wanyu/IteraTeR_v2 huggingface dataset:
Original:  A hypergraph%DIFDELCMD < {\cal %%% H is said to be 1-Sperner if every two distinct hyperedges e,f of%DIFDELCMD < {\cal %%% H satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences , including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Revised:  A hypergraph%DIFDELCMD < {\cal %%% H is said to be 1-Sperner if every two distinct hyperedges e,f of%DIFDELCMD < {\cal %%% satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences , including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Edit intent: fluency
Original:  A hypergraph%DIFDELCMD < {\cal %%% H is said to be 1-Sperner if every two distinct hyperedges e,f of%DIFDELCMD < {\cal %%% H satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences , including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Revised:  A hypergraph%DIFDELCMD < {\cal %%% H is said to be 1-Sperner if every two distinct hyperedges e,f of%DIFDELCMD < {\cal %%% H satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem and derive several consequences from it. In particular, we obtain bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Edit intent: clarity
Original: We compare the visibility and performance of Latin American and Caribbean (LAC) publications in the Core collection indexes included in the Web of Science (WoS) -- Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index -- and the Scielo Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Revised: We compare the visibility of Latin American and Caribbean (LAC) publications in the Core collection indexes included in the Web of Science (WoS) -- Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index -- and the Scielo Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Edit intent: clarity
Original: We compare the visibility and performance of Latin American and Caribbean (LAC) publications in the Core collection indexes included in the Web of Science (WoS) -- Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index -- and the Scielo Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Revised: We compare the visibility and performance of Latin American and Caribbean (LAC) publications in the Core Collection indexes of the Web of Science (WoS) -- Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index -- and the Scielo Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Edit intent: clarity
Original: We compare the visibility and performance of Latin American and Caribbean (LAC) publications in the Core collection indexes included in the Web of Science (WoS) -- Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index -- and the Scielo Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Revised: We compare the visibility and performance of Latin American and Caribbean (LAC) publications in the Core collection indexes included in the Web of Science (WoS) --Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index -- and the Scielo Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Edit intent: fluency
Original: We compare the visibility and performance of Latin American and Caribbean (LAC) publications in the Core collection indexes included in the Web of Science (WoS) -- Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index -- and the Scielo Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Revised: We compare the visibility and performance of Latin American and Caribbean (LAC) publications in the Core collection indexes included in the Web of Science (WoS) -- Science Citation Index Expanded, Social Sciences Citation Index, and Arts & Humanities Citation Index--and the SciELO Citation Index (SciELO CI) which was integrated into the larger WoS platform in 2014.
Edit intent: fluency
Original:  How is the regional level of ScieLO CI related to the global one of WoS?
Revised:  How is the regional level of SciELO CI related to the global one of WoS?
Edit intent: fluency
Original:  How is the regional level of ScieLO CI related to the global one of WoS?
Revised:  How is the regional level of ScieLO CI related to the global range of WoS?
Edit intent: clarity
Original:  The articulation of SciELO into WoS may improve the international standardization (for example, of referencing) in the regional journals, but comes at the price of losing independence of the journal inclusion criteria.
Revised:  The articulation of SciELO into WoS may improve the international visibility of the regional journals, but comes at the price of losing independence of the journal inclusion criteria.
Edit intent: clarity
Original:  The articulation of SciELO into WoS may improve the international standardization (for example, of referencing) in the regional journals, but comes at the price of losing independence of the journal inclusion criteria.
Revised:  The articulation of SciELO into WoS may improve the international standardization (for example, of referencing) in the regional journals, but at the cost of independent journal inclusion criteria.
Edit intent: coherence
Original: Gene coexpression is a common feature employed in predicting buffering relationships that explain genetic interactions , which constitute an important mechanism behind the robustness of cells to genetic perturbations.
Revised: Genetic interactions confer robustness on cells in response to genetic perturbations.
Edit intent: clarity
Original:  Yet, partial correlation values convey no information on the (linear) influence of the association within the entire multivariate system or, in other words, of the represented edge within the entire network.
Revised:  Yet, partial correlations convey no information on the (linear) influence of the association within the entire multivariate system or, in other words, of the represented edge within the entire network.
Edit intent: clarity
Original:  Yet, partial correlation values convey no information on the (linear) influence of the association within the entire multivariate system or, in other words, of the represented edge within the entire network.
Revised:  Yet, partial correlation values convey no information about the (linear) influence of the association within the entire multivariate system or, in other words, of the represented edge within the entire network.
Edit intent: fluency
Original:  We show that this new quantity correlates better with quantitative genetic interactions in yeast than classical coexpression measures .
Revised:  We show that this new quantity correlates better with quantitative genetic interactions in yeast .
Edit intent: clarity
Original: We report some preliminary computational results comparing parallel and sequential codes for vertex/facet enumeration problems for convex polyhedra.
Revised: We report some computational results comparing parallel and sequential codes for vertex/facet enumeration problems for convex polyhedra.
Edit intent: clarity
Original: The possible recognition between double stranded (ds) DNA with homologous sequences was many times invoked to explain different biological observations.
Revised: Molecular recognition between two double stranded (ds) DNA with homologous sequences was many times invoked to explain different biological observations.
Edit intent: clarity
Original:  This mechanism agrees with experimental data and explains several puzzling observations on the sequence dependence and the involvement of topoisomerases in the recognition.
Revised:  This mechanism agrees with experimental data and shed light upon the sequence effects and the possible involvement of topoisomerase II in the recognition.
Edit intent: clarity
Original:  Botnet-size independence enables two end hosts to set up communication regardless of the size of distributed botnets in any AS in the world . SIBRA thus ends the arms race between DDoS attackers and defenders.
Revised:  Botnet-size independence enables two end hosts to set up communication regardless of the size of distributed botnets in any Autonomous System in the Internet . SIBRA thus ends the arms race between DDoS attackers and defenders.
Edit intent: clarity
Original:  However, traditional indicators are not much based on the analysis of the processes intended to measure and the practical goals of the measurement.
Revised:  However, traditional indicators do not much rely on the analysis of the processes intended to measure and the practical goals of the measurement.
Edit intent: clarity
Original: The stochastic block model for one community with parameters n , K, p, and q is considered: K out of n vertices are in the community;
Revised: Community detection is considered for a stochastic block model for one community with parameters n , K, p, and q is considered: K out of n vertices are in the community;
Edit intent: clarity
Original:  An estimator based on observation of the graph G=(V, E) is said to achieve weak recovery if the mean number of misclassified vertices is o(K) as n%DIFDELCMD < \to %%% \infty.
Revised:  An estimator based on observation of the graph G=(V, E) is said to achieve weak recovery if the mean number of misclassified vertices is o(K) %DIFDELCMD < \to %%% \infty.
Edit intent: clarity
Original:  The main focus of the paper is on weak recovery in the sublinear regime K= \leq K \leq } o(n) and np = n^{o(1) . It is shown that weak recovery is provided by a belief propagation algorithm running for \log^\ast (n) +O(1) iterations, if \lambda > 1/e, with the total time complexity O(|E| \log^*n).
Revised:  The main focus of the paper is on weak recovery in the sublinear regime K= \leq K \leq } o(n) . It is shown that weak recovery is provided by a belief propagation algorithm running for \log^\ast (n) +O(1) iterations, if \lambda > 1/e, with the total time complexity O(|E| \log^*n).
Edit intent: coherence
Original:  The main focus of the paper is on weak recovery in the sublinear regime K= \leq K \leq } o(n) and np = n^{o(1) . It is shown that weak recovery is provided by a belief propagation algorithm running for \log^\ast (n) +O(1) iterations, if \lambda > 1/e, with the total time complexity O(|E| \log^*n).
Revised:  The main focus of the paper is on weak recovery in the sublinear regime K= \leq K \leq } o(n) and np = n^{o(1) . It is shown that such recovery is attainable by a belief propagation algorithm running for \log^\ast (n) +O(1) iterations, if \lambda > 1/e, with the total time complexity O(|E| \log^*n).
Edit intent: clarity
Original:  The main focus of the paper is on weak recovery in the sublinear regime K= \leq K \leq } o(n) and np = n^{o(1) . It is shown that weak recovery is provided by a belief propagation algorithm running for \log^\ast (n) +O(1) iterations, if \lambda > 1/e, with the total time complexity O(|E| \log^*n).
Revised:  The main focus of the paper is on weak recovery in the sublinear regime K= \leq K \leq } o(n) and np = n^{o(1) . It is shown that weak recovery is provided by a belief propagation algorithm running for \log^\ast n +O(1) iterations, if \lambda > 1/e, with the total time complexity O(|E| \log^*n).
Edit intent: fluency
Original:  Conversely,  no local algorithm with radius t of interaction satisfying t = o(\frac{\log n{\log(2+np)}) } can asymptotically outperform trivial random guessing if \lambda \leq 1/e . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge {\log n} }\left(  +o(1) }\right)
Revised:  Conversely, if \lambda \leq 1/e, no local algorithm with radius t of interaction satisfying t = o(\frac{\log n{\log(2+np)}) } can asymptotically outperform trivial random guessing if \lambda \leq 1/e . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge {\log n} }\left( +o(1) }\right)
Edit intent: coherence
Original:  Conversely,  no local algorithm with radius t of interaction satisfying t = o(\frac{\log n{\log(2+np)}) } can asymptotically outperform trivial random guessing if \lambda \leq 1/e . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge {\log n} }\left(  +o(1) }\right)
Revised:  Conversely, no local algorithm {\log(2+np)}) } can asymptotically outperform trivial random guessing if \lambda \leq 1/e . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge {\log n} }\left( +o(1) }\right)
Edit intent: clarity
Original:  Conversely,  no local algorithm with radius t of interaction satisfying t = o(\frac{\log n{\log(2+np)}) } can asymptotically outperform trivial random guessing if \lambda \leq 1/e . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge {\log n} }\left(  +o(1) }\right)
Revised:  Conversely, no local algorithm with radius t of interaction satisfying t = o(\frac{\log n{\log(2+np)}) } can asymptotically outperform trivial random guessing . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge {\log n} }\left( +o(1) }\right)
Edit intent: clarity
Original:  Conversely,  no local algorithm with radius t of interaction satisfying t = o(\frac{\log n{\log(2+np)}) } can asymptotically outperform trivial random guessing if \lambda \leq 1/e . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge {\log n} }\left(  +o(1) }\right)
Revised:  Conversely, no local algorithm with radius t of interaction satisfying t = o(\frac{\log n{\log(2+np)}) } can asymptotically outperform trivial random guessing if \lambda \leq 1/e . By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph, we provide evidence to suggest that spectral methods fail to provide weak recovery if \lambda \leq 1. \ge \frac{n{\log n} }\left( +o(1) }\right)
Edit intent: clarity
Original:  It is shown that such recovery is attainable by a belief propagation algorithm running for \log^\ast n+O(1) iterations, if \lambda=K^2(p-q)^2/((n-K)q), the signal-to-noise ratio, exceeds 1  /  e  , with the total time complexity O(|E| \log^*n)  . Conversely, if \lambda \leq 1/e, no local algorithm can asymptotically outperform trivial random guessing.
Revised:  A critical parameter is the effective signal-to-noise ratio \lambda=K^2(p-q)^2/((n-K)q), the signal-to-noise ratio, exceeds 1 / e , with the total time complexity O(|E| \log^*n) . Conversely, if \lambda \leq 1/e, no local algorithm can asymptotically outperform trivial random guessing.
Edit intent: clarity
Original:  It is shown that such recovery is attainable by a belief propagation algorithm running for \log^\ast n+O(1) iterations, if \lambda=K^2(p-q)^2/((n-K)q), the signal-to-noise ratio, exceeds 1  /  e  , with the total time complexity O(|E| \log^*n)  . Conversely, if \lambda \leq 1/e, no local algorithm can asymptotically outperform trivial random guessing.
Revised:  It is shown that such recovery is attainable by a belief propagation algorithm running for \log^\ast n+O(1) iterations, if \lambda=K^2(p-q)^2/((n-K)q), with \lambda= 1 / e , with the total time complexity O(|E| \log^*n) . Conversely, if \lambda \leq 1/e, no local algorithm can asymptotically outperform trivial random guessing.
Edit intent: coherence
Original:  It is shown that such recovery is attainable by a belief propagation algorithm running for \log^\ast n+O(1) iterations, if \lambda=K^2(p-q)^2/((n-K)q), the signal-to-noise ratio, exceeds 1  /  e  , with the total time complexity O(|E| \log^*n)  . Conversely, if \lambda \leq 1/e, no local algorithm can asymptotically outperform trivial random guessing.
Revised:  It is shown that such recovery is attainable by a belief propagation algorithm running for \log^\ast n+O(1) iterations, if \lambda=K^2(p-q)^2/((n-K)q), the signal-to-noise ratio, exceeds 1 / e . The belief propagation algorithm only needs to run for \log^\ast n+O(1) iterations , with the total time complexity O(|E| \log^*n) . Conversely, if \lambda \leq 1/e, no local algorithm can asymptotically outperform trivial random guessing.
Edit intent: coherence
Original:  By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph , we provide evidence to suggest that spectral methods fail to recovery the community if \lambda \leq 1.
Revised:  Furthermore, a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph , we provide evidence to suggest that spectral methods fail to recovery the community if \lambda \leq 1.
Edit intent: clarity
Original:  By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph , we provide evidence to suggest that spectral methods fail to recovery the community if \lambda \leq 1.
Revised:  By analyzing a linear message-passing algorithm that corresponds to applying power iteration to the non-backtracking matrix of the graph is shown to attain weak recovery if and only if \lambda> 1.
Edit intent: clarity
Original:  Along the way , we develop an automated procedure for proving a/b-power-freeness for morphisms of a certain form  .
Revised:  To accomplish this , we develop an automated procedure for proving a/b-power-freeness for morphisms of a certain form .
Edit intent: clarity
Original:  We also outline a new connection between group testing schemes and combinatorial designs.
Revised:  We also provide a new connection between group testing schemes and combinatorial designs.
Edit intent: clarity
Original: Recent advances on Transmission Network Expansion Planning (TNEP) demonstrate that the use of robust optimization, in contrast with respect to stochastic programming methods, make the expansion planning problem computationally tractable for real systems.
Revised: Recent breakthroughs in Transmission Network Expansion Planning (TNEP) demonstrate that the use of robust optimization, in contrast with respect to stochastic programming methods, make the expansion planning problem computationally tractable for real systems.
Edit intent: clarity
Original: Recent advances on Transmission Network Expansion Planning (TNEP) demonstrate that the use of robust optimization, in contrast with respect to stochastic programming methods, make the expansion planning problem computationally tractable for real systems.
Revised: Recent advances on Transmission Network Expansion Planning (TNEP) have demonstrated that the use of robust optimization, in contrast with respect to stochastic programming methods, make the expansion planning problem computationally tractable for real systems.
Edit intent: clarity
Original: Recent advances on Transmission Network Expansion Planning (TNEP) demonstrate that the use of robust optimization, in contrast with respect to stochastic programming methods, make the expansion planning problem computationally tractable for real systems.
Revised: Recent advances on Transmission Network Expansion Planning (TNEP) demonstrate that the use of robust optimization, as opposed to stochastic programming methods, make the expansion planning problem computationally tractable for real systems.
Edit intent: coherence
Original: Recent advances on Transmission Network Expansion Planning (TNEP) demonstrate that the use of robust optimization, in contrast with respect to stochastic programming methods, make the expansion planning problem computationally tractable for real systems.
Revised: Recent advances on Transmission Network Expansion Planning (TNEP) demonstrate that the use of robust optimization, in contrast with respect to stochastic programming methods, renders the expansion planning problem computationally tractable for real systems.
Edit intent: clarity
Original:  State-of-the-art robust methods treat the problem as stationary during the study period, making all the required investments on expansion of lines  at the beginning of the project horizon.
Revised:  State-of-the-art robust methods treat this problem as stationary during the study period, making all the required investments on expansion of lines at the beginning of the project horizon.
Edit intent: fluency
Original:  State-of-the-art robust methods treat the problem as stationary during the study period, making all the required investments on expansion of lines  at the beginning of the project horizon.
Revised:  State-of-the-art robust methods treat the problem as stationary throughout the study period, making all the required investments on expansion of lines at the beginning of the project horizon.
Edit intent: clarity
Original:  State-of-the-art robust methods treat the problem as stationary during the study period, making all the required investments on expansion of lines  at the beginning of the project horizon.
Revised:  State-of-the-art robust methods treat the problem as stationary during the study period, with all the required investments on expansion of lines at the beginning of the project horizon.
Edit intent: coherence
Original:  State-of-the-art robust methods treat the problem as stationary during the study period, making all the required investments on expansion of lines  at the beginning of the project horizon.
Revised:  State-of-the-art robust methods treat the problem as stationary during the study period, making all the required investments on expansion of lines being made at the beginning of the project horizon.
Edit intent: clarity
Original:  However, it is well-known that socioeconomic and environmental constraints might change considerably during the network lifetime , such as planned increments of wind-power generation capacities, variations of environmental conditions due to climate change or growing trends on consumption patterns, and these changes might also affect the optimal capacity expansion planning.
Revised:  However, it is common knowledge that socioeconomic and environmental constraints might change considerably during the network lifetime , such as planned increments of wind-power generation capacities, variations of environmental conditions due to climate change or growing trends on consumption patterns, and these changes might also affect the optimal capacity expansion planning.
Edit intent: clarity