraction theory and specifically use them in the cases where the analyzed systems are weakly contractive (i.e., has zero contraction rate) and/or converge to specific points belonging to a subspace of equilibria .
Revised:  To support our analyses, we introduce novel results on contraction theory and specifically use them in the cases where the analyzed systems are weakly contractive (i.e., has zero contraction rate) and/or converge to specific points belonging to a subspace of equilibria .
Edit intent: clarity
Original:  To support our convergence analyses, we introduce novel results on contraction theory and specifically use them in the cases where the analyzed systems are weakly contractive (i.e., has zero contraction rate) and/or converge to specific points belonging to a subspace of equilibria .
Revised:  To support our convergence analyses, we introduce novel results on contraction theory .
Edit intent: coherence
Original:  We also propose a simple trick to reduce the complexity of processing each training sample from O(S !) to O(1 ), where S is the number of the speakers in the training sample, by using the start times of the constituent source utterances.
Revised:  We also propose a simple trick to reduce the complexity of processing each training sample from O(S ), where S is the number of the speakers in the training sample, by using the start times of the constituent source utterances.
Edit intent: coherence
Original:  Our theoretical and numerical results shed light on how the controllability of the network opinion depends on the parameters such as the size and the connectivity of the network, and the sparsity constraints faced by the manipulative agent.
Revised:  Our theoretical and numerical results shed light on how controllability of the network opinion depends on the parameters such as the size and the connectivity of the network, and the sparsity constraints faced by the manipulative agent.
Edit intent: fluency
Original: Gradual type systems seamlessly integrate statically-typed programs with dynamically-typed programs.
Revised: Information flow type systems enforce the security property of noninterference by detecting unauthorized data flows at compile-time. However, they require precise type annotations, making them difficult to use in practice as much of the legacy infrastructure is written in untyped or dynamically-typed programs.
Edit intent: coherence
Original:  The runtime for gradual type systems can be viewed as a monitor which refines and enforces constraints to ensure type-preservation . Gradual typing  has been applied to information flow types , where information flow monitors are derived from gradual information flow types.
Revised:  The runtime for gradual type systems can be viewed as a monitor which refines and enforces constraints to ensure type-preservation . Gradual typing has been applied to information flow control , where information flow monitors are derived from gradual information flow types.
Edit intent: clarity
Original:  In this paper , we re-examine the connection between gradual information flow types and information flow monitors , and identify the root cause for the tension between satisfying gradual guarantees and noninterference.
Revised:  In this paper , we re-examine the connection between gradual information flow types and information flow monitors to identify the root cause for the tension between satisfying gradual guarantees and noninterference.
Edit intent: coherence
Original:  In this paper , we re-examine the connection between gradual information flow types and information flow monitors , and identify the root cause for the tension between satisfying gradual guarantees and noninterference.
Revised:  In this paper , we re-examine the connection between gradual information flow types and information flow monitors , and identify the root cause of the tension between satisfying gradual guarantees and noninterference.
Edit intent: fluency
Original:  In this paper , we re-examine the connection between gradual information flow types and information flow monitors , and identify the root cause for the tension between satisfying gradual guarantees and noninterference.
Revised:  In this paper , we re-examine the connection between gradual information flow types and information flow monitors , and identify the root cause for the tension between the gradual guarantees and noninterference.
Edit intent: clarity
Original:  We develop a runtime semantics for a simple imperative language with gradual information flow types that provides both noninterference and the dynamic gradual guarantee .
Revised:  We develop runtime semantics for a simple imperative language with gradual information flow types that provides both noninterference and the dynamic gradual guarantee .
Edit intent: fluency
Original:  We develop a runtime semantics for a simple imperative language with gradual information flow types that provides both noninterference and the dynamic gradual guarantee .
Revised:  We develop a runtime semantics for a simple imperative language with gradual information flow types that provides both noninterference and gradual guarantees .
Edit intent: clarity
Original:  We leverage a proof technique developed for FlowML , which reduces noninterference proofs to preservation proofs , to prove the key security property .
Revised:  We leverage a proof technique developed for FlowML and reduce noninterference proofs to preservation proofs , to prove the key security property .
Edit intent: coherence
Original:  We leverage a proof technique developed for FlowML , which reduces noninterference proofs to preservation proofs , to prove the key security property .
Revised:  We leverage a proof technique developed for FlowML , which reduces noninterference proofs to preservation proofs .
Edit intent: coherence
Original:  NAS adopts a search strategy to effectively explore predefined search space to find architecture in search space with outstanding performance with minimum searching cost . Bayesian optimization and evolutionary algorithms are two commonly used search strategies, but they suffer from computationally expensive, challenge to implement , and inefficient exploration ability.
Revised:  NAS adopts a search strategy to explore the predefined search space to find architecture in search space with outstanding performance with minimum searching cost . Bayesian optimization and evolutionary algorithms are two commonly used search strategies, but they suffer from computationally expensive, challenge to implement , and inefficient exploration ability.
Edit intent: clarity
Original:  NAS adopts a search strategy to effectively explore predefined search space to find architecture in search space with outstanding performance with minimum searching cost . Bayesian optimization and evolutionary algorithms are two commonly used search strategies, but they suffer from computationally expensive, challenge to implement , and inefficient exploration ability.
Revised:  NAS adopts a search strategy to effectively explore predefined search space to find outstanding performance architecture with the minimum searching costs . Bayesian optimization and evolutionary algorithms are two commonly used search strategies, but they suffer from computationally expensive, challenge to implement , and inefficient exploration ability.
Edit intent: clarity
Original:  NAS adopts a search strategy to effectively explore predefined search space to find architecture in search space with outstanding performance with minimum searching cost . Bayesian optimization and evolutionary algorithms are two commonly used search strategies, but they suffer from computationally expensive, challenge to implement , and inefficient exploration ability.
Revised:  NAS adopts a search strategy to effectively explore predefined search space to find architecture in search space with outstanding performance with minimum searching cost . Bayesian optimization and evolutionary algorithms are two commonly used search strategies, but they suffer from computationally expensive, challenge to implement or inefficient exploration ability.
Edit intent: fluency
Original:  In this paper, we propose to combine evolutionary algorithm with a neural predictor that can significantly improve the exploration ability of evolutionary algorithms for NAS . We designed a graph-based neural predictor with uncertainty estimation and adopted an acquisition function defined from this neural predictor to guide the evolutionary algorithm to efficiently explore the search space.
Revised:  In this paper, we propose a neural predictor that can significantly improve the exploration ability of evolutionary algorithms for NAS . We designed a graph-based neural predictor with uncertainty estimation and adopted an acquisition function defined from this neural predictor to guide the evolutionary algorithm to efficiently explore the search space.
Edit intent: coherence
Original:  In this paper, we propose to combine evolutionary algorithm with a neural predictor that can significantly improve the exploration ability of evolutionary algorithms for NAS . We designed a graph-based neural predictor with uncertainty estimation and adopted an acquisition function defined from this neural predictor to guide the evolutionary algorithm to efficiently explore the search space.
Revised:  In this paper, we propose to combine evolutionary algorithm with a neural predictor guided evolutionary algorithm to enhance the exploration ability of evolutionary algorithms for NAS . We designed a graph-based neural predictor with uncertainty estimation and adopted an acquisition function defined from this neural predictor to guide the evolutionary algorithm to efficiently explore the search space.
Edit intent: clarity
Original:  Larger datasets to be collected in e.g. the LHC's Run 3 will enable measurements with higher precision, but will require faster data processing to keep fitting times stable.
Revised:  Larger datasets to be collected at e.g. the LHC's Run 3 will enable measurements with higher precision, but will require faster data processing to keep fitting times stable.
Edit intent: fluency
Original:  This will allow to fit the larger datasets of Run 3 in the same time or faster than today's fits.
Revised:  This will allow to fit larger datasets of Run 3 in the same time or faster than today's fits.
Edit intent: fluency
Original:  This will allow to fit the larger datasets of Run 3 in the same time or faster than today's fits.
Revised:  This will allow to fit the larger datasets of the future in the same time or faster than today's fits.
Edit intent: clarity
Original:  In this paper, we provide a finer analysis and extension of this framework , where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature.
Revised:  We propose a finer analysis and extension of this framework , where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature.
Edit intent: clarity
Original:  In this paper, we provide a finer analysis and extension of this framework , where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature.
Revised:  In this paper, we provide a finer analysis of how belief can be based on information , where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature.
Edit intent: clarity
Original:  We combine Belnap-Dunn logic and non-standard probabilities to account for potentially contradictory information  within a two-layer modal logical framework to account for belief .
Revised:  We use Belnap-Dunn logic and non-standard probabilities to account for potentially contradictory information within a two-layer modal logical framework to account for belief .
Edit intent: clarity
Original:  To further improve the performance, the interior of the tub was spray-painted with chrome paint, forming a low quality-factor (Q) fabry-perot optical cavity.
Revised:  To further improve the performance, the interior of the tub was spray-painted with chrome paint, forming a low quality-factor (Q) Fabry-Perot optical cavity.
Edit intent: fluency
Original:  Namely, the comparison is made with rank, quantile , cyclic LOESS (locally estimated scatterplot smoothing), and MAD (median absolute deviation) normalization methods  .
Revised:  Namely, the comparison is made with Rank, Quantile , cyclic LOESS (locally estimated scatterplot smoothing), and MAD (median absolute deviation) normalization methods .
Edit intent: fluency
Original:  } [x_{1, 1}, \ldots, x_{n, n}] } of degree at most poly(n) such that every matrix M which can be written as a sum of a matrix of rank at most n/100 and  sparsity at most n^2/100 satisfies P(M) = 0. This confirms a conjecture of Gesmundo, Hauenstein, Ikenmeyer and Landsberg [GHIL16] and improves the best upper bound known for this problem down from \exp(n^2) [KLPS14, GHIL16] to poly(n).
Revised:  } [x_{1, 1}, \ldots, x_{n, n}] } of degree at most poly(n) such that every matrix M which can be written as a sum of a matrix of rank at most n/100 and a matrix of sparsity at most n^2/100 satisfies P(M) = 0. This confirms a conjecture of Gesmundo, Hauenstein, Ikenmeyer and Landsberg [GHIL16] and improves the best upper bound known for this problem down from \exp(n^2) [KLPS14, GHIL16] to poly(n).
Edit intent: fluency
Original:  This attractor network is used to identify the most efficient (total intervention volume minimizing) protocol to drive the system from one basin to another.
Revised:  This attractor network is used to identify efficient (total intervention volume minimizing) protocol to drive the system from one basin to another.
Edit intent: clarity
Original:  This attractor network is used to identify the most efficient (total intervention volume minimizing) protocol to drive the system from one basin to another.
Revised:  This attractor network is used to identify the most efficient (total intervention volume minimizing) protocols that drive the system from one basin to another.
Edit intent: fluency
Original:  It is based on a biologically motivated Markov model for genetic sequence evolution.
Edit intent: coherence
Original:  As a point set, this space comprises the previously developed Billera-Holmes-Vogtmann (BHV) tree space while its geometry is motivated from the edge-product space.
Revised:  As a point set, wald space contains the previously developed Billera-Holmes-Vogtmann (BHV) tree space while its geometry is motivated from the edge-product space.
Edit intent: clarity
Original:  Comparison with the BHV geometry shows that our canonical and biologically motived space is substantially different.
Revised:  Comparison with the BHV geometry shows that our canonical and biologically motivated space is substantially different.
Edit intent: fluency
Original: L\'evy walks are random walks processes whose step length follows a long-tailed power law distribution.
Revised: L\'evy walks are random walk processes whose step-lengths follow a long-tailed power law distribution.
Edit intent: fluency
Original: L\'evy walks are random walks processes whose step length follows a long-tailed power law distribution.
Revised: L\'evy walks are random walks processes whose step length follows a long-tailed power-law distribution.
Edit intent: fluency
Original:  Due to their abundance as movement patterns of biological organisms, significant theoretical efforts have been devoted to identify the foraging circumstances that would make such patterns advantageous Viswanathan et al.
Revised:  Due to their abundance as movement patterns of biological organisms, significant theoretical efforts have been devoted to identifying the foraging circumstances that would make such patterns advantageous Viswanathan et al.
Edit intent: fluency
Original:  Nature, 1999 . Despite numerous attempts , there is currently no conclusive analytical evidence that L\'evy flights are preferable strategies in higher dimensions than one.
Revised:  Nature, 1999 . However, despite extensive research , there is currently no conclusive analytical evidence that L\'evy flights are preferable strategies in higher dimensions than one.
Edit intent: clarity
Original:  Nature, 1999 . Despite numerous attempts , there is currently no conclusive analytical evidence that L\'evy flights are preferable strategies in higher dimensions than one.
Revised:  Nature, 1999 . Despite numerous attempts , there is currently no mathematical proof indicating that L\'evy flights are preferable strategies in higher dimensions than one.
Edit intent: clarity
Original:  Reviews of Modern Physics, 2011%DIFDELCMD < ]%%% , this strategy optimally finds sparse targets of any size and shape.
Revised:  Reviews of Modern Physics, 2011%DIFDELCMD < ]%%% walk strategy is extremely efficient at finding sparse targets of any size and shape.
Edit intent: clarity
Original:  Our results thus provide strong theoretical support for the optimality and robustness of intermittent\emph{  L\'evy walks under general conditions .
Revised:  Our results shed new light on the\emph{ L\'evy walks under general conditions .
Edit intent: clarity
Original:  Our results thus provide strong theoretical support for the optimality and robustness of intermittent\emph{  L\'evy walks under general conditions .
Revised:  Our results thus provide strong theoretical support for the optimality and robustness of intermittent\emph{ L\'evy walks .
Edit intent: clarity