wanyu/IteraTeR_v2 huggingface dataset:
Original:  [Social Network Analysis and Mining, 2013] that it is possible to compute an optimal sized target set in O(2^{(2^{t}+1)t}\cdot m) time, where m and t denote the number of edges and the cardinality of a minimum vertex cover, respectively, of the graph under consideration .
Revised:  [Social Network Analysis and Mining, 2013] that it is possible to compute an optimal-sized target set in O(2^{(2^{t}+1)t}\cdot m) time, where m and t denote the number of edges and the cardinality of a minimum vertex cover, respectively, of the graph under consideration .
Edit intent: fluency
Original:  [Social Network Analysis and Mining, 2013] that it is possible to compute an optimal sized target set in O(2^{(2^{t}+1)t}\cdot m) time, where m and t denote the number of edges and the cardinality of a minimum vertex cover, respectively, of the graph under consideration .
Revised:  [Social Network Analysis and Mining, 2013] that it is possible to compute an optimal sized target set in O(2^{(2^{t}+1)t}\cdot m) time, where t denotes the cardinality of a minimum vertex cover, respectively, of the graph under consideration .
Edit intent: clarity
Original:  We improve this result by designing an algorithm that computes an optimal sized target set in 2^{O(t\log t)}n^{O(1)} time, where n denotes the number of vertices of the graph under consideration . - We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% \% On the Approximability of Influence in Social Networks.
Revised:  We improve this result by designing an algorithm running in time 2^{O(t\log t)}n^{O(1)} time, where n denotes the number of vertices of the graph under consideration . - We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% \% On the Approximability of Influence in Social Networks.
Edit intent: clarity
Original:  We improve this result by designing an algorithm that computes an optimal sized target set in 2^{O(t\log t)}n^{O(1)} time, where n denotes the number of vertices of the graph under consideration . - We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% \% On the Approximability of Influence in Social Networks.
Revised:  We improve this result by designing an algorithm that computes an optimal sized target set in 2^{O(t\log t)}n^{O(1)} . - We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% \% On the Approximability of Influence in Social Networks.
Edit intent: clarity
Original:  We improve this result by designing an algorithm that computes an optimal sized target set in 2^{O(t\log t)}n^{O(1)} time, where n denotes the number of vertices of the graph under consideration . - We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% \% On the Approximability of Influence in Social Networks.
Revised:  We improve this result by designing an algorithm that computes an optimal sized target set in 2^{O(t\log t)}n^{O(1)} time, where n denotes the number of vertices of the graph under consideration . - SIDMA, 2009%DIFDELCMD < ] %%% \% On the Approximability of Influence in Social Networks.
Edit intent: coherence
Original:  We improve this result by designing an algorithm that computes an optimal sized target set in 2^{O(t\log t)}n^{O(1)} time, where n denotes the number of vertices of the graph under consideration . - We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% \% On the Approximability of Influence in Social Networks.
Revised:  We improve this result by designing an algorithm that computes an optimal sized target set in 2^{O(t\log t)}n^{O(1)} time, where n denotes the number of vertices of the graph under consideration . - We show that the TSS Problem on bipartite graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O(\log n_{min SIDMA, 2009%DIFDELCMD < ] %%% On the Approximability of Influence in Social Networks.
Edit intent: coherence
Original:  SIAM Journal on Discrete Mathematics, 23(3):1400-1415, 2009%DIFDELCMD < ] %%% had shown that the TSS Problem on general graphs does not admit an approximation algorithm with a performance guarantee asymptotically better than O( 2 ^{\log^{1 - \epsilon n}), where n is the number of vertices of the graph under consideration, unless NP \subseteq DTIME(n^{polylog(n)})}  .
Revised:  SIAM Journal on Discrete Mathematics, 23(3):1400-1415, 2009%DIFDELCMD < ] %%% > We design a 2 ^{\log^{1 - \epsilon n}), where n is the number of vertices of the graph under consideration, unless NP \subseteq DTIME(n^{polylog(n)})} .
Edit intent: coherence
Original:  Proteins may thus acquire a latent potential for allosteric regulation and evolutionary adaptation  .
Revised:  Proteins can thus acquire a latent potential for allosteric regulation and evolutionary adaptation .
Edit intent: clarity
Original:  An elementary physical model is presented that illustrates this evolutionary scenario and its implications.
Revised:  A physical model is presented that illustrates this evolutionary scenario and its implications.
Edit intent: clarity
Original:  Based on minimal assumptions, the model recapitulates and links several well-known features of proteins and makes new predictions amenable to experimental tests .
Revised:  The scenario can be implemented in experiments of protein evolution to directly test its predictions .
Edit intent: clarity
Original: In unsupervised outlier ensembles, the absence of ground truth makes the combination of base  detectors a challenging task.
Revised: In unsupervised outlier ensembles, the absence of ground truth makes the combination of base outlier detectors a challenging task.
Edit intent: clarity
Original:  In this paper, we propose a framework---called Locally Selective Combination in Parallel Outlier Ensembles (LSCP)---which addresses this issue by defining a local region around a test instance using the consensus of its nearest neighbors in randomly generated feature spaces .
Revised:  In this paper, we propose a framework---called Locally Selective Combination in Parallel Outlier Ensembles (LSCP)---which addresses the issue by defining a local region around a test instance using the consensus of its nearest neighbors in randomly generated feature spaces .
Edit intent: fluency
Original:  In this paper, we propose a framework---called Locally Selective Combination in Parallel Outlier Ensembles (LSCP)---which addresses this issue by defining a local region around a test instance using the consensus of its nearest neighbors in randomly generated feature spaces .
Revised:  In this paper, we propose a framework---called Locally Selective Combination in Parallel Outlier Ensembles (LSCP)---which addresses this issue by defining a local region around a test instance using the consensus of its nearest neighbors in randomly selected feature subspaces .
Edit intent: clarity
Original:  Four variants of the LSCP framework are compared with six widely used combination algorithms for parallel ensembles . Experimental results demonstrate that one of these LSCP variantsconsistently outperforms baseline algorithms on the majority of eighteen real-world datasets.
Revised:  Four variants of the LSCP framework are compared with seven widely used parallel frameworks . Experimental results demonstrate that one of these LSCP variantsconsistently outperforms baseline algorithms on the majority of eighteen real-world datasets.
Edit intent: clarity
Original: Optimal sensor and actuator placement is a central challenge in high-dimensional estimation and control.
Revised: Optimal sensor and actuator selection is a central challenge in high-dimensional estimation and control.
Edit intent: clarity
Original:  In this work, we exploit balanced model reduction and greedy optimization to efficiently determine sensor and actuator placements that optimize observability and controllability.
Revised:  In this work, we exploit balanced model reduction and greedy optimization to efficiently determine sensor and actuator selections that optimize observability and controllability.
Edit intent: clarity
Original:  The results are demonstrated on the linearized Ginzburg-Landau system, for which our algorithm approximates well-known optimal placements computed using costly gradient descent methods.
Revised:  The results are demonstrated on the linearized Ginzburg-Landau system, for which our algorithm approximates known optimal placements computed using costly gradient descent methods.
Edit intent: clarity
Original: A set P = H \cup \{w\} of n+1 points in general position in the plane is called a wheel set if all points but w are extreme.
Revised: A set P = H \cup \{w\} of n+1 points in general position in the plane is called a wheel set if all points but w are extreme.
Edit intent: fluency
Original:  We show that for the purpose of counting crossing-free geometric graphs on  P, it suffices to know the so-calledfrequency vector of P.
Revised:  We show that for the purpose of counting crossing-free geometric graphs on P, it suffices to know the frequency vector of P.
Edit intent: clarity
Original:  We show that for the purpose of counting crossing-free geometric graphs on  P, it suffices to know the so-calledfrequency vector of P.
Revised:  We show that for the purpose of counting crossing-free geometric graphs on P, it suffices to know the so-calledfrequency vector of P.
Edit intent: fluency
Original:  We give simple formulas in terms of the frequency vector for the number of crossing-free spanning cycles, matchings, w-embracing triangles , and many more.
Revised:  We give simple formulas in terms of the frequency vector for the number of crossing-free spanning cycles, matchings, triangulations , and many more.
Edit intent: clarity
Original:  Based on these formulas , the corresponding numbers of graphs can be computed efficiently.
Revised:  Based on that , the corresponding numbers of graphs can be computed efficiently.
Edit intent: clarity
Original:  While the concept of frequency vectors does not generalize easily, we show how to apply similar methods in higher dimensions .
Revised:  While the concept of frequency vectors does not generalize easily, we show how to use similar ideas in R^d for any fixed d .
Edit intent: clarity
Original: The diameter , vertex eccentricities, and the radius of a graph are some of the most fundamental graph parameters.
Revised: The diameter of a graph are some of the most fundamental graph parameters.
Edit intent: clarity
Original:  Roditty and Williams STOC 2013%DIFDELCMD < ] %%% gave an O(mn) time algorithm for computing a 1.5 approximation of graph diameter.
Revised:  Roditty and Williams %DIFDELCMD < ] %%% gave an O(mn) time algorithm for computing a 1.5 approximation of graph diameter.
Edit intent: clarity
Original:  Backurs et al. }%DIFDELCMD < [%%% STOC 2018 gave an%DIFDELCMD < \tilde %%% O(m\sqrt{n) time algorithm for computing 2-approximation of eccentricities.
Revised:  Backurs et al. }%DIFDELCMD < [%%% gave an%DIFDELCMD < \tilde %%% O(m\sqrt{n) time algorithm for computing 2-approximation of eccentricities.
Edit intent: clarity
Original:  Backurs et al. }%DIFDELCMD < [%%% STOC 2018 gave an%DIFDELCMD < \tilde %%% O(m\sqrt{n) time algorithm for computing 2-approximation of eccentricities.
Revised:  Backurs et al. }%DIFDELCMD < [%%% STOC 2018 %DIFDELCMD < \tilde %%% O(m\sqrt{n) time algorithm for computing 2-approximation of eccentricities.
Edit intent: clarity
Original:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter-spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex  directed graph G  we can compute a sparse subgraph H which is a (1.5) -diameter-spanner of Gand contains at most \tilde O(n^{1.5}) edges.
Revised:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex directed graph G we can compute a sparse subgraph H which is a (1.5) -diameter-spanner of Gand contains at most \tilde O(n^{1.5}) edges.
Edit intent: fluency
Original:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter-spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex  directed graph G  we can compute a sparse subgraph H which is a (1.5) -diameter-spanner of Gand contains at most \tilde O(n^{1.5}) edges.
Revised:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter-spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex directed graph G , we can compute a sparse subgraph H which is a (1.5) -diameter-spanner of Gand contains at most \tilde O(n^{1.5}) edges.
Edit intent: fluency
Original:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter-spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex  directed graph G  we can compute a sparse subgraph H which is a (1.5) -diameter-spanner of Gand contains at most \tilde O(n^{1.5}) edges.
Revised:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter-spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex directed graph G we can compute a sparse subgraph H that is a (1.5) -diameter-spanner of Gand contains at most \tilde O(n^{1.5}) edges.
Edit intent: fluency
Original:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter-spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex  directed graph G  we can compute a sparse subgraph H which is a (1.5) -diameter-spanner of Gand contains at most \tilde O(n^{1.5}) edges.
Revised:  Given a graph G=(V,E), a subgraph H=(V, E0 ) is defined to be a %DIFDELCMD < {\em %%% t-diameter-spanner if the diameter of H is at most t times the diameter of G. We show that for any n-vertex directed graph G we can compute a sparse subgraph H which is a (1.5) -diameter spanner of G, such that H contains at most \tilde O(n^{1.5}) edges.
Edit intent: clarity
Original:  The intercell flux is obtained using additional degrees of freedom distributed along the  boundary.
Revised:  The intercell flux is obtained using additional degrees of freedom distributed along the cell boundary.
Edit intent: fluency
Original:  Although recent attempts at formulating generative models of video have had some success, current progress is hampered by (1) the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples, and (2) the wide gap between purely synthetic video datasets and challenging real-world datasets in terms of complexity.
Revised:  While recent attempts at formulating generative models of video have had some success, current progress is hampered by (1) the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples, and (2) the wide gap between purely synthetic video datasets and challenging real-world datasets in terms of complexity.
Edit intent: fluency
Original:  Although recent attempts at formulating generative models of video have had some success, current progress is hampered by (1) the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples, and (2) the wide gap between purely synthetic video datasets and challenging real-world datasets in terms of complexity.
Revised:  Although recent attempts at formulating generative models of video have had some success, current progress is hampered by (1) the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples, and (2) the wide gap between purely synthetic video data sets and challenging real-world datasets in terms of complexity.
Edit intent: clarity
Original:  Although recent attempts at formulating generative models of video have had some success, current progress is hampered by (1) the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples, and (2) the wide gap between purely synthetic video datasets and challenging real-world datasets in terms of complexity.
Revised:  Although recent attempts at formulating generative models of video have had some success, current progress is hampered by (1) the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples, and (2) the wide gap between purely synthetic video datasets and challenging real-world data sets in terms of complexity.
Edit intent: clarity
Original:  To this extent we propose Fr\'echet Video Distance (FVD), a new metric for generative models of video based on FID , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the capabilities of the current iteration of generative models for video.
Revised:  To this extent we propose Fr\'{e Video Distance (FVD), a new metric for generative models of video based on FID , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the capabilities of the current iteration of generative models for video.
Edit intent: fluency
Original:  To this extent we propose Fr\'echet Video Distance (FVD), a new metric for generative models of video based on FID , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the capabilities of the current iteration of generative models for video.
Revised:  To this extent we propose Fr\'echet Video Distance (FVD), a new metric for generative models of video , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the capabilities of the current iteration of generative models for video.
Edit intent: clarity
Original:  To this extent we propose Fr\'echet Video Distance (FVD), a new metric for generative models of video based on FID , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the capabilities of the current iteration of generative models for video.
Revised:  To this extent we propose Fr\'echet Video Distance (FVD), a new metric for generative models of video based on FID , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the current capabilities of generative models of the current iteration of generative models for video.
Edit intent: fluency
Original:  To this extent we propose Fr\'echet Video Distance (FVD), a new metric for generative models of video based on FID , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the capabilities of the current iteration of generative models for video.
Revised:  To this extent we propose Fr\'echet Video Distance (FVD), a new metric for generative models of video based on FID , and StarCraft 2 Videos (SCV), a collection of progressively harder datasets that challenge the capabilities of video.
Edit intent: clarity
Original:  We conduct a large-scale human study, which confirms that FVD correlates well with qualitative human judgment of generated videos, and provide initial benchmark results on SCV.
Revised:  We contribute a large-scale human study, which confirms that FVD correlates well with qualitative human judgment of generated videos, and provide initial benchmark results on SCV.
Edit intent: clarity
Original:  Preliminary results demonstrate that 8-bit posit has better accuracy that 8-bit fixed or floating-point for three different low-dimensional datasets.
Revised:  Preliminary results demonstrate that 8-bit posit has better accuracy than 8-bit fixed or floating-point for three different low-dimensional datasets.
Edit intent: fluency
Original:  Moreover, the accuracy is comparable to 32-bit floating-point on a Xilinx Virtex-7 FGPA device.
Revised:  Moreover, the accuracy is comparable to 32-bit floating-point on a Xilinx Virtex-7 FPGA device.
Edit intent: fluency
Original:  The trade-offs between DNN performance and hardware resources, i.e. latency, power, and resource utilization, show that posit outperforms in accuracy and latency at 8-bit and below.
Revised:  The trade-offs between DNN performance and hardware resources, i.e. latency, power, and resource utilization, show that posit outperforms in accuracy and latency at 8-bit and below.
Edit intent: fluency
Original:  The input is an asymmetric metric (V,c), root r  \in V, monotone submodular function f:2^V \xrightarrow{ R_+ and budget B.
Revised:  The input is an asymmetric metric (V,c), root r \in V, monotone submodular function f:2^V \rightarrow R_+ and budget B.
Edit intent: fluency
Original:  Our main result is a  quasi-polynomial time O(\frac{\log k}{\log\log k})-approximation algorithm for this problem, where k\le |V| is the number of vertices in an optimal solution.
Revised:  Our main result is a simple quasi-polynomial time O(\frac{\log k}{\log\log k})-approximation algorithm for this problem, where k\le |V| is the number of vertices in an optimal solution.
Edit intent: coherence
Original:  As a consequence we obtain a simple O(\log^2 k{\log\log k})-approximation algorithm for directed (polymatroid) Steiner tree in quasi-polynomial time.
Revised:  As a consequence we obtain an O(\log^2 k{\log\log k})-approximation algorithm for directed (polymatroid) Steiner tree in quasi-polynomial time.
Edit intent: clarity
Original:   For the usual directed Steiner tree problem, this matches the best previous result known.
Revised:  For the usual directed Steiner tree problem, our result matches the best previous result known.
Edit intent: clarity
Original:  For the polymatroid generalization ] , our result improves prior results by a logarithmic factor.
Revised:  For the polymatroid generalization ] , our result improves prior approximation ratios by a logarithmic factor.
Edit intent: clarity
Original:  Our approximation ratiois tight for quasi-polynomial algorithms under certain complexity assumptions .
Revised:  Our approximation ratiois tight for quasi-polynomial algorithms .
Edit intent: clarity
Original: The derivatives of differential equation solutions are commonly used as model diagnostics and as part of parameter estimation routines .
Revised: Derivatives of differential equation solutions are commonly used as model diagnostics and as part of parameter estimation routines .
Edit intent: clarity
Original:  In this manuscript we investigate an implementation of Discrete local Sensitivity Analysis via Automatic Differentiation (DSAAD)  . A non-stiff Lotka-Volterra model, a discretization of the two dimensional (N \times N) Brusselator stiff reaction-diffusion PDE , a stiff non-linear air pollution and a non-stiff pharmacokinetic/pharmacodynamic (PK/PD) model were used as prototype models for this investigation.
Revised:  In this manuscript we investigate the performance characteristics of Discrete Local Sensitivity Analysis implemented via Automatic Differentiation (DSAAD) . A non-stiff Lotka-Volterra model, a discretization of the two dimensional (N \times N) Brusselator stiff reaction-diffusion PDE , a stiff non-linear air pollution and a non-stiff pharmacokinetic/pharmacodynamic (PK/PD) model were used as prototype models for this investigation.
Edit intent: clarity