wanyu/IteraTeR_full_sent huggingface dataset:
Original: In the maximum n-times coverage problem , we are provided a set of elements, a weight for each element, and a set of overlays where each overlay specifies an element specific coverage of zero or more times.
Revised: We introduce the maximum n-times coverage problem , we are provided a set of elements, a weight for each element, and a set of overlays where each overlay specifies an element specific coverage of zero or more times.
Edit intent: coherence
Original: In the maximum n-times coverage problem , we are provided a set of elements, a weight for each element, and a set of overlays where each overlay specifies an element specific coverage of zero or more times. The goal is to select up to k overlays such that the sum of the weights of elements that are covered at least n times is maximized .
Revised: In the maximum n-times coverage problem that selects k overlays to maximize the summed coverage of weighted elements, where each element must be covered at least n times is maximized .
Edit intent: clarity
Original:  We frame the design of a peptide vaccine for COVID-19 as maximum n-times coverage using machine learning defined candidate peptide sets, and show that our solution is superior to 29 other published COVID-19 peptide vaccine designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.
Revised:  We show that maximum n-times coverage using machine learning defined candidate peptide sets, and show that our solution is superior to 29 other published COVID-19 peptide vaccine designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.
Edit intent: clarity
Original:  We frame the design of a peptide vaccine for COVID-19 as maximum n-times coverage using machine learning defined candidate peptide sets, and show that our solution is superior to 29 other published COVID-19 peptide vaccine designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.
Revised:  We frame the design of a peptide vaccine for COVID-19 as maximum n-times coverage is a natural way to frame peptide vaccine design, and find that it produces a pan-strain COVID-19 vaccine design that is superior to 29 other published COVID-19 peptide vaccine designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.
Edit intent: meaning-changed
Original:  We frame the design of a peptide vaccine for COVID-19 as maximum n-times coverage using machine learning defined candidate peptide sets, and show that our solution is superior to 29 other published COVID-19 peptide vaccine designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.
Revised:  We frame the design of a peptide vaccine for COVID-19 as maximum n-times coverage using machine learning defined candidate peptide sets, and show that our solution is superior to 29 other published designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules.
Edit intent: fluency
Original:  The proposed model outperformed all the state-of-the-art methods by achieving the average accuracy of 88.4\% and 88.6\% on the 2008 BCI Competition IV 2a (four-classes) and 2b datasets (binary-classes), respectively.
Revised:  The proposed model outperforms all the state-of-the-art methods by achieving the average accuracy of 88.4\% and 88.6\% on the 2008 BCI Competition IV 2a (four-classes) and 2b datasets (binary-classes), respectively.
Edit intent: fluency
Original:  Moreover, the classification standard deviation for nine different subjects achieved the lowest value of 5.5 for the 2b dataset and 7.1 for the 2a dataset, validating that the proposed method is highly robust.
Revised:  Moreover, the classification standard deviation for nine different subjects achieves the lowest value of 5.5 for the 2b dataset and 7.1 for the 2a dataset, validating that the proposed method is highly robust.
Edit intent: fluency
Original:  Moreover, the classification standard deviation for nine different subjects achieved the lowest value of 5.5 for the 2b dataset and 7.1 for the 2a dataset, validating that the proposed method is highly robust.
Revised:  Moreover, the classification standard deviation for nine different subjects achieved the lowest value of 5.5 for the 2b dataset and 7.1 for the 2a dataset, which validates that the proposed method is highly robust.
Edit intent: coherence
Original:  Optimizing the trade-off between information gain and energy cost (e.g., control effort, energy expenditure, distance travelled) is desirable but leads to a non-monotone objective function in the set of robot trajectories.
Revised:  Optimizing the trade-off between information gain and energy cost (e.g., control effort, distance travelled) is desirable but leads to a non-monotone objective function in the set of robot trajectories.
Edit intent: clarity
Original:  Our results show up to 60\% communication reduction and 80-92\% computation reduction on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy expenditure .
Revised:  Compared to the naive distributed execution of local search, our approach saves up to 60\% communication reduction and 80-92\% computation reduction on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy expenditure .
Edit intent: meaning-changed
Original:  Our results show up to 60\% communication reduction and 80-92\% computation reduction on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy expenditure .
Revised:  Our results show up to 60\% communication and 80--92\% computation on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy expenditure .
Edit intent: clarity
Original:  Our results show up to 60\% communication reduction and 80-92\% computation reduction on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy expenditure .
Revised:  Our results show up to 60\% communication reduction and 80-92\% computation reduction on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy cost .
Edit intent: clarity
Original:  We demonstrate the utility of this framework by applying it to an original dataset of statutes and regulations from two different countries, the United States and Germany, spanning more than twenty years ( 1998--2019 ).
Revised:  We demonstrate the utility of this framework by applying it to an original dataset of statutes and regulations from two different countries, the United States and Germany, spanning more than twenty years ( 1998-2019 ).
Edit intent: fluency
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised:  Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks %DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Edit intent: coherence
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% A k-apex graph is a graph with a subset of k vertices, called apices, whose removal makes the graph planar. We present an O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^2 n \log^3 n)-time algorithm that, given a directed k-apex graph G with n vertices, arc capacities, a set of sources S and a set of sinks T, computes a maximum flow from S to T in G. This improves by a factor of k on the fastest algorithm previously known for this problem ] O(k ^4n \text{ polylog ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog Borradaile et al., FOCS 2012, SICOMP 2017] O(k ^4n \text{ polylog ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ]. Our improvement is achieved by introducing a new variant of the push-relabel algorithm for computing maximum flows. We use our improved algorithm for maximum flow in k-apex graphs, together with additional insights, to obtain an O(k ^4n \text{ polylog ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^3 n \ ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylogpolylog ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog(nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks. This improves by a factor of k^2 over the fastest algorithm previously known for this problem ]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog Wang, SODA 2019]
Edit intent: meaning-changed
Original: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ]
Revised: The most efficient algorithm currently known for computing maximum integer flows in planar graphs with vertex capacities and multiple sources and sinks Wang, SODA 2019%DIFDELCMD < ] %%% runs in O(k ^5n \text{ polylog ] O(k ^4n \text{ polylog ].
Edit intent: fluency
Original:  We design  a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates  with respect to the number of degrees of freedom as well as the computational cost.
Revised:  We design and analyze a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates with respect to the number of degrees of freedom as well as the computational cost.
Edit intent: meaning-changed
Original:  We design  a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates  with respect to the number of degrees of freedom as well as the computational cost.
Revised:  We design a goal-oriented adaptive finite element method , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates with respect to the number of degrees of freedom as well as the computational cost.
Edit intent: clarity
Original:  We design  a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates  with respect to the number of degrees of freedom as well as the computational cost.
Revised:  We design a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method or geometric multigrid . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates with respect to the number of degrees of freedom as well as the computational cost.
Edit intent: meaning-changed
Original:  We design  a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates  with respect to the number of degrees of freedom as well as the computational cost.
Revised:  We design a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates . Unlike prior work, we do not only consider rates with respect to the number of degrees of freedom as well as the computational cost.
Edit intent: meaning-changed
Original:  We design  a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates  with respect to the number of degrees of freedom as well as the computational cost.
Revised:  We design a goal-oriented adaptive finite element method (GOAFEM) , which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG) . We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates with respect to the number of degrees of freedom but even prove optimal complexity, i.e., optimal convergence rates with respect to the total computational cost.
Edit intent: meaning-changed
Original: The Shortest Path Problem, in real-life applications, has to deal with multiple criteria.
Revised: The Shortest Path Problem, in real-life applications, has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such attack over an edge, probabilities that can differ across edges. Furthermore, usage of a single shortest path (for routing) implies possible traffic bottleneck, which should be avoided if possible, which we term pathneck security avoidance.
Edit intent: meaning-changed
Original:  In the second part, we show a polynomial-time algorithm that, given an undirected graph G and a pair of vertices (s,t), finds prioritized multi-criteria 2-disjoint (vertex/edge) shortest  paths between s and t.
Revised:  In the second part, we show a polynomial-time algorithm that, given an undirected graph G and a pair of vertices (s,t), finds prioritized multi-criteria 2-disjoint (vertex/edge) shortest secure paths between s and t.
Edit intent: meaning-changed
Original:  In the third part of the paper, we introduce the k-disjoint all-criteria-shortest  paths problem, which is solved in time O( min (k|E|, |E|^{3/2})).
Revised:  In the third part of the paper, we introduce the k-disjoint all-criteria-shortest secure paths problem, which is solved in time O( min (k|E|, |E|^{3/2})).
Edit intent: meaning-changed
Original:  In the third part of the paper, we introduce the k-disjoint all-criteria-shortest  paths problem, which is solved in time O( min (k|E|, |E|^{3/2})).
Revised:  In the third part of the paper, we introduce the k-disjoint all-criteria-shortest paths problem, which is solved in time O( \min (k|E|, |E|^{3/2})).
Edit intent: meaning-changed
Original: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex (  none, when n = 4) breaking the otherwise fully regular lattice.
Revised: We analyze the problem of quadrangulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex ( none, when n = 4) breaking the otherwise fully regular lattice.
Edit intent: fluency
Original: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex (  none, when n = 4) breaking the otherwise fully regular lattice.
Revised: We analyze the problem of quadtragulating a n-sided patch, each side at its boundary , with a single internal irregular vertex ( none, when n = 4) breaking the otherwise fully regular lattice.
Edit intent: clarity
Original: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex (  none, when n = 4) breaking the otherwise fully regular lattice.
Revised: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary subdivided into a given number of edges, using a single irregular vertex ( none, when n = 4) breaking the otherwise fully regular lattice.
Edit intent: meaning-changed
Original: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex (  none, when n = 4) breaking the otherwise fully regular lattice.
Revised: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex ( or none, when n = 4) breaking the otherwise fully regular lattice.
Edit intent: fluency
Original: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex (  none, when n = 4) breaking the otherwise fully regular lattice.
Revised: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex ( none, when n = 4) that breaks the otherwise fully regular lattice.
Edit intent: clarity
Original:  We derive, in  analytical closed-form, (1) the necessary and sufficient conditions that a patch must meet to admit this quadrangulation, and (2) a full description of the resulting tessellation  .
Revised:  We derive, in an analytical closed-form, (1) the necessary and sufficient conditions that a patch must meet to admit this quadrangulation, and (2) a full description of the resulting tessellation .
Edit intent: fluency
Original:  We derive, in  analytical closed-form, (1) the necessary and sufficient conditions that a patch must meet to admit this quadrangulation, and (2) a full description of the resulting tessellation  .
Revised:  We derive, in analytical closed-form, (1) the necessary and sufficient conditions that a patch must meet to admit this quadrangulation, and (2) a full description of the resulting tessellation (s) .
Edit intent: meaning-changed