wanyu/IteraTeR_full_sent huggingface dataset:
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total %DIFDELCMD < \bigl(%%% n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Edit intent: fluency
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%% expected time O ( n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Edit intent: fluency
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%% n^2 K^5{s}(\log s+ K2^{O(\log^* K))) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Edit intent: meaning-changed
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%% n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% ) . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Edit intent: fluency
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%% n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Edit intent: fluency
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%% n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl(( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Edit intent: fluency
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%% n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (i.e., k=1).
Edit intent: fluency
Original:  We assess the size and power of the backtests in realistic sample sizes, and in particular demonstrate the tradeoff between power and specificity in validating quantile forecasts  .
Revised:  We assess the size and power of the backtests in realistic sample sizes, and in particular demonstrate the tradeoff between power and specificity in validating quantile forecasts L of ten bank trading portfolios. For some portfolios, test results depend materially on the choice of kernel .
Edit intent: meaning-changed
Original: We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices  , decorrelation of moves in different points on the forward curve, and implied volatility skew and smile.
Revised: We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure , decorrelation of moves in different points on the forward curve, and implied volatility skew and smile.
Edit intent: meaning-changed
Original:  In addition to an efficient numerical scheme for calculating European vanilla and early-exercise option prices, we describe an algorithm for Monte Carlo-based pricing of more generic derivative prices which involves an efficient approximation for the risk neutral drift that avoids having to simulate drifts for every forward settlement date required for pricing.
Revised:  In addition to an efficient numerical scheme for calculating European vanilla and early-exercise option prices, we describe an algorithm for Monte Carlo-based pricing of more generic derivative payoffs which involves an efficient approximation for the risk neutral drift that avoids having to simulate drifts for every forward settlement date required for pricing.
Edit intent: clarity
Original:  In overcoming this restrictive assumption, here we study equilibrium points in random games with correlated entries. Namely, we analyse the mean value and the distribution of the number of (stable) internal equilibria in multi-player two-strategy evolutionary games where the payoff matrix entries are correlated random variables.
Revised:  In this paper, we overcome this restrictive assumption by considering multi-player two-strategy evolutionary games where the payoff matrix entries are correlated random variables.
Edit intent: clarity
Original:  We then characterise the asymptotic behaviour of this important quantity  and study the effect of the correlation  .
Revised:  We then characterise the asymptotic behaviour of this important quantity and study the effect of the correlation . Our results show that decreasing the correlation among payoffs (namely, of a strategist for different group compositions) leads to larger mean numbers of (stable) equilibrium points, suggesting that the system or population behavioural diversity can be promoted by increasing independence of the payoff entries .
Edit intent: meaning-changed
Original:  Recent results have shown, in the dual (spectrally positive  ) model,  the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times  if and only if the surplus is above some level.
Revised:  In the dual (spectrally positive ) model, the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level.
Edit intent: coherence
Original:  Recent results have shown, in the dual (spectrally positive  ) model,  the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times  if and only if the surplus is above some level.
Revised:  Recent results have shown, in the dual (spectrally positive L\'evy ) model, the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level.
Edit intent: meaning-changed
Original:  Recent results have shown, in the dual (spectrally positive  ) model,  the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times  if and only if the surplus is above some level.
Revised:  Recent results have shown, in the dual (spectrally positive ) model, recent results have shown the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level.
Edit intent: meaning-changed
Original:  Recent results have shown, in the dual (spectrally positive  ) model,  the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times  if and only if the surplus is above some level.
Revised:  Recent results have shown, in the dual (spectrally positive ) model, the optimality of a periodic barrier strategy , which pays dividends at Poissonian dividend-decision times if and only if the surplus is above some level.
Edit intent: meaning-changed
Original:  Recent results have shown, in the dual (spectrally positive  ) model,  the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times  if and only if the surplus is above some level.
Revised:  Recent results have shown, in the dual (spectrally positive ) model, the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times , if and only if the surplus is above some level.
Edit intent: fluency
Original: We introduce methods that rapidly evaluate a battery of information-theoretic and algorithmic complexity measures on DNA sequences in application to potential binding sites for nucleosomes. The first application of this new tool demonstrates structure beyond GC content on DNA sequences in the context of nucleosome binding. We tested the measures on well-studied genomic sequences of size 20K and 100K bps .
Revised: We introduce methods that rapidly evaluate a battery of information-theoretic and algorithmic complexity nature applied to DNA sequences to identify their potential capabilities to determine nucleosomal binding sites. We test our measures on well-studied genomic sequences of size 20K and 100K bps .
Edit intent: clarity
Original:  The measures reveal the known in vivo versus in vitro predictive discrepancies , but they also uncover the internal structure of G and C within the nucleosome length , thus disclosing more than simply GC content when one examines alphabet transformations that separate and scramble the GC content signal and the DNA sequence .
Revised:  The measures reveal the known in vivo versus in vitro predictive discrepancies and uncover their potential to pinpoint (high) nucleosome occupancy. We explore different possible signals within and beyond the nucleosome length , thus disclosing more than simply GC content when one examines alphabet transformations that separate and scramble the GC content signal and the DNA sequence .
Edit intent: meaning-changed
Original:  The measures reveal the known in vivo versus in vitro predictive discrepancies , but they also uncover the internal structure of G and C within the nucleosome length , thus disclosing more than simply GC content when one examines alphabet transformations that separate and scramble the GC content signal and the DNA sequence . Most current prediction methods are based upon training (e.g. k-mer discovery), the one here advanced, however, is a training-free approach to investigating informative measures of DNA information content in connection with structural nucleosomic packing .
Revised:  The measures reveal the known in vivo versus in vitro predictive discrepancies , but they also uncover the internal structure of G and C within the nucleosome length and find that complexity indices are informative of nucleosome occupancy. We compare against the gold standard (Kaplan model) and find similar and complementary results with the main difference that our sequence complexity approach. For example, for high occupancy, complexity-based scores outperform the Kaplan model for predicting binding representing a significant advancement in predicting the highest nucleosome occupancy following a training-free approach to investigating informative measures of DNA information content in connection with structural nucleosomic packing .
Edit intent: meaning-changed
Original:  such that uv is an edge in G if and only if there exists a Manhattan path between f(u) and f(v) in Z^2 avoiding the obstacles of O . The grid obstacle number of a graph is the smallest number of obstacles needed for the grid obstacle representation of G. This work shows that planar graphs admit such a representation while there exists some non-planar graphs that do not admit such a representation.
Revised:  such that uv is an edge in G if and only if there exists a Manhattan path between f(u) and f(v) in Z^2 avoiding the obstacles of O and points in f(V). This work shows that planar graphs admit such a representation while there exists some non-planar graphs that do not admit such a representation.
Edit intent: meaning-changed
Original:  such that uv is an edge in G if and only if there exists a Manhattan path between f(u) and f(v) in Z^2 avoiding the obstacles of O . The grid obstacle number of a graph is the smallest number of obstacles needed for the grid obstacle representation of G. This work shows that planar graphs admit such a representation while there exists some non-planar graphs that do not admit such a representation.
Revised:  such that uv is an edge in G if and only if there exists a Manhattan path between f(u) and f(v) in Z^2 avoiding the obstacles of O . The grid obstacle number of a graph is the smallest number of obstacles needed for the grid obstacle representation of G. This work shows that planar graphs admit such a representation while there exist some non-planar graphs that do not admit such a representation.
Edit intent: fluency
Original:  In this work we investigate how gene conservation, essentiality and functional repertoire are reflected in the connectivity k of the corresponding proteins in the PPI networks  of 42 evolutionarily unrelated bacterial species .
Revised:  In this work we investigate how gene conservation, essentiality and functional repertoire of a gene to the connectivity k of the corresponding proteins in the PPI networks of 42 evolutionarily unrelated bacterial species .
Edit intent: meaning-changed
Original:  In this work we investigate how gene conservation, essentiality and functional repertoire are reflected in the connectivity k of the corresponding proteins in the PPI networks  of 42 evolutionarily unrelated bacterial species .
Revised:  In this work we investigate how gene conservation, essentiality and functional repertoire are reflected in the connectivity k of the corresponding protein in the PPI networks of 42 evolutionarily unrelated bacterial species .
Edit intent: fluency
Original:  In this work we investigate how gene conservation, essentiality and functional repertoire are reflected in the connectivity k of the corresponding proteins in the PPI networks  of 42 evolutionarily unrelated bacterial species .
Revised:  In this work we investigate how gene conservation, essentiality and functional repertoire are reflected in the connectivity k of the corresponding proteins in the PPI networks . Focusing on a set of 42 evolutionarily unrelated bacterial species .
Edit intent: clarity
Original:  In this work we investigate how gene conservation, essentiality and functional repertoire are reflected in the connectivity k of the corresponding proteins in the PPI networks  of 42 evolutionarily unrelated bacterial species . We investigate three issues: i) the degree distribution and densities of the PPI subnetworks of essential and nonessential genes;
Revised:  In this work we investigate how gene conservation, essentiality and functional repertoire are reflected in the connectivity k of the corresponding proteins in the PPI networks of 42 bacterial species with reasonably separated evolutionary trajectories, we investigate three issues: i) the degree distribution and densities of the PPI subnetworks of essential and nonessential genes;
Edit intent: meaning-changed
Original:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s  ) is related to the the degree of the corresponding protein in the PPI network ;
Revised:  ii) how gene conservation , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s ) is related to the the degree of the corresponding protein in the PPI network ;
Edit intent: fluency
Original:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s  ) is related to the the degree of the corresponding protein in the PPI network ;
Revised:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressures (evaluated through the ratio K_a/K_s ) is related to the the degree of the corresponding protein in the PPI network ;
Edit intent: clarity
Original:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s  ) is related to the the degree of the corresponding protein in the PPI network ;
Revised:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s and ENC plots ) is related to the the degree of the corresponding protein in the PPI network ;
Edit intent: meaning-changed
Original:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s  ) is related to the the degree of the corresponding protein in the PPI network ;
Revised:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s ) is related to the the connectivity of the corresponding protein in the PPI network ;
Edit intent: clarity
Original:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s  ) is related to the the degree of the corresponding protein in the PPI network ;
Revised:  ii) how the conservationof genes , measured both by the evolutionary retention index (ERI) and by evolutionary pressure (as represented by the ratio K_a/K_s ) is related to the the degree of the corresponding protein ;
Edit intent: clarity
Original:  Noteworthy, a phase transition is observed such that, for  k\ge40, bacterial PPI network are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG J, a category of genes which is related to ribosomal functions and to the processing of genetic information.
Revised:  Noteworthy, a structural transition in the network is observed such that, for k\ge40, bacterial PPI network are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG J, a category of genes which is related to ribosomal functions and to the processing of genetic information.
Edit intent: meaning-changed
Original:  Noteworthy, a phase transition is observed such that, for  k\ge40, bacterial PPI network are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG J, a category of genes which is related to ribosomal functions and to the processing of genetic information.
Revised:  Noteworthy, a phase transition is observed such that, for connectivities k\ge40, bacterial PPI network are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG J, a category of genes which is related to ribosomal functions and to the processing of genetic information.
Edit intent: meaning-changed
Original:  Noteworthy, a phase transition is observed such that, for  k\ge40, bacterial PPI network are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG J, a category of genes which is related to ribosomal functions and to the processing of genetic information.
Revised:  Noteworthy, a phase transition is observed such that, for k\ge40, bacterial PPI networks are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG J, a category of genes which is related to ribosomal functions and to the processing of genetic information.
Edit intent: fluency
Original:  Noteworthy, a phase transition is observed such that, for  k\ge40, bacterial PPI network are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG J, a category of genes which is related to ribosomal functions and to the processing of genetic information.
Revised:  Noteworthy, a phase transition is observed such that, for k\ge40, bacterial PPI network are mostly populated by genes that are conserved, essential and which, in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.
Edit intent: clarity