wanyu/IteraTeR_v2 huggingface dataset:
Original:  To facilitate the synthesis, we introduce the Scriven Model, which separates each criterion into an evaluated entity (i.e. the object of the evaluation) and an evaluation criterion (i.e. the dimension along which an entity is evaluated).
Revised:  To facilitate the synthesis, we introduce the Scriven Model, which separates each criterion into an evaluated entity (i.e. the object of evaluation) and an evaluation criterion (i.e. the dimension along which an entity is evaluated).
Edit intent: clarity
Original: A bipartite graph G(X,Y,E) with vertex partition (X,Y) is said to have the Normalized Matching Property (NMP) if for any subset S\subseteq X  we have |N(S)|{|Y|}\ge|S|{|X|}.
Revised: A bipartite graph G(X,Y,E) with vertex partition (X,Y) states that for any subset S\subseteq X we have |N(S)|{|Y|}\ge|S|{|X|}.
Edit intent: clarity
Original: A bipartite graph G(X,Y,E) with vertex partition (X,Y) is said to have the Normalized Matching Property (NMP) if for any subset S\subseteq X  we have |N(S)|{|Y|}\ge|S|{|X|}.
Revised: A bipartite graph G(X,Y,E) with vertex partition (X,Y) is said to have the Normalized Matching Property (NMP) if for any subset S\subseteq X , we have |N(S)|{|Y|}\ge|S|{|X|}.
Edit intent: fluency
Original:  In this paper, we investigate the Normalized Matching Property in two classes of bipartite graphs.
Revised:  In this paper, we show the following results about having the Normalized Matching Property in two classes of bipartite graphs.
Edit intent: clarity
Original:  1. The random bipartite graph G(k,n,p)  with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Revised:  1. We establish p=\frac{\log n G(k,n,p) with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Edit intent: clarity
Original:  1. The random bipartite graph G(k,n,p)  with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Revised:  1. The random bipartite graph G(k,n,p) , which is the graph with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Edit intent: clarity
Original:  1. The random bipartite graph G(k,n,p)  with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Revised:  1. The random bipartite graph G(k,n,p) with |X|=k,|Y|=n (assuming k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Edit intent: coherence
Original:  1. The random bipartite graph G(k,n,p)  with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Revised:  1. The random bipartite graph G(k,n,p) with |X|=k,|Y|=n , and k\le n \leq \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Edit intent: clarity
Original:  1. The random bipartite graph G(k,n,p)  with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Revised:  1. The random bipartite graph G(k,n,p) with |X|=k,|Y|=n , and k\le n < \exp(o(k)) ), and in which each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Edit intent: fluency
Original:  1. The random bipartite graph G(k,n,p)  with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Revised:  1. The random bipartite graph G(k,n,p) with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y is an edge independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Edit intent: clarity
Original:  1. The random bipartite graph G(k,n,p)  with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for the existence of a perfect matching in \mathbb{G}(n,n,p).
Revised:  1. The random bipartite graph G(k,n,p) with |X|=k,|Y|=n , and k\le n < \exp(o(k)) , and each pair (x,y)\in X\times Y being an edge in \mathbb{G independently with probability p has p=\frac{\log n . This generalizes a classic result of Erd\H{o}s-R\'enyi on the \frac{\log n}{n} threshold for having a perfect matching in \mathbb{G}(n,n,p).
Edit intent: clarity
Original:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following a paper of Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if every x\in X has degree at least pn and every pair of distinct x, x'\in X have at most (1+\varepsilon)p^2n common neighbors.
Revised:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following A. Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if every x\in X has degree at least pn and every pair of distinct x, x'\in X have at most (1+\varepsilon)p^2n common neighbors.
Edit intent: clarity
Original:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following a paper of Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if every x\in X has degree at least pn and every pair of distinct x, x'\in X have at most (1+\varepsilon)p^2n common neighbors.
Revised:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following a paper of Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if each x\in X has degree at least pn and every pair of distinct x, x'\in X have at most (1+\varepsilon)p^2n common neighbors.
Edit intent: fluency
Original:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following a paper of Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if every x\in X has degree at least pn and every pair of distinct x, x'\in X have at most (1+\varepsilon)p^2n common neighbors.
Revised:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following a paper of Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if every x\in X has degree at least pn and each pair of distinct x, x'\in X have at most (1+\varepsilon)p^2n common neighbors.
Edit intent: fluency
Original:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following a paper of Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if every x\in X has degree at least pn and every pair of distinct x, x'\in X have at most (1+\varepsilon)p^2n common neighbors.
Revised:  2. A bipartite graph G(X,Y), with k=|X|\le |Y|=n, is said to be Thomason pseudorandom (following a paper of Thomason (Discrete Math., 1989)) with parameters (p,\varepsilon) if every x\in X has degree at least pn and every pair of distinct x, x'\in X has at most (1+\varepsilon)p^2n common neighbors.
Edit intent: fluency
Original:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Revised:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% %DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Edit intent: coherence
Original:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Revised:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% %DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Edit intent: coherence
Original:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Revised:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y _X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Edit intent: clarity
Original:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Revised:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% such that the subgraph G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Edit intent: clarity
Original:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Revised:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP , provided p \gg\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Edit intent: clarity
Original:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Revised:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k}. En route , we prove an 'almost' vertex decomposition theorem:
Edit intent: fluency
Original:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an 'almost' vertex decomposition theorem:
Revised:  Given \varepsilon>0 and n%DIFDELCMD < \ge %%% k\gg 0, there exist functions f,g with f(x),g(x)%DIFDELCMD < \to %%% 0 as x%DIFDELCMD < \to %%% 0, and sets \mathrm{Del}_X\subset X, \ \mathrm{Del}_Y\subset Y with |\mathrm{Del_X|}%DIFDELCMD < \le %%% f(\varepsilon)k,\ |\mathrm{Del_Y|}%DIFDELCMD < \le %%% g(\varepsilon)n such that G(X\setminus \mathrm{Del}_X,Y\setminus \mathrm{Del}_Y) has NMP . Enroute\tfrac{1}{k} , we prove an "almost" vertex decomposition theorem:
Edit intent: fluency
Original:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{  trees that have NMP  and which arise organically through the Euclidean GCD algorithm.
Revised:  Every such Thomason pseudorandom graph admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{ trees that have NMP and which arise organically through the Euclidean GCD algorithm.
Edit intent: clarity
Original:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{  trees that have NMP  and which arise organically through the Euclidean GCD algorithm.
Revised:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - excluding a negligible portion of its vertex set - a partition of its vertex set into \emph{ trees that have NMP and which arise organically through the Euclidean GCD algorithm.
Edit intent: clarity
Original:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{  trees that have NMP  and which arise organically through the Euclidean GCD algorithm.
Revised:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into graphs that we call\emph{ trees that have NMP and which arise organically through the Euclidean GCD algorithm.
Edit intent: clarity
Original:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{  trees that have NMP  and which arise organically through the Euclidean GCD algorithm.
Revised:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{ . These are trees that have NMP and which arise organically through the Euclidean GCD algorithm.
Edit intent: coherence
Original:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{  trees that have NMP  and which arise organically through the Euclidean GCD algorithm.
Revised:  Every Thomason pseudorandom bipartite graph G(X,Y) admits - except for a negligible portion of its vertex set - a partition of its vertex set into \emph{ trees that have NMP , and which arise organically through the Euclidean GCD algorithm.
Edit intent: fluency
Original:  En route, we prove an "almost" vertex decomposition theorem: Every such Thomason pseudorandom graph admits - excluding a negligible portion of its vertex set - a partition of its vertex set into graphs that we call Euclidean trees .
Revised:  En route, we prove an "almost" vertex decomposition theorem: Every such Thomason pseudorandom graph admits - excluding a negligible portion of its vertex set - a partition of its vertex set into graphs that we call Euclidean trees .
Edit intent: fluency
Original: More than hundred years ago the "classic physics" was it its full power, with just a few unexplained phenomena;
Revised: More than hundred years ago the 'classic physics' was it in its full power, with just a few unexplained phenomena;
Edit intent: fluency
Original:  which however lead to a revolution and developing the "modern physics" .
Revised:  which however led to a revolution and developing the "modern physics" .
Edit intent: fluency
Original:  which however lead to a revolution and developing the "modern physics" .
Revised:  which however lead to a revolution and the development of the 'modern physics' .
Edit intent: fluency
Original:  In the physics studying the nature under extreme conditions (like approaching the speed of light, studying atomic and sub-atomic interactions, considering objects on the scale of the Universe) has lead to the understanding of the relativistic and quantal behavior.
Revised:  In physics studying the nature under extreme conditions (like approaching the speed of light, studying atomic and sub-atomic interactions, considering objects on the scale of the Universe) has lead to the understanding of the relativistic and quantal behavior.
Edit intent: coherence
Original:  In the physics studying the nature under extreme conditions (like approaching the speed of light, studying atomic and sub-atomic interactions, considering objects on the scale of the Universe) has lead to the understanding of the relativistic and quantal behavior.
Revised:  In the physics studying the nature under extreme conditions has lead to the understanding of the relativistic and quantal behavior.
Edit intent: clarity
Original:  Quite similarly , in the computing some phenomena, acquired in connection with extreme (computing) conditions, cannot be understood on the basis of the " classic computing paradigm ". Using analogies with the classic vs. modern physics, the need for a "modern computing paradigm" is introduced and underpinned.
Revised:  Quite similarly in computing some phenomena, acquired in connection with extreme (computing) conditions, cannot be understood on the basis of the " classic computing paradigm ". Using analogies with the classic vs. modern physics, the need for a "modern computing paradigm" is introduced and underpinned.
Edit intent: fluency
Original:  Quite similarly , in the computing some phenomena, acquired in connection with extreme (computing) conditions, cannot be understood on the basis of the " classic computing paradigm ". Using analogies with the classic vs. modern physics, the need for a "modern computing paradigm" is introduced and underpinned.
Revised:  Quite similarly , in the computing some phenomena, acquired in connection with extreme (computing) conditions, cannot be understood based on of the ' classic computing paradigm ". Using analogies with the classic vs. modern physics, the need for a "modern computing paradigm" is introduced and underpinned.
Edit intent: fluency
Original:  Rather, the paper wants to call the attention to both that under extreme conditions qualitatively different behavior may be encountered in both worlds, and that pinpointing certain, formerly unnoticed or neglected aspects enable to explain the new phenomena .
Revised:  Rather, the paper wants to call the attention to both that under extreme conditions qualitatively different behaviors may be encountered in both worlds, and that pinpointing certain, formerly unnoticed or neglected aspects enable to explain the new phenomena .
Edit intent: fluency
Original: In microbial communities, each species may have multiple, distinct phenotypes .
Revised: In microbial communities, each species often has multiple, distinct phenotypes .
Edit intent: clarity
Original:  Here, we address this question theoretically, showing that simple models with subpopulation structure and averaged versions thereof generically give contradictory linear stability results.
Revised:  Here, we show that such implicit averaging over phenotypes leads to incorrect linear stability results.
Edit intent: clarity
Original:  Specialising to the bacterial persister phenotype, we analyse stochastic switching between phenotypes in detail in an asymptotic limit .
Revised:  We then analyze the effect of phenotypic switching in detail in an asymptotic limit .
Edit intent: clarity
Original:  Finally, we extend these results by showing numerically that subpopulations also modify the stability of the system to large perturbations such as antibiotic treatments.
Revised:  Finally, we extend these results by showing how phenotypic variation modifies the stability of the system to large perturbations such as antibiotic treatments.
Edit intent: clarity
Original:  Based on previous research, this paper proposes a new quasi-best fast TT decomposition algorithm for large-scale sparse tensors with proven correctness and for which the upper bound of its complexity  derived.
Revised:  Based on previous research, this paper proposes a new quasi-best fast TT decomposition algorithm for large-scale sparse tensors with proven correctness and the upper bound of its complexity derived.
Edit intent: clarity