wanyu/IteraTeR_v2 huggingface dataset:
Original:  In a seminal paper, Kempe, Kleinberg, and Kumar ( JCSS 2002 ) asked whether, given such a labeled graph, a %DIFDELCMD < {\em %%% sparse subset of edges can always be found that preserves temporal connectivity if the other edges are removed -- we call such subsets%DIFDELCMD < {\em %%% temporal spanners . Recently, Axiotis and Fotakis (ICALP 2016) answered negatively , exhibiting a family of minimally connected temporal graphs with \Omega (n^2) edges .
Revised:  In a seminal paper, Kempe, Kleinberg, and Kumar ( JCSS 2002 ) asked whether, given such a labeled graph, a %DIFDELCMD < {\em %%% sparse subset of edges can always be found that preserves temporal connectivity if the other edges are removed -- we call such subsets%DIFDELCMD < {\em %%% temporal spanners . Recently, Axiotis and Fotakis (ICALP 2016) answered negatively by exhibiting a family of minimally connected temporal graphs with \Omega (n^2) edges .
Edit intent: fluency
Original:  In a seminal paper, Kempe, Kleinberg, and Kumar ( JCSS 2002 ) asked whether, given such a labeled graph, a %DIFDELCMD < {\em %%% sparse subset of edges can always be found that preserves temporal connectivity if the other edges are removed -- we call such subsets%DIFDELCMD < {\em %%% temporal spanners . Recently, Axiotis and Fotakis (ICALP 2016) answered negatively , exhibiting a family of minimally connected temporal graphs with \Omega (n^2) edges .
Revised:  In a seminal paper, Kempe, Kleinberg, and Kumar ( JCSS 2002 ) asked whether, given such a labeled graph, a %DIFDELCMD < {\em %%% sparse subset of edges can always be found that preserves temporal connectivity if the other edges are removed -- we call such subsets%DIFDELCMD < {\em %%% temporal spanners . Recently, Axiotis and Fotakis (ICALP 2016) answered negatively , exhibiting a family of minimally connected temporal graphs with \Omega (n^2) .
Edit intent: clarity
Original:  The natural question then becomes whether sparse spanners can be found in specific classes of dense graphs.
Revised:  The natural question is then whether sparse temporal spanners can always be found in specific classes of dense graphs.
Edit intent: clarity
Original:  The natural question then becomes whether sparse spanners can be found in specific classes of dense graphs.
Revised:  The natural question then becomes whether sparse spanners can be found in some classes of dense graphs.
Edit intent: clarity
Original:  In this article, we settle the question%DIFDELCMD < {\em %%% positively for complete graphs, showing that one can always remove all but o(n ^2)edges, whatever the labels, while preserving temporal connectivity .
Revised:  In this %DIFDELCMD < {\em %%% positively for complete graphs, showing that one can always remove all but o(n ^2)edges, whatever the labels, while preserving temporal connectivity .
Edit intent: clarity
Original:  In this article, we settle the question%DIFDELCMD < {\em %%% positively for complete graphs, showing that one can always remove all but o(n ^2)edges, whatever the labels, while preserving temporal connectivity .
Revised:  In this article, we settle the question%DIFDELCMD < {\em %%% for complete graphs, showing that one can always remove all but o(n ^2)edges, whatever the labels, while preserving temporal connectivity .
Edit intent: coherence
Original:  Then, using a completely different approach, we establish a gradual set of results, showing that a quarter of the edges can be removed, then half of the edges, and eventually { %DIFDELCMD < \em %%% all\choose  } but\lfloor \rfloor  O(n \log n) edges.
Revised:  Then, using a completely different approach, we establish a gradual set of results, showing that a quarter of the edges can be removed, then half of the edges, and eventually { %DIFDELCMD < \em %%% n\choose } but\lfloor \rfloor O(n \log n) edges.
Edit intent: fluency
Original:  Then, using a completely different approach, we establish a gradual set of results, showing that a quarter of the edges can be removed, then half of the edges, and eventually { %DIFDELCMD < \em %%% all\choose  } but\lfloor \rfloor  O(n \log n) edges.
Revised:  Then, using a completely different approach, we establish a gradual set of results, showing that a quarter of the edges can be removed, then half of the edges, and eventually { %DIFDELCMD < \em %%% all\choose } -\lfloor \rfloor O(n \log n) edges.
Edit intent: coherence
Original:  Then, using a completely different approach, we establish a gradual set of results, showing that a quarter of the edges can be removed, then half of the edges, and eventually { %DIFDELCMD < \em %%% all\choose  } but\lfloor \rfloor  O(n \log n) edges.
Revised:  Then, using a completely different approach, we establish a gradual set of results, showing that a quarter of the edges can be removed, then half of the edges, and eventually { %DIFDELCMD < \em %%% all\choose } but\lfloor \rfloor = O(n \log n) edges.
Edit intent: coherence
Original:  Such a labeled graph { %DIFDELCMD < \cal %%% G \em  } =(G,\lambda) is said to be temporally connected if a path exists with non-decreasing times from every vertex to every other vertex.
Revised:  Such a graph is { %DIFDELCMD < \cal %%% G \em } =(G,\lambda) is said to be temporally connected if a path exists with non-decreasing times from every vertex to every other vertex.
Edit intent: clarity
Original:  Such a labeled graph { %DIFDELCMD < \cal %%% G \em  } =(G,\lambda) is said to be temporally connected if a path exists with non-decreasing times from every vertex to every other vertex.
Revised:  Such a labeled graph { %DIFDELCMD < \cal %%% \em } =(G,\lambda) is said to be temporally connected if a path exists with non-decreasing times from every vertex to every other vertex.
Edit intent: clarity
Original:  Such a labeled graph { %DIFDELCMD < \cal %%% G \em  } =(G,\lambda) is said to be temporally connected if a path exists with non-decreasing times from every vertex to every other vertex.
Revised:  Such a labeled graph { %DIFDELCMD < \cal %%% G \em } if a path exists with non-decreasing times from every vertex to every other vertex.
Edit intent: clarity
Original:  In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a sparse {\em  subset of edges can always be found whose labels suffice to preserve temporal connectivity---a temporal spanner {\em  .
Revised:  In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a {\em subset of edges can always be found whose labels suffice to preserve temporal connectivity---a temporal spanner {\em .
Edit intent: clarity
Original:  In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a sparse {\em  subset of edges can always be found whose labels suffice to preserve temporal connectivity---a temporal spanner {\em  .
Revised:  In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a sparse {\em subset of edges always exists whose labels suffice to preserve temporal connectivity---a temporal spanner {\em .
Edit intent: clarity
Original:  In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a sparse {\em  subset of edges can always be found whose labels suffice to preserve temporal connectivity---a temporal spanner {\em  .
Revised:  In a seminal paper, Kempe, Kleinberg, and Kumar (STOC 2000) asked whether, given such a temporal graph, a sparse {\em subset of edges can always be found whose labels suffice to preserve temporal connectivity---a {\em .
Edit intent: fluency
Original:  The natural question is then whether sparse temporal spanners can always be found in some classes of dense graphs.
Edit intent: coherence
Original:  In this paper, we answer this question affirmatively , by showing that if the underlying graph G is a complete graph, then one can always find temporal spanners of density O(n \log n).
Revised:  In this paper, we answer this question affirmatively , by showing that if G is a complete graph, then one can always find temporal spanners of density O(n \log n).
Edit intent: clarity
Original:  In this paper, we answer this question affirmatively , by showing that if the underlying graph G is a complete graph, then one can always find temporal spanners of density O(n \log n).
Revised:  In this paper, we answer this question affirmatively , by showing that if the underlying graph G is a complete graph, then one can always find a temporal spanner of density O(n \log n).
Edit intent: fluency
Original:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Revised:  The n%DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Edit intent: clarity
Original:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Revised:  The best known result for complete graphs so far was that spanners of density %DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Edit intent: fluency
Original:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Revised:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Edit intent: coherence
Original:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Revised:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% 2 %DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Edit intent: coherence
Original:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% n/4%DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Revised:  The best known result for complete graphs so far was that spanners of density n%DIFDELCMD < \choose %%% 2 -%DIFDELCMD < \lfloor %%% %DIFDELCMD < \rfloor %%% = O(n^2) always exist.
Edit intent: coherence
Original:  The proofs are constructive and directly adaptable as an algorithm .
Revised:  The proofs are constructive .
Edit intent: coherence
Original:  In a seminal paper, Kempe, Kleinberg, and Kumar ~ KKK02 asked whether, given such a temporal graph, a {\em sparse} subset of edges always exists whose labels suffice to preserve temporal connectivity---a {\em temporal spanner}.
Revised:  In a seminal paper, Kempe, Kleinberg, and Kumar KKK02 asked whether, given such a temporal graph, a {\em sparse} subset of edges always exists whose labels suffice to preserve temporal connectivity---a {\em temporal spanner}.
Edit intent: fluency
Original:  In a seminal paper, Kempe, Kleinberg, and Kumar ~ KKK02 asked whether, given such a temporal graph, a {\em sparse} subset of edges always exists whose labels suffice to preserve temporal connectivity---a {\em temporal spanner}.
Revised:  In a seminal paper, Kempe, Kleinberg, and Kumar ~ KKK02 asked whether, given such a temporal graph, a {\em sparse} subset of edges always exists whose labels suffice to preserve temporal connectivity -- a {\em temporal spanner}.
Edit intent: fluency
Original:  Axiotis and Fotakis ~ AF16 answered negatively by exhibiting a family of \Theta(n^2)-dense temporal graphs which admit no temporal spanner of density o(n^2).
Revised:  Axiotis and Fotakis AF16 answered negatively by exhibiting a family of \Theta(n^2)-dense temporal graphs which admit no temporal spanner of density o(n^2).
Edit intent: fluency
Original: This paper considers a collaborative tracking control problem using a group of fixed-wing UAVs with constant and non-identical speeds.
Revised: This paper considers a collaborative tracking control problem using a group of fixed-wing unmanned aerial vehicles (UAVs) with constant and non-identical speeds.
Edit intent: clarity
Original:  The dynamics of fixed-wing UAVs are modelled by unicycle-type equations, with nonholonomic constraints by assuming that UAVs fly at constant attitudes in the nominal operation mode.
Revised:  The dynamics of fixed-wing UAVs are modelled by unicycle-type equations, with nonholonomic constraints by assuming that UAVs fly at constant altitudes in the nominal operation mode.
Edit intent: fluency
Original:  Trade-offs  and performance limitations of the target tracking control due to the constant-speed constraint are also discussed in detail.
Revised:  Trade-offs in the controller design and performance limitations of the target tracking control due to the constant-speed constraint are also discussed in detail.
Edit intent: clarity
Original:  The dynamics of fixed-wing UAVs are modelled by unicycle-type equations , with nonholonomic constraints by assuming that UAVs fly at constant altitudes in the nominal operation mode.
Revised:  The dynamics of fixed-wing UAVs are modelled by unicycle-type equations with nonholonomic constraints by assuming that UAVs fly at constant altitudes in the nominal operation mode.
Edit intent: fluency
Original:  The dynamics of fixed-wing UAVs are modelled by unicycle-type equations , with nonholonomic constraints by assuming that UAVs fly at constant altitudes in the nominal operation mode.
Revised:  The dynamics of fixed-wing UAVs are modelled by unicycle-type equations , with nonholonomic constraints , assuming that UAVs fly at constant altitudes in the nominal operation mode.
Edit intent: coherence
Original:  The control focus is on the design of a collective tracking controller such that all fixed-wing UAVs as a group can collaboratively track a desired target's position and velocity.
Revised:  The controller is designed such that all fixed-wing UAVs as a group can collaboratively track a desired target's position and velocity.
Edit intent: clarity
Original:  Experimental results with three fixed-wing UAVs tracking a target rotorcraft are shown to validate the effectiveness and performance of the proposed tracking controllers .
Revised:  Experimental results with three fixed-wing UAVs tracking a target rotorcraft are provided .
Edit intent: clarity
Original:  In this paper  we present an on-line algorithm that partitions posets of width w into w^{O(\log{w})} chains.
Revised:  In this paper , we present an on-line algorithm that partitions posets of width w into w^{O(\log{w})} chains.
Edit intent: fluency
Original: An on-line chain partitioning algorithm receives the vertices of a poset one at a time, and when a vertex is received, irrevocably assigns it to one of the chains.
Revised: An on-line chain partitioning algorithm receives the elements of a poset one at a time, and when a vertex is received, irrevocably assigns it to one of the chains.
Edit intent: clarity
Original: An on-line chain partitioning algorithm receives the vertices of a poset one at a time, and when a vertex is received, irrevocably assigns it to one of the chains.
Revised: An on-line chain partitioning algorithm receives the vertices of a poset one at a time, and when an element is received, irrevocably assigns it to one of the chains.
Edit intent: clarity
Original:  Unfortunately, state of the art acoustic radiation force techniques  are limited to high end ultrasound hardware due to high power requirements , are extremely sensitive to patient and sonographer motion  and generally suffer from low frame rates.
Revised:  Unfortunately, state of the art acoustic radiation force techniques are limited to high end ultrasound hardware due to high power requirements ; are extremely sensitive to patient and sonographer motion and generally suffer from low frame rates.
Edit intent: fluency
Original:  Unfortunately, state of the art acoustic radiation force techniques  are limited to high end ultrasound hardware due to high power requirements , are extremely sensitive to patient and sonographer motion  and generally suffer from low frame rates.
Revised:  Unfortunately, state of the art acoustic radiation force techniques are limited to high end ultrasound hardware due to high power requirements , are extremely sensitive to patient and sonographer motion ; and generally suffer from low frame rates.
Edit intent: fluency
Original:  Using pressure waves removes the need for generating shear waves, in turn, enabling elasticity based diagnostic techniques on portable and low cost devices.
Revised:  Using pressure waves removes the need for generating shear waves, which in turn enables elasticity based diagnostic techniques on portable and low cost devices.
Edit intent: coherence
Original:  However, current travel time tomography and full waveform inversion techniques for recovering pressure wave velocities , require a full circumferential field of view.
Revised:  However, current travel time tomography and full waveform inversion techniques for recovering pressure wave velocities require a full circumferential field of view.
Edit intent: fluency
Original:  Focus based techniques  on the other hand  provide only localized measurements, and are sensitive to the intermediate medium  .
Revised:  Focus based techniques , on the other hand provide only localized measurements, and are sensitive to the intermediate medium .
Edit intent: fluency
Original:  Focus based techniques  on the other hand  provide only localized measurements, and are sensitive to the intermediate medium  .
Revised:  Focus based techniques on the other hand , provide only localized measurements, and are sensitive to the intermediate medium .
Edit intent: fluency
Original:  Focus based techniques  on the other hand  provide only localized measurements, and are sensitive to the intermediate medium  .
Revised:  Focus based techniques on the other hand provide only localized measurements, are sensitive to the intermediate medium .
Edit intent: coherence
Original:  This is the first step towards a full waveform solver using a deep learning framework for the elastic and viscoelastic inverse problem.
Revised:  This is the first step towards a full waveform solver using a Deep Learning framework for the elastic and viscoelastic inverse problem.
Edit intent: fluency
Original:  Ultrasound elastography is gaining traction as an accessible and useful diagnostic tool for such things as cancer detection and differentiation as well as liver and thyroid disease diagnostics.
Revised: Objective: Ultrasound elastography is gaining traction as an accessible and useful diagnostic tool for such things as cancer detection and differentiation as well as liver and thyroid disease diagnostics.
Edit intent: clarity
Original:  Ultrasound elastography is gaining traction as an accessible and useful diagnostic tool for such things as cancer detection and differentiation as well as liver and thyroid disease diagnostics.
Revised:  Ultrasound elastography is gaining traction as an accessible and useful diagnostic tool for such things as cancer detection and differentiation and thyroid disease diagnostics.
Edit intent: coherence
Original:  Researchers have shown that pressure wave velocity possesses similar diagnostic abilities to shear wave velocity.
Revised:  Researchers have shown that pressure wave velocity carries similar diagnostic abilities to shear wave velocity.
Edit intent: clarity
Original:  Unfortunately, state of the art shear wave imaging techniques, essential to promote this goal, are limited to high end ultrasound hardware due to high power requirements;
Revised:  Unfortunately, state of the art shear wave imaging techniques, essential to promote this goal, are limited to high-end ultrasound hardware due to high power requirements;
Edit intent: fluency
Original:  Methods: In this paper, we present a single sided sound speed inversion solution using a fully convolutional deep neural network.
Revised:  Methods: In this paper, we present a single-sided sound speed inversion solution using a fully convolutional deep neural network.
Edit intent: fluency
Original:  We use simulations for training, allowing the generation of large volumes of ground truth data.
Revised:  We use simulations for training, allowing the generation of limitless ground truth data.
Edit intent: clarity
Original:  Results: We show that it is possible to invert for longitudinal sound speed in soft tissue at super real time frame rates.
Revised:  Results: We show that it is possible to invert for longitudinal sound speed in soft tissue at high frame rates.
Edit intent: clarity
Original:  Our method shows exceptional results on simulated data , and highly encouraging initial results on real data.
Revised:  We validate the method on simulated data , and highly encouraging initial results on real data.
Edit intent: clarity
Original:  Our method shows exceptional results on simulated data , and highly encouraging initial results on real data.
Revised:  Our method shows exceptional results on simulated data . We present highly encouraging results on limited real data.
Edit intent: clarity
Original:  Utilizing pressure sound speed and deep learning technologies , brings the same quality diagnostic abilities to low power devices at real time frame rates.
Revised:  longitudinal sound speed and deep learning technologies , brings the same quality diagnostic abilities to low power devices at real time frame rates.
Edit intent: coherence
Original:  We further regulate the inferences made by the neural network through a simple ` sanity check' routine, which guarantees both flow rate admissibility within the network's capacity region and minimum service levels.
Revised:  We further regulate the inferences made by the neural network through a simple ' sanity check' routine, which guarantees both flow rate admissibility within the network's capacity region and minimum service levels.
Edit intent: fluency
Original:  To do so, we propose a class of regularizations we call \textit{Graph Spectral Regularizations that impose graph structure on latent layers.
Revised:  To do so, we propose a class of regularizations we call \textit{Graph Spectral Regularizations that impose graph structure on latent layers.
Edit intent: fluency
Original:  Here we propose a novel class of Graph Spectral Regularizations for making hidden layers interpretable --- and even informative of phenotypic state space.
Revised:  Here we propose Graph Spectral Regularization for making hidden layers interpretable --- and even informative of phenotypic state space.
Edit intent: clarity
Original:  This regularization uses a graph Laplacian and encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data itself via co-activations of a hidden layer of the neural network.
Revised:  This regularization uses a graph Laplacian that encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data itself via co-activations of a hidden layer of the neural network.
Edit intent: fluency
Original:  This regularization uses a graph Laplacian and encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data itself via co-activations of a hidden layer of the neural network.
Revised:  This regularization uses a graph Laplacian and encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data via co-activations of a hidden layer of the neural network.
Edit intent: clarity
Original:  We show numerous uses for this including 1) cluster indication 2) trajectory finding and 3) visualization in biological and image data sets.
Revised:  We show numerous uses for this including cluster indication and visualization in biological and image data sets.
Edit intent: clarity