wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this way, we fuse the structural features and visual features in the consistent bird-eye view frame, yielding a semantic feature representationwith sensible geometry , namely CORAL.  Comparisons on the Oxford RobotCar show that CORAL has superior performance against other state-of-the-art methods.
Revised:  In this way, we fuse the structural features and visual features in the consistent bird-eye view frame, yielding a semantic feature representationwith sensible geometry , namely CORAL. Comparisons on the Oxford RobotCar show that CORAL-VLAD has superior performance against other state-of-the-art methods.
Edit intent: meaning-changed
Original:  Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation  does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems.
Revised:  Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation , does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems.
Edit intent: fluency
Original:  Furthermore, it is possible to further increase the accuracy of the solutions in 2D by increasing the support of the integrals containing the bubble functions .
Revised:  Furthermore, it is possible to further increase the accuracy of the solutions in 2D with a simple modification of the RFB method. We provide analysis to show how the modified-RFB method mitigates the pollution error. The analysis gave rise to a fourth order accurate finite difference scheme that uses seven-point stencil .
Edit intent: meaning-changed
Original:  A new two-level finite element method is introduced for the approximations of the residual-free bubble (RFB) functionsand its application to the Helmholtz equation with large wave numbers is considered.
Revised: An adapted bubble approach which is a modifiation of the residual-free bubbles (RFB) method, is proposed for the Helmhotz problem in 2D. A new two-level finite element method is introduced for the approximations of the residual-free bubble (RFB) functionsand its application to the Helmholtz equation with large wave numbers is considered.
Edit intent: meaning-changed
Original:  A new two-level finite element method is introduced for the approximations of the residual-free bubble (RFB) functionsand its application to the Helmholtz equation with large wave numbers is considered. Altough this approach was considered for the Helmholtz equation before, our new insights show that some of its important properties have remained hidden.
Revised:  A new two-level finite element method is introduced for the approximations of the bubble functions.
Edit intent: coherence
Original:  Furthermore, it is possible to further increase the accuracy of the solutions in 2D with a simple modification of the RFB method. We provide analysis to show how the modified-RFB method mitigates the pollution error. The analysis gave rise to a fourth order accurate finite difference scheme that uses seven-point stencil. The modified-RFB is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size  .
Revised:  Furthermore, it is possible to further increase the accuracy of the solutions in 2D with a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. The AB method is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size .
Edit intent: meaning-changed
Original:  The modified-RFB is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size  .
Revised:  The modified-RFB is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size . We provide analysis to show how the AB method mitigates the pollution error .
Edit intent: meaning-changed
Original: A data analysis of the COVID-19 epidemic is proposed on the basis of the dashboard publicly accessible at URL that focuses on the characterization of the first and second epidemic outbreaks in Italy . The scope of this tool, which provides an immediate appreciation of the past epidemic development together with its current trends , is to foster a deeper interpretation of available data as well as to provide a hint on the near future evolution of the most relevant epidemic indicators.
Revised: A data analysis of the COVID-19 epidemic is proposed on the basis of the dashboard publicly accessible at URL that focuses on the characterization of the first and second epidemic outbreaks in Italy from late February 2020. Our analysis provides an immediate appreciation of the past epidemic development together with its current trends , is to foster a deeper interpretation of available data as well as to provide a hint on the near future evolution of the most relevant epidemic indicators.
Edit intent: meaning-changed
Original:  The scope of this tool, which provides an immediate appreciation of the past epidemic development together with its current trends , is to foster a deeper interpretation of available data as well as to provide a hint on the near future evolution of the most relevant epidemic indicators.
Revised:  The scope of this tool, which provides an immediate appreciation of the past epidemic development together with its current trends and fosters a deeper interpretation of available data as well as to provide a hint on the near future evolution of the most relevant epidemic indicators.
Edit intent: clarity
Original:  The scope of this tool, which provides an immediate appreciation of the past epidemic development together with its current trends , is to foster a deeper interpretation of available data as well as to provide a hint on the near future evolution of the most relevant epidemic indicators.
Revised:  The scope of this tool, which provides an immediate appreciation of the past epidemic development together with its current trends , is to foster a deeper interpretation of available data as well as to provide a hint on the near future evolution of critical and meaningful epidemic indicators.
Edit intent: clarity
Original:  Our analysis provides an immediate appreciation of the past epidemic development  together with its current trends and fosters a deeper interpretation of available data as well as to provide a hint on the near future evolution of critical and meaningful epidemic indicators .
Revised:  Our analysis provides an immediate appreciation of the past epidemic development , together with its current trends and fosters a deeper interpretation of available data as well as to provide a hint on the near future evolution of critical and meaningful epidemic indicators .
Edit intent: fluency
Original:  Our analysis provides an immediate appreciation of the past epidemic development  together with its current trends and fosters a deeper interpretation of available data as well as to provide a hint on the near future evolution of critical and meaningful epidemic indicators .
Revised:  Our analysis provides an immediate appreciation of the past epidemic development together with its current trends by fostering a deeper interpretation of available data as well as to provide a hint on the near future evolution of critical and meaningful epidemic indicators .
Edit intent: coherence
Original:  Our analysis provides an immediate appreciation of the past epidemic development  together with its current trends and fosters a deeper interpretation of available data as well as to provide a hint on the near future evolution of critical and meaningful epidemic indicators .
Revised:  Our analysis provides an immediate appreciation of the past epidemic development together with its current trends and fosters a deeper interpretation of available data through several critical epidemic indicators. In addition, we complement the epiMOX dashboard with a predictive tool based on an epidemiological compartmental model, named SUIHTER, for the forecast on the near future epidemic evolution .
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: _{\pi}[f] of a } {\rm )}(}{\cal {\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: coherence
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } We introduce a novel statistical measure for MCMC-mean estimation, the inter-trace variance{\rm )}(}{\cal {\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm trv )}(}{\cal {\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm ^{(\tau_{rel)}(}{\cal {\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal M {\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: clarity
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal ,f), which depends on a Markov chain{\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: clarity
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal {\cal M function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal {\cal and a function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal {\cal function f: S \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal {\cal function f: \Omega \to [a,b] . mean-estimation), to within \varepsilon additive error (w.h.p.).
Edit intent: meaning-changed
Original: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.). Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal {\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . The inter-trace variance can be efficiently estimated from observed data and leads to a more efficient MCMC-mean estimator. Prior MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: meaning-changed
Original:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators %DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: clarity
Original:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% }{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: meaning-changed
Original:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} receive, as input, upper-bounds on \tau _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: meaning-changed
Original:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} _{ %DIFDELCMD < \rm %%% mix } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: fluency
Original:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} _{ %DIFDELCMD < \rm %%% rel } or \tau_{rel the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: clarity
Original:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: clarity
Original:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau}  _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% \frac{TR{\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Revised:  Letting R \doteq b-a, standard variance-agnostic MCMC mean-estimators run the chain for%DIFDELCMD < \cal O%%% (\frac{TR^{2}{\varepsilon^{2}}) steps, when given as inputan (often loose) upper-bound T on the relaxation time \tau} _{ %DIFDELCMD < \rm %%% rel } . When an upper-bound V on the stationary variance v_{\pi \doteq \mathbb{V}_{\pi}[f] is known, }%DIFDELCMD < \tilde{\cal O}\bigl(%%% {\varepsilon}+\frac{TV}{\varepsilon^{2}}}%DIFDELCMD < \bigr) %%% steps suffice.
Edit intent: fluency