wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We demonstrate how to incorporate this heterogeneity into a wide class of epidemiological models , and derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. Persistent heterogeneity has three important consequences compared to the effects of short-term overdispersion: (1) It results in a major modification of the early epidemic dynamics; (2) It significantly suppresses the herd immunity threshold; (3) It also significantly reduces the final size of the epidemic.
Revised:  We demonstrate how to incorporate this heterogeneity into a wide class of epidemiological models , and derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic.
Edit intent: clarity
Original:  We estimate social and biological contributions to persistent heterogeneity using data on real-life face-to-face contact networks and age variation of the incidence rate during the COVID-19 epidemic. In addition, empirical data from the COVID-19 epidemic in New York City (NYC) and Chicago, as well as 50 US states provide a consistent characterization of the level of heterogeneity.
Revised:  However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Transient and long-term levels of heterogeneity are estimated by using empirical data from the COVID-19 epidemic in New York City (NYC) and Chicago, as well as 50 US states provide a consistent characterization of the level of heterogeneity.
Edit intent: meaning-changed
Original:  In addition, empirical data from the COVID-19 epidemic in New York City (NYC) and Chicago, as well as 50 US states provide a consistent characterization of the level of heterogeneity. Our estimates suggest that the hardest-hit areas, such as NYC, are close to the heterogeneity-modified herd immunity threshold following the first wave of the epidemic .
Revised:  In addition, empirical data from the COVID-19 epidemic in New York City (NYC) and Chicago, as well as from real-life face-to-face contact networks. These results suggest that the hardest-hit areas, such as NYC, are close to the heterogeneity-modified herd immunity threshold following the first wave of the epidemic .
Edit intent: clarity
Original:  Our estimates suggest that the hardest-hit areas, such as NYC, are close to the heterogeneity-modified herd immunity threshold following the first wave of the epidemic . However, this type of immunity is fragile as it wanes over time if the pattern of social interactions changes substantially .
Revised:  Our estimates suggest that the hardest-hit areas, such as NYC, are close to the heterogeneity-modified herd immunity threshold following the first wave of the epidemic , but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves .
Edit intent: meaning-changed
Original:  For random TLSE problems , numerical experiments illustrate the sharpness of the estimates based on normwise condition numbers , while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Revised:  With TLSE problems solved by the classical QR-SVD or randomized algorithms , numerical experiments illustrate the sharpness of the estimates based on normwise condition numbers , while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Edit intent: meaning-changed
Original:  For random TLSE problems , numerical experiments illustrate the sharpness of the estimates based on normwise condition numbers , while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Revised:  For random TLSE problems , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution , while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Edit intent: meaning-changed
Original:  Explicit condition number expressions and perturbation bound for the TLS problem can be recovered from our estimates. With TLSE problems solved by the classical QR-SVD or randomized algorithms , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Revised:  Explicit condition number expressions and perturbation bound for the TLS problem . For TLSE problems with equilibratory input data , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Edit intent: clarity
Original:  With TLSE problems solved by the classical QR-SVD or randomized algorithms , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Revised:  With TLSE problems solved by the classical QR-SVD or randomized algorithms , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, mixed and componentwise condition numbers are much tighter.
Edit intent: clarity
Original:  With TLSE problems solved by the classical QR-SVD or randomized algorithms , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
Revised:  With TLSE problems solved by the classical QR-SVD or randomized algorithms , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers-based estimations are much tighter.
Edit intent: clarity
Original:  Indeed, we theoretically prove that nodes of high-degree  are disproportionately in the Removed state after a first wave of infection, which has very positive consequences.
Revised:  Indeed, human contact networks exhibit a powerlaw structure, which means immunizing nodes at random is extremely ineffective at slowing the epidemic, while immunizing high-degree nodes can efficiently guarantee herd immunity. We theoretically prove that nodes of high-degree are disproportionately in the Removed state after a first wave of infection, which has very positive consequences.
Edit intent: meaning-changed
Original:  Indeed, we theoretically prove that nodes of high-degree  are disproportionately in the Removed state after a first wave of infection, which has very positive consequences. In particular, powerlaw graphs do not retain their structure after a few waves of infection, which implies second and third waves may be of much smaller amplitude than the first wave.
Revised:  Indeed, we theoretically prove that nodes of high-degree are disproportionately in the Removed state , which is a form of targeted immunization. Even if quarantines are declared too early, subsequent waves of infection spread slower than the first wave.
Edit intent: meaning-changed
Original:  In particular, powerlaw graphs do not retain their structure after a few waves of infection, which implies second and third waves may be of much smaller amplitude than the first wave. We propose an opening and closing strategy aiming at immunizing the graph while infecting the minimum number of individuals, while guaranteeing the population is now robust to future infections.
Revised:  In particular, powerlaw graphs do not retain their structure after a few waves of infection, which implies second and third waves may be of much smaller amplitude than the first waves. This leads us to propose an opening and closing strategy aiming at immunizing the graph while infecting the minimum number of individuals, while guaranteeing the population is now robust to future infections.
Edit intent: coherence
Original: In the k-Vertex Disjoint Shortest Paths problem, a set of  terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths.
Revised: In the k-Disjoint Shortest Paths problem, a set of terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths.
Edit intent: clarity
Original: In the k-Vertex Disjoint Shortest Paths problem, a set of  terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths.
Revised: In the k-Vertex Disjoint Shortest Paths problem, a set of source terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths.
Edit intent: fluency
Original:  In this work we provide a simple algorithm to solve the k-Disjonit Shortest Paths with Congestion-c problem in time f(k) n^{O(k-c)} on DAGs.
Revised:  We provide a simple algorithm to solve the k-Disjonit Shortest Paths with Congestion-c problem in time f(k) n^{O(k-c)} on DAGs.
Edit intent: clarity
Original:  Along this way, we significantly simplify the argument that is used in the previous work for k-Disjoint Paths with Congestion-c by Amiri et al  .
Revised:  Along this way, we significantly simplify the argument that is used in the previous work for k-Disjoint Paths with Congestion-c IPL 2019, MFCS 2016 .
Edit intent: meaning-changed
Original:  Along this way, we significantly simplify the argument that is used in the previous work for k-Disjoint Paths with Congestion-c by Amiri et al  .
Revised:  Along this way, we significantly simplify the argument that is used in the previous work for k-Disjoint Paths with Congestion-c by Amiri et al , but we significantly simplify their argument .
Edit intent: meaning-changed
Original: In the k-Disjoint Shortest Paths problem, a set of source terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths .
Revised: In the k-Disjoint Shortest Paths problem, a set of terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths .
Edit intent: clarity
Original: In the k-Disjoint Shortest Paths problem, a set of source terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths .
Revised: In the k-Disjoint Shortest Paths problem, a set of source terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of them .
Edit intent: clarity
Original:  Our algorithm is based on the earlier algorithm for k-Disjonit Paths with Congestion-c[ IPL 2019, MFCS 2016 ], but we significantly simplify their argument.
Revised:  Using the techniques for DAGs, we show the problem is solvable in time f(k) n^{O(k) is based on the earlier algorithm for k-Disjonit Paths with Congestion-c[ IPL 2019, MFCS 2016 ], but we significantly simplify their argument.
Edit intent: meaning-changed
Original:  Our algorithm is based on the earlier algorithm for k-Disjonit Paths with Congestion-c[ IPL 2019, MFCS 2016 ], but we significantly simplify their argument.
Revised:  Our algorithm is based on the earlier algorithm for k-Disjoint Paths with Congestion-c[ IPL 2019, MFCS 2016 ], but we significantly simplify their argument.
Edit intent: fluency
Original:  Our algorithm is based on the earlier algorithm for k-Disjonit Paths with Congestion-c[ IPL 2019, MFCS 2016 ], but we significantly simplify their argument.
Revised:  Our algorithm is based on the earlier algorithm for k-Disjonit Paths with Congestion-c[ IPL2019 ], but we significantly simplify their argument.
Edit intent: coherence
Original:  We also discuss the hardness of the problem , achieving a better lower bound than the previous one [ IPL 2019 ] . We believe our simplified method of analysis can be helpful to deal with similar problems on general undirected graphs .
Revised:  Then we prove that it is not possible to improve the algorithm significantly by showing that for every constant c the problem is W [ IPL 2019 ] . We believe our simplified method of analysis can be helpful to deal with similar problems on general undirected graphs .
Edit intent: meaning-changed
Original:  We also discuss the hardness of the problem , achieving a better lower bound than the previous one [ IPL 2019 ] . We believe our simplified method of analysis can be helpful to deal with similar problems on general undirected graphs .
Revised:  We also discuss the hardness of the problem , achieving a better lower bound than the previous one [ 1 ] . We believe our simplified method of analysis can be helpful to deal with similar problems on general undirected graphs .
Edit intent: meaning-changed
Original:  We also discuss the hardness of the problem , achieving a better lower bound than the previous one [ IPL 2019 ] . We believe our simplified method of analysis can be helpful to deal with similar problems on general undirected graphs .
Revised:  We also discuss the hardness of the problem , achieving a better lower bound than the previous one [ IPL 2019 ] -hard w.r.t.\ parameter k-c. We also consider the problem on acyclic planar graphs, but this time we restrict ourselves to the edge-disjoint shortest paths problem. We show that even on acyclic planar graphs there is no f(k)n^{o(k) .
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Original:  We show lower bounds 3, 11/3 and 4 (> 3.44948), 4+\sqrt{73}{3} (>4.18133) and 13{3} (>4.33333) } on the competitive ratio when the numbers of servers are 3, 4 and 5, respectively.
Revised:  We show lower bounds 1+ \sqrt{6 (> 3.44948), 4+\sqrt{73}{3} (>4.18133) and 13{3} (>4.33333) } on the competitive ratio when the numbers of servers are 3, 4 and 5, respectively.
Edit intent: meaning-changed
Original: The modular subset sum problem consists of deciding, given a modulus m, a multiset S of n integers in 0.. m , and a target integer t, whether there exists a subset of S with elements summing to t \mod  , and to report such a set if it exists.
Revised: The modular subset sum problem consists of deciding, given a modulus m, a multiset S of n integers in 0.. m-1 , and a target integer t, whether there exists a subset of S with elements summing to t \mod , and to report such a set if it exists.
Edit intent: meaning-changed
Original: The modular subset sum problem consists of deciding, given a modulus m, a multiset S of n integers in 0.. m , and a target integer t, whether there exists a subset of S with elements summing to t \mod  , and to report such a set if it exists.
Revised: The modular subset sum problem consists of deciding, given a modulus m, a multiset S of n integers in 0.. m , and a target integer t, whether there exists a subset of S with elements summing to t \mod m , and to report such a set if it exists.
Edit intent: fluency
Original:  This builds on and improves on a previous (m ) w.h.p. algorithm from Axiotis, Backurs, Jin, Tzamos, and Wu (SODA 19).
Revised:  This builds on and improves on a previous O(m \log^7 m ) w.h.p. algorithm from Axiotis, Backurs, Jin, Tzamos, and Wu (SODA 19).
Edit intent: meaning-changed
Original:  However, multiplexing compute-resources across microservices is still challenging in production because contention for shared resources can cause latency spikes that violate the service-level objectives (SLOs) of user requests.
Revised:  However, multiplexing of compute resources across microservices is still challenging in production because contention for shared resources can cause latency spikes that violate the service-level objectives (SLOs) of user requests.
Edit intent: fluency
Original:  FIRM leverages online telemetry data and machine-learning methods to adaptively (a) detect/localize microservices that cause SLO-violations , (b) identify low-level resources in contention, and (c) take actions to mitigate SLO-violations by dynamic reprovisioning.
Revised:  FIRM leverages online telemetry data and machine-learning methods to adaptively (a) detect/localize microservices that cause SLO violations , (b) identify low-level resources in contention, and (c) take actions to mitigate SLO-violations by dynamic reprovisioning.
Edit intent: fluency
Original:  FIRM leverages online telemetry data and machine-learning methods to adaptively (a) detect/localize microservices that cause SLO-violations , (b) identify low-level resources in contention, and (c) take actions to mitigate SLO-violations by dynamic reprovisioning.
Revised:  FIRM leverages online telemetry data and machine-learning methods to adaptively (a) detect/localize microservices that cause SLO-violations , (b) identify low-level resources in contention, and (c) take actions to mitigate SLO violations via dynamic reprovisioning.
Edit intent: fluency
Original: One of the current state-of-the-art multilingual document embedding model is the bidirectional LSTM-based multilingual neural machine translation model (LASER) . This paper presents a transformer-based sentence/document embedding model, T-LASER, which makes three significant improvements.
Revised: One of the current state-of-the-art multilingual document embedding model LASER is based on the bidirectional LSTM neural machine translation model (LASER) . This paper presents a transformer-based sentence/document embedding model, T-LASER, which makes three significant improvements.
Edit intent: clarity
Original: One of the current state-of-the-art multilingual document embedding model is the bidirectional LSTM-based multilingual neural machine translation model (LASER) . This paper presents a transformer-based sentence/document embedding model, T-LASER, which makes three significant improvements.
Revised: One of the current state-of-the-art multilingual document embedding model is the bidirectional LSTM-based multilingual neural machine translation model . This paper presents a transformer-based sentence/document embedding model, T-LASER, which makes three significant improvements.
Edit intent: clarity
Original: We study sketching schemes for the cardinality estimation problem in data streams, and advocate for measuring the efficiency of such a scheme in terms of its MVP: Memory-Variance Product, i. e., the product of its space, in bits , and the relative variance of its estimates.
Revised: Cardinality estimation is perhaps the simplest non-trivial statistical problem that can be solved via sketching. Industrially-deployed sketches like HyperLogLog, MinHash, and PCSA are mergeable, which means that large data sets can be sketched in a distributed environment, and then merged into a single sketch of the whole data set. In the last decade a variety of sketches have been developed that are non-mergeable, but attractive for other reasons. They are simpler, their cardinality estimates are strictly unbiased, and they have substantially lower variance. We evaluate sketching schemes on a reasonably level playing field, in terms of its MVP: Memory-Variance Product, i. e., the product of its space, in bits , and the relative variance of its estimates.
Edit intent: meaning-changed
Original: We study sketching schemes for the cardinality estimation problem in data streams, and advocate for measuring the efficiency of such a scheme in terms of its MVP: Memory-Variance Product, i. e., the product of its space, in bits , and the relative variance of its estimates. Under this natural metric, the celebrated HyperLogLog sketch of Flajolet et al. (2007 ) has an MVP approaching 6(3\ln 2-1)\approx 6.48 for estimating cardinalities up to 2^{64.
Revised: We study sketching schemes for the cardinality estimation problem in data streams, and advocate for measuring the efficiency of such a scheme in terms of their memory-variance product (MVP). E.g., a sketch that occupies 5m bits and whose relative variance is 2/m (standard error \sqrt{2/m ) has an MVP approaching 6(3\ln 2-1)\approx 6.48 for estimating cardinalities up to 2^{64.
Edit intent: meaning-changed
Original:  Under this natural metric, the celebrated HyperLogLog sketch of Flajolet et al. (2007 ) has an MVP approaching 6(3\ln 2-1)\approx 6.48 for estimating cardinalities up to 2^{64.
Revised:  Under this natural metric, the celebrated HyperLogLog sketch of Flajolet et al. (2007 ) has an MVP .
Edit intent: clarity
Original:  We develop a new class of "curtain" sketchesthat are a bit more complex than Martingale LogLog but with substantially better }%DIFDELCMD < \MVPs%%% , e. g., Martingale Curtain has MVP \approx 2.31. We also prove that Martingale Fishmonger has   an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
Revised:  We develop a new class of "curtain" sketchesthat are a bit more complex than Martingale LogLog but with substantially better }%DIFDELCMD < \MVPs%%% of 10. Our contributions are as follows. Cohen and Ting independently discovered what we call the Martingale transform for converting a mergeable sketch into a non-mergeable sketch. We present a simpler way to analyze the limiting MVP of Martingale-type sketches. We prove that the an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
Edit intent: meaning-changed
Original:  We also prove that Martingale Fishmonger has   an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
Revised:  We also prove that Martingale Fishmonger has transform is optimal in the non-mergeable world, and that an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
Edit intent: meaning-changed
Original:  We also prove that Martingale Fishmonger has   an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
Revised:  We also prove that Martingale Fishmonger has in particular is optimal among linearizable sketches, with an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
Edit intent: meaning-changed