wanyu/IteraTeR_full_sent huggingface dataset:
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Revised:  CHM is not only a fundamental problem in Linear Programming, Computational Geometry, Machine Learning and Statistics, it also serves as a query problem in many applications e.g. Topic Modeling, LP Feasibility, Data Reduction. The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Edit intent: meaning-changed
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Revised:  The {\it Triangle Algorithm} (TA) %DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Edit intent: clarity
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Revised:  The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% %DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Edit intent: fluency
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Revised:  The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% %DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Edit intent: meaning-changed
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Revised:  The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% %DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Edit intent: coherence
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Revised:  The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% \mbox{%DIFAUXCMD kalantari2015characterization {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Edit intent: meaning-changed
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
Revised:  The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it , i. e. the orthogonal bisector of pp' separates p from conv(S).
Edit intent: fluency
Original:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S). By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Revised:  The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either%DIFDELCMD < \Vert %%% p'- p%DIFDELCMD < \Vert %%% \leq \varepsilon R, R= \max \{%DIFDELCMD < \Vert %%% p -v%DIFDELCMD < \Vert%%% : v\in S\ {\it witness %DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Edit intent: coherence
Original:  By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Revised:  By the%DIFDELCMD < {\it %%% Spherical}-CHM is a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Edit intent: clarity
Original:  By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Revised:  By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 %DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Edit intent: fluency
Original:  By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Revised:  By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% %DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Edit intent: fluency
Original:  By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% =1, \forall v \in S . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Revised:  By the%DIFDELCMD < {\it %%% Spherical}-CHM we mean a CHM, where p=0 ,%DIFDELCMD < \Vert %%% v%DIFDELCMD < \Vert%%% and each point in S has unit norm . First, we prove the equivalence of exact and approximate versions of CHM and Spherical-CHM.
Edit intent: meaning-changed
Original:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Revised:  On the other hand, %DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Edit intent: clarity
Original:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Revised:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% %DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Edit intent: fluency
Original:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Revised:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% %DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Edit intent: meaning-changed
Original:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Revised:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% %DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Edit intent: coherence
Original:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% \geq \sqrt{1+ \varepsilon to O(1/\varepsilon).
Revised:  On the other hand, using this iteration complexity we prove if for each p' \in conv(S) with%DIFDELCMD < \Vert %%% p%DIFDELCMD < \Vert %%% > \varepsilon that is not a witness there is v \in S with%DIFDELCMD < \Vert %%% p' - v%DIFDELCMD < \Vert %%% we prove that under the satisfiability of a simple condition in each iteration, the complexity improves to O(1/\varepsilon).
Edit intent: meaning-changed
Original:  Lastly, as an application of TA, we show how to solve strict LP feasibility as a dual of CHM. In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  This suggests the\textit{ Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Edit intent: coherence
Original:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  In summary, TA and the\textit{Spherical-TA Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Edit intent: meaning-changed
Original:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  In summary, TA and the\textit{ which first converts a given CHM into a Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Edit intent: meaning-changed
Original:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  In summary, TA and the\textit{ Spherical-CHM before applying the algorithm. Next we introduce a series of applications of Spherical-TA. In particular, Spherical-TA serves as a fast version of vanilla TA to boost its efficiency. As an example, this results in a fast version of\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Edit intent: meaning-changed
Original:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  In summary, TA and the\textit{ Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{AVTA }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Edit intent: meaning-changed
Original:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  In summary, TA and the\textit{ Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ \mbox{%DIFAUXCMD \cite{awasthi2018robust}\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Edit intent: meaning-changed
Original:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  In summary, TA and the\textit{ Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{AVTA^+ }\hspace{0pt}%DIFAUXCMD } .
Edit intent: meaning-changed
Original:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
Revised:  In summary, TA and the\textit{ Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ for solving exact or approximate irredundancy problem. Computationally, we have considered CHM, LP and Strict LP Feasibility and the Irredundancy problem. Based on substantial amount of computing, Spherical-TA achieves better efficiency than state of the art algorithms. Leveraging on the efficiency of Spherical-TA, we propose AVTA^+ as a pre-processing step for data reduction which arises in such applications as in computing the Minimum Volume Enclosing Ellipsoid \mbox{%DIFAUXCMD \cite{moshtagh2005minimum}\hspace{0pt}%DIFAUXCMD } .
Edit intent: meaning-changed
Original: This paper develops a consistent  Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models against nonparametric alternatives . Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods.
Revised: This paper develops a consistent heteroskedasticity robust Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models against nonparametric alternatives . Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods.
Edit intent: meaning-changed
Original: This paper develops a consistent  Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models against nonparametric alternatives . Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods.
Revised: This paper develops a consistent Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models . Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods.
Edit intent: clarity
Original:  The test is simple to implement, because it requires estimating only the restricted semiparametric model and because the asymptotic distribution of the test statistic is pivotal. The projection interpretation of series estimators allows me to derive a degrees of freedom correction.
Revised:  The test is asymptotically standard normal under the null. Compared with the earlier literature on series-based specification tests in parametric models, I rely on the projection property of series estimators allows me to derive a degrees of freedom correction.
Edit intent: meaning-changed
Original:  The projection interpretation of series estimators allows me to derive a degrees of freedom correction. This correction allows me to account for the estimation variance and develop refined asymptotic results. It also substantially improves the finite sample performance of the test .
Revised:  The projection interpretation of series estimators and derive a different normalization of the test statistic. Compared with the recent test in Gupta (2018), I use a different way of accounting for heteroskedasticity. I demonstrate using Monte Carlo studies that my test has superior finite sample performance of the test .
Edit intent: meaning-changed
Original:  More specifically, we map the equilibrium condition of a  financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with 2-body interactions, i.e., a Quadratic Unconstrained Binary Optimization (QUBO) problem.
Revised:  More specifically, we map the equilibrium condition of a toy-model financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with 2-body interactions, i.e., a Quadratic Unconstrained Binary Optimization (QUBO) problem.
Edit intent: meaning-changed
Original:  More specifically, we map the equilibrium condition of a  financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with 2-body interactions, i.e., a Quadratic Unconstrained Binary Optimization (QUBO) problem.
Revised:  More specifically, we map the equilibrium condition of a financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with 2-body interactions, i.e., a quadratic unconstrained binary optimization (QUBO) problem.
Edit intent: fluency
Original:  We report a peptide generation framework PepCVAE, based on a semi-supervised variational autoen- coder (VAE) model, for designing novel antimicrobial peptide (AMP) sequences.
Revised:  We report a peptide generation framework PepCVAE, based on a semi-supervised variational autoencoder (VAE) model, for designing novel antimicrobial peptide (AMP) sequences.
Edit intent: fluency
Original:  Extensive analysis of the PepCVAE-generated sequences reveals superior performance of our model in comparison to a plain VAE, as PepCVAE generates novel AMP sequences with higher long-range diversity, while being closer to the training distribution of bio- logical peptides.
Revised:  Extensive analysis of the PepCVAE-generated sequences reveals superior performance of our model in comparison to a plain VAE, as PepCVAE generates novel AMP sequences with higher long-range diversity, while being closer to the training distribution of biological peptides.
Edit intent: clarity
Original:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ]  temporary price impact with a modified market depth .
Revised:  The correct scaling turns out to keep the market depth parameter constant while resilience over fixed periods of time grows in inverse proportion with the duration between trading times. For vanilla options, the scaling limit is found to coincide with the scaling limit for ] temporary price impact with a modified market depth .
Edit intent: meaning-changed
Original:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ]  temporary price impact with a modified market depth .
Revised:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the one obtained by PDE methods in ] temporary price impact with a modified market depth .
Edit intent: meaning-changed
Original:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ]  temporary price impact with a modified market depth .
Revised:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for 12] temporary price impact with a modified market depth .
Edit intent: meaning-changed
Original:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ]  temporary price impact with a modified market depth .
Revised:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ] for models with purely temporary price impact with a modified market depth .
Edit intent: clarity
Original:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ]  temporary price impact with a modified market depth .
Revised:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ] temporary price impact . These models are a special case of our framework and so our probabilistic scaling limit argument allows one to expand the scope of the scaling limit result to path-dependent options .
Edit intent: meaning-changed
Original:  To demonstrate this, we show that for the distributive phosphorylation of a protein at two binding sites multistationarity is only possible if the total concentration of the substrate is larger than either the  concentration of the kinase or the  phosphatase.
Revised:  To demonstrate this, we show that for the distributive phosphorylation of a protein at two binding sites multistationarity is only possible if the total concentration of the substrate is larger than either the total concentration of the kinase or the phosphatase.
Edit intent: fluency