wanyu/IteraTeR_v2 huggingface dataset:
Original:  Specifically, cumulative non-decreasing measures like the h-index contain intrinsic spurious autocorrelation, resulting in a significant overestimation of their "predictive power".
Revised:  Specifically, cumulative non-decreasing measures like the h-index contain intrinsic spurious autocorrelation, resulting in significant overestimation of their "predictive power".
Edit intent: fluency
Original:  Applying the model to a scientist's annual h-index change (a non-cumulative measure), the models exhibit far less predictive power.
Edit intent: coherence
Original:  Moreover, the predictive power of these models vary greatly with the career ageof scientists , producing least accurate estimates for already risk-burdened early career researchers.
Revised:  Moreover, the predictive power of these models depend heavily upon scientists' career age , producing least accurate estimates for already risk-burdened early career researchers.
Edit intent: clarity
Original:  These results place in doubt the suitability of linear regression modelsof future h-index for real application in recruitment decisions and indicate that more effort is needed to develop and benchmark career predictability algorithms .
Revised:  These results place in doubt the suitability of such models, and indicate further investigation is required before they can be used in recruiting decisions .
Edit intent: clarity
Original:  An {\it additive number} of G , denoted by \eta(G), is the minimum number k such that G has a additive labeling \ell :V(G) %DIFDELCMD < \to \lbrace %%% 1,. ..,k%DIFDELCMD < \rbrace %%% . An {\it additive choosability number } of a graph G, denoted by \ell(G) , is the smallest number k such that G has an additive labeling from any assignment of lists of size k to the vertices of G  . Seamone (2012) a80 conjectured that for every graph G, \eta(G)= \ell(G).
Revised:  The {\it additive number} of G , denoted by \eta(G), is the minimum number k such that G has a additive labeling \ell :V(G) %DIFDELCMD < \to \lbrace %%% 1,. ..,k%DIFDELCMD < \rbrace %%% . An {\it additive choosability number } of a graph G, denoted by \ell(G) , is the smallest number k such that G has an additive labeling from any assignment of lists of size k to the vertices of G . Seamone (2012) a80 conjectured that for every graph G, \eta(G)= \ell(G).
Edit intent: fluency
Original:  An {\it additive number} of G , denoted by \eta(G), is the minimum number k such that G has a additive labeling \ell :V(G) %DIFDELCMD < \to \lbrace %%% 1,. ..,k%DIFDELCMD < \rbrace %%% . An {\it additive choosability number } of a graph G, denoted by \ell(G) , is the smallest number k such that G has an additive labeling from any assignment of lists of size k to the vertices of G  . Seamone (2012) a80 conjectured that for every graph G, \eta(G)= \ell(G).
Revised:  An {\it additive number} of G , denoted by \eta(G), is the minimum number k such that G has a additive labeling \ell :V(G) %DIFDELCMD < \to \lbrace %%% 1,. ..,k%DIFDELCMD < \rbrace %%% . An {\it additive choosability } of a graph G, denoted by \ell(G) , is the smallest number k such that G has an additive labeling from any assignment of lists of size k to the vertices of G . Seamone (2012) a80 conjectured that for every graph G, \eta(G)= \ell(G).
Edit intent: fluency
Original:  An {\it additive number} of G , denoted by \eta(G), is the minimum number k such that G has a additive labeling \ell :V(G) %DIFDELCMD < \to \lbrace %%% 1,. ..,k%DIFDELCMD < \rbrace %%% . An {\it additive choosability number } of a graph G, denoted by \ell(G) , is the smallest number k such that G has an additive labeling from any assignment of lists of size k to the vertices of G  . Seamone (2012) a80 conjectured that for every graph G, \eta(G)= \ell(G).
Revised:  An {\it additive number} of G , denoted by \eta(G), is the minimum number k such that G has a additive labeling \ell :V(G) %DIFDELCMD < \to \lbrace %%% 1,. ..,k%DIFDELCMD < \rbrace %%% . An {\it additive choosability number } of a graph G, denoted by \ell(G) , is the smallest number k such that G has an additive labeling for any assignment of lists of size k to the vertices of G . Seamone (2012) a80 conjectured that for every graph G, \eta(G)= \ell(G).
Edit intent: fluency
Original:  We show that it is \mathbf{NP} -complete to decide whether a (0,1)-additive labeling exists for some families of graphs such as  planar triangle-free graphs and perfect graphs .
Revised:  We show that it is \mathbf{NP} -complete to decide whether a (0,1)-additive labeling exists for some families of graphs such as planar triangle-free graphs .
Edit intent: clarity
Original:  For a graph G with some (0,1)-additive labelings, the (0,1)-additive number of G is defined as \eta _{1} (G) = \min_{\ell \in \Gamma}\sum_{v\in V(G)}\ell(v) where \Gamma is the set of (0,1)-additive labelings of G. We prove that given a planar graph that contains a (0,1)-additive labeling, for all \varepsilon >0 , approximating the (0,1)-additive number within n^{1-\varepsilon} is \mathbf{NP} -hard.
Revised:  For a graph G with some (0,1)-additive labelings, the (0,1)-additive number of G is defined as \eta _{1} (G) = \min_{\ell \in \Gamma}\sum_{v\in V(G)}\ell(v) where \Gamma is the set of (0,1)-additive labelings of G. We prove that given a planar graph that admits a (0,1)-additive labeling, for all \varepsilon >0 , approximating the (0,1)-additive number within n^{1-\varepsilon} is \mathbf{NP} -hard.
Edit intent: clarity
Original: Two financial networks, namely, cross-border long-term debt and equity securities portfolio investment networks are analysed  .
Revised: Cross-border equity and long-term debt and equity securities portfolio investment networks are analysed .
Edit intent: clarity
Original: Two financial networks, namely, cross-border long-term debt and equity securities portfolio investment networks are analysed  .
Revised: Two financial networks, namely, cross-border long-term debt securities portfolio investment networks are analysed .
Edit intent: clarity
Original:  They serve as proxies for measuring the interdependence of financial markets and the robustness of the global financial system from 2002 to 2012, covering the 2008 global financial crisis.
Revised:  They serve as proxies for measuring the robustness of the global financial system from 2002 to 2012, covering the 2008 global financial crisis.
Edit intent: clarity
Original:  The spread of certain financial derivative products, such as credit default swaps and equity-linked derivatives, scales with the edge density of the long-term debt securities network .
Revised:  The spread of certain financial derivative products, such as credit default swaps and equity-linked derivatives, scales with the edge density of the debt securities network .
Edit intent: clarity
Original: In this note we  show that, without a major change, the Elekes-Sharir framework , developed for tackling  Erdos's distinct distances problem, does not seem capable to lead to a lower boundfor the distinct distances problem that is larger than the one obtained by Guth and Katz .
Revised: In this note we show that, without a major change, this framework Erdos's distinct distances problem, does not seem capable to lead to a lower boundfor the distinct distances problem that is larger than the one obtained by Guth and Katz .
Edit intent: clarity
Original: In this note we  show that, without a major change, the Elekes-Sharir framework , developed for tackling  Erdos's distinct distances problem, does not seem capable to lead to a lower boundfor the distinct distances problem that is larger than the one obtained by Guth and Katz .
Revised: In this note we show that, without a major change, the Elekes-Sharir framework , developed for tacklingcannot Erdos's distinct distances problem, does not seem capable to lead to a lower boundfor the distinct distances problem that is larger than the one obtained by Guth and Katz .
Edit intent: fluency
Original: In this note we  show that, without a major change, the Elekes-Sharir framework , developed for tackling  Erdos's distinct distances problem, does not seem capable to lead to a lower boundfor the distinct distances problem that is larger than the one obtained by Guth and Katz .
Revised: In this note we show that, without a major change, the Elekes-Sharir framework , developed for tackling lead to Erdos's distinct distances problem, does not seem capable to lead to a lower boundfor the distinct distances problem that is larger than the one obtained by Guth and Katz .
Edit intent: fluency
Original:  When considering Erdos's lattice construction, the gap between this bound and the actual bound  arises from an application of the Cauchy-Schwarz inequality (which is an integral part of the Elekes-Sharir framework).
Revised:  When considering Erdos's lattice construction, the gap between this bound and the actual bound of Erdos arises from an application of the Cauchy-Schwarz inequality (which is an integral part of the Elekes-Sharir framework).
Edit intent: clarity
Original: Given a Markov Decision Process (MDP) with n states and m actions per state, we study the number of iterations needed by Policy Iteratio n (PI) algorithms to converge.
Revised: Given a Markov Decision Process (MDP) with n states and m actions per state, we study the number of iterations needed by Policy Iteration (PI) algorithms to converge.
Edit intent: fluency
Original:  We consider two variations of PI: Howard's PI that changes all the actions with a positive advantage, and Sim plex-PI that only changes one action with maximal advantage.
Revised:  We consider two variations of PI: Howard's PI that changes all the actions with a positive advantage, and Simplex-PI that only changes one action with maximal advantage.
Edit intent: fluency
Original:  %DIFDELCMD < \lceil %%% \frac{1{1-\gamma}\log (1{1-\gamma} ) }%DIFDELCMD < \rceil %%% \left \lceil {1-\gamma}\log }\left( {1-\gamma} }\right)
Revised:  %DIFDELCMD < \lceil %%% {1-\gamma}\log (1{1-\gamma} ) }%DIFDELCMD < \rceil %%% \left \lceil {1-\gamma}\log }\left( {1-\gamma} }\right)
Edit intent: coherence
Original:  %DIFDELCMD < \lceil %%% \frac{1{1-\gamma}\log (1{1-\gamma} ) }%DIFDELCMD < \rceil %%% \left \lceil {1-\gamma}\log }\left( {1-\gamma} }\right)
Revised:  %DIFDELCMD < \lceil %%% \frac{1{1-\gamma}\log (1{1-\gamma} ) }%DIFDELCMD < \rceil %%% \left \lceil \frac{1{1-\gamma}\log }\left( {1-\gamma} }\right)
Edit intent: fluency
Original:  %DIFDELCMD < \lceil %%% \frac{1{1-\gamma}\log (1{1-\gamma} ) }%DIFDELCMD < \rceil %%% \left \lceil {1-\gamma}\log }\left( {1-\gamma} }\right)
Revised:  %DIFDELCMD < \lceil %%% \frac{1{1-\gamma}\log (1{1-\gamma} ) }%DIFDELCMD < \rceil %%% \left \lceil {1-\gamma}\log }\left( \frac{1{1-\gamma} }\right)
Edit intent: fluency
Original:  \right \rceil iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1) %DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{n{1-\gamma} \log (n{1-\gamma} )}%DIFDELCMD < \rceil %%% \left\lceil {1-\gamma} \log }\left( {1-\gamma} }\right)\right\rceil iterations, improving by a factor 2 a result by Ye (2011).
Revised:  \right \rceil iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1) %DIFDELCMD < \lceil %DIFDELCMD < %%% {1-\gamma} \log (n{1-\gamma} )}%DIFDELCMD < \rceil %%% \left\lceil {1-\gamma} \log }\left( {1-\gamma} }\right)\right\rceil iterations, improving by a factor 2 a result by Ye (2011).
Edit intent: clarity
Original:  \right \rceil iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1) %DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{n{1-\gamma} \log (n{1-\gamma} )}%DIFDELCMD < \rceil %%% \left\lceil {1-\gamma} \log }\left( {1-\gamma} }\right)\right\rceil iterations, improving by a factor 2 a result by Ye (2011).
Revised:  \right \rceil iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1) %DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{n{1-\gamma} \log (n{1-\gamma} )}%DIFDELCMD < \rceil %%% \left\lceil \frac{n{1-\gamma} \log }\left( {1-\gamma} }\right)\right\rceil iterations, improving by a factor 2 a result by Ye (2011).
Edit intent: fluency
Original:  \right \rceil iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1) %DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{n{1-\gamma} \log (n{1-\gamma} )}%DIFDELCMD < \rceil %%% \left\lceil {1-\gamma} \log }\left( {1-\gamma} }\right)\right\rceil iterations, improving by a factor 2 a result by Ye (2011).
Revised:  \right \rceil iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1) %DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{n{1-\gamma} \log (n{1-\gamma} )}%DIFDELCMD < \rceil %%% \left\lceil {1-\gamma} \log }\left( \frac{n{1-\gamma} }\right)\right\rceil iterations, improving by a factor 2 a result by Ye (2011).
Edit intent: fluency
Original:  We then consider bounds that are independent of the discount factor  \gamma.
Revised:  We then consider bounds that are independent of the discount factor ~ \gamma.
Edit intent: fluency
Original:  We generalize this result to general MDPsunder some structural assumptions : given a measure of the maximal transient time \tau_t and the maximal time \tau_r to revisit states in recurrent classes under all policies, we show that Simplex-PI terminates after at most n^2 m (m-1) ( \left( \lceil \tau_r \log (n \tau_r) \rceil +\lceil \tau_r \log (n \tau_t) \rceil ) \right) \lceil {\tau_t} \log (n (\tau_t+1)) \rceil = \tilde O ( n^2 \tau_t \tau_r m^2 ) iterations.
Revised:  We generalize this result to general MDPsunder some structural assumptions : given a measure of the maximal transient time \tau_t and the maximal time \tau_r to revisit states in recurrent classes under all policies, we show that Simplex-PI terminates after at most n^2 m (m-1) \left( \lceil \tau_r \log (n \tau_r) \rceil +\lceil \tau_r \log (n \tau_t) \rceil ) \right) \lceil {\tau_t} \log (n (\tau_t+1)) \rceil = \tilde O ( n^2 \tau_t \tau_r m^2 ) iterations.
Edit intent: fluency
Original:  We generalize this result to general MDPsunder some structural assumptions : given a measure of the maximal transient time \tau_t and the maximal time \tau_r to revisit states in recurrent classes under all policies, we show that Simplex-PI terminates after at most n^2 m (m-1) ( \left( \lceil \tau_r \log (n \tau_r) \rceil +\lceil \tau_r \log (n \tau_t) \rceil ) \right) \lceil {\tau_t} \log (n (\tau_t+1)) \rceil = \tilde O ( n^2 \tau_t \tau_r m^2 ) iterations.
Revised:  We generalize this result to general MDPsunder some structural assumptions : given a measure of the maximal transient time \tau_t and the maximal time \tau_r to revisit states in recurrent classes under all policies, we show that Simplex-PI terminates after at most n^2 m (m-1) ( \left( \lceil \tau_r \log (n \tau_r) \rceil +\lceil \tau_r \log (n \tau_t) \rceil \right) \lceil {\tau_t} \log (n (\tau_t+1)) \rceil = \tilde O ( n^2 \tau_t \tau_r m^2 ) iterations.
Edit intent: fluency
Original:  Finally, under the additional (restrictive) assumption that the MDP is weakly-communicating, we show that Simplex-PI and Howard's PI terminate after at most n(m-1) ( \left( \lceil \tau_t \log n \tau_t \rceil + \lceil \tau_r \log n \tau_r \rceil ) \right) =\tilde O(nm (\tau_t+\tau_r)) iterations.
Revised:  Finally, under the additional (restrictive) assumption that the MDP is weakly-communicating, we show that Simplex-PI and Howard's PI terminate after at most n(m-1) \left( \lceil \tau_t \log n \tau_t \rceil + \lceil \tau_r \log n \tau_r \rceil ) \right) =\tilde O(nm (\tau_t+\tau_r)) iterations.
Edit intent: fluency
Original:  Finally, under the additional (restrictive) assumption that the MDP is weakly-communicating, we show that Simplex-PI and Howard's PI terminate after at most n(m-1) ( \left( \lceil \tau_t \log n \tau_t \rceil + \lceil \tau_r \log n \tau_r \rceil ) \right) =\tilde O(nm (\tau_t+\tau_r)) iterations.
Revised:  Finally, under the additional (restrictive) assumption that the MDP is weakly-communicating, we show that Simplex-PI and Howard's PI terminate after at most n(m-1) ( \left( \lceil \tau_t \log n \tau_t \rceil + \lceil \tau_r \log n \tau_r \rceil \right) =\tilde O(nm (\tau_t+\tau_r)) iterations.
Edit intent: fluency
Original:  We consider two variations of PI: Howard's PI that changes all the actions with a positive advantage, and Simplex-PI that only changes one action with maximal advantage.
Revised:  We consider two variations of PI: Howard's PI that changes the actions in all states with a positive advantage, and Simplex-PI that only changes one action with maximal advantage.
Edit intent: clarity
Original:  We show that Howard's PI terminates after at most n(m-1)%DIFDELCMD < \left \lceil %%% \frac{1{1-\gamma}\log }%DIFDELCMD < \left( %DIFDELCMD < %%% \frac{1{1-\gamma}}%DIFDELCMD < \right)
Revised:  We show that Howard's PI terminates after at most n(m-1)%DIFDELCMD < \left \lceil %%% {1-\gamma}\log }%DIFDELCMD < \left( %DIFDELCMD < %%% \frac{1{1-\gamma}}%DIFDELCMD < \right)
Edit intent: fluency
Original:  We show that Howard's PI terminates after at most n(m-1)%DIFDELCMD < \left \lceil %%% \frac{1{1-\gamma}\log }%DIFDELCMD < \left( %DIFDELCMD < %%% \frac{1{1-\gamma}}%DIFDELCMD < \right)
Revised:  We show that Howard's PI terminates after at most n(m-1)%DIFDELCMD < \left \lceil %%% \frac{1{1-\gamma}\log }%DIFDELCMD < \left( %DIFDELCMD < %%% {1-\gamma}}%DIFDELCMD < \right)
Edit intent: fluency
Original:  \right \rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1)%DIFDELCMD < \left\lceil %%% \frac{n{1-\gamma} \log }%DIFDELCMD < \left( %%% \frac{n{1-\gamma} }%DIFDELCMD < \right)\right\rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor 2 a result by Ye (2011).
Revised:  \right \rceil %%% O (\frac{n m{1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1)%DIFDELCMD < \left\lceil %%% \frac{n{1-\gamma} \log }%DIFDELCMD < \left( %%% \frac{n{1-\gamma} }%DIFDELCMD < \right)\right\rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor 2 a result by Ye (2011).
Edit intent: clarity
Original:  \right \rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1)%DIFDELCMD < \left\lceil %%% \frac{n{1-\gamma} \log }%DIFDELCMD < \left( %%% \frac{n{1-\gamma} }%DIFDELCMD < \right)\right\rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor 2 a result by Ye (2011).
Revised:  \right \rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1)%DIFDELCMD < \left\lceil %%% {1-\gamma} \log }%DIFDELCMD < \left( %%% \frac{n{1-\gamma} }%DIFDELCMD < \right)\right\rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor 2 a result by Ye (2011).
Edit intent: fluency
Original:  \right \rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1)%DIFDELCMD < \left\lceil %%% \frac{n{1-\gamma} \log }%DIFDELCMD < \left( %%% \frac{n{1-\gamma} }%DIFDELCMD < \right)\right\rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor 2 a result by Ye (2011).
Revised:  \right \rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor O(\log n) a result by Hansen et al. (2013), while Simplex-PI terminates after at most n(m-1)%DIFDELCMD < \left\lceil %%% \frac{n{1-\gamma} \log }%DIFDELCMD < \left( %%% {1-\gamma} }%DIFDELCMD < \right)\right\rceil %%% {1-\gamma} \log (1{1-\gamma})) } iterations, improving by a factor 2 a result by Ye (2011).
Edit intent: fluency
Original:  When the MDP is deterministic, we show that Simplex-PI terminates after at most 2 n^2 m (m-1)%DIFDELCMD < \lceil %%% 2 (n-1) \log n%DIFDELCMD < \rceil \lceil %%% 2 n \log n%DIFDELCMD < \rceil %%% = O(n^4 m^2 \log^2 n) iterations, improving by a factor O(n) a bound obtained by Post and Ye (2012).
Revised:  When the MDP is deterministic, we show that Simplex-PI terminates after at most 2 n^2 m (m-1)%DIFDELCMD < \lceil %%% %DIFDELCMD < \rceil \lceil %%% 2 n \log n%DIFDELCMD < \rceil %%% = O(n^4 m^2 \log^2 n) iterations, improving by a factor O(n) a bound obtained by Post and Ye (2012).
Edit intent: clarity
Original:  When the MDP is deterministic, we show that Simplex-PI terminates after at most 2 n^2 m (m-1)%DIFDELCMD < \lceil %%% 2 (n-1) \log n%DIFDELCMD < \rceil \lceil %%% 2 n \log n%DIFDELCMD < \rceil %%% = O(n^4 m^2 \log^2 n) iterations, improving by a factor O(n) a bound obtained by Post and Ye (2012).
Revised:  When the MDP is deterministic, we show that Simplex-PI terminates after at most 2 n^2 m (m-1)%DIFDELCMD < \lceil %%% 2 (n-1) \log n%DIFDELCMD < \rceil \lceil %%% %DIFDELCMD < \rceil %%% = O(n^4 m^2 \log^2 n) iterations, improving by a factor O(n) a bound obtained by Post and Ye (2012).
Edit intent: clarity
Original:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le  .
Revised:  %DIFDELCMD < \rceil %%% %DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le .
Edit intent: coherence
Original:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le  .
Revised:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% %DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le .
Edit intent: fluency
Original:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le  .
Revised:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le .
Edit intent: fluency
Original:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le  .
Revised:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% %DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le .
Edit intent: coherence
Original:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le  .
Revised:  %DIFDELCMD < \rceil %%% +%DIFDELCMD < \lceil %DIFDELCMD < %%% \tau_r \log (n \tau_t)%DIFDELCMD < \rceil \right) \lceil {%%% \tau_t \log (n (\tau_t+1))%DIFDELCMD < \rceil %%% =%DIFDELCMD < \tilde %%% O ( n^2 \tau_t \tau_r m^2 ) iterations \le \le n .
Edit intent: clarity