wanyu/IteraTeR_v2 huggingface dataset:
Original: Beliefs are not facts, but they are factive -- feel like facts.
Revised: Beliefs are not facts, but they are -- feel like facts.
Edit intent: fluency
Original: Beliefs are not facts, but they are factive -- feel like facts.
Revised: Beliefs are not facts, but they are factive factive - they feel like facts.
Edit intent: clarity
Original:  In this paper, we present a mechanism to produce maps of belief places , where populations agree on salient features of fictional environments, and belief spaces, where subgroups have related but distinct perspectives.
Revised:  In this paper, we present a mechanism to produce maps of belief places , where populations agree on salient features of fictional environments, and belief spaces, where subgroups have related but distinct perspectives.
Edit intent: fluency
Original:  We analytically study two distinguished limits---the %DIFDELCMD < \epsilon %%%  \to 0 limit which is relevant for macroscopic domains and the %DIFDELCMD < \epsilon %%%  \to \infty limit which is relevant for nano-scale domains.
Revised:  We analytically study two distinguished limits---the %DIFDELCMD < \epsilon %%% \to 0 limit relevant for macroscopic domains and the %DIFDELCMD < \epsilon %%% \to \infty limit which is relevant for nano-scale domains.
Edit intent: fluency
Original:  We analytically study two distinguished limits---the %DIFDELCMD < \epsilon %%%  \to 0 limit which is relevant for macroscopic domains and the %DIFDELCMD < \epsilon %%%  \to \infty limit which is relevant for nano-scale domains.
Revised:  We analytically study two distinguished limits---the %DIFDELCMD < \epsilon %%% \to 0 limit which is relevant for macroscopic domains and the %DIFDELCMD < \epsilon %%% \to \infty limit relevant for nano-scale domains.
Edit intent: fluency
Original:  We also investigate relaxation mechanisms for non-trivial topologies and how such mechanisms are dominated by defect annihilation, near vertices or in the interior, or through transient almost isotropic states and such relaxation mechanisms have potential relevance for switching mechanisms in nematic-based devices .
Revised:  We also introduce the concept of ` non-trivial topologies and how such mechanisms are dominated by defect annihilation, near vertices or in the interior, or through transient almost isotropic states and such relaxation mechanisms have potential relevance for switching mechanisms in nematic-based devices .
Edit intent: clarity
Original:  We also investigate relaxation mechanisms for non-trivial topologies and how such mechanisms are dominated by defect annihilation, near vertices or in the interior, or through transient almost isotropic states and such relaxation mechanisms have potential relevance for switching mechanisms in nematic-based devices .
Revised:  We also investigate relaxation mechanisms for non-trivial ' topologies and the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics .
Edit intent: clarity
Original: In petroleum reservoir simulation, the standard preconditioner, the Constrained Pressure Residual (CPR) method , is a two-stage process which involves solving a restricted pressure system.
Revised: In petroleum reservoir simulation, the Constrained Pressure Residual (CPR) method , is a two-stage process which involves solving a restricted pressure system.
Edit intent: coherence
Original: In petroleum reservoir simulation, the standard preconditioner, the Constrained Pressure Residual (CPR) method , is a two-stage process which involves solving a restricted pressure system.
Revised: In petroleum reservoir simulation, the standard preconditioner, the Constrained Pressure Residual (CPR) method , is a two-stage process involving the solution of a restricted pressure system.
Edit intent: coherence
Original:  Initially designed for isothermal models, this approach is often used in the thermal case .
Revised:  While initially designed for the isothermal case, CPR is also the standard for thermal cases .
Edit intent: clarity
Original: Dynamical low-rank algorithm are a class of numerical methods that compute low-rank approximations of dynamical systems.
Revised: Dynamical low-rank algorithms are a class of numerical methods that compute low-rank approximations of dynamical systems.
Edit intent: fluency
Original:  Recently, efficient dynamical low-rank algorithms have been applied   to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort, while often maintaining good accuracy.
Revised:  Recently, efficient dynamical low-rank algorithms have been applied in to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort, while often maintaining good accuracy.
Edit intent: fluency
Original:  We will prove that the scheme dynamically and automatically captures the low-rank structure of the solution, and preserves the fluid limit on the numerical level.
Revised:  We will prove that the scheme dynamically and automatically captures the low-rank structure of the solution, and preserves the diffusion limit on the numerical level.
Edit intent: clarity
Original:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Revised:  Recently, efficient dynamical low-rank algorithms have been applied 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Edit intent: coherence
Original:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Revised:  Recently, efficient dynamical low-rank algorithms have been applied in to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Edit intent: coherence
Original:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Revised:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low-rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Edit intent: fluency
Original:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Revised:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce numerical cost , while often maintaining good accuracy.
Edit intent: clarity
Original:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining good accuracy.
Revised:  Recently, efficient dynamical low-rank algorithms have been applied in 11,15 to treat kinetic equations, including the Vlasov--Poisson and the Boltzmann equation, where it was demonstrated that the methods are able to capture the low rank structure of the solution and significantly reduce the numerical effort , while often maintaining high accuracy.
Edit intent: clarity
Original:  In this paper, we perform an error analysis for a dynamical low-rank algorithm applied to  a classical model in kinetic theory , namely the radiative transfer equation.
Revised:  In this paper, we investigate the error analysis for a dynamical low-rank algorithm applied to a classical model in kinetic theory , namely the radiative transfer equation.
Edit intent: clarity
Original:  We will prove that the scheme  dynamically and automatically captures the low-rank structure of the solution, and preserves the diffusion limit on the numerical level .
Revised:  We will prove that the scheme dynamically and automatically capture this low-rank structure of the solution, and preserves the diffusion limit on the numerical level .
Edit intent: coherence
Original:  We will prove that the scheme  dynamically and automatically captures the low-rank structure of the solution, and preserves the diffusion limit on the numerical level .
Revised:  We will prove that the scheme dynamically and automatically captures the low-rank structure .
Edit intent: clarity
Original:  This work thus serves as the first mathematical error analysis for a dynamical low rank approximation applied to a kinetic problem.
Revised:  This work thus serves as the first mathematical error analysis for a dynamical low-rank approximation applied to a kinetic problem.
Edit intent: fluency
Original: We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the B\"uhlmann 's classical notion of an Equilibrium Risk Exchange.
Revised: We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the B\"uhlmann 's classical notion of an Equilibrium Risk Exchange.
Edit intent: fluency
Original:  In both the B\"uhlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint.
Revised:  In both the B\"uhlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint.
Edit intent: fluency
Original:  In Buhlmann 's definition the vector that assigns the budget constraint is given a priori.
Revised:  In B\"uhlmann 's definition the vector that assigns the budget constraint is given a priori.
Edit intent: fluency
Original:  The most commonly cited example of a promise CSP is the approximate graph coloring problem--which has recently benefited from multiple breakthroughs [BKO19, WZ19 ] due to a systematic study of promise CSPs under the lens of "polymorphisms," operations that map tuples in the strict form of each constraint to a tuple in its weak form.
Revised:  The most commonly cited example of a promise CSP is the approximate graph coloring problem--which has recently seen exciting progress [BKO19, WZ19 ] due to a systematic study of promise CSPs under the lens of "polymorphisms," operations that map tuples in the strict form of each constraint to a tuple in its weak form.
Edit intent: clarity
Original:  The most commonly cited example of a promise CSP is the approximate graph coloring problem--which has recently benefited from multiple breakthroughs [BKO19, WZ19 ] due to a systematic study of promise CSPs under the lens of "polymorphisms," operations that map tuples in the strict form of each constraint to a tuple in its weak form.
Revised:  The most commonly cited example of a promise CSP is the approximate graph coloring problem--which has recently benefited from multiple breakthroughs [BKO19, WZ19 ] benefiting from a systematic algebraic approach to promise CSPs based on "polymorphisms," operations that map tuples in the strict form of each constraint to a tuple in its weak form.
Edit intent: clarity
Original:  The most commonly cited example of a promise CSP is the approximate graph coloring problem--which has recently benefited from multiple breakthroughs [BKO19, WZ19 ] due to a systematic study of promise CSPs under the lens of "polymorphisms," operations that map tuples in the strict form of each constraint to a tuple in its weak form.
Revised:  The most commonly cited example of a promise CSP is the approximate graph coloring problem--which has recently benefited from multiple breakthroughs [BKO19, WZ19 ] due to a systematic study of promise CSPs under the lens of "polymorphisms," operations that map tuples in the strict form of each constraint to tuples in the corresponding weak form.
Edit intent: clarity
Original:  It is known that computing the  Hamming distance between a pattern and a streaming text exactly requires \Omega(n) space  .
Revised:  It is known that computing the exact Hamming distance between a pattern and a streaming text exactly requires \Omega(n) space .
Edit intent: fluency
Original:  It is known that computing the  Hamming distance between a pattern and a streaming text exactly requires \Omega(n) space  .
Revised:  It is known that computing the Hamming distance between a pattern and a streaming text requires \Omega(n) space .
Edit intent: clarity
Original:  Recent advances in hardware technology allow generating such data at a very high speed, but unfortunately, the produced data may contain about 10\\%DIF < of noise~[Biol. %DIF > of   Direct.'07, Klebanov and Yakovlev].
Revised:  Recent advances in hardware technology allow generating such data at a very high speed, but unfortunately, the produced data may contain about 10\\%DIF < of noise~[Biol. %DIF > of noise~ Direct.'07, Klebanov and Yakovlev].
Edit intent: fluency
Original:  Recent advances in hardware technology allow generating such data at a very high speed, but unfortunately, the produced data may contain about 10\\%DIF < of noise~[Biol. %DIF > of   Direct.'07, Klebanov and Yakovlev].
Revised:  Recent advances in hardware technology allow generating such data at a very high speed, but unfortunately, the produced data may contain about 10\\%DIF < of noise~[Biol. %DIF > of Biol. Direct.'07, Klebanov and Yakovlev].
Edit intent: fluency
Original:  A possible workaround for this issue is  (1\pm\varepsilon)-approximation.
Revised:  A possible workaround for this issue is the (1\pm\varepsilon)-approximation.
Edit intent: fluency
Original:  This line of research was initiated in [ICALP'16, Clifford and Starikovskaya] who gave a (1\pm\varepsilon)-approximation algorithm with space  (\varepsilon^{-5}n).
Revised:  This line of research was initiated in [ICALP'16, Clifford and Starikovskaya] who gave a (1\pm\varepsilon)-approximation algorithm with space ~ (\varepsilon^{-5}n).
Edit intent: fluency
Original:  In this work, we show a suite of new streaming algorithms for computing the Hamming, L_1, L_2 and general L_p (0 < p %DIFDELCMD < \le %%%  2) distances between the pattern and the text.
Revised:  In this work, we show a suite of new streaming algorithms for computing the Hamming, L_1, L_2 and general L_p (0 < p %DIFDELCMD < \le %%% < 2) distances between the pattern and the text.
Edit intent: fluency
Original:  In particular, for the Hamming distance case and for the L_p distance when 0 < p \le 1 we show a streaming algorithm that uses (\varepsilon^{-2}n) space for polynomial-size alphabets.
Revised:  In particular, for the Hamming distance and for the L_p distance when 0 < p \le 1 we show a streaming algorithm that uses (\varepsilon^{-2}n) space for polynomial-size alphabets.
Edit intent: clarity
Original:  This improves the time complexity of the overall algorithm as compared to previous analyses of AKS algorithm in \ell_p norm Blomer and Naewe ( 2009 ),Arvind and Joglekar(2008)
Revised:  Prior to these works Blomer and Naewe ( 2009 ),Arvind and Joglekar(2008)
Edit intent: clarity
Original:  This improves the time complexity of the overall algorithm as compared to previous analyses of AKS algorithm in \ell_p norm Blomer and Naewe ( 2009 ),Arvind and Joglekar(2008)
Revised:  This improves the time complexity of the overall algorithm as compared to previous analyses of AKS algorithm in \ell_p norm Blomer and Naewe 2009 ),Arvind and Joglekar(2008)
Edit intent: fluency
Original:  This improves the time complexity of the overall algorithm as compared to previous analyses of AKS algorithm in \ell_p norm Blomer and Naewe ( 2009 ),Arvind and Joglekar(2008)
Revised:  This improves the time complexity of the overall algorithm as compared to previous analyses of AKS algorithm in \ell_p norm Blomer and Naewe ( 2009 
Edit intent: coherence
Original:  ] . In the \ell_2 norm, using the birthday paradox we achieve a time complexity of 2^{ 2.49 n+o(n)}, as compared to the time complexity of 2^{ 2.571 n+o(n) %DIFDELCMD < \MBLOCKRIGHTBRACE %%% of AKS (using birthday paradox) Hanrot et al. (2011)%DIFDELCMD < ]%%% . We further modify our linear sieving technique and introduce a mixed sieving procedure.
Revised:  ] . In the \ell_2 norm, using the birthday paradox we achieve a time complexity of 2^{ 2.49 n+o(n)}, while our algorithm has a running time 2^{ 2.571 n+o(n) %DIFDELCMD < \MBLOCKRIGHTBRACE %%% of AKS (using birthday paradox) Hanrot et al. (2011)%DIFDELCMD < ]%%% . We further modify our linear sieving technique and introduce a mixed sieving procedure.
Edit intent: clarity
Original:  ] . In the \ell_2 norm, using the birthday paradox we achieve a time complexity of 2^{ 2.49 n+o(n)}, as compared to the time complexity of 2^{ 2.571 n+o(n) %DIFDELCMD < \MBLOCKRIGHTBRACE %%% of AKS (using birthday paradox) Hanrot et al. (2011)%DIFDELCMD < ]%%% . We further modify our linear sieving technique and introduce a mixed sieving procedure.
Revised:  ] . In the \ell_2 norm, using the birthday paradox we achieve a time complexity of 2^{ 2.49 n+o(n)}, as compared to the time complexity of 2^{ 2.571 n+o(n) %DIFDELCMD < \MBLOCKRIGHTBRACE %%% Hanrot et al. (2011)%DIFDELCMD < ]%%% . We further modify our linear sieving technique and introduce a mixed sieving procedure.
Edit intent: coherence
Original:  ] . In the \ell_2 norm, using the birthday paradox we achieve a time complexity of 2^{ 2.49 n+o(n)}, as compared to the time complexity of 2^{ 2.571 n+o(n) %DIFDELCMD < \MBLOCKRIGHTBRACE %%% of AKS (using birthday paradox) Hanrot et al. (2011)%DIFDELCMD < ]%%% . We further modify our linear sieving technique and introduce a mixed sieving procedure.
Revised:  ] . In the \ell_2 norm, using the birthday paradox we achieve a time complexity of 2^{ 2.49 n+o(n)}, as compared to the time complexity of 2^{ 2.571 n+o(n) %DIFDELCMD < \MBLOCKRIGHTBRACE %%% of AKS (using birthday paradox) Hanrot et al. (2011)%DIFDELCMD < ]%%% . We further modify our linear sieving technique and introduce a mixed sieving procedure.
Edit intent: fluency
Original:  At first a point is mapped to a hypercube within a sphere (as done in linear sieve) and then within each hypercube we perform a quadratic sieve like AKS.
Revised:  At first a point is mapped to a hypercube within a sphere (as done in linear sieve) and then within each hypercube we perform a quadratic seve like AKS.
Edit intent: fluency
Original:  This helps us achieve a timecomplexity of 2^{2.25n+o(n) \ell_2 norm, which is better than the time complexity of  List Sieve Birthday (2^{2.465n+o(n) [Pujol and Stehle( 2009 ), Hanrot et al.
Revised:  This helps us achieve a timecomplexity of 2^{2.25n+o(n) \ell_2 norm, which is better than the time complexity of 2^{2.25n+o(n) List Sieve Birthday (2^{2.465n+o(n) [Pujol and Stehle( 2009 ), Hanrot et al.
Edit intent: fluency
Original:  This helps us achieve a timecomplexity of 2^{2.25n+o(n) \ell_2 norm, which is better than the time complexity of  List Sieve Birthday (2^{2.465n+o(n) [Pujol and Stehle( 2009 ), Hanrot et al.
Revised:  This helps us achieve a timecomplexity of 2^{2.25n+o(n) \ell_2 norm, which is better than the time complexity of List Sieve Birthday (2^{2.465n+o(n) [Pujol an Stehle, 2009 ), Hanrot et al.
Edit intent: clarity
Original:  The arising system of governing equations can be solved accurately with a monolithic approach using mixed finite elements and Newton's method.
Revised:  The governing equations can be solved accurately with a monolithic approach using mixed finite elements and Newton's method.
Edit intent: clarity
Original:  This contribution instead separates mesh refinement from nonlinear problem regularization and provides a robust continuation procedure to obtain accurate solutions on  uniform meshes.
Revised:  This contribution instead separates mesh refinement from nonlinear problem regularization and provides a continuation procedure which robustly obtains accurate solutions on uniform meshes.
Edit intent: clarity
Original:  Simulations are presented with comparison to two experimental data sets  , one for the melting of octadecane and another for the freezing of water.
Revised:  Simulations are presented with comparison to experimental data sets , one for the melting of octadecane and another for the freezing of water.
Edit intent: clarity
Original:  Furthermore, the robust solution procedure admits detailed sensitivity studies with respect to key numerical parameters  .
Revised:  Sensitivities to key numerical parameters .
Edit intent: coherence
Original:  Furthermore, the robust solution procedure admits detailed sensitivity studies with respect to key numerical parameters  .
Revised:  Furthermore, the robust solution procedure admits detailed sensitivity studies with respect to key numerical parameters are presented .
Edit intent: coherence
Original: For a fixed connected graph H, the \{H\{\cal  {\cal  -M-DELETION problem asks, given a graph G, for the minimum number of vertices that intersect all minor models of H in G . It is known that{\cal   this problem can be solved in time f  (tw)\cdot n^{O(1)}, where tw is the treewidth of G . We determine the asymptotically optimal function f(tw), for each possible choice of H. Namely, we prove that, under the ETH, f(tw) =2^{\Theta(tw)} depending on }{\cal  }.
Revised: For a fixed finite collection of graphs{\cal {\cal -M-DELETION problem asks, given a graph G, for the minimum number of vertices that intersect all minor models of H in G . It is known that{\cal this problem can be solved in time f (tw)\cdot n^{O(1)}, where tw is the treewidth of G . We determine the asymptotically optimal function f(tw), for each possible choice of H. Namely, we prove that, under the ETH, f(tw) =2^{\Theta(tw)} depending on }{\cal }.
Edit intent: clarity