wanyu/IteraTeR_v2 huggingface dataset:
Original:  blocks . Previous ]  I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [  [  Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [   Fadel et al., TCS '99 ].
Revised:  blocks . Previous ] I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [ ,[ Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [ Fadel et al., TCS '99 ].
Edit intent: fluency
Original:  blocks . Previous ]  I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [  [  Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [   Fadel et al., TCS '99 ].
Revised:  blocks . Previous ] I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [ [ , Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [ Fadel et al., TCS '99 ].
Edit intent: fluency
Original:  blocks . Previous ]  I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [  [  Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [   Fadel et al., TCS '99 ].
Revised:  blocks . Previous ] I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [ [ Kumar and Schwabe, SPDP 1996 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [ Fadel et al., TCS '99 ].
Edit intent: fluency
Original:  blocks . Previous ]  I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [  [  Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [   Fadel et al., TCS '99 ].
Revised:  blocks . Previous ] I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [ [ Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% {B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [ Fadel et al., TCS '99 ].
Edit intent: fluency
Original:  blocks . Previous ]  I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [  [  Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [   Fadel et al., TCS '99 ].
Revised:  blocks . Previous ] I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [ [ Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [ , Fadel et al., TCS '99 ].
Edit intent: fluency
Original:  blocks . Previous ]  I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [  [  Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [   Fadel et al., TCS '99 ].
Revised:  blocks . Previous ] I/O-efficient priority queues either support these operations in O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os [ [ Kumar and Schwabe, SPDP '96 ] or support only operations Insert, Delete and Extract-Min in optimal O%DIFDELCMD < \left( %%% \frac{1{B}\log_{\frac{M}{B}} \frac{N}{B}}%DIFDELCMD < \right) %%% amortized I/Os, however without supporting Decrease-Key [ Fadel et al., TCS 1999 ].
Edit intent: fluency
Original:  We also present buffered repository trees that support on a multi-set of N elements, operation Insert \textsc{ in O \left(\frac{1}{B}\log_{ \frac{M } \frac{N}{B}\right)
Revised:  We also present buffered repository trees that support on a multi-set of N elements, operation \textsc{ in O \left(\frac{1}{B}\log_{ \frac{M } \frac{N}{B}\right)
Edit intent: fluency
Original:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Revised:  I/Os and operation \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Edit intent: fluency
Original:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Revised:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( \log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Edit intent: clarity
Original:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Revised:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} \frac{\lambda^{\varepsilon}{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Edit intent: fluency
Original:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Revised:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + \frac{K \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Edit intent: fluency
Original:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Revised:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% %DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Edit intent: coherence
Original:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Revised:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% {B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Edit intent: fluency
Original:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ] Buchsbaum et al., SODA '00].
Revised:  I/Os and operation Extract \textsc{ on K extracted elements in O \left( M^{\varepsilon\log} }{B} \log} _{ \frac{M } \frac{N}{B} + K/B \right) amortized I/Os, using O \left(\frac{N}{B}\right) blocks . Previous results achieve O%DIFDELCMD < \left(%%% \frac{1{B}\log_2 \frac{N}{B}}%DIFDELCMD < \right) %%% I/Os and O%DIFDELCMD < \left( %%% \log_2 \frac{N{B} + \frac{K}{B}}%DIFDELCMD < \right) %%% I/Os, respectively [ ], Buchsbaum et al., SODA '00].
Edit intent: fluency
Original:  Our results imply improved O \left( \frac{E{B}\log} \right)\left({B}\log} _{ \frac{M } \frac{E}{B}\right)
Revised:  Our results imply improved O \left( {B}\log} \right)\left({B}\log} _{ \frac{M } \frac{E}{B}\right)
Edit intent: fluency
Original:  Our results imply improved O \left( \frac{E{B}\log} \right)\left({B}\log} _{ \frac{M } \frac{E}{B}\right)
Revised:  Our results imply improved O \left( \frac{E{B}\log} \right)\left(\frac{E{B}\log} _{ \frac{M } \frac{E}{B}\right)
Edit intent: fluency
Original:  I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs %DIFDELCMD < \left(%%%  V,E %DIFDELCMD < \right) %%% with E = \Omega %DIFDELCMD < \left( %%% V ^{1+\varepsilon}%DIFDELCMD < \right)%%% , \varepsilon > 0 and V = \Omega%DIFDELCMD < \left( %%% M%DIFDELCMD < \right)%%% , which is equal to the I/O-optimal bound for sorting E values in external memory .
Revised:  I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs %DIFDELCMD < \left(%%% ( V,E %DIFDELCMD < \right) %%% with E = \Omega %DIFDELCMD < \left( %%% V ^{1+\varepsilon}%DIFDELCMD < \right)%%% , \varepsilon > 0 and V = \Omega%DIFDELCMD < \left( %%% M%DIFDELCMD < \right)%%% , which is equal to the I/O-optimal bound for sorting E values in external memory .
Edit intent: fluency
Original:  I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs %DIFDELCMD < \left(%%%  V,E %DIFDELCMD < \right) %%% with E = \Omega %DIFDELCMD < \left( %%% V ^{1+\varepsilon}%DIFDELCMD < \right)%%% , \varepsilon > 0 and V = \Omega%DIFDELCMD < \left( %%% M%DIFDELCMD < \right)%%% , which is equal to the I/O-optimal bound for sorting E values in external memory .
Revised:  I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs %DIFDELCMD < \left(%%% V,E %DIFDELCMD < \right) %%% with E = \Omega %DIFDELCMD < \left( %%% V ^{1+\varepsilon}%DIFDELCMD < \right)%%% , \varepsilon > 0 and V = %DIFDELCMD < \left( %%% M%DIFDELCMD < \right)%%% , which is equal to the I/O-optimal bound for sorting E values in external memory .
Edit intent: fluency
Original:  Then, we characterize minimal well-indumatched graphs of girth at least 9 and show subsequently that there is no well-indumatched graph of odd girth g greater than or equal to 9 and different from 11.
Revised:  Then, we characterize minimal well-indumatched graphs of girth at least 9 and show subsequently that for an odd integer g greater than or equal to 9 and different from 11.
Edit intent: clarity
Original:  Then, we characterize minimal well-indumatched graphs of girth at least 9 and show subsequently that there is no well-indumatched graph of odd girth g greater than or equal to 9 and different from 11.
Revised:  Then, we characterize minimal well-indumatched graphs of girth at least 9 and show subsequently that there is no well-indumatched graph of odd girth g greater than or equal to 9 and different from 11, there is no well-indumatched graph of girth g.
Edit intent: clarity
Original: Heterogeneous knowledge naturally arises among different agents in cooperative multiagent reinforcement learning .
Revised: In cooperative multiagent reinforcement learning .
Edit intent: clarity
Original:  As such, learning can be greatly improved if agents can effectively pass their knowledge on to other agents.
Revised:  As such, learning can be greatly improved if agents can effectively exchange their knowledge to other agents.
Edit intent: clarity
Original:  Existing work has demonstrated that peer-to-peer knowledge transfer , a process referred to as action advising , improves team-wide learning.
Revised:  In particular, recent work showed that action advising, a form of peer-to-peer knowledge transfer , a process referred to as action advising , improves team-wide learning.
Edit intent: clarity
Original:  Our empirical evaluations show that HMAT accelerates team-wide learning progress in difficult environments that are more complex than those explored in previous work.
Revised:  Our empirical evaluations show that HMAT accelerates team-wide learning progress in environments that are more complex than those explored in previous work.
Edit intent: clarity
Original:  HMAT also learns teaching policies that can be transferred to different teammates/tasks and can even teach teammates with heterogeneous action spaces.
Revised:  HMAT also learns teaching policies that can be transferred to different teammates/tasks , even when teammates have heterogeneous action spaces.
Edit intent: coherence
Original:  This paper introduces a novel learning-to-teach framework, called hierarchical multiagent teaching (HMAT), in which the teacher  advice may include extended action sequences over multiple levels of temporal abstraction.
Revised:  This paper introduces a novel learning-to-teach framework, called hierarchical multiagent teaching (HMAT), in which the teacher 's advice may include extended action sequences over multiple levels of temporal abstraction.
Edit intent: fluency
Original:  Learning across the team can be greatly improved if agents can effectively exchange their knowledge to other agents .
Revised:  Learning across the team can be greatly enhanced when agents effectively exchange knowledge with their peers .
Edit intent: clarity
Original:  In particular, recent work showed that action advising, a form of peer-to-peer knowledge transfer from teacher agents to student agents, improves team-wide learning.
Revised:  In particular, recent work studying agents that learn to teach other teammates has demonstrated that action advising accelerates team-wide learning.
Edit intent: clarity
Original:  The empirical evaluations show that HMAT accelerates team-wide learning progress in environments that are more complex than considered in previous learning-to-teach research.
Revised:  Our empirical evaluations demonstrate that HMAT improves team-wide learning progress in environments that are more complex than considered in previous learning-to-teach research.
Edit intent: clarity
Original:  HMAT is also shown to learn teaching policies that can be transferred to different teammates / tasks, even when  teammates have heterogeneous action spaces.
Revised:  HMAT is also shown to learn teaching policies that can effectively transfer knowledge to different teammates / tasks, even when teammates have heterogeneous action spaces.
Edit intent: clarity
Original:  HMAT is also shown to learn teaching policies that can be transferred to different teammates / tasks, even when  teammates have heterogeneous action spaces.
Revised:  HMAT is also shown to learn teaching policies that can be transferred to different teammates / tasks, even when the teammates have heterogeneous action spaces.
Edit intent: clarity
Original:  However, the prior work has simplified the learning of advising policies by using simple function approximations and only considering advising with primitive (low-level) actions, limiting the scalability of learning and teaching to complex domains.
Revised:  However, the prior work has simplified the learning of advising policies by using simple function approximations and only considered advising with primitive (low-level) actions, limiting the scalability of learning and teaching to complex domains.
Edit intent: fluency
Original:  In this paper, we propose a language that can express a wide range of physical database layouts, going well beyond the row- and column- based methods that are widely used in database management systems.
Revised:  In this paper, we propose a language that can express a wide range of physical database layouts, going well beyond the row- and column-based methods that are widely used in database management systems.
Edit intent: fluency
Original:  We demonstrate our method on a 3D brain registration task for both images and anatomical surfaces, and provide extensive empirical analyses of the algorithm .
Revised:  We demonstrate our method on a 3D brain registration task for both images and anatomical surfaces, and provide extensive empirical analyses .
Edit intent: clarity
Original:  Our implementation is available online at URL
Revised:  Our implementation is available at URL
Edit intent: clarity
Original: Feature hashing and more general projection schemes are commonly used in machine learning to reduce the dimensionality of feature vectors.
Revised: Feature hashing and more general projection schemes are commonly used to reduce the dimensionality of feature vectors.
Edit intent: clarity
Original:  In practice, feature vectors often have a low \ell_\infty-to-\ell_2 norm ratio, and for this restricted set of vectors, many sparse JL-based schemes can achieve the norm-preserving objective with smaller dimension m than is necessary for the scheme on the full space R^n. A line of work introduced by Weinberger et. al (ICML '09)
Revised:  A line of work introduced by Weinberger et. al (ICML '09)
Edit intent: coherence
Original:  analyzes the sparse JL transform with one nonzero entry per column, which is a standard feature hashing scheme . Recently, Freksen, Kamma, and Larsen ( NIPS '18) closed this line of work by proving an essentially tight tradeoff between \ell_\infty-to-\ell_2 norm ratio , distortion, failure probability, and dimension m for this feature hashing scheme.
Revised:  analyzes the sparse JL transform with one nonzero entry per column, which is a standard feature hashing scheme . Recently, Freksen, Kamma, and Larsen ( NIPS '18) closed this line of work by proving a tight tradeoff between \ell_\infty-to-\ell_2 norm ratio , distortion, failure probability, and dimension m for this feature hashing scheme.
Edit intent: clarity
Original:  Our main result is an essentially tight tradeoff between \ell_\infty-to-\ell_2 norm ratio , distortion, failure probability, and dimension m for a general sparsity s, that  generalizes the result of Freksen et. al.
Revised:  Our main result is a tight tradeoff between \ell_\infty-to-\ell_2 norm ratio , distortion, failure probability, and dimension m for a general sparsity s, that generalizes the result of Freksen et. al.
Edit intent: clarity
Original:  Our main result is an essentially tight tradeoff between \ell_\infty-to-\ell_2 norm ratio , distortion, failure probability, and dimension m for a general sparsity s, that  generalizes the result of Freksen et. al.
Revised:  Our main result is an essentially tight tradeoff between \ell_\infty-to-\ell_2 norm ratio and accuracy for a general sparsity s, that generalizes the result of Freksen et. al.
Edit intent: clarity
Original:  However, including the TPQ into an XQuery compiler is not a straightforward problem and current XML DBMSs process XQueries without any TPQ detection.
Revised:  However, including the TPQ into an XQuery compiler is not a straightforward task and current XML DBMSs process XQueries without any TPQ detection.
Edit intent: clarity
Original: As the computational power of toady's devices increases , real-time physically-based rendering becomes possible, and is rapidly gaining attention across a variety of domains.
Revised: With the increasing computational power of toady's devices increases , real-time physically-based rendering becomes possible, and is rapidly gaining attention across a variety of domains.
Edit intent: clarity