wanyu/IteraTeR_v2 huggingface dataset:
Original:  (iv) } the local boxicity of a graph, one in terms of the number of vertices and the other in terms of the number of edges\emph{ {2} \log{n}.
Revised:  (iv) } the local boxicity of a graph, one in terms of the number of vertices and the other in terms of the number of edgesproduct dimension\emph{ {2} \log{n}.
Edit intent: clarity
Original: Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the mean time to extinction is an important characteristic of any natural population.
Revised: Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population.
Edit intent: clarity
Original:  Here we consider the simplest and the most popular model in population dynamics, the logistic model, under both demographic and bounded environmental stochasticity.
Revised:  Here we consider logistic and logistic-like systems under the combined effect of demographic and bounded environmental stochasticity.
Edit intent: clarity
Original:  Our preliminary analysis studies the complexity of split-correctness over regular spanners.
Revised:  Our analysis studies the complexity of split-correctness over regular spanners.
Edit intent: clarity
Original:  We also discuss different variants of split-correctness, for instance, in the presence of black-box extractors with so-called split constraints.
Revised:  We also discuss different variants of split-correctness, for instance, in the presence of black-box extractors with split constraints.
Edit intent: clarity
Original: The paper studies normal and structured matrices under unitary and  structure-preserving similarity transformations .
Revised: Structured canonical forms under unitary and structure-preserving similarity transformations .
Edit intent: clarity
Original: Understanding the mechanisms responsible for dynamics of the Z-ring is important for our understanding of cell division in prokaryotic cells.
Revised: Understanding the mechanisms responsible for dynamics of the Z-ring is important for gaining insight into the cell division in prokaryotic cells.
Edit intent: clarity
Original:  Hydrolysis is known to regulate the dynamics of other tubulin polymers like microtubules .
Revised:  In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules .
Edit intent: coherence
Original:  Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events , irrespective of the mechanism of hydrolysis . Based on our model, we conclude that the Z-ring undergoes random breaking and closing during the process of cell division .
Revised:  Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events , irrespective of the mechanism of hydrolysis .
Edit intent: clarity
Original: Effective Hamiltonians arise in multiple problems, including homogenization of Hamilton-Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry-Mather theory.
Revised: Effective Hamiltonians arise in several problems, including homogenization of Hamilton-Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry-Mather theory.
Edit intent: fluency
Original: Effective Hamiltonians arise in multiple problems, including homogenization of Hamilton-Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry-Mather theory.
Revised: Effective Hamiltonians arise in multiple problems, including homogenization of Hamilton--Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry-Mather theory.
Edit intent: fluency
Original: Effective Hamiltonians arise in multiple problems, including homogenization of Hamilton-Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry-Mather theory.
Revised: Effective Hamiltonians arise in multiple problems, including homogenization of Hamilton-Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry--Mather theory.
Edit intent: fluency
Original:  In Aubry-Mather theory, related objects, Mather measures, are also of great importance.
Revised:  In Aubry--Mather theory, related objects, Mather measures, are also of great importance.
Edit intent: fluency
Original:  We prove the existence and convergence of the Hessian Riemannian flow .
Revised:  We prove the convergence of the Hessian Riemannian flow .
Edit intent: clarity
Original:  In addition, we explore the relation between the Hessian Riemannian flow and a variant of Newton's method that greatly improves the performance of our numerical methods .
Revised:  In addition, we explore the relation between the Hessian Riemannian flow . In addition, we explore a variant of Newton's method that greatly improves the performance of our numerical methods .
Edit intent: coherence
Original:  In addition, we explore the relation between the Hessian Riemannian flow and a variant of Newton's method that greatly improves the performance of our numerical methods .
Revised:  In addition, we explore the relation between the Hessian Riemannian flow and a variant of Newton's method that greatly improves the performance of the Hessian Riemannian flow .
Edit intent: clarity
Original:  In our numerical experiments, we see that our algorithms preserve the non-negativity of Mather measures and are more stable than previous methods in problems that are close to singular  .
Revised:  In our numerical experiments, we see that our algorithms preserve the non-negativity of Mather measures and are more stable than related methods in problems that are close to singular .
Edit intent: clarity
Original: This paper introduces NSGA-Net , an evolutionary approach for neural architecture search (NAS).
Revised: This paper introduces NSGA-Net -- an evolutionary approach for neural architecture search (NAS).
Edit intent: fluency
Original:  NSGA-Net is designed with three goals in mind: (1) a NAS procedure for multiple , possibly conflicting , objectives, (2) efficient exploration and exploitation of the space of potential neural network architectures, and (3) output of a diverse set of network architectures spanning a trade-off frontier of the objectives in a single run.
Revised:  NSGA-Net is designed with three goals in mind: (1) a procedure considering multiple and conflicting objectives, (2) efficient exploration and exploitation of the space of potential neural network architectures, and (3) output of a diverse set of network architectures spanning a trade-off frontier of the objectives in a single run.
Edit intent: clarity
Original:  NSGA-Net is designed with three goals in mind: (1) a NAS procedure for multiple , possibly conflicting , objectives, (2) efficient exploration and exploitation of the space of potential neural network architectures, and (3) output of a diverse set of network architectures spanning a trade-off frontier of the objectives in a single run.
Revised:  NSGA-Net is designed with three goals in mind: (1) a NAS procedure for multiple , possibly conflicting , objectives, (2) an efficient procedure balancing exploration and exploitation of the space of potential neural network architectures, and (3) output of a diverse set of network architectures spanning a trade-off frontier of the objectives in a single run.
Edit intent: clarity
Original:  NSGA-Net is designed with three goals in mind: (1) a NAS procedure for multiple , possibly conflicting , objectives, (2) efficient exploration and exploitation of the space of potential neural network architectures, and (3) output of a diverse set of network architectures spanning a trade-off frontier of the objectives in a single run.
Revised:  NSGA-Net is designed with three goals in mind: (1) a NAS procedure for multiple , possibly conflicting , objectives, (2) efficient exploration and exploitation of the space of potential neural network architectures, and (3) a procedure finding a diverse set of network architectures spanning a trade-off frontier of the objectives in a single run.
Edit intent: clarity
Original:  NSGA-Net is designed with three goals in mind: (1) a NAS procedure for multiple , possibly conflicting , objectives, (2) efficient exploration and exploitation of the space of potential neural network architectures, and (3) output of a diverse set of network architectures spanning a trade-off frontier of the objectives in a single run.
Revised:  NSGA-Net is designed with three goals in mind: (1) a NAS procedure for multiple , possibly conflicting , objectives, (2) efficient exploration and exploitation of the space of potential neural network architectures, and (3) output of a diverse set of trade-off network architectures achieved in a single run.
Edit intent: clarity
Original:  an exploration step comprising crossover and mutation of architectures  and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network prior . Experimental results suggest that combining the  objectives of minimizing both an error metric and computational complexity,
Revised:  an exploration step comprising crossover and mutation of architectures , and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network prior . Experimental results suggest that combining the objectives of minimizing both an error metric and computational complexity,
Edit intent: fluency
Original:  an exploration step comprising crossover and mutation of architectures  and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network prior . Experimental results suggest that combining the  objectives of minimizing both an error metric and computational complexity,
Revised:  an exploration step comprising crossover and mutation of architectures and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network . Experimental results suggest that combining the objectives of minimizing both an error metric and computational complexity,
Edit intent: clarity
Original:  an exploration step comprising crossover and mutation of architectures  and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network prior . Experimental results suggest that combining the  objectives of minimizing both an error metric and computational complexity,
Revised:  an exploration step comprising crossover and mutation of architectures and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network prior . Experimental results suggest that combining the dual objectives of minimizing both an error metric and computational complexity,
Edit intent: clarity
Original:  an exploration step comprising crossover and mutation of architectures  and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network prior . Experimental results suggest that combining the  objectives of minimizing both an error metric and computational complexity,
Revised:  an exploration step comprising crossover and mutation of architectures and finally an exploitation step that applies the entire history of evaluated neural architectures in the form of a Bayesian Network prior . Experimental results suggest that combining the objectives of minimizing an error metric and computational complexity,
Edit intent: clarity
Original:  as measured by FLOPS , allows NSGA-Net to find competitive neural architectures near the Pareto front of both objectives on two different tasks, object classification and object alignment.
Revised:  as measured by FLOPs , allows NSGA-Net to find competitive neural architectures near the Pareto front of both objectives on two different tasks, object classification and object alignment.
Edit intent: fluency
Original:  as measured by FLOPS , allows NSGA-Net to find competitive neural architectures near the Pareto front of both objectives on two different tasks, object classification and object alignment.
Revised:  as measured by FLOPS , allows NSGA-Net to find competitive neural architectures . Moreover,
Edit intent: coherence
Original:  NSGA-Net obtains networks that achieve 3.72\% (at 4.5 million FLOP) error on CIFAR-10 classification and 8.64\% (at 26.6 million FLOP) error on the CMU-Car alignment task.
Revised:  NSGA-Net achieves error rate on the CMU-Car alignment task.
Edit intent: clarity
Original:  Andoni, Krauthgamer  and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within  approximation factor poly(\log n).
Revised:  Andoni, Krauthgamer , and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within approximation factor poly(\log n).
Edit intent: fluency
Original:  Andoni, Krauthgamer  and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within  approximation factor poly(\log n).
Revised:  Andoni, Krauthgamer and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within an approximation factor poly(\log n).
Edit intent: fluency
Original:  vertices and O(n) edges that preserves all non-trivial min-cuts of G . We show a very  simple argument that improves this contraction-based sparsifier by eliminating the poly-logarithmic factors, that is, we show a contraction-based sparsification that leaves O(n/\delta) vertices and O(n) edges, preserves all non-trivial min-cuts and can be computed in near-linear time O( |E(G)|).
Revised:  vertices and O(n) edges that preserves all non-trivial min-cuts of G . We show a very hides logarithmic factors. We present a simple argument that improves this contraction-based sparsifier by eliminating the poly-logarithmic factors, that is, we show a contraction-based sparsification that leaves O(n/\delta) vertices and O(n) edges, preserves all non-trivial min-cuts and can be computed in near-linear time O( |E(G)|).
Edit intent: clarity
Original:  ExaHyPE combines dynamically adaptive meshes (AMR) with ADER-DG. It is parallelised using tasks, and it is cache efficient.
Revised:  ExaHyPE combines dynamically adaptive meshes (AMR) with ADER-DG. It is parallelized using tasks, and it is cache efficient.
Edit intent: fluency
Original:  Despite this inhomogeneous character, our code benefits from AVX vectorization, though it suffers from memory access bursts.
Revised:  Despite this inhomogeneous character, our code benefits from AVX vectorization, though we suffer from memory access bursts.
Edit intent: fluency
Original:  We show that a frequency reduction of the chip does not mitigate burst effects although it improves the code's energy-to-solution.
Revised:  A frequency reduction of the chip does not mitigate burst effects although it improves the code's energy-to-solution.
Edit intent: coherence
Original:  We show that a frequency reduction of the chip does not mitigate burst effects although it improves the code's energy-to-solution.
Revised:  We show that a frequency reduction of the chip improves the code's energy-to-solution.
Edit intent: clarity
Original:  Even worse, the burst 's latency dependence becomes worse once we add Optane.
Revised:  Yet, it does not mitigate burst effects. The bursts' latency penalty becomes worse once we add Optane.
Edit intent: clarity
Original:  However, in cases where memory-intense and computationally expensive tasks overlap, ExaHype 's cache-oblivious implementation can exploit the Intel Memory Drive Technology (IMDT) virtualizing the extra memory layer, and it suffers only from a less than 3x performance decline per degree of freedom versus pure DDR4 memory .
Revised:  However, in cases where memory-intense and computationally expensive tasks overlap, ExaHyPE 's cache-oblivious implementation can exploit the Intel Memory Drive Technology (IMDT) virtualizing the extra memory layer, and it suffers only from a less than 3x performance decline per degree of freedom versus pure DDR4 memory .
Edit intent: clarity
Original:  We thus propose that upcoming supercomputing simulation codes with dynamic, inhomogeneous task graphs require algorithms and task schedulers which actively prefetch data, intermix tasks of different  character, and apply frequency control to or switch off the memory if appropriate .
Revised:  We thus propose that upcoming supercomputing simulation codes with dynamic, inhomogeneous task graphs are actively supported by thread runtimes in intermixing tasks of different character, and apply frequency control to or switch off the memory if appropriate .
Edit intent: clarity
Original:  We thus propose that upcoming supercomputing simulation codes with dynamic, inhomogeneous task graphs require algorithms and task schedulers which actively prefetch data, intermix tasks of different  character, and apply frequency control to or switch off the memory if appropriate .
Revised:  We thus propose that upcoming supercomputing simulation codes with dynamic, inhomogeneous task graphs require algorithms and task schedulers which actively prefetch data, intermix tasks of different compute character, and apply frequency control to or switch off the memory if appropriate .
Edit intent: clarity
Original:  We then focus on the average delay of enumeration algorithms and show that we can bring down the dependency of the average delay to the square root of the formula sizeand even to a logarithmic dependency for monotone formulas .
Revised:  We then focus on the average delay of enumeration algorithms and show that we can bring down the dependency of the average delay to the square root of the formula sizeand even to a logarithmic dependency for monotone formulas .
Edit intent: fluency
Original:  For convex minimization variational problems  , the duality gap between the primal and dual functionals is a perfect a posteriori error estimator.
Revised:  For convex minimization variational problems , the primal-dual gap between the primal and dual functionals is a perfect a posteriori error estimator.
Edit intent: clarity
Original:  For convex minimization variational problems  , the duality gap between the primal and dual functionals is a perfect a posteriori error estimator.
Revised:  For convex minimization variational problems , the duality gap between the primal and dual functionals can be used as a posteriori error estimator.
Edit intent: clarity
Original:  This primal dual error estimator is robust with respect to the parameters of the problem, and it can be used for both the mesh refinements of finite element methods and the true RB error certification.
Revised:  This primal dual error estimator is robust with respect to the parameters of the problem, and it can be used for both mesh refinements of finite element methods and the true RB error certification.
Edit intent: fluency
Original:  The present work interpolates between these two extremes by quantitatively characterizing the tradeoff between the degree of decentralization and the performance of the distributed algorithm.
Revised:  The present work interpolates between these two extremes by quantifying the tradeoff between the degree of decentralization and the performance of the distributed algorithm.
Edit intent: clarity
Original: Full Approximation Scheme (FAS)  is a widely used multigrid method for nonlinear problems.
Revised: Full Approximation Scheme (FAS) scheme is a widely used multigrid method for nonlinear problems.
Edit intent: clarity
Original:  In this paper, a new framework to analyze FAS for convex optimization problems is developed.
Revised:  In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed.
Edit intent: clarity
Original: We consider the FDA approved Glucose-Insulin-Glucagon nonlinear model which  describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes.
Revised: The Glucose-Insulin-Glucagon nonlinear model which describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes.
Edit intent: coherence
Original: We consider the FDA approved Glucose-Insulin-Glucagon nonlinear model which  describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes.
Revised: We consider the FDA approved Glucose-Insulin-Glucagon nonlinear model which accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes.
Edit intent: clarity
Original:  Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon ( dual-therapy ) that can optimally maintain the blood glucose level after consuming a meal within healthy limits and prevent the onset of both hypoglycemia and hyperglycemia.
Revised:  Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon ( dual therapy ) that can optimally maintain the blood glucose level after consuming a meal within healthy limits and prevent the onset of both hypoglycemia and hyperglycemia.
Edit intent: fluency
Original:  Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon ( dual-therapy ) that can optimally maintain the blood glucose level after consuming a meal within healthy limits and prevent the onset of both hypoglycemia and hyperglycemia.
Revised:  Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon ( dual-therapy ) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia.
Edit intent: clarity
Original:  The problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package \mathcal{PSOPT .
Revised:  This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package \mathcal{PSOPT .
Edit intent: fluency
Original:  The problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package \mathcal{PSOPT .
Revised:  The problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT .
Edit intent: coherence
Original:  Interestingly, in the case of monotherapy,  the optimal solution we find is nearly identical to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal.
Revised:  Interestingly, in the case of monotherapy, we find the optimal solution we find is nearly identical to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal.
Edit intent: fluency
Original:  Interestingly, in the case of monotherapy,  the optimal solution we find is nearly identical to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal.
Revised:  Interestingly, in the case of monotherapy, the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal.
Edit intent: clarity
Original:  We also find that the optimal dual-therapy (using both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone.
Revised:  We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone.
Edit intent: clarity
Original:  We also propose a rule for both dosage and time of delivery for the dual-therapy.
Revised:  We also propose an ad-hoc rule for both dosage and time of delivery for the dual-therapy.
Edit intent: clarity
Original:  We also propose a rule for both dosage and time of delivery for the dual-therapy.
Revised:  We also propose a rule for both the dosage and the time of delivery for the dual-therapy.
Edit intent: fluency