wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting tough connection of the problem with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: clarity
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem , an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: clarity
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: fluency
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: meaning-changed
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: coherence
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: clarity
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)-time and O\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: fluency
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left(\frac{|E|^2\log|E|{\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Edit intent: fluency
Original:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right) based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting its tough connection with the geometric Hitting Set problem we give \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O ( \left(\left( |E| ^4\log{\varepsilon^2}+\log|E|{\varepsilon^3}}\right) |E| )-time and O(|E| ^2\log|E| ) spa\-ce algorithm \right)\left({\varepsilon}}\right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Edit intent: coherence
Original:  More accurate (34+24\sqrt{2}+\varepsilon)-, \left(12+6\sqrt{3}+\varepsilon\right)- and \left(34+38\sqrt{\frac{15}{19}}+\varepsilon\right) -ap\-pro\-xi\-mate algorithms are proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant  .
Revised:  More accurate (34+24\sqrt{2}+\varepsilon)-, \left(12+6\sqrt{3}+\varepsilon\right)- and \left(34+38\sqrt{\frac{15}{19}}+\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant .
Edit intent: clarity
Original:  More accurate (34+24\sqrt{2}+\varepsilon)-, \left(12+6\sqrt{3}+\varepsilon\right)- and \left(34+38\sqrt{\frac{15}{19}}+\varepsilon\right) -ap\-pro\-xi\-mate algorithms are proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant  .
Revised:  More accurate (34+24\sqrt{2}+\varepsilon)-, \left(12+6\sqrt{3}+\varepsilon\right)- and \left(34+38\sqrt{\frac{15}{19}}+\varepsilon\right) -ap\-pro\-xi\-mate algorithms are proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant . Related work only tackles the case where E consists of axis-parallel segments, resulting in an O(|E|\log|E|)-time and O(|E|\log|E|)-space 8-approximation .
Edit intent: meaning-changed
Original: Fast constant factor approximation algorithms are devised for an NP- and W[1]-hard problem of intersecting a set of  straight line segments with the smallest cardinality set of disks of fixed radii r>0, where the set of segments forms a straight line drawing G=(V,E) of a planar graph without edge crossings.
Revised: Fast constant factor approximation algorithms are devised for an NP- and W[1]-hard problem of intersecting a set of n straight line segments with the smallest cardinality set of disks of fixed radii r>0, where the set of segments forms a straight line drawing G=(V,E) of a planar graph without edge crossings.
Edit intent: meaning-changed
Original:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}}  \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}}  \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% {\varepsilon^2}+\log|E|{\varepsilon^3}} \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}} \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Edit intent: fluency
Original:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}}  \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}}  \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}} n^4\log n \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}} \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Edit intent: meaning-changed
Original:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}}  \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}}  \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}} \right) %DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}} \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Edit intent: coherence
Original:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}}  \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}}  \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}} \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( {\varepsilon}} \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Edit intent: fluency
Original:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}}  \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}}  \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Revised:  Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+\varepsilon\right)-approximate O\left( %DIFDELCMD < \left(%%% |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}} \right) |E|^2\log |E|%DIFDELCMD < \right)%%% -time and O\left( \frac{|E|^2\log|E|{\varepsilon}} n^2\log n \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
Edit intent: meaning-changed
Original:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Revised:  More accurate (34+242+\varepsilon)- %DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Edit intent: fluency
Original:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Revised:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% +\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Edit intent: coherence
Original:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Revised:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Edit intent: fluency
Original:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Revised:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 44\sqrt{\frac{6 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Edit intent: meaning-changed
Original:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Revised:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approxi\-mate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Edit intent: fluency
Original:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Revised:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for cases where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Edit intent: fluency
Original:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Revised:  More accurate (34+242+\varepsilon)- ,%DIFDELCMD < \left(%%% 12+6\sqrt{3+\varepsilon}%DIFDELCMD < \right)%%% - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also proposed for the case where G is any subgraph of either an outerplane graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant.
Edit intent: meaning-changed
Original:  Related work only tackles the case where E consists of axis-parallel segments, resulting in an O( |E|\log |E| )-time and O( |E|\log |E| )-space 8-approximation.
Revised:  Moreover, an O(n^2\log n)-time and O(n^2)-space 18-approximation is designed for the case where G is any subgraph of a Gabriel graph. To the best of our knowledge, related work only tackles the case where E consists of axis-parallel segments, resulting in an O( |E|\log |E| )-time and O( |E|\log |E| )-space 8-approximation.
Edit intent: meaning-changed
Original:  Related work only tackles the case where E consists of axis-parallel segments, resulting in an O( |E|\log |E| )-time and O( |E|\log |E| )-space 8-approximation.
Revised:  Related work only tackles the case where E consists of axis-parallel segments, resulting in an O( n\log n )-time and O( |E|\log |E| )-space 8-approximation.
Edit intent: meaning-changed
Original:  Related work only tackles the case where E consists of axis-parallel segments, resulting in an O( |E|\log |E| )-time and O( |E|\log |E| )-space 8-approximation.
Revised:  Related work only tackles the case where E consists of axis-parallel segments, resulting in an O( |E|\log |E| )-time and O( n\log n )-space 8-approximation.
Edit intent: meaning-changed
Original:  In this setting, our principal goals reside in describing as explicit as possible the set of all deflators (i.e. the dual set of all wealth processes) and the log-optimal portfolio for the stopped model S^{\tau}.
Revised:  In this setting, our principal goal resides in describing as explicit as possible the set of all deflators (i.e. the dual set of all wealth processes) and the log-optimal portfolio for the stopped model S^{\tau}.
Edit intent: fluency
Original:  In this setting, our principal goals reside in describing as explicit as possible the set of all deflators (i.e. the dual set of all wealth processes) and the log-optimal portfolio for the stopped model S^{\tau}.
Revised:  In this setting, our principal goals reside in describing as explicit as possible the set of all deflators , which constitutes the dual set of all wealth processes) and the log-optimal portfolio for the stopped model S^{\tau}.
Edit intent: clarity
Original:  In this setting, our principal goals reside in describing as explicit as possible the set of all deflators (i.e. the dual set of all wealth processes) and the log-optimal portfolio for the stopped model S^{\tau}.
Revised:  In this setting, our principal goals reside in describing as explicit as possible the set of all deflators (i.e. the dual set of all "admissible" wealth processes, for the stopped model S^{\tau}.
Edit intent: clarity
Original:  Since the death time and the default time  can be seen when they occur only, the progressive enlargement of \mathbb F with \tau , that we denote by \mathbb G, sounds taylor-fit for modelling the new flow of information that incorporates both \mathbb F and \tau.
Revised:  Since the death time and the default time (that \tau might represent) can be seen when they occur only, the progressive enlargement of \mathbb F with \tau , that we denote by \mathbb G, sounds taylor-fit for modelling the new flow of information that incorporates both \mathbb F and \tau.
Edit intent: meaning-changed
Original:  Since the death time and the default time  can be seen when they occur only, the progressive enlargement of \mathbb F with \tau , that we denote by \mathbb G, sounds taylor-fit for modelling the new flow of information that incorporates both \mathbb F and \tau.
Revised:  Since the death time and the default time can be seen when they occur only, the progressive enlargement of \mathbb F with \tau sounds tailor-fit for modelling the new flow of information that incorporates both \mathbb F and \tau.
Edit intent: clarity
Original:  Thanks to the deep results of Choulli et al (2016) on the ] martingales classification and representation for progressive enlarged filtration, we completely and explicitly describe all the deflators for (S ^{\tau,\mathbb G) in terms of the deflators of the initial market model (S} ,\mathbb F) .
Revised:  Thanks to the deep results of Choulli et al . ] martingales classification and representation for progressive enlarged filtration, we completely and explicitly describe all the deflators for (S ^{\tau,\mathbb G) in terms of the deflators of the initial market model (S} ,\mathbb F) .
Edit intent: coherence