wanyu/IteraTeR_full_sent huggingface dataset:
Original: This paper proposes a multiscale method for solving the numerical solution of mean field games  . Starting from an approximate solution at the coarsest level, the method constructs approximations on successively finer grids via alternating sweeping  .
Revised: This paper proposes a multiscale method for solving the numerical solution of mean field games . Starting from an approximate solution at the coarsest level, the method constructs approximations on successively finer grids via alternating sweeping , which not only allows for the use of classical time marching numerical schemes but also enables applications to both local and nonlocal problems .
Edit intent: meaning-changed
Original:  An example of  application of text mining in poetry is the usage of features derived from their individual word in order to capture the lexical, sublexical and interlexical meaning, and infer the General Affective Meaning (GAM) of the text.
Revised:  An example of an application of text mining in poetry is the usage of features derived from their individual word in order to capture the lexical, sublexical and interlexical meaning, and infer the General Affective Meaning (GAM) of the text.
Edit intent: fluency
Original:  An example of  application of text mining in poetry is the usage of features derived from their individual word in order to capture the lexical, sublexical and interlexical meaning, and infer the General Affective Meaning (GAM) of the text.
Revised:  An example of application of text mining in poetry is the usage of features derived from their individual words in order to capture the lexical, sublexical and interlexical meaning, and infer the General Affective Meaning (GAM) of the text.
Edit intent: fluency
Original:  These challenges can be mitigated by extensive testing. We study testing policies that optimize a fixed budget of tests within a single institution (e. g., business, school, nursing home, etc.) by varying the number of batches that the tests are split into. We prove that, in an exponential spread model and for reasonable parameter values, the expected size of an outbreak at initial detection is smaller when random subgroups of the population are tested frequently, as opposed to periodic testing of the entire population.
Revised:  These challenges can be mitigated through testing, testing budget is often limited. Here we study how institutions, such as nursing homes, should utilize a fixed test budget for early detection of an outbreak at initial detection is smaller when random subgroups of the population are tested frequently, as opposed to periodic testing of the entire population.
Edit intent: clarity
Original:  We prove that, in an exponential spread model and for reasonable parameter values, the expected size of an outbreak at initial detection is smaller when random subgroups of the population are tested frequently, as opposed to periodic testing of the entire population. We also simulate the effect of different policies in a network SEIR modeltaking into account factors such as variable connectivity between individuals, incubation period, and inaccurate testing results. We show that under a broad set of early-outbreak scenarios, given a certain budget of tests, increasing testing frequency of random samples of the population will reduce the societal risk, defined as the number of infection opportunities until first detection.
Revised:  We prove that, in an exponential spread model and for reasonable parameter values, the expected size of an outbreak . Using an extended network-SEIR model, we show that given a certain budget of tests, increasing testing frequency of random samples of the population will reduce the societal risk, defined as the number of infection opportunities until first detection.
Edit intent: clarity
Original:  We show that under a broad set of early-outbreak scenarios, given a certain budget of tests, increasing testing frequency of random samples of the population will reduce the societal risk, defined as the number of infection opportunities until first detection. For example, testing a quarter of the institution members every week is generally better than testing the entire institution every month.
Revised:  We show that under a broad set of early-outbreak scenarios, given a certain budget of tests, it is generally better than testing the entire institution every month.
Edit intent: clarity
Original:  For example, testing a quarter of the institution members every week is generally better than testing the entire institution every month. In fact, in many settings, sufficiently frequent testing (combined with mitigation once an outbreak is detected) can decrease the risk even compared to the baseline when the institution is closed and testing is not conducted. The bottom-line is a simple policy prescription for institutions: distribute the total tests over several batches instead of using them all at once  .
Revised:  For example, testing a quarter of the institution members every week is generally better to test smaller subgroups of the population frequently than to test larger groups but less frequently. The numerical results are consistent with an analytical expression we derive for the size of the outbreak at detection in an exponential spread model. Our work provides a simple guideline for institutions: distribute the total tests over several batches instead of using them all at once .
Edit intent: meaning-changed
Original:  The bottom-line is a simple policy prescription for institutions: distribute the total tests over several batches instead of using them all at once  .
Revised:  The bottom-line is a simple policy prescription for institutions: distribute the total tests over several batches instead of using them all at once . We expect that in the appropriate scenarios, this easy-to-implement policy recommendation will lead to earlier detection and better mitigation of local COVID-19 outbreaks .
Edit intent: meaning-changed
Original:  For example, GEGL manages to solve the penalized octanol-water partition coefficient optimization with a score of 31.82 , while the best-known score in the literature is 26.1 . Besides, for the GuacaMol benchmark with 20 tasks, our method achieves the highest score for 19 tasks, in comparison with state-of-the-art methods, and newly obtains the perfect score for three tasks.
Revised:  For example, GEGL manages to solve the penalized octanol-water partition coefficient optimization with a score of 31.40 , while the best-known score in the literature is 26.1 . Besides, for the GuacaMol benchmark with 20 tasks, our method achieves the highest score for 19 tasks, in comparison with state-of-the-art methods, and newly obtains the perfect score for three tasks.
Edit intent: meaning-changed
Original:  For example, GEGL manages to solve the penalized octanol-water partition coefficient optimization with a score of 31.82 , while the best-known score in the literature is 26.1 . Besides, for the GuacaMol benchmark with 20 tasks, our method achieves the highest score for 19 tasks, in comparison with state-of-the-art methods, and newly obtains the perfect score for three tasks.
Revised:  For example, GEGL manages to solve the penalized octanol-water partition coefficient optimization with a score of 31.82 , while the best-known score in the literature is 27.22 . Besides, for the GuacaMol benchmark with 20 tasks, our method achieves the highest score for 19 tasks, in comparison with state-of-the-art methods, and newly obtains the perfect score for three tasks.
Edit intent: meaning-changed
Original: We consider the Budgeted Submodular Maximization problem , that seeks to maximize an increasing submodular function subject to budget constraints. Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha  , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Revised: We consider the Budgeted Submodular Maximization problem , that seeks to maximize an increasing submodular function subject to a knapsack constraint, which is also known as the Budgeted Submodular Maximization (BSM) problem. Sviridenko (2004) showed that by guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Edit intent: meaning-changed
Original:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha  , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Revised:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 appropriate elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Edit intent: clarity
Original:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha  , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Revised:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution , and then executing a greedy algorithm, one can obtain the optimal approximation ratio of \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Edit intent: meaning-changed
Original:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha  , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Revised:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-1/e \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Edit intent: clarity
Original:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha  , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Revised:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 for BSM. However, the need to guess (by enumeration) 3 elements makes the algorithm of Sviridenko impractical as it leads to a time complexity of O(n^5) (which can be slightly improved using the thresholding technique of Badanidiyuru , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Edit intent: meaning-changed
Original:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha  , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Revised:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha Vondrak (2014), but only to roughly O(n^4)). Our main results in this paper show that fewer guesses suffice. Specifically, by making only 2 guesses, we get the same optimal approximation ratio of \alpha with an improved time complexity of roughly O(n^3). Furthermore, by making only a single guess , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing.
Edit intent: meaning-changed
Original:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha  , 1 guesssuffices to achieve ratio 0.899 \alpha \approx 0.568, while ratio 0.68\alpha \approx 0.43 can be achieved without any guessing. We note that ratio \alpha  -\epsilon can be achieved using  {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Revised:  Extending a result of Khuller, Moss, and Naor for the Budgeted Coverage problem, Sviridenko showed that the greedy algorithm combined with guessing 3 most profitable elements of an optimal solution has approximation ratio \alpha = 1-\frac{1 \approx 0.632 . We show that just 2 guesses sufficeto achieve ratio \alpha , we get an almost as good approximation ratio of 0.6174>0.9767\alpha in roughly O(n^2) time. Prior to our work, the only algorithms that were known to obtain an approximation ratio close to \alpha for BSM were the algorithm of Sviridenko and an algorithm of Ene -\epsilon can be achieved using {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Edit intent: meaning-changed
Original:  We note that ratio \alpha  -\epsilon can be achieved using  {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Revised:  We note that ratio \alpha Nguyen (2019) that achieves (\alpha -\epsilon can be achieved using {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Edit intent: meaning-changed
Original:  We note that ratio \alpha  -\epsilon can be achieved using  {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Revised:  We note that ratio \alpha -\epsilon )-approximation. However, the algorithm of Ene {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Edit intent: meaning-changed
Original:  We note that ratio \alpha  -\epsilon can be achieved using  {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Revised:  We note that ratio \alpha -\epsilon can be achieved using Nguyen requires {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Edit intent: meaning-changed
Original:  We note that ratio \alpha  -\epsilon can be achieved using  {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Revised:  We note that ratio \alpha -\epsilon can be achieved using {(1/\epsilon)}^{O(1/\epsilon^4)}n\log ^2 n time, and hence, is of theoretical interest only as } values of \epsilon.
Edit intent: meaning-changed
Original:  We note that ratio \alpha  -\epsilon can be achieved using  {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Revised:  We note that ratio \alpha -\epsilon can be achieved using {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large (1/\epsilon)} values of \epsilon.
Edit intent: fluency
Original:  We note that ratio \alpha  -\epsilon can be achieved using  {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large } values of \epsilon.
Revised:  We note that ratio \alpha -\epsilon can be achieved using {(1/\epsilon)}^{O(1/\epsilon^4)}n\log n value oracle calls, but this algorithm is impractical already for large }^{O(1/\epsilon^4) values of \epsilon.
Edit intent: fluency
Original:  Among practical algorithms  , our is the currently best known one .
Revised:  In contrast, all the algorithms we analyze are simple and parallelizable, which makes them good candidates for practical use. Recently, Tang et al. (2020) studied a simple greedy algorithm that already has a long research history, and proved that its approximation ratio is at least 0.405. We improve over this result, and show that the approximation ratio of this algorithm is within the range , our is the currently best known one .
Edit intent: meaning-changed
Original: The Ensemble Kalman Filter (EnKF) is a Bayesian filtering algorithm utilized in estimating unknown model states and parameters for nonlinear systems. An important component of the EnKF is the observation function , which connects the unknown system variables with the observed data.
Revised: The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting the unknown system variables with the observed data.
Edit intent: clarity
Original:  These functions take different forms based on modeling assumptions with respect to the available data and relevant system parameters. The goal of this research is to analyze the effects of observation function selection in the EnKF in the settingof epidemic modeling, where a variety of observation functions are used in the literature.
Revised:  Key differences in observed data and modeling assumptions have led to the use of different observation functions in the epidemic modeling literature. In this work, we present a novel computational analysis demonstrating the effects of observation function selection in the EnKF in the settingof epidemic modeling, where a variety of observation functions are used in the literature.
Edit intent: clarity
Original:  The goal of this research is to analyze the effects of observation function selection in the EnKF in the settingof epidemic modeling, where a variety of observation functions are used in the literature. In particular, four observation functions of different forms and various levels of complexity are examined in connection with the classic Susceptible-Infectious-Recovered (SIR)
Revised:  The goal of this research is to analyze the effects of observation function selection when using the EnKF for state and parameter estimation in this setting. In examining the use of four epidemiologically-inspired observation functions of different forms and various levels of complexity are examined in connection with the classic Susceptible-Infectious-Recovered (SIR)
Edit intent: clarity
Original:  model  . Results demonstrate the importance of choosing an observation function that well interprets the available data on the corresponding EnKF estimates in several filtering scenarios, including state estimation with known parameters, and combined state and parameter estimation with both constant and time-varying parameters.
Revised:  model , we show how incorrect observation modeling assumptions (i.e., fitting incidence data with a prevalence model, or neglecting under-reporting) can lead to inaccurate filtering estimates and forecast predictions . Results demonstrate the importance of choosing an observation function that well interprets the available data on the corresponding EnKF estimates in several filtering scenarios, including state estimation with known parameters, and combined state and parameter estimation with both constant and time-varying parameters.
Edit intent: meaning-changed
Original:  Our algorithm uses imperfect evaluations of the target function to direct further evaluations of the target function either at new sites in the function's domain or to improve the quality of evaluations at already-evaluated sites. We establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method both to synthetic test cases and to a real-world example of uncertainty quantification for aerodynamic design.
Revised:  We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method both to synthetic test cases and to a real-world example of uncertainty quantification for aerodynamic design.
Edit intent: clarity
Original: We generalize a graph-based multiclass semi-supervised classification technique based on diffuse interface methods to multilayer graphs allowing for a very high number of layers . Besides the treatment of various applications with an inherent multilayer structure, we present a very flexible approach that interprets high-dimensional data in a low-dimensional multilayer graph representation.
Revised: We generalize a graph-based multiclass semi-supervised classification technique based on diffuse interface methods to multilayer graphs . Besides the treatment of various applications with an inherent multilayer structure, we present a very flexible approach that interprets high-dimensional data in a low-dimensional multilayer graph representation.
Edit intent: coherence
Original:  Highly efficient numerical methods involving the spectral decomposition of the corresponding differential graph operators as well as fast matrix-vector products based on the nonequispaced fast Fourier transform (NFFT) enable the rapid treatment of very large data sets and make the algorithm independent of specialized hardware as well as scalable to even larger problems. We test the performance of our method on a variety of large and high-dimensional data sets .
Revised:  Highly efficient numerical methods involving the spectral decomposition of the corresponding differential graph operators as well as fast matrix-vector products based on the nonequispaced fast Fourier transform (NFFT) enable the rapid treatment of large and high-dimensional data sets. We perform various numerical tests putting a special focus on image segmentation. In particular, we test the performance of our method on a variety of large and high-dimensional data sets .
Edit intent: meaning-changed