wanyu/IteraTeR_full_sent huggingface dataset:
Original:  It runs in O(n^{2\omega})\leq O(n^{4.75}) time, where \omega \approx  2.373  is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n\log n).
Revised:  It runs in O(n^{2\omega})\leq O(n^{4.75}) time, where \omega \approx 2.373 ) is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n\log n).
Edit intent: fluency
Original:  Our algorithm is also conceptually simpler than Fulek and Kyn\v{c : We perform a sequence of \emph{local operations} that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Revised:  Our algorithm is also conceptually simpler Fulek and Kyn\v{c : We perform a sequence of \emph{local operations} that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Edit intent: coherence
Original:  Our algorithm is also conceptually simpler than Fulek and Kyn\v{c : We perform a sequence of \emph{local operations} that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Revised:  Our algorithm is also conceptually simpler than : We perform a sequence of \emph{local operations} that gradually "untangles" the image \varphi(G) into an embedding \psi(G), or reports that \varphi is not a weak embedding.
Edit intent: coherence
Original:  It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon Akitaya et al., 2016%DIFDELCMD < ]%%% , and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.
Revised:  It Akitaya et al., 2016%DIFDELCMD < ]%%% , and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.
Edit intent: coherence
Original:  It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon Akitaya et al., 2016%DIFDELCMD < ]%%% , and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.
Revised:  It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon %DIFDELCMD < ]%%% , and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.
Edit intent: coherence
Original:  It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon Akitaya et al., 2016%DIFDELCMD < ]%%% , and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.
Revised:  It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon Akitaya et al., 2016%DIFDELCMD < ]%%% combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.
Edit intent: coherence
Original: Let P be a set of n points in the plane and _{\theta}(P), has minimum (or maximum) area in optimal O(n\log n) time and O(n) space, improving the previous O(n^2) bound.
Revised: Let P be a set of n points in the plane . We compute the value of \theta\in _{\theta}(P), has minimum (or maximum) area in optimal O(n\log n) time and O(n) space, improving the previous O(n^2) bound.
Edit intent: meaning-changed
Original: Let P be a set of n points in the plane and _{\theta}(P), has minimum (or maximum) area in optimal O(n\log n) time and O(n) space, improving the previous O(n^2) bound.
Revised: Let P be a set of n points in the plane and 0,2\pi) for which the rectilinear convex hull of P, denoted by \mathcal{RH_{\theta}(P), has minimum (or maximum) area in optimal O(n\log n) time and O(n) space, improving the previous O(n^2) bound.
Edit intent: meaning-changed
Original:  Let } O be a set of k lines passing through the origin . We show=\pi-\alpha_i and \Theta=\min\{\Theta_i:i=1,\ldots,2k\}.
Revised:  Let } O be a set of k lines passing through the origin sorted by slope and let \alpha_i be the aperture angles of the 2k sectors defined by every pair of two consecutive lines. Let \Theta_{i=\pi-\alpha_i and \Theta=\min\{\Theta_i:i=1,\ldots,2k\}.
Edit intent: meaning-changed
Original:  We further obtain} : (1) How such that \Theta}\ge to compute the O -hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Revised:  We further obtain} : (1) Given a set \mathcal{O such that \Theta}\ge to compute the O -hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Edit intent: meaning-changed
Original:  We further obtain} : (1) How such that \Theta}\ge to compute the O -hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Revised:  We further obtain} : (1) How such that \Theta}\ge\frac{\pi to compute the O -hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Edit intent: meaning-changed
Original:  We further obtain} : (1) How such that \Theta}\ge to compute the O -hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Revised:  We further obtain} : (1) How such that \Theta}\ge to compute the O -convex hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Edit intent: meaning-changed
Original:  We further obtain} : (1) How such that \Theta}\ge to compute the O -hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Revised:  We further obtain} : (1) How such that \Theta}\ge to compute the O -hull of P in optimal O (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Edit intent: meaning-changed
Original:  We further obtain} : (1) How such that \Theta}\ge to compute the O -hull of P in \Theta (n\log n) time and O(n) space, ({2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Revised:  We further obtain} : (1) How such that \Theta}\ge to compute the O -hull of P in \Theta (n\log n) time and O(n) space, while if \Theta<\frac{\pi{2} the complexities are O(\frac{n}{\Theta}\log n) time and O(\frac{n}{\Theta}) space.
Edit intent: meaning-changed
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) Given a set \mathcal{O such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) } }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: meaning-changed
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) how to such that \Theta}\ge\frac{\pi compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) } }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: meaning-changed
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) how to such that \Theta}\ge compute and maintain the _{\theta}(P ) } }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: clarity
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) } boundary of the }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: meaning-changed
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) } \mathcal{O}} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: meaning-changed
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) } }}_{\theta for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: meaning-changed
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) } }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, or in O(k\frac{n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: meaning-changed
Original:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) }  }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( n) space a value of \theta for which the rectilinear convex hull, \mathcal{RH_{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Revised:  (} 2) how to such that \Theta}\ge compute and maintain the rotated hull \mathcal{OH_{\theta}(P ) } }} for \theta\in [0,2\pi) in O(kn\log n) time and O(kn) space, and (3) how to compute in \Theta(n{\Theta}} \log n) time and O( _{\theta}(P ), has minimum area, thus improving the previously best O(n^2) algorithm presented by Bae et al.in 2009.
Edit intent: meaning-changed
Original: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Revised: } k\frac{n{\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Edit intent: meaning-changed
Original: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Revised: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge\frac{\pi }}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Edit intent: meaning-changed
Original: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Revised: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge \mathcal{O}}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Edit intent: meaning-changed
Original: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Revised: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}_{\theta-convex hull of P of minimum (or maximum) area over all \theta\in }[
Edit intent: meaning-changed
Original: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}-convex hull of P of minimum (or maximum) area over all \theta\in }[
Revised: } {\Theta}) space if \Theta<\frac{\pi}{2}. (3) Finally, given a set \mathcal{O} such that \Theta}\ge }}-convex hull of P of minimum (or maximum) area over all \theta\in }[0,2\pi) in O(kn\log n) time and O(kn) space.
Edit intent: meaning-changed
Original: Many experiments randomly assign individuals to either a treatment group with access to a program or a control group without such access. I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Revised: I develop tools to learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Edit intent: clarity
Original:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Revised:  I study what we can learn about the average effects of providing an offer to participate in a program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Edit intent: clarity
Original:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Revised:  I study what we can learn about the average effects of providing access to the program given data from an experiment that randomizes offers. I allow for the complication that individuals may not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Edit intent: meaning-changed
Original:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Revised:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status in the sense that those who are not provided an offer may receive one from outside the experiment, and that the data may only provide partial information on the receipt of program access across individuals.
Edit intent: meaning-changed
Original:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Revised:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may provide only partial information on the receipt of program access across individuals.
Edit intent: fluency
Original:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of program access across individuals.
Revised:  I study what we can learn about the average effects of providing access to the program given data from such experiments when individuals do not comply with their assigned status and when the data may only provide partial information on the receipt of an offer across individuals.
Edit intent: clarity
Original:   I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Revised:  To do so, I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Edit intent: clarity
Original:   I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Revised:  I propose a new nonparametric selection model with unobserved choice sets that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Edit intent: meaning-changed
Original:   I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Revised:  I propose a new nonparametric multiple treatment selection model that provides a conceptual framework to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Edit intent: clarity
Original:   I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Revised:  I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of an offer, exploit the partial information the data may provide on where access was received .
Edit intent: clarity
Original:   I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information the data may provide on where access was received .
Revised:  I propose a new nonparametric multiple treatment selection model that provides a general setup to define a range of parameters evaluating the effects of program access and to exploit the partial information available on offer receipt, and also consider an array of identifying assumptions .
Edit intent: meaning-changed
Original:  I illustrate how a computational procedure can be used to learn about these parameters in this model. Using the developed framework , I analyze the effects of providing access to the Head Start preschool program given data from the Head Start Impact Study.
Revised:  I illustrate how a computational procedure can be used to sharply learn about the parameters under the various assumptions. Using these tools , I analyze the effects of providing access to the Head Start preschool program given data from the Head Start Impact Study.
Edit intent: clarity
Original:  I find that providing access to Head Start can have positive effects on test scores and that these effects can negatively depend on whether access to an alternative preschool was available. In addition , I find that the earning benefits associated with the test score gains can outweigh the net costs for various policies providing access to Head Start .
Revised:  I find that providing access to Head Start can have positive effects on test scores . These effects primarily arise from children who do not have any preschool as an outside option. Performing a cost-benefit analysis , I find that the earning benefits associated with the test score gains can outweigh the net costs for various policies providing access to Head Start .
Edit intent: meaning-changed