wanyu/IteraTeR_v2 huggingface dataset:
Original:  We show that this problem can be solved in polynomial time for both discrete and interval uncertainty, but that the same problem becomes NP-hard when each coefficient can independently assume only a finite number of values.
Revised:  We show that the problem can be solved in polynomial time for both discrete and interval uncertainty, but that the same problem becomes NP-hard when each coefficient can independently assume only a finite number of values.
Edit intent: fluency
Original:  In particular, this demonstrates that placing uncertainty sets by their convex hulls may change the problem significantly, in contrast to the situation in classical single-level robust optimization.
Revised:  In particular, this demonstrates that replacing uncertainty sets by their convex hulls may change the problem significantly, in contrast to the situation in classical single-level robust optimization.
Edit intent: clarity
Original:  The main technique in this result uses explicit pseudo-random generators that are believed to be quantum-secure to construct concept classes that are hard to learn quantumly under the uniform distribution.
Revised:  The main technique in this result uses explicit pseudo-random functions that are believed to be quantum-secure to construct concept classes that are hard to learn quantumly under the uniform distribution.
Edit intent: clarity
Original:  This gives a strong conditional negative answer to one of the "Ten Semi-Grand Challenges for Quantum Computing Theory" raised by Aaronson [Aar05], who asked if AC^0 and TC^0 can be PAC-learned in quantum polynomial time.
Revised:  This gives a strong (conditional) negative answer to one of the "Ten Semi-Grand Challenges for Quantum Computing Theory" raised by Aaronson [Aar05], who asked if AC^0 and TC^0 can be PAC-learned in quantum polynomial time.
Edit intent: fluency
Original:  For instance, 3GPP released its first specification on VR to enable 360-degree video streaming over 5G networks while relying on several technologies specified in ISO/IEC 23090-2, also known as MPEG-OMAF.
Revised:  For instance, 3GPP released its first VR specification to enable 360-degree video streaming over 5G networks while relying on several technologies specified in ISO/IEC 23090-2, also known as MPEG-OMAF.
Edit intent: clarity
Original:  For instance, 3GPP released its first specification on VR to enable 360-degree video streaming over 5G networks while relying on several technologies specified in ISO/IEC 23090-2, also known as MPEG-OMAF.
Revised:  For instance, 3GPP released its first specification on VR to enable 360-degree video streaming over 5G networks which relies on several technologies specified in ISO/IEC 23090-2, also known as MPEG-OMAF.
Edit intent: coherence
Original:  While some implementations of OMAF-compatible players have already been demonstrated at several trade shows, we have not yet seen any implementations of viewport-dependent media profile in a web browser .
Revised:  While some implementations of OMAF-compatible players have already been demonstrated at several trade shows, so far, no web browser-based implementations have been presented .
Edit intent: clarity
Original:  In this demo paper we describe how we implemented the most advanced media profile from OMAF: HEVC-based viewport-dependent OMAF video profile  with multi-resolution HEVC-tiles, using only JavaScript .
Revised:  In this demo paper we describe how we implemented the most advanced media profile of OMAF: HEVC-based viewport-dependent OMAF video profile with multi-resolution HEVC-tiles, using only JavaScript .
Edit intent: clarity
Original:  In this demo paper we describe how we implemented the most advanced media profile from OMAF: HEVC-based viewport-dependent OMAF video profile  with multi-resolution HEVC-tiles, using only JavaScript .
Revised:  In this demo paper we describe how we implemented the most advanced media profile from OMAF: HEVC-based viewport-dependent OMAF video profile with multi-resolution HEVC tiles .
Edit intent: coherence
Original:  We also describe how to overcome certain missing features that HTML5 browsers do not provide today to fully support OMAF.
Revised:  We also describe the applied workarounds for the implementation challenges we encountered with state-of-the-art HTML5 browsers do not provide today to fully support OMAF.
Edit intent: clarity
Original:  The implementation was tested on Safari browser with support of HEVC video through  HTML5 Media Source Extensions API.
Revised:  The implementation was tested in the Safari browser with support of HEVC video through HTML5 Media Source Extensions API.
Edit intent: fluency
Original:  The implementation was tested on Safari browser with support of HEVC video through  HTML5 Media Source Extensions API.
Revised:  The implementation was tested on Safari browser with support of HEVC video through the HTML5 Media Source Extensions API.
Edit intent: fluency
Original:  In addition, the WebGL API is used for rendering, using region-wise packing metadata  defined in OMAF.
Revised:  In addition, the WebGL API was used for rendering, using region-wise packing metadata defined in OMAF.
Edit intent: fluency
Original:  In addition, the WebGL API is used for rendering, using region-wise packing metadata  defined in OMAF.
Revised:  In addition, the WebGL API is used for rendering, using region-wise packing metadata as defined in OMAF.
Edit intent: clarity
Original:  We provide an exact algorithm of O(m^2 \log n) time by showing the connection of agony to the capacitated circulation problem .
Revised:  We solve the problem by showing the connection of agony to the capacitated circulation problem .
Edit intent: clarity
Original:  We provide an exact algorithm of O(m^2 \log n) time by showing the connection of agony to the capacitated circulation problem .
Revised:  We provide an exact algorithm of O(m^2 \log n) time by showing the connection to the capacitated circulation problem .
Edit intent: clarity
Original:  We propose a machine learning algorithm, based on deep artificial neural networks, that learns the underlying input parameters to observable map from a few training samples (computed realizations of this map).
Revised:  We propose a machine learning algorithm, based on deep artificial neural networks, that predicts the underlying map from a few training samples (computed realizations of this map).
Edit intent: clarity
Original:  We propose a machine learning algorithm, based on deep artificial neural networks, that learns the underlying input parameters to observable map from a few training samples (computed realizations of this map).
Revised:  We propose a machine learning algorithm, based on deep artificial neural networks, that learns the underlying input parameters to observableinput parameters to observable map from a few training samples (computed realizations of this map).
Edit intent: fluency
Original:  Numerical experiments for realistic high dimensional test problems, demonstrate that even with approximately 100 training samples, the resulting neural networks have a prediction error of less than one to two percent, at a computational cost which is several orders of magnitude lower than the cost of the underlying PDE solver.
Revised:  Numerical experiments are presented to demonstrate low prediction errors for the trained network networks, even when the network has been trained with a few samples, at a computational cost which is several orders of magnitude lower than the cost of the underlying PDE solver.
Edit intent: clarity
Original:  Numerical experiments for realistic high dimensional test problems, demonstrate that even with approximately 100 training samples, the resulting neural networks have a prediction error of less than one to two percent, at a computational cost which is several orders of magnitude lower than the cost of the underlying PDE solver.
Revised:  Numerical experiments for realistic high dimensional test problems, demonstrate that even with approximately 100 training samples, the resulting neural networks have a prediction error of less than one to two percent, at a computational cost which is several orders of magnitude lower than the underlying PDE solver.
Edit intent: clarity
Original: We devise a method to obtain a robust estimate of forces in a heterogeneous environment based on experimentally recorded  trajectories.
Revised: We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded trajectories.
Edit intent: clarity
Original:  Here, the observed force includes a "spurious" force term due to heterogeneous diffusivity .
Revised:  Here, the observed drift includes a "spurious" force term due to heterogeneous diffusivity .
Edit intent: clarity
Original:  We show how Bayesian inference can be leveraged to reliably infer forces by taking into account various noise sources including such spurious forces  .
Revised:  We show how Bayesian inference can be leveraged to reliably infer forces by taking into account such spurious forces .
Edit intent: clarity
Original:  The method is based on the marginalization of the force posterior over all possible spurious force contributions.
Revised:  The method is based on marginalizing the force posterior over all possible spurious force contributions.
Edit intent: clarity
Original:  in O\left( 1{B}\frac{M{B}} N{B} \right) amortized I/Os , operation Extract-Min  in O\left( \lceil M^{\varepsilon}{B} \frac{M{B}} N{B} \rceil  \right) amortized I/Os and operation Delete in O%DIFDELCMD < \left({%%% \frac{M^{\varepsilon}{B}\log^2_{M{B}} N{B}}%DIFDELCMD < }\right) %DIFDELCMD < %%% amortized I/Os, for any real \varepsilon \in \left(0,1\right), using O\left( N{B}\frac{M{B}} N{B} \right) blocks.
Revised:  in O\left( 1{B}\frac{M{B}} N{B} \right) amortized I/Os and operations Extract-Min in O\left( \lceil M^{\varepsilon}{B} \frac{M{B}} N{B} \rceil \right) amortized I/Os and operation Delete in O%DIFDELCMD < \left({%%% \frac{M^{\varepsilon}{B}\log^2_{M{B}} N{B}}%DIFDELCMD < }\right) %DIFDELCMD < %%% amortized I/Os, for any real \varepsilon \in \left(0,1\right), using O\left( N{B}\frac{M{B}} N{B} \right) blocks.
Edit intent: fluency
Original:  in O\left( 1{B}\frac{M{B}} N{B} \right) amortized I/Os , operation Extract-Min  in O\left( \lceil M^{\varepsilon}{B} \frac{M{B}} N{B} \rceil  \right) amortized I/Os and operation Delete in O%DIFDELCMD < \left({%%% \frac{M^{\varepsilon}{B}\log^2_{M{B}} N{B}}%DIFDELCMD < }\right) %DIFDELCMD < %%% amortized I/Os, for any real \varepsilon \in \left(0,1\right), using O\left( N{B}\frac{M{B}} N{B} \right) blocks.
Revised:  in O\left( 1{B}\frac{M{B}} N{B} \right) amortized I/Os , operation Extract-Min in O\left( \lceil M^{\varepsilon}{B} \frac{M{B}} N{B} \rceil \right) %DIFDELCMD < \left({%%% \frac{M^{\varepsilon}{B}\log^2_{M{B}} N{B}}%DIFDELCMD < }\right) %DIFDELCMD < %%% amortized I/Os, for any real \varepsilon \in \left(0,1\right), using O\left( N{B}\frac{M{B}} N{B} \right) blocks.
Edit intent: coherence
Original:  in O\left( 1{B}\frac{M{B}} N{B} \right) amortized I/Os , operation Extract-Min  in O\left( \lceil M^{\varepsilon}{B} \frac{M{B}} N{B} \rceil  \right) amortized I/Os and operation Delete in O%DIFDELCMD < \left({%%% \frac{M^{\varepsilon}{B}\log^2_{M{B}} N{B}}%DIFDELCMD < }\right) %DIFDELCMD < %%% amortized I/Os, for any real \varepsilon \in \left(0,1\right), using O\left( N{B}\frac{M{B}} N{B} \right) blocks.
Revised:  in O\left( 1{B}\frac{M{B}} N{B} \right) amortized I/Os , operation Extract-Min in O\left( \lceil M^{\varepsilon}{B} \frac{M{B}} N{B} \rceil \right) amortized I/Os and operation Delete in O%DIFDELCMD < \left({%%% }{B}\log^2_{M{B}} N{B}}%DIFDELCMD < }\right) %DIFDELCMD < %%% amortized I/Os, for any real \varepsilon \in \left(0,1\right), using O\left( N{B}\frac{M{B}} N{B} \right) blocks.
Edit intent: fluency
Original:  Previous I/O-efficient priority queues either support these operations in O\left( 1{B}\log_2 \frac{N}{B} \right) amortized I/Os [Kumar and Schwabe, SPDP '96] , or support only operations Insert, Delete and Extract-Min in optimal O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) amortized I/Os, however without supporting Decrease-Key [Fadel et al., TCS '99].
Revised:  Previous I/O-efficient priority queues either support these operations in O\left( 1{B}\log_2 \frac{N}{B} \right) amortized I/Os [Kumar and Schwabe, SPDP '96] or support only operations Insert, Delete and Extract-Min in optimal O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) amortized I/Os, however without supporting Decrease-Key [Fadel et al., TCS '99].
Edit intent: fluency
Original:  We also present buffered repository trees that support on a multi-set of N elements, operations Insert and Extract (on K extracted elements) in O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) and O\left( %DIFDELCMD < {%%%  \log_{\frac{M}{B}} \frac{N}{B} + K/B %DIFDELCMD < }%%% \right) amortized I/Os, respectively, using O \left( %DIFDELCMD < {%%% \frac{N \right) blocks.
Revised:  We also present buffered repository trees that support on a multi-set of N elements, operation Insert in O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) and O\left( %DIFDELCMD < {%%% \log_{\frac{M}{B}} \frac{N}{B} + K/B %DIFDELCMD < }%%% \right) amortized I/Os, respectively, using O \left( %DIFDELCMD < {%%% \frac{N \right) blocks.
Edit intent: clarity
Original:  We also present buffered repository trees that support on a multi-set of N elements, operations Insert and Extract (on K extracted elements) in O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) and O\left( %DIFDELCMD < {%%%  \log_{\frac{M}{B}} \frac{N}{B} + K/B %DIFDELCMD < }%%% \right) amortized I/Os, respectively, using O \left( %DIFDELCMD < {%%% \frac{N \right) blocks.
Revised:  We also present buffered repository trees that support on a multi-set of N elements, operations Insert and Extract (on K extracted elements) in O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) and O\left( %DIFDELCMD < {%%% \log_{\frac{M}{B}} \frac{N}{B} + K/B %DIFDELCMD < }%%% \right) amortized I/Os, using O \left( %DIFDELCMD < {%%% \frac{N \right) blocks.
Edit intent: coherence
Original:  We also present buffered repository trees that support on a multi-set of N elements, operations Insert and Extract (on K extracted elements) in O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) and O\left( %DIFDELCMD < {%%%  \log_{\frac{M}{B}} \frac{N}{B} + K/B %DIFDELCMD < }%%% \right) amortized I/Os, respectively, using O \left( %DIFDELCMD < {%%% \frac{N \right) blocks.
Revised:  We also present buffered repository trees that support on a multi-set of N elements, operations Insert and Extract (on K extracted elements) in O\left( \frac{1}{B}\log_{\frac{M}{B}} \frac{N}{B} \right) and O\left( %DIFDELCMD < {%%% \log_{\frac{M}{B}} \frac{N}{B} + K/B %DIFDELCMD < }%%% \right) amortized I/Os, respectively, using O \left( %DIFDELCMD < {%%% \frac{N \right) blocks.
Edit intent: fluency
Original:  This improves upon the previous\left({B}\log_2 \frac{N}{B}}\right) I/ O-bounds that achieve a base-2 logarithm instead\left( {B} + \frac{K}{B}}\right)  [Buchsbaum et al., SODA '00].
Revised:  This improves upon the previous\left({B}\log_2 \frac{N}{B}}\right) I/ Os and O\left( {B} + \frac{K}{B}}\right) [Buchsbaum et al., SODA '00].
Edit intent: clarity
Original:  This improves upon the previous\left({B}\log_2 \frac{N}{B}}\right) I/ O-bounds that achieve a base-2 logarithm instead\left( {B} + \frac{K}{B}}\right)  [Buchsbaum et al., SODA '00].
Revised:  This improves upon the previous\left({B}\log_2 \frac{N}{B}}\right) I/ O-bounds that achieve a base-2 logarithm instead\left( \log_2 \frac{N{B} + \frac{K}{B}}\right) [Buchsbaum et al., SODA '00].
Edit intent: fluency
Original:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right)  = \Omega ( M ^{\varepsilon}%DIFDELCMD < }%%% ) \left( }\right)\left( \right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Revised:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right) with E = \Omega ( M ^{\varepsilon}%DIFDELCMD < }%%% ) \left( }\right)\left( \right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Edit intent: clarity
Original:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right)  = \Omega ( M ^{\varepsilon}%DIFDELCMD < }%%% ) \left( }\right)\left( \right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Revised:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right) = \Omega M ^{\varepsilon}%DIFDELCMD < }%%% ) \left( }\right)\left( \right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Edit intent: fluency
Original:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right)  = \Omega ( M ^{\varepsilon}%DIFDELCMD < }%%% ) \left( }\right)\left( \right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Revised:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right) = \Omega ( M ^{\varepsilon}%DIFDELCMD < }%%% \left( }\right)\left( \right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Edit intent: fluency
Original:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right)  = \Omega ( M ^{\varepsilon}%DIFDELCMD < }%%% ) \left( }\right)\left( \right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Revised:  Our results imply improved O\left( %DIFDELCMD < {%%% \frac{E}{B}\log_{\frac{M}{B}} \frac{E}{B} %DIFDELCMD < }%%% \right) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed graphs with an edge-to-node ratio \frac{E\left(\right) = \Omega ( M ^{\varepsilon}%DIFDELCMD < }%%% ) \left( }\right)\left( M\right) , which is equal to the I/O-optimal bound for sorting E values in external memory.
Edit intent: coherence
Original: We present priority queues in the  external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and Decrease-Key   ) in O \left(1{B} \frac{M{B } N{B}\right)
Revised: We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation UPDATE ) in O \left(1{B} \frac{M{B } N{B}\right)
Edit intent: coherence
Original: We present priority queues in the  external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and Decrease-Key   ) in O \left(1{B} \frac{M{B } N{B}\right)
Revised: We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and Decrease-Key and ) in O \left(1{B} \frac{M{B } N{B}\right)
Edit intent: fluency
Original:  amortized I/Os and operations Extract-Min and Delete  in O \left(\lceil \frac{M^{\varepsilon}{B} \log} }{B} \log} _{ \frac{M } \frac{N}{B} \rceil \log_{ \frac{M } \frac{N}{B}\right)
Revised:  amortized I/Os and operations EXTRACT-MIN in O \left(\lceil \frac{M^{\varepsilon}{B} \log} }{B} \log} _{ \frac{M } \frac{N}{B} \rceil \log_{ \frac{M } \frac{N}{B}\right)
Edit intent: coherence
Original:  amortized I/Os and operations Extract-Min and Delete  in O \left(\lceil \frac{M^{\varepsilon}{B} \log} }{B} \log} _{ \frac{M } \frac{N}{B} \rceil \log_{ \frac{M } \frac{N}{B}\right)
Revised:  amortized I/Os and operations Extract-Min and Delete and in O \left(\lceil \frac{M^{\varepsilon}{B} \log} }{B} \log} _{ \frac{M } \frac{N}{B} \rceil \log_{ \frac{M } \frac{N}{B}\right)
Edit intent: fluency
Original:  amortized I/Os, for any real \varepsilon \in%DIFDELCMD < \left(%%% 0,1%DIFDELCMD < \right)%%% , using O \left(\frac{N}{B}\log_{ \frac{M } \frac{N}{B}\right)
Revised:  amortized I/Os, for any real \varepsilon \in%DIFDELCMD < \left(%%% 0,1%DIFDELCMD < \right)%%% using O \left(\frac{N}{B}\log_{ \frac{M } \frac{N}{B}\right)
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 %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: clarity
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(%%% {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