wanyu/IteraTeR_v2 huggingface dataset:
Original:  We also find that the final wealth distribution of all traders corresponds to the well-known Pareto power law, while that one of random traders only is exponential.
Revised:  We also find that the final wealth distribution of all traders corresponds to the well-known Pareto power law, while that one of random traders is exponential.
Edit intent: clarity
Original:  Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered (SIR) dynamics on finite tree-like networks .
Revised:  Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered dynamics on finite tree-like networks .
Edit intent: clarity
Original:  Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered (SIR) dynamics on finite tree-like networks .
Revised:  Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered (SIR) dynamics on finite trees .
Edit intent: clarity
Original: A drawing D of the complete graph K_n is}\left\lfloor {2}}\right\rfloor \left\lfloor{2}}\right\rfloor \left\lfloor {2}}\right\rfloor\left\lfloor {2}}\right\rfloor {\em  {\em s -shellable} if there exists a subset S = \{v_1,v_2,\ldots,v_ s\} of the vertices and a region R of D with the following property .
Revised: A drawing D of the complete graph K_n is}\left\lfloor {2}}\right\rfloor \left\lfloor{2}}\right\rfloor \left\lfloor {2}}\right\rfloor\left\lfloor {2}}\right\rfloor {\em . We say that a drawing D of K_n is{\em s -shellable} if there exists a subset S = \{v_1,v_2,\ldots,v_ s\} of the vertices and a region R of D with the following property .
Edit intent: coherence
Original: A drawing D of the complete graph K_n is}\left\lfloor {2}}\right\rfloor \left\lfloor{2}}\right\rfloor \left\lfloor {2}}\right\rfloor\left\lfloor {2}}\right\rfloor {\em  {\em s -shellable} if there exists a subset S = \{v_1,v_2,\ldots,v_ s\} of the vertices and a region R of D with the following property .
Revised: A drawing D of the complete graph K_n is}\left\lfloor {2}}\right\rfloor \left\lfloor{2}}\right\rfloor \left\lfloor {2}}\right\rfloor\left\lfloor {2}}\right\rfloor {\em {\em s -shellable} if there exist a subset S = \{v_1,v_2,\ldots,v_ s\} of the vertices and a region R of D with the following property .
Edit intent: fluency
Original:  For 1 \leq i < j \leq s, let D_{ij the drawing obtained from D by removing v_1,v_2,\ldots v_{i-1},v_{j+1}, v_{j+2 \ldots,v_{s} ;
Revised:  For 1 \leq i < j \leq s, if D_{ij the drawing obtained from D by removing v_1,v_2,\ldots v_{i-1},v_{j+1}, v_{j+2 \ldots,v_{s} ;
Edit intent: coherence
Original:  For 1 \leq i < j \leq s, let D_{ij the drawing obtained from D by removing v_1,v_2,\ldots v_{i-1},v_{j+1}, v_{j+2 \ldots,v_{s} ;
Revised:  For 1 \leq i < j \leq s, let D_{ij the drawing obtained from D by removing v_1,v_2,\ldots v_{i-1},v_{j+1}, \ldots,v_{s} ;
Edit intent: fluency
Original:  then for all 1 \leq i < j \leq s, v_i and v_j are incident with the region of D_{ij} that contains R.
Revised:  then for all 1 \leq i < j \leq s, v_i and v_j are on the boundary of the region of D_{ij} that contains R.
Edit intent: clarity
Original:  We prove that for s\geq n/2  the number of crossings of any s -
Revised:  For s\geq n/2 the number of crossings of any s -
Edit intent: clarity
Original:  We prove that for s\geq n/2  the number of crossings of any s -
Revised:  We prove that for s\geq n/2 , we prove that the number of crossings of any s -
Edit intent: style
Original: shellable drawing of K_n is at least the long-conjectured value of the crossing number of K_n, namely Z%DIFDELCMD < \left(%%% n%DIFDELCMD < \right) %%% :
Revised: shellable drawing of K_n is at least the long-conjectured value %DIFDELCMD < \left(%%% n%DIFDELCMD < \right) %%% :
Edit intent: clarity
Original: shellable drawing of K_n is at least the long-conjectured value of the crossing number of K_n, namely Z%DIFDELCMD < \left(%%% n%DIFDELCMD < \right) %%% :
Revised: shellable drawing of K_n is at least the long-conjectured value of the crossing number of K_n, namely Z%DIFDELCMD < \left(%%% %DIFDELCMD < \right) %%% :
Edit intent: clarity
Original: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Revised: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% {2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Edit intent: fluency
Original: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Revised: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% {2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Edit intent: fluency
Original: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Revised: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% {2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Edit intent: fluency
Original: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Revised: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Edit intent: coherence
Original: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n is s-shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Revised: =\frac{1{4}}%DIFDELCMD < \left\lfloor %DIFDELCMD < %%% \frac{n{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-1{2}}%DIFDELCMD < \right\rfloor \left\lfloor %DIFDELCMD < %%% \frac{n-2{2}}%DIFDELCMD < \right\rfloor \left\lfloor %%% \frac{n-3{2}}%DIFDELCMD < \right\rfloor%%% . We also prove that every crossing minimal cylindricaldrawing of K_n are s -shellable for some s\geq n/2 . From these results it follows that the cylindrical crossing number of K_n is Z(n)
Edit intent: fluency
Original:  , thus settling the Harary-Hill conjecture for cylindrical drawings of K_n. Moreover, the techniques developed provide an unified proof verifying the Harary-Hill conjecture also for 2-page, monotone, and x-bounded drawings.
Revised:  Moreover, the techniques developed provide an unified proof verifying the Harary-Hill conjecture also for 2-page, monotone, and x-bounded drawings.
Edit intent: coherence
Original:  , thus settling the Harary-Hill conjecture for cylindrical drawings of K_n. Moreover, the techniques developed provide an unified proof verifying the Harary-Hill conjecture also for 2-page, monotone, and x-bounded drawings.
Revised:  , thus settling the Harary-Hill conjecture for cylindrical drawings of K_n. crossings. The techniques developed provide an unified proof verifying the Harary-Hill conjecture also for 2-page, monotone, and x-bounded drawings.
Edit intent: coherence
Original:  , thus settling the Harary-Hill conjecture for cylindrical drawings of K_n. Moreover, the techniques developed provide an unified proof verifying the Harary-Hill conjecture also for 2-page, monotone, and x-bounded drawings.
Revised:  , thus settling the Harary-Hill conjecture for cylindrical drawings of K_n. Moreover, the techniques developed provide a unified proof of the Harary-Hill conjecture also for 2-page, monotone, and x-bounded drawings.
Edit intent: clarity
Original:  , thus settling the Harary-Hill conjecture for cylindrical drawings of K_n. Moreover, the techniques developed provide an unified proof verifying the Harary-Hill conjecture also for 2-page, monotone, and x-bounded drawings.
Revised:  , thus settling the Harary-Hill conjecture for cylindrical drawings of K_n. Moreover, the techniques developed provide an unified proof verifying the Harary-Hill conjecture for these classes of drawings.
Edit intent: clarity
Original:  A monochromatic strong matching of S with rectangles is any set of pairwise disjoint axis-aligned rectangles such that each rectangle contains exactly two points of S from the same color class, and every element of S is contained in at most one rectangle .
Revised:  A monochromatic strong matching of S with rectangles is any set of pairwise-disjoint axis-aligned rectangles such that each rectangle contains exactly two points of S from the same color class, and every element of S is contained in at most one rectangle .
Edit intent: fluency
Original:  We prove that this problem is NP-hard and provide an algorithm that constructs a matching with at least1 / 16 of the number of rectangles of an optimal matching.
Revised:  We prove that this problem is NP-hard and provide an algorithm that constructs a matching with at least 1 / 16 of the number of rectangles of an optimal matching.
Edit intent: fluency
Original:  The "common input" problem presents the major roadblock: it is difficult to reliably distinguish causal connections between pairs of observed neurons from correlations induced by common input from unobserved neurons.
Revised:  The `common input' problem presents the major roadblock: it is difficult to reliably distinguish causal connections between pairs of observed neurons from correlations induced by common input from unobserved neurons.
Edit intent: fluency
Original:  This work proposes a "shotgun" experimental design, in which we observe multiple subnetworks briefly, in a serial manner.
Revised:  This work proposes a `shotgun' experimental design, in which we observe multiple subnetworks briefly, in a serial manner.
Edit intent: fluency
Original:  This work proposes a "shotgun" experimental design, in which we observe multiple subnetworks briefly, in a serial manner.
Revised:  This work proposes a "shotgun" experimental design, in which we observe multiple sub-networks briefly, in a serial manner.
Edit intent: fluency
Original:  We develop Bayesian methods based on generalized linear models (GLM) and "spike-and-slab" sparse priors to perform network inference given this type of data, and demonstrate in simulation that this shotgun experimental design can in fact eliminate the biases induced by common input effects.
Revised:  We develop Bayesian methods based on generalized linear models (GLM) and "spike-and-slab" sparse priors to perform network inference given this type of data, and demonstrate in simulation that this shotgun experimental design can eliminate the biases induced by common input effects.
Edit intent: clarity
Original: Crossing individuals from genetically distinct populations often results in improvements in quantitative traits, such as growth rate, biomass production and stress resistance ;
Revised: In biology, crossing individuals from genetically distinct populations often results in improvements in quantitative traits, such as growth rate, biomass production and stress resistance ;
Edit intent: clarity
Original:  These artificial regulatory networks exhibit biologically realistic topological properties and fitness is measured as the ability of a network to respond to external inputs in the correct way.
Revised:  These artificial regulatory networks exhibit topological properties that reflect those observed in biology, and fitness is measured as the ability of a network to respond to external inputs in the correct way.
Edit intent: clarity
Original:  Our model reproduced experimental observations from the literature on heterosis using only biologically meaningful parameters, such as mutation rates.
Revised:  Our model reproduced experimental observations from the literature on heterosis using only biologically justified parameters, such as mutation rates.
Edit intent: clarity
Original:  Hybrid vigor was observed, its extent was seen to increase as parental populations diverged until it collapses when the two populations have become incompatible .
Revised:  Hybrid vigor was observed, its extent was seen to increase as parental populations diverged and it reached a point where it collapsed .
Edit intent: clarity
Original:  We also reproduce  for the first time in a model  the fact that hybrid vigor cannot easily be fixed by crossing hybrids, which is currently an important drawback of the use of hybrid crops.
Revised:  We also reproduce , for the first time in a model the fact that hybrid vigor cannot easily be fixed by crossing hybrids, which is currently an important drawback of the use of hybrid crops.
Edit intent: fluency
Original:  We also reproduce  for the first time in a model  the fact that hybrid vigor cannot easily be fixed by crossing hybrids, which is currently an important drawback of the use of hybrid crops.
Revised:  We also reproduce for the first time in a model , the fact that hybrid vigor cannot easily be fixed by crossing hybrids, which is currently an important drawback of the use of hybrid crops.
Edit intent: fluency
Original:  We also reproduce  for the first time in a model  the fact that hybrid vigor cannot easily be fixed by crossing hybrids, which is currently an important drawback of the use of hybrid crops.
Revised:  We also reproduce for the first time in a model the fact that hybrid vigor cannot easily be fixed by within a breeding line, currently an important drawback of the use of hybrid crops.
Edit intent: clarity
Original:  We also reproduce  for the first time in a model  the fact that hybrid vigor cannot easily be fixed by crossing hybrids, which is currently an important drawback of the use of hybrid crops.
Revised:  We also reproduce for the first time in a model the fact that hybrid vigor cannot easily be fixed by crossing hybrids, which is currently an important limitation of the use of hybrid crops.
Edit intent: clarity
Original:  The simulation allows us to study the effects of three standard models for the genetic basis of heterosis , dominance, over-dominance, and epistasis.
Revised:  The simulation allowed us to study the effects of three standard models for the genetic basis of heterosis , dominance, over-dominance, and epistasis.
Edit intent: fluency
Original:  The simulation allows us to study the effects of three standard models for the genetic basis of heterosis , dominance, over-dominance, and epistasis.
Revised:  The simulation allows us to study the effects of three standard models for the genetic basis of heterosis : dominance, over-dominance, and epistasis.
Edit intent: fluency
Original:  This phenomenon is known as heterosis or hybrid vigor .
Revised:  Heterosis has become a very useful tool in global agriculture, but its genetic basis remains controversial and its effects hard to predict .
Edit intent: clarity
Original:  We have taken a computational approach to explore the mechanisms underlying heterosis, developing a simulation of evolution, independent reassortment of alleles and hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework.
Revised:  We have taken a computational approach to studying heterosis, developing a simulation of evolution, independent reassortment of alleles and hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework.
Edit intent: clarity
Original:  These artificial regulatory networks exhibit topological properties that reflect those observed in biology, and fitness is measured as the ability of a network to respond to external inputs in the correct way.
Revised:  Fitness is measured as the ability of a network to respond to external inputs in the correct way.
Edit intent: coherence
Original:  These artificial regulatory networks exhibit topological properties that reflect those observed in biology, and fitness is measured as the ability of a network to respond to external inputs in the correct way.
Revised:  These artificial regulatory networks exhibit topological properties that reflect those observed in biology, and fitness is measured as the ability of a network to respond to external inputs in a pre-defined way.
Edit intent: clarity
Original:  Our model reproduced experimental observations from the literature on heterosis using only biologically justified parameters , such as mutation rates .
Revised:  Our model reproduced common experimental observations on heterosis using only biologically justified parameters , such as mutation rates .
Edit intent: clarity
Original:  Our model reproduced experimental observations from the literature on heterosis using only biologically justified parameters , such as mutation rates .
Revised:  Our model reproduced experimental observations from the literature on heterosis using only biologically justified parameters .
Edit intent: clarity
Original:  Hybrid vigor was observed , its extent was seen to increase as parental populations diverged and it reached a point where it collapsed.
Revised:  Hybrid vigor was observed and its extent was seen to increase as parental populations diverged and it reached a point where it collapsed.
Edit intent: fluency
Original:  Accordingly, a key new objective that we pursue is efficient design of the stochastic grids formed by the simulated sample paths of the underlying state process.
Revised:  Accordingly, a key new objective that we pursue is efficient design of the stochastic grids anchoring the simulated sample paths of the underlying state process.
Edit intent: clarity
Original:   To this end, we introduce active learning schemes that adaptively place new grid points close to the stopping boundaries.
Revised:  To this end, we introduce active learning schemes that adaptively place new design points close to the stopping boundaries.
Edit intent: clarity
Original:  The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of total grid size can be achieved.
Revised:  The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved.
Edit intent: clarity
Original:  Using this, we show that a reaction network has critical siphons iff it has "drainable" or "self-replicable" siphons.
Revised:  Using this, we show that a reaction network has critical siphons iff it has "drainable" and "self-replicable" siphons.
Edit intent: fluency
Original:  Consequently, we obtain a new, elementary proof for the persistence of non-catalytic weakly-reversible chemical reaction networks .
Revised:  Consequently, we obtain a new, elementary proof for the persistence of non-catalytic weakly-reversible networks are persistent .
Edit intent: clarity
Original:  It is not known how the observed clones may differ with respect to cell properties such as proliferation and self-renewal.
Revised:  Nevertheless it is not known how the observed clones may differ with respect to cell properties such as proliferation and self-renewal.
Edit intent: coherence
Original:  Furthermore, we suggest, based on systematic simulations, that even too weak spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network.
Revised:  Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter- burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network.
Edit intent: clarity
Original:  By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it is possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.
Revised:  By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.
Edit intent: clarity
Original:  We consider three  fundamental visibility structures:  the visibility map, the colored visibility map, and the Voronoi visibility map  .
Revised:  We consider threevisible fundamental visibility structures: the visibility map, the colored visibility map, and the Voronoi visibility map .
Edit intent: fluency
Original: Several variation of the Watterson estimator of variability for Next Generation Sequencing (NGS) data have been proposed in the literature.
Revised: Several variations of the Watterson estimator of variability for Next Generation Sequencing (NGS) data have been proposed in the literature.
Edit intent: fluency
Original: We study the complexity of several parameterizations for as well as for some related satisfiability problems \textsc{ . Given a family of subsets \mathcal S=\{S_1,\ldots,S_m\} over a set of elements X=\{x_1,\ldots,x_n\} and an integer p, consists of finding a set \mathcal T of at most k subsets covering at least p elements.
Revised: We study the complexity of several parameterizations for \textsc{ . Given a family of subsets \mathcal S=\{S_1,\ldots,S_m\} over a set of elements X=\{x_1,\ldots,x_n\} and an integer p, consists of finding a set \mathcal T of at most k subsets covering at least p elements.
Edit intent: clarity
Original:  This problem, when parameterized by k, can be easily shown to be W[2]-hard.
Revised:  This problem, when parameterized by k, is W[2]-hard.
Edit intent: clarity