wanyu/IteraTeR_v2 huggingface dataset:
Original:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil  k + 1. We also\rceil  show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Revised:  For k \geq 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil k + 1. We also\rceil show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Edit intent: clarity
Original:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil  k + 1. We also\rceil  show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Revised:  For k >= 1 we bound the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil k + 1. We also\rceil show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Edit intent: clarity
Original:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil  k + 1. We also\rceil  show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Revised:  For k >= 1 we improve the upper bound on the maximum thickness of semi-bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil k + 1. We also\rceil show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Edit intent: fluency
Original:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil  k + 1. We also\rceil  show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Revised:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs between\lceil k + 1. We also\rceil show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Edit intent: coherence
Original:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil  k + 1. We also\rceil  show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Revised:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil k + 1)\rceil show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Edit intent: coherence
Original:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil  k + 1. We also\rceil  show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Revised:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil k + 1. We also\rceil and 2k. In addition we show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Edit intent: coherence
Original:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil  k + 1. We also\rceil  show that the maximum thickness of semi-bar k-visibility graphs is between the ceiling of 2 (k+1) /3 and 2k.
Revised:  For k >= 1 we improve the upper bound on the maximum thickness of bar k-visibility graphs from 2k(9k-1) to 6k, and prove that the maximum thickness must be at least\lceil k + 1. We also\rceil show that the maximum thickness of semi-bar k-visibility graphs on n vertices is at most (k+1) /3 and 2k.
Edit intent: clarity
Original:  \choose  
Revised:  n\choose 
Edit intent: fluency
Original: It is shown that it is decidable if a given configuration of a pushdown automaton ( pda) with no epsilon-transitions is bisimulation equivalent with some unspecified finite-state process .
Revised: The problem if a given configuration of a pushdown automaton ( pda) with no epsilon-transitions is bisimulation equivalent with some unspecified finite-state process .
Edit intent: clarity
Original:  It might be worth to note that the first-order grammars here can be viewed as describing machine behaviours in a more "syntax-independent" way than in the classical works like by Courcelle (1995), and the regularity question is thus more abstract than there.
Edit intent: coherence
Original:  However, a reliable clock must be designed through two conflicting properties: entrainability to properly respond to external stimuli such as sunlight, and regularity to oscillate with a precise period.
Revised:  However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic stimuli such as sunlight, and regularity to oscillate with a precise period.
Edit intent: clarity
Original:  Our result indicates an existence of a dead zone, i.e., a time during which external stimuli neither advance nor delay the clock.
Revised:  Our result indicates an existence of a dead zone, i.e., a time period during which input stimuli neither advance nor delay the clock.
Edit intent: clarity
Original:  This result is independent of model details and a dead zone appears only when the input stimuli obey the time course of actual insolation .
Revised:  A dead zone appears only when the input stimuli obey the time course of actual insolation .
Edit intent: coherence
Original:  This result is independent of model details and a dead zone appears only when the input stimuli obey the time course of actual insolation .
Revised:  This result is independent of model details and a dead zone appears only when input stimuli obey the time course of actual insolation .
Edit intent: fluency
Original: In the Boundary Labeling problem, we are given a set of  n points, referred to as sites , inside an axis-parallel rectangle  R, and a set of  n pairwise disjoint rectangular labels that are attached to  R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of n points, referred to as sites , inside an axis-parallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside.
Edit intent: fluency
Original: In the Boundary Labeling problem, we are given a set of  n points, referred to as sites , inside an axis-parallel rectangle  R, and a set of  n pairwise disjoint rectangular labels that are attached to  R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites , inside an axis-parallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside.
Edit intent: fluency
Original: In the Boundary Labeling problem, we are given a set of  n points, referred to as sites , inside an axis-parallel rectangle  R, and a set of  n pairwise disjoint rectangular labels that are attached to  R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of n points, referred to as sites , inside an axis-parallel rectangle ~ R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside.
Edit intent: clarity
Original: In the Boundary Labeling problem, we are given a set of  n points, referred to as sites , inside an axis-parallel rectangle  R, and a set of  n pairwise disjoint rectangular labels that are attached to  R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of n points, referred to as sites , inside an axis-parallel rectangle R, and a set of ~ n pairwise disjoint rectangular labels that are attached to R from the outside.
Edit intent: fluency
Original: In the Boundary Labeling problem, we are given a set of  n points, referred to as sites , inside an axis-parallel rectangle  R, and a set of  n pairwise disjoint rectangular labels that are attached to  R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of n points, referred to as sites , inside an axis-parallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Edit intent: fluency
Original:  The task is to connect the sites to the labels by non-intersecting rectilinear paths, so-called leaders , with at most one bend.
Revised:  The task is to connect the sites to the labels by non-intersecting rectilinear paths, so-called leaders , with at most one bend.
Edit intent: fluency
Original:  In this paper, we study the Multi-Sided Boundary Labeling problem, with labels lying on at least two sides of the enclosing rectangle.
Revised:  In this paper, we study the Multi-Sided Boundary Labeling problem, with labels lying on at least two sides of the enclosing rectangle.
Edit intent: fluency
Original:  So far, such an algorithm has only been known for the cases that labels lie on one side or on two opposite sides of R (where a crossing-free solution always exists).
Revised:  So far, such an algorithm has only been known for the cases in which labels lie on one side or on two opposite sides of R (where a crossing-free solution always exists).
Edit intent: fluency
Original:  So far, such an algorithm has only been known for the cases that labels lie on one side or on two opposite sides of R (where a crossing-free solution always exists).
Revised:  So far, such an algorithm has only been known for the cases that labels lie on one side or on two opposite sides of ~R (here a crossing-free solution always exists).
Edit intent: clarity
Original:  For the more difficult case where labels  lie on adjacent sides , we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length  .
Revised:  The case where labels lie on adjacent sides , we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length .
Edit intent: clarity
Original:  For the more difficult case where labels  lie on adjacent sides , we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length  .
Revised:  For the more difficult case where labels may lie on adjacent sides , we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length .
Edit intent: clarity
Original:  For the more difficult case where labels  lie on adjacent sides , we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length  .
Revised:  For the more difficult case where labels lie on adjacent sides , we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length in a crossing-free layout .
Edit intent: clarity
Original: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites, inside an axis-parallel rectangle ~ R, and a set of ~ n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of n points, referred to as sites, inside an axis-parallel rectangle ~ R, and a set of ~ n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Edit intent: fluency
Original: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites, inside an axis-parallel rectangle ~ R, and a set of ~ n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites, inside an axis-parallel rectangle R, and a set of ~ n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Edit intent: fluency
Original: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites, inside an axis-parallel rectangle ~ R, and a set of ~ n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites, inside an axis-parallel rectangle ~ R, and a set of n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Edit intent: fluency
Original: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites, inside an axis-parallel rectangle ~ R, and a set of ~ n pairwise disjoint rectangular labels that are attached to ~ R from the outside.
Revised: In the Boundary Labeling problem, we are given a set of ~ n points, referred to as sites, inside an axis-parallel rectangle ~ R, and a set of ~ n pairwise disjoint rectangular labels that are attached to R from the outside.
Edit intent: fluency
Original:  So far, such an algorithm has only been known for the cases in which labels lie on one side or on two opposite sides of ~ R (here a crossing-free solution always exists).
Revised:  So far, such an algorithm has only been known for the cases in which labels lie on one side or on two opposite sides of R (here a crossing-free solution always exists).
Edit intent: fluency
Original:  We give a closely-matching upper bound U on the number of colours such that with probability that tends to 1, the Glauber dynamics mixes slowly on random Delta-regular graphs when at most U colours are used.
Revised:  We give a closely-matching upper bound U on the number of colours such that with probability that tends to 1, the Glauber dynamics mixes slowly on random \Delta-regular graphs when at most U colours are used.
Edit intent: fluency
Original:  We derive a lower bound on the minimax risk for the noiseless case and an upper bound for the special caseof metric graphs embedded in R2 . The upper bound is based on the reconstruction algorithm given in Aanjaneya et al. (2012).
Revised:  We derive lower and upper bounds on the minimax risk for the noiseless case and an upper bound for the special caseof metric graphs embedded in R2 . The upper bound is based on the reconstruction algorithm given in Aanjaneya et al. (2012).
Edit intent: clarity
Original: The great importance international rankings have  in the research policy arena calls for caution as they present many flaws and shortcomings  .
Revised: The great importance international rankings have achieved in the research policy arena calls for caution as they present many flaws and shortcomings .
Edit intent: clarity
Original: The great importance international rankings have  in the research policy arena calls for caution as they present many flaws and shortcomings  .
Revised: The great importance international rankings have in the research policy arena warns against many threats consequence of the flaws and shortcomings .
Edit intent: clarity
Original:  For this, we describe the Spanish university system as a study case presenting the I-UGR Rankings for Spanish universities by fields and subfields.
Revised:  For this, we analyze the Spanish university system as a study case presenting the I-UGR Rankings for Spanish universities by fields and subfields.
Edit intent: clarity
Original: The perfect phylogeny problem is a classic problem in com- putational biology, where we seek an unrooted phylogeny that is com- patible with a set of qualitative characters.
Revised: The perfect phylogeny problem is a classic problem in computational biology, where we seek an unrooted phylogeny that is com- patible with a set of qualitative characters.
Edit intent: fluency
Original: The perfect phylogeny problem is a classic problem in com- putational biology, where we seek an unrooted phylogeny that is com- patible with a set of qualitative characters.
Revised: The perfect phylogeny problem is a classic problem in com- putational biology, where we seek an unrooted phylogeny that is compatible with a set of qualitative characters.
Edit intent: fluency
Original:  Bor- dewich , Huber, and Semple showed how to use the partition intersection graph to find a maximum compatible set of characters.
Revised:  Bordewich , Huber, and Semple showed how to use the partition intersection graph to find a maximum compatible set of characters.
Edit intent: fluency
Original:  Our characterization is stated in terms of minimal triangulations of the partition intersection graph that are uniquely representable, also known as ur-chordal graphs , and we extend this characterization to maximal subsets of characters that have a unique perfect phylogeny .
Revised:  Our characterization is stated in terms of minimal triangulations of the partition intersection graph that are uniquely representable, also known as ur-chordal graphs .
Edit intent: coherence
Original:  Our characterization is motivated by the structure of ur-chordal graphs, and the fact that the block struc- ture of minimal triangulations is mirrored in the graph that has been triangulated.
Revised:  Our characterization is motivated by the structure of ur-chordal graphs, and the fact that the block structure of minimal triangulations is mirrored in the graph that has been triangulated.
Edit intent: fluency
Original:  It builds on  MPI for distributing the workload across the nodes of the cluster.
Revised:  It builds on MPI for distributing the workload across the nodes in a cluster.
Edit intent: clarity
Original:  Apart from fast execution, memory use is highly optimized, enabling training large emergent maps even on a single node .
Revised:  Apart from fast execution, memory use is highly optimized, enabling training large emergent maps even on a single computer .
Edit intent: clarity
Original: Automated tracking of multiple moving targets is the key experimental gateway to quantitative dynamical information in fields as diverse as collective behavior in biology, turbulence , crowd and traffic control.
Revised: Tracking multiple moving targets is the key experimental gateway to quantitative dynamical information in fields as diverse as collective behavior in biology, turbulence , crowd and traffic control.
Edit intent: clarity
Original: Automated tracking of multiple moving targets is the key experimental gateway to quantitative dynamical information in fields as diverse as collective behavior in biology, turbulence , crowd and traffic control.
Revised: Automated tracking of multiple moving targets allows quantitative measure of the dynamic behavior in systems as diverse as collective behavior in biology, turbulence , crowd and traffic control.
Edit intent: clarity
Original:  In three dimensions tracking is hard because of optical occlusions : when two featureless targets  overlap for several frames , loss of identity is likely .
Revised:  In three dimensions , tracking several targets becomes increasingly hard since optical occlusions are very likely, i.e. two featureless targets overlap for several frames , loss of identity is likely .
Edit intent: clarity
Original:  In three dimensions tracking is hard because of optical occlusions : when two featureless targets  overlap for several frames , loss of identity is likely .
Revised:  In three dimensions tracking is hard because of optical occlusions : when two featureless targets frequently overlap for several frames , loss of identity is likely .
Edit intent: clarity
Original:  In three dimensions tracking is hard because of optical occlusions : when two featureless targets  overlap for several frames , loss of identity is likely .
Revised:  In three dimensions tracking is hard because of optical occlusions : when two featureless targets overlap for several frames .
Edit intent: clarity
Original:  Occlusions are  frequent in biological groups as flocks, schools and swarms, a fact that has severely limited collective animal behavior field studies in the past.
Revised:  Occlusions are particularly frequent in biological groups as flocks, schools and swarms, a fact that has severely limited collective animal behavior field studies in the past.
Edit intent: clarity
Original:  Here we present a new tracking method in three dimensions able to cope with the most severe occlusions.
Revised:  This paper presents a 3d tracking method that is robust in the case of severe occlusions.
Edit intent: clarity
Original:  The excellent results for both birds and midges prove the potential applicability of our method to the most diverse experimental situations.
Revised:  The excellent results for both birds and midges show the potential applicability of our method to the most diverse experimental situations.
Edit intent: coherence
Original:  This paper presents a 3d tracking method that is robust in the case of severe occlusions.
Revised:  This paper presents a 3D tracking method that is robust in the case of severe occlusions.
Edit intent: fluency
Original:  We tested our algorithm both with synthetic data and with experimental data of bird flocks and insect swarms  , and show that our system yields high quality trajectories for hundreds of moving targets with severe overlap.
Revised:  We tested our algorithm with synthetic data and with experimental data of bird flocks and insect swarms , and show that our system yields high quality trajectories for hundreds of moving targets with severe overlap.
Edit intent: clarity
Original:  We tested our algorithm both with synthetic data and with experimental data of bird flocks and insect swarms  , and show that our system yields high quality trajectories for hundreds of moving targets with severe overlap.
Revised:  We tested our algorithm both with synthetic data , with experimental data of bird flocks and insect swarms , and show that our system yields high quality trajectories for hundreds of moving targets with severe overlap.
Edit intent: coherence
Original: The paper presents a non-linear quantization method for detail components in the JPEG2000 standard.
Revised: The paper presents a non-uniform quantization method for detail components in the JPEG2000 standard.
Edit intent: clarity
Original: The paper presents a non-linear quantization method for detail components in the JPEG2000 standard.
Revised: The paper presents a non-linear quantization method for the Detail components in the JPEG2000 standard.
Edit intent: fluency
Original:  The quantization step sizes are determined by  actual statistics of the wavelet coefficients.
Revised:  The quantization step sizes are determined by the actual statistics of the wavelet coefficients.
Edit intent: fluency
Original:  Moreover, weighted mean of the coefficients lying within the step size is chosen as quantized value - contrary to the uniform quantizer.
Revised:  Moreover, the mean of the coefficients lying within the step size is chosen as quantized value - contrary to the uniform quantizer.
Edit intent: clarity
Original:  Moreover, weighted mean of the coefficients lying within the step size is chosen as quantized value - contrary to the uniform quantizer.
Revised:  Moreover, weighted mean of the coefficients lying within the step size is chosen as the quantized value, contrary to the uniform quantizer.
Edit intent: fluency