wanyu/IteraTeR_full_sent huggingface dataset:
Original:  This problem was introduced by Funke, Krumpe, and Storandt IWOCA 2016 . We provide the first general subquadratic algorithm for computing the times and the order of disappearance.
Revised:  This problem was introduced by Funke, Krumpe, and Storandt The goal is to determine the elimination order, i.e., the order in which the disks disappear . We provide the first general subquadratic algorithm for computing the times and the order of disappearance.
Edit intent: meaning-changed
Original:  This problem was introduced by Funke, Krumpe, and Storandt IWOCA 2016 . We provide the first general subquadratic algorithm for computing the times and the order of disappearance. This algorithm also works for other shapes ( such as rectangles)and in any fixed dimension.
Revised:  This problem was introduced by Funke, Krumpe, and Storandt IWOCA 2016 . We provide the first general subquadratic algorithm for this problem. Our solution extends to other shapes ( such as rectangles)and in any fixed dimension.
Edit intent: clarity
Original:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Revised:  We also describe an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Edit intent: clarity
Original:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Revised:  Using quadtrees, we provide an alternative algorithm that is based on quadtrees. Its running time is O\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Edit intent: meaning-changed
Original:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Revised:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(n\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Edit intent: meaning-changed
Original:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Revised:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\log n + \min \{ \log \Delta, \log \Phi \}\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Edit intent: meaning-changed
Original:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Revised:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big), where \Delta is the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Edit intent: meaning-changed
Original:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them).
Revised:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest and the slowest growth rate and \Phi is the ratio of the maximum to the minimum distance between them).
Edit intent: meaning-changed
Original:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them). Our result improves the running times of previous algorithms by Funke, Krumpe, and Storandt [IWOCA 2016], Bahrdt et al.
Revised:  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the largest and the smallest distance between two disk centers. This improves the running times of previous algorithms by Funke, Krumpe, and Storandt [IWOCA 2016], Bahrdt et al.
Edit intent: clarity
Original: We devise  dynamic algorithms for the following (weak ) visibility polygon computation problems: * Maintaining visibility polygon of a fixed point located interior to  simple polygon amid vertex insertions and deletions to  simple polygon.
Revised: We devise dynamic algorithms for both maintaining as well as querying for the visibility and weak visibility polygons amid vertex insertions and/or deletions to the simple polygon. * Maintaining visibility polygon of a fixed point located interior to simple polygon amid vertex insertions and deletions to simple polygon.
Edit intent: meaning-changed
Original: We devise  dynamic algorithms for the following (weak ) visibility polygon computation problems: * Maintaining visibility polygon of a fixed point located interior to  simple polygon amid vertex insertions and deletions to  simple polygon.
Revised: We devise dynamic algorithms for the following (weak ) visibility polygon computation problems: * A fully-dynamic algorithm for maintaining the visibility polygon of a fixed point located interior to simple polygon amid vertex insertions and deletions to simple polygon.
Edit intent: meaning-changed
Original:   * Answering visibility polygon query corresponding to any point located exterior to simple polygon amid vertex insertions and deletions to  simple polygon.
Revised:  The time complexity to update the visibility polygon of a point q due to the insertion (resp. deletion) of vertex v to (resp. from) the current simple polygon is expressed in terms of the number of combinatorial changes needed to the visibility polygon of q due to the insertion (resp. deletion) of v. * Answering visibility polygon query corresponding to any point located exterior to simple polygon amid vertex insertions and deletions to simple polygon.
Edit intent: meaning-changed
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  If p is not exterior to the current simple polygon then the visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any line segment located interior to simple polygon amid both vertex insertions and deletions to simple polygon.
Edit intent: meaning-changed
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  * Maintaining weak visibility polygon of p is computed. Otherwise, our algorithm outputs the visibility polygon corresponding to the exterior visibility of p . * Answering weak visibility polygon query corresponding to any line segment located interior to simple polygon amid both vertex insertions and deletions to simple polygon.
Edit intent: meaning-changed
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * An output-sensitive algorithm to compute the weak visibility polygon query corresponding to any line segment located interior to simple polygon amid both vertex insertions and deletions to simple polygon.
Edit intent: meaning-changed
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon corresponding to any line segment located interior to simple polygon amid both vertex insertions and deletions to simple polygon.
Edit intent: clarity
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any query line segment located interior to simple polygon amid both vertex insertions and deletions to simple polygon.
Edit intent: meaning-changed
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any line segment located interior to the simple polygon amid both vertex insertions and deletions to simple polygon.
Edit intent: clarity
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any line segment located interior to simple polygon amid both the vertex insertions and deletions to simple polygon.
Edit intent: fluency
Original:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
Revised:  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any line segment located interior to simple polygon amid both vertex insertions and deletions to the simple polygon.
Edit intent: fluency
Original:  * Maintaining visibility polygon of a fixed point located in the free space of the polygonal domain amid vertex insertions to simple polygons in that polygonal domain. The proposed algorithms are output-sensitive, and the time complexities of algorithms for (weak) visibility polygon maintenance are expressed in terms of change in output complexity .
Revised:  Each of these algorithms require preprocessing the initial simple polygon. And, the algorithms that maintain the visibility polygon (resp. weak visibility polygon) compute the visibility polygon (resp. weak visibility polygon) with respect to the initial simple polygon during the preprocessing phase .
Edit intent: clarity
Original: In the  circle packing problem for triangular containers , one asks whether a given set of circles can be packed into a given triangle . Packing problems like this have been shown to be NP-hard.
Revised: In the classic circle packing problem for triangular containers , one asks whether a given set of circles can be packed into a given triangle . Packing problems like this have been shown to be NP-hard.
Edit intent: meaning-changed
Original:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
Revised:  In this paper, we present new sufficient conditions for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
Edit intent: fluency
Original:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
Revised:  In this paper, we present a new sufficient condition for packing circles into square and triangular containers, using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
Edit intent: clarity
Original:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
Revised:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the sum of the circles' areas: For square containers, it is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
Edit intent: meaning-changed
Original:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
Revised:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any set of circles with a combined area of up to approximately 53.90\% of the square's area. And when the container is a right or obtuse triangle, any set of circles whose combined area does not exceed the triangle's incircle .
Edit intent: meaning-changed
Original:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle . This area condition is tight, in the sense that for any larger area , there are instances which cannot be packed.
Revised:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle can be packed. These area conditions are tight, in the sense that for any larger area , there are instances which cannot be packed.
Edit intent: clarity
Original:  A similar result for square containers has been established earlier this year, using the versatile, divide-and-conquer-based Split Packing algorithm.
Revised:  Similar results have long been known for squares, but to the best of our knowledge, we give the first results of this type for circular objects. Our proofs are constructive: We describe a versatile, divide-and-conquer-based Split Packing algorithm.
Edit intent: meaning-changed
Original:  A similar result for square containers has been established earlier this year, using the versatile, divide-and-conquer-based Split Packing algorithm. In this paper, we present a generalized, weighted version of this approach, allowing us to construct packings of circles into asymmetric triangles. It seems crucial to the success of these results that Split Packingdoes not depend on an orthogonal subdivision structure. Beside realizing all packings below the critical density bound, our algorithm can also be used as a constant-factor approximation algorithm when looking for the smallest non-acute triangle of a given side ratio in which a given set of circles can be packed .
Revised:  A similar result for square containers has been established earlier this year, using the versatile, divide-and-conquer-based algorithm for packing circles into various container shapes with optimal worst-case density. It employs an elegant subdivision scheme that recursively splits the circles into two groups and then packs these into subcontainers. We call this algorithm "Split Packing". It can be used as a constant-factor approximation algorithm when looking for the smallest non-acute triangle of a given side ratio in which a given set of circles can be packed .
Edit intent: meaning-changed
Original:  Beside realizing all packings below the critical density bound, our algorithm can also be used as a constant-factor approximation algorithm when looking for the smallest non-acute triangle of a given side ratio in which a given set of circles can be packed .
Revised:  Beside realizing all packings below the critical density bound, our algorithm can also be used as a constant-factor approximation algorithm when looking for the smallest container in which a given set of circles can be packed .
Edit intent: clarity
Original:  Beside realizing all packings below the critical density bound, our algorithm can also be used as a constant-factor approximation algorithm when looking for the smallest non-acute triangle of a given side ratio in which a given set of circles can be packed . An interactive visualization of the Split Packing approach and other related material can be found at URL
Revised:  Beside realizing all packings below the critical density bound, our algorithm can also be used as a constant-factor approximation algorithm when looking for the smallest non-acute triangle of a given side ratio in which a given set of circles can be packed , due to its polynomial runtime. A browser-based, interactive visualization of the Split Packing approach and other related material can be found at URL
Edit intent: meaning-changed
Original: We investigate the dynamical effects of non-Gaussian asymmetric stable L\'evy noisy fluctuations on the evolution of the transcription factor activator in the kinetic concentration model of a single genetic regulation system.
Revised: We investigate the dynamical effects of non-Gaussian asymmetric stable L\'evy fluctuations on the evolution of the transcription factor activator in the kinetic concentration model of a single genetic regulation system.
Edit intent: clarity
Original:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP),  to examine the transition events from low to high concentration state under the influence of L\'evy noise.
Revised:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), in order to examine the transition events from low to high concentration state under the influence of L\'evy noise.
Edit intent: coherence
Original:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP),  to examine the transition events from low to high concentration state under the influence of L\'evy noise.
Revised:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), to examine the likelihood for transcriptions: The mean time scale for the system exits the low concentration state (the longer the exit time, the less likely for transcription) and the switch probability from low concentration states to high concentration state under the influence of L\'evy noise.
Edit intent: meaning-changed
Original:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP),  to examine the transition events from low to high concentration state under the influence of L\'evy noise.We find that the fluctuations of the synthesis reaction rate lead to peculiar transitions to higher concentrations (i.e., higher likelihood for transcriptions)
Revised:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), to examine the transition events from low to high concentration states (corresponding to likelihood for transcription). By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that the fluctuations of the synthesis reaction rate lead to peculiar transitions to higher concentrations (i.e., higher likelihood for transcriptions)
Edit intent: meaning-changed