wanyu/IteraTeR_full_sent huggingface dataset:
Original:    Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Revised:  How then do we isolate these Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Edit intent: meaning-changed
Original:    Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Revised:  invisible Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Edit intent: fluency
Original:    Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Revised:  pre-symptomatic spreaders? Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Edit intent: meaning-changed
Original:    Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Revised:  Here we propose an alternating quarantine strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down.
Edit intent: clarity
Original:    Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and lock-down. All symptomatic individuals continue to remain in isolation.
Revised:  Here we propose an alternating lock-down strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and quarantine.
Edit intent: clarity
Original:  Hence this strategy isolates the majority of exposed individuals during their asymptomatic phase. We find that when complemented with behavioral norms to reduce infection, such as avoiding physical contact or observing personal hygiene, this strategy not only overcomes the pandemic, but also allows for some level of flexibility, withstanding a fraction of defectors or essential workers that remain continuously active . We examine our strategy based on current epidemiological models with parameter relevant for COVID-19. We wish, however, following this communication, to further test and fine-tune our scheme based on real-time human interaction data, and assess its actual effectiveness.
Revised:  Hence this strategy isolates the majority of exposed individuals during their 
Edit intent: coherence
Original: We first revisit the problem of kernel estimation of spot volatility in a general continuous It\^o semimartingale model in the absence of microstructure noise, and prove a Central Limit Theorem with optimal convergence rate , which is an extension of Figueroa and Li (2020)
Revised: We first revisit the problem of estimating the spot volatility of an It\^o semimartingale model in the absence of microstructure noise, and prove a Central Limit Theorem with optimal convergence rate , which is an extension of Figueroa and Li (2020)
Edit intent: clarity
Original: We first revisit the problem of kernel estimation of spot volatility in a general continuous It\^o semimartingale model in the absence of microstructure noise, and prove a Central Limit Theorem with optimal convergence rate , which is an extension of Figueroa and Li (2020)
Revised: We first revisit the problem of kernel estimation of spot volatility in a general continuous It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate , which is an extension of Figueroa and Li (2020)
Edit intent: clarity
Original: We first revisit the problem of kernel estimation of spot volatility in a general continuous It\^o semimartingale model in the absence of microstructure noise, and prove a Central Limit Theorem with optimal convergence rate , which is an extension of Figueroa and Li (2020) as we allow for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
Revised: We first revisit the problem of kernel estimation of spot volatility in a general continuous It\^o semimartingale model in the absence of microstructure noise, and prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
Edit intent: coherence
Original:  as we allow for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
Revised:  as we allow for a general two-sided kernel . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
Edit intent: clarity
Original:  as we allow for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
Revised:  as we allow for a general two-sided kernel function . Next, we introduce a new pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
Edit intent: clarity
Original:  as we allow for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise .
Revised:  as we allow for a general two-sided kernel function . Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility to handle the microstructure noise of ultra high-frequency observations .
Edit intent: clarity
Original:  We prove Central Limit Theorems for the estimation error with an optimal rate and study the problems of optimal bandwidth and kernel selection. As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator  is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Revised:  We prove Central Limit Theorems for the estimation error with an optimal rate and study the problems of optimal bandwidth and kernel functions. We show that the asymptotic variance of the pre-averaging/kernel estimator is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Edit intent: clarity
Original:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator  is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Revised:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the pre-averaging/kernel estimator is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Edit intent: clarity
Original:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator  is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Revised:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator 's asymptotic variance is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Edit intent: meaning-changed
Original:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator  is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Revised:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator is minimal for exponential kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Edit intent: clarity
Original:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator  is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
Revised:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator is minimal for exponential or Laplace kernels, hence, justifying the need of working with kernels of unbounded support as proposed in this work.
Edit intent: clarity
Original:  This problem was first studied in \mbox{%DIFAUXCMD lubars2018correcting0pt%DIFAUXCMD where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% \frac{8{3}p,
Revised:  0pt%DIFAUXCMD where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% \frac{8{3}p,
Edit intent: coherence
Original:  This problem was first studied in \mbox{%DIFAUXCMD lubars2018correcting0pt%DIFAUXCMD where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% \frac{8{3}p,
Revised:  This problem was first studied in \mbox{%DIFAUXCMD lubars2018correcting0pt%DIFAUXCMD where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% {3}p,
Edit intent: meaning-changed
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% %DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Edit intent: coherence
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% {n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Edit intent: coherence
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% %DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Edit intent: meaning-changed
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% /{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np.
Edit intent: coherence
Original: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% , our improved condition still requires that \beta must increase inversely proportional to np. In order to improve the matching performance for sparse graphs, we propose a new algorithm that uses "witnesses"
Revised: 16\log{n}{nps^2}}%DIFDELCMD < \right\}%%% . We improve their condition to \beta\geq\max%DIFDELCMD < \left\{%%% 30\sqrt{\frac{\log n{n(1-p)^2s^2}},\frac{45\log{n}}{np(1-p)^2s^2}}%DIFDELCMD < \right)%%% . However, when p=O%DIFDELCMD < \left( %%% \sqrt{{\log n/{ns^2}}}%DIFDELCMD < \right)%%% We first analyze a simple algorithm that matches vertices based on the number of common seeds in the 1-hop neighborhoods, and then further propose a new algorithm that uses "witnesses"
Edit intent: meaning-changed
Original:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Revised:  in the 2-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Edit intent: meaning-changed
Original:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Revised:  in the 2-hop neighborhood, instead of only 1-hop }\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Edit intent: coherence
Original:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Revised:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% {s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Edit intent: meaning-changed
Original:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Revised:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and 2-hop algorithms, showing that our new 2-hop algorithm requires substantially fewer correct seeds than the 1-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the 1-hop and 2-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results in \mbox{%DIFAUXCMD \cite{10.14778/2794367.2794371,lubars2018correcting }\hspace{0pt}%DIFAUXCMD when p}\ge .
Edit intent: meaning-changed
Original:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge .
Revised:  in the 2-hop neighborhood, instead of only 1-hop neighborhood as in \mbox{%DIFAUXCMD \cite{lubars2018correcting}\hspace{0pt}%DIFAUXCMD . We show that when np^2\leq\frac{1}{135\log n}, our new algorithm can achieve perfect recovery with high probability if \beta\geq\max}%DIFDELCMD < \left\{%%% 900\sqrt{\frac{np^3(1-s)\log n{s}}, 600\sqrt{\frac{\log n}{ns^4}}, \frac{1200\log n}{n^2p^2s^4}}%DIFDELCMD < \right\} %%% and nps^2\geq 128\log n }\hspace{0pt}%DIFAUXCMD when p}\ge n^{-5/6.
Edit intent: meaning-changed
Original:  For instance, when p is a constant or p=n^{-3/4}, we show that only \Omega(\sqrt{n\log n}) correct seeds suffice for perfect matching, while the previously best-known results demand \Omega(n) and \Omega(n^{3/4}\log n) correct seeds, respectively} . Numerical experiments on both synthetic and real graphs corroborate our theoretical findings and show that our 2-hop algorithm significantly outperforms the 1-hop algorithm when the graphsare relatively sparse .
Revised:  For instance, when p is a constant or p=n^{-3/4}, we show that only \Omega(\sqrt{n\log n}) correct seeds suffice for perfect matching, while the previously best-known results demand \Omega(n) and \Omega(n^{3/4}\log n) correct seeds, respectively} . Numerical experiments corroborate our theoretical findings and show that our 2-hop algorithm significantly outperforms the 1-hop algorithm when the graphsare relatively sparse .
Edit intent: meaning-changed
Original:  For instance, when p is a constant or p=n^{-3/4}, we show that only \Omega(\sqrt{n\log n}) correct seeds suffice for perfect matching, while the previously best-known results demand \Omega(n) and \Omega(n^{3/4}\log n) correct seeds, respectively} . Numerical experiments on both synthetic and real graphs corroborate our theoretical findings and show that our 2-hop algorithm significantly outperforms the 1-hop algorithm when the graphsare relatively sparse .
Revised:  For instance, when p is a constant or p=n^{-3/4}, we show that only \Omega(\sqrt{n\log n}) correct seeds suffice for perfect matching, while the previously best-known results demand \Omega(n) and \Omega(n^{3/4}\log n) correct seeds, respectively} . Numerical experiments on both synthetic and real graphs corroborate our theoretical findings , demonstrating the superiority of our 2-hop algorithm significantly outperforms the 1-hop algorithm when the graphsare relatively sparse .
Edit intent: clarity