wanyu/IteraTeR_v2 huggingface dataset:
Original:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)}  up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth  5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Revised:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)} up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})}. In a second part, we prove that in any graph G of minimum degree \delta and girth 5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Edit intent: fluency
Original:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)}  up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth  5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Revised:  For d-regular graphs and further classes of graphs , this bound is improved to%DIFDELCMD < \M%%% (G)\leq n-%DIFDELCMD < n{\Theta(d^{3/2})}%%% . Moreover, if G is regular and has no vertices sharing the same neighbours, we show that the conjecture holds n{\Theta(d)} up to constants , i. e. \M(G)\leq n- %DIFDELCMD < n{\Theta(d)}%%% . In the n{\Theta(d^{3})} second part, we prove that in any graph G of minimum degree \delta and girth at least 5, \M(G)\leq(1+o_\delta(1))3\log\delta{2\delta}n.
Edit intent: clarity
Original:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that  if a connected graph G has n vertices and maximum degree d and admits an identifying code, then \M(G)\leq n-n{d}+ O(1) . We use probabilistic tools to show that for sufficiently large d , \M(G)\leq n-n{\Theta(d)} holds for a large class of graphs containing, among others, all regular graphs and all graphs of bounded clique number.
Revised:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that there exists a constant c such that if a connected graph G has n vertices and maximum degree d and admits an identifying code, then \M(G)\leq n-n{d}+ O(1) . We use probabilistic tools to show that for sufficiently large d , \M(G)\leq n-n{\Theta(d)} holds for a large class of graphs containing, among others, all regular graphs and all graphs of bounded clique number.
Edit intent: clarity
Original:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that  if a connected graph G has n vertices and maximum degree d and admits an identifying code, then \M(G)\leq n-n{d}+ O(1) . We use probabilistic tools to show that for sufficiently large d , \M(G)\leq n-n{\Theta(d)} holds for a large class of graphs containing, among others, all regular graphs and all graphs of bounded clique number.
Revised:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that if a connected graph G with n vertices and maximum degree d and admits an identifying code, then \M(G)\leq n-n{d}+ O(1) . We use probabilistic tools to show that for sufficiently large d , \M(G)\leq n-n{\Theta(d)} holds for a large class of graphs containing, among others, all regular graphs and all graphs of bounded clique number.
Edit intent: fluency
Original:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that  if a connected graph G has n vertices and maximum degree d and admits an identifying code, then \M(G)\leq n-n{d}+ O(1) . We use probabilistic tools to show that for sufficiently large d , \M(G)\leq n-n{\Theta(d)} holds for a large class of graphs containing, among others, all regular graphs and all graphs of bounded clique number.
Revised:  Foucaud, R. Klasing, A. Kosowski and A. Raspaud that if a connected graph G has n vertices and maximum degree d admits an identifying code, then \M(G)\leq n-n{d}+ O(1) . We use probabilistic tools to show that for sufficiently large d , \M(G)\leq n-n{\Theta(d)} holds for a large class of graphs containing, among others, all regular graphs and all graphs of bounded clique number.
Edit intent: coherence
Original:  Given  two points s and t and h splinegons of totally n verticeswith pairwise disjoint interior , we compute a shortest s-to-t path avoiding the splinegons, in O(n+h\log^{1+\epsilon}h+k) time, where k is a parameter sensitive to the structures of the input splinegons and is bounded by O(h^2).
Revised:  Given in the plane two points s and t and h splinegons of totally n verticeswith pairwise disjoint interior , we compute a shortest s-to-t path avoiding the splinegons, in O(n+h\log^{1+\epsilon}h+k) time, where k is a parameter sensitive to the structures of the input splinegons and is bounded by O(h^2).
Edit intent: clarity
Original:  Given  two points s and t and h splinegons of totally n verticeswith pairwise disjoint interior , we compute a shortest s-to-t path avoiding the splinegons, in O(n+h\log^{1+\epsilon}h+k) time, where k is a parameter sensitive to the structures of the input splinegons and is bounded by O(h^2).
Revised:  Given two points s and t and a set of h pairwise disjoint splinegons with a total of n vertices , we compute a shortest s-to-t path avoiding the splinegons, in O(n+h\log^{1+\epsilon}h+k) time, where k is a parameter sensitive to the structures of the input splinegons and is bounded by O(h^2).
Edit intent: clarity
Original:  Given  two points s and t and h splinegons of totally n verticeswith pairwise disjoint interior , we compute a shortest s-to-t path avoiding the splinegons, in O(n+h\log^{1+\epsilon}h+k) time, where k is a parameter sensitive to the structures of the input splinegons and is bounded by O(h^2).
Revised:  Given two points s and t and h splinegons of totally n verticeswith pairwise disjoint interior , we compute a shortest s-to-t path avoiding the splinegons, in O(n+h\log^{1+\epsilon}h+k) time, where k is a parameter sensitive to the structures of the input splinegons and is upper-bounded by O(h^2).
Edit intent: clarity
Original:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h  ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm  takes O(n+h^2\log n) time.
Revised:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons with a total of n vertices. Our algorithm runs in O(n+ k+ h\log h ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm takes O(n+h^2\log n) time.
Edit intent: clarity
Original:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h  ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm  takes O(n+h^2\log n) time.
Revised:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ h\log h ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm takes O(n+h^2\log n) time.
Edit intent: fluency
Original:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h  ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm  takes O(n+h^2\log n) time.
Revised:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h ) time and O(n) space, where k is the number of all free common tangents . Even for the special case when all splinegons are convex polygons, the previously best algorithm takes O(n+h^2\log n) time.
Edit intent: coherence
Original:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h  ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm  takes O(n+h^2\log n) time.
Revised:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case where all splinegons are convex polygons, the previously best algorithm takes O(n+h^2\log n) time.
Edit intent: fluency
Original:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h  ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm  takes O(n+h^2\log n) time.
Revised:  (3) We give an optimal algorithm for a basic visibility problem of computing all free common tangents among h pairwise disjoint convex splinegons of totally n vertices, in O(n+ k+ h\log h ) time and O(n) space, where k is the number of all free common tangents (and k=O(h^2)) . Even for the special case when all splinegons are convex polygons, the previously best algorithm for this visibility problem takes O(n+h^2\log n) time.
Edit intent: clarity
Original:  We describe the `stratified B-tree', which beats  the CoW B-tree in every way .
Revised:  We describe the `stratified B-tree', which beats the CoW B-tree .
Edit intent: clarity
Original: In this paper we consider optimal allocation problem for the perennial plants.
Revised: In this paper we consider optimal allocation problem for perennial plants.
Edit intent: fluency
Original:  In the second part of the paper we extend the model developed in previous sections to the case, when the plant controls not only the distribution of allocated carbohydrates, but also the size of a seed.
Revised:  In the second part of the paper we extend the model developed in previous sections to the case, when a plant controls not only the distribution of allocated carbohydrates, but also the size of a seed.
Edit intent: fluency
Original:  In the second part of the paper we extend the model developed in previous sections to the case, when the plant controls not only the distribution of allocated carbohydrates, but also the size of a seed.
Revised:  In the second part of the paper we extend the model developed in previous sections to the case, when the plant controls not only a distribution of allocated carbohydrates, but also the size of a seed.
Edit intent: fluency
Original:  In the second part of the paper we extend the model developed in previous sections to the case, when the plant controls not only the distribution of allocated carbohydrates, but also the size of a seed.
Revised:  In the second part of the paper we extend the model developed in previous sections to the case, when the plant controls not only the distribution of allocated carbohydrates, but also a size of a seed.
Edit intent: fluency
Original:  The opposite strategy, namely to produce the seeds as large as possible, was also considered.
Revised:  The opposite strategy, namely to produce the seeds as large as possible, is also considered.
Edit intent: fluency
Original: In this paper we propose a novel optimal allocation problem for perennial plants  .
Revised: We present a novel optimal allocation problem for perennial plants .
Edit intent: clarity
Original: In this paper we propose a novel optimal allocation problem for perennial plants  .
Revised: In this paper we propose a novel optimal allocation model for perennial plants .
Edit intent: clarity
Original:  We do not restrict ourselves to consider only the periods favorable for photosynthesis, but analyze the whole life period of a perennial plant.
Revised:  We do not restrict considerations purely to periods favourable for photosynthesis, but analyze the whole life period of a perennial plant.
Edit intent: clarity
Original:  This provides more information about the strategies of a plant during transitions between the favorable and unfavorable seasons.
Revised:  This provides more information about plants' strategies during transitions between the favorable and unfavorable seasons.
Edit intent: clarity
Original:  This provides more information about the strategies of a plant during transitions between the favorable and unfavorable seasons.
Revised:  This provides more information about the strategies of a plant during transitions between favourable and unfavourable seasons.
Edit intent: fluency
Original:  One of predictions of the model is that a plant can begin re-establishment of vegetative tissues some time before the beginning of the favorable conditions, so as to come into the better environmental conditions with a certain amount of already developed vegetative tissues.
Revised:  One of the model's predictions is that a plant can begin re-establishment of vegetative tissues some time before the beginning of the favorable conditions, so as to come into the better environmental conditions with a certain amount of already developed vegetative tissues.
Edit intent: clarity
Original: Regulatory dynamics in systems biology is often described by continuous rate equations for continuously varying chemical concentrations.
Revised: Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations.
Edit intent: clarity
Original:  In the latter, the distinction between stable and unstable dynamics is usually made by checking damage after flip perturbations .
Revised:  In the latter, the dynamics has been called unstable if flip perturbations lead to damage spreading .
Edit intent: clarity
Original:  Here we point out that this notion of stability is incompatible with the stability properties of the original continuous dynamics probed by small perturbations .
Revised:  Here we find that this stability classification strongly differs from the stability properties of the original continuous dynamics probed by small perturbations .
Edit intent: clarity
Original:  Here we point out that this notion of stability is incompatible with the stability properties of the original continuous dynamics probed by small perturbations .
Revised:  Here we point out that this notion of stability is incompatible with the stability properties of the original continuous dynamics under small perturbations of the state vector .
Edit intent: clarity
Original:  In particular, random networks of nodes with large sensitivity yield stable dynamics , in contrast to the prediction of chaos obtained by flip perturbationsin Boolean networks .
Revised:  In particular, random networks of nodes with large sensitivity yield stable dynamics under small perturbations .
Edit intent: clarity
Original:  We also prove the termination of each iteration of the procedure , thus confirming semi-decidability of the synthesis problem .
Revised:  We also prove the termination of each iteration of the procedure .
Edit intent: coherence
Original:  Some promising experimental results are presented, based on an implementation of the fixpoint algorithm on top of the tool PHAVer.
Revised:  Some promising experimental results are presented, based on an implementation of the fixpoint procedure on top of the tool PHAVer.
Edit intent: clarity
Original: Considering the recent experimental discovery of Green et al that present day non-Africans have 1 to 4\% of their nuclear DNA of Neandertal origin, we propose here a model which is able to quantify the interbreeding events between the two subpopulations .
Revised: Considering the recent experimental discovery of Green et al that present day non-Africans have 1 to 4\% of their nuclear DNA of Neanderthal origin, we propose here a model which is able to quantify the interbreeding events between the two subpopulations .
Edit intent: fluency
Original:  By simulating the  model we are able to apply it to the interbreeding of African and Neandertal subpopulations and estimate the only parameter of the model, which is the number of individuals per generation exchanged between subpopulations.
Revised:  By simulating the model we are able to apply it to the interbreeding of African and Neanderthal subpopulations and estimate the only parameter of the model, which is the number of individuals per generation exchanged between subpopulations.
Edit intent: fluency
Original:  Our results indicate that the amount of Neandertal DNA in non-Africans can be explained with maximum probability by the exchange of a single pair of individuals between the subpopulations at each 77 generations, but larger exchange frequencies are also allowed with sizable probability .
Revised:  Our results indicate that the amount of Neanderthal DNA in non-Africans can be explained with maximum probability by the exchange of a single pair of individuals between the subpopulations at each 77 generations, but larger exchange frequencies are also allowed with sizable probability .
Edit intent: fluency
Original:  This version corrects a small typo at the end of the proof of Theorem 1.
Edit intent: coherence
Original:  Using percentiles (e.g., top-1\%, top-10\%, etc.), an integrated impact indicator (I3) can be based on integration of the citation curves after normalization to the same scale.
Revised:  Using percentile ranks (e.g., top-1\%, top-10\%, etc.), an integrated impact indicator (I3) can be based on integration of the citation curves after normalization to the same scale.
Edit intent: clarity
Original:  Using percentiles (e.g., top-1\%, top-10\%, etc.), an integrated impact indicator (I3) can be based on integration of the citation curves after normalization to the same scale.
Revised:  Using percentiles (e.g., top-1\%, top-10\%, etc.), an integrated impact indicator (I3) can be based on integration of the citation curves , but after normalization of the citation curves to the same scale.
Edit intent: coherence
Original:  In addition to comparing I3  with IFs for the journals in two ISI Subject Categories ("Information Science & Library Science" and "Multidisciplinary Sciences") , we show that the summations can transparently be decomposed in terms of the contributions of institutional units such as nations(universities, etc. ) because percentiles provide us with a paper-based measure .
Revised:  I3 with IFs for the journals in two ISI Subject Categories ("Information Science & Library Science" and "Multidisciplinary Sciences") , we show that the summations can transparently be decomposed in terms of the contributions of institutional units such as nations(universities, etc. ) because percentiles provide us with a paper-based measure .
Edit intent: coherence
Original: Escherichia coli ( {\sl  {\sl E. coli ) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past.
Revised:  {\sl {\sl E. coli ) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past.
Edit intent: clarity
Original: Escherichia coli ( {\sl  {\sl E. coli ) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past.
Revised: Escherichia coli ( {\sl ({\sl E. coli ) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past.
Edit intent: fluency
Original:  A number of such earlier studies assume that a bacterium resets its memory at tumbles -- a fact not borne out by experiment -- and make use of approximate coarse-grained descriptions.
Revised:  A number of earlier studies assume that a bacterium resets its memory at tumbles -- a fact not borne out by experiment -- and make use of approximate coarse-grained descriptions.
Edit intent: clarity
Original:  In all cases, the apparent contradiction between favorable drift and favorable accumulationis resolved .
Revised:  In the adaptive case, favorable drift occurs together with favorable accumulation .
Edit intent: coherence
Original: Single-nucleotide-resolution chemical mapping is a classic approach to characterizing structured RNA molecules that is being advanced by new chemistries, faster readouts, and coupling to computational algorithms.
Revised: Single-nucleotide-resolution chemical mapping for structured RNA is being rapidly advanced by new chemistries, faster readouts, and coupling to computational algorithms.
Edit intent: clarity
Original:  Recent tests have suggested that 2' -OH acylation data (SHAPE) can give near-zero error rates ( 0-4 \%) in modeling  RNA secondary structure.
Revised:  Recent tests have shown that selective 2' -OH acylation data (SHAPE) can give near-zero error rates ( 0-4 \%) in modeling RNA secondary structure.
Edit intent: clarity
Original:  Here, we benchmark the method on six RNAs for which crystallographic data are available: tRNAphe and 5S rRNA from E. coli;
Revised:  Here, we benchmark the method using six molecules for which crystallographic data are available: tRNAphe and 5S rRNA from E. coli;
Edit intent: clarity
Original:  Here, we benchmark the method on six RNAs for which crystallographic data are available: tRNAphe and 5S rRNA from E. coli;
Revised:  Here, we benchmark the method on six RNAs for which crystallographic data are available: tRNAphe and 5S rRNA from Escherichia coli,
Edit intent: clarity
Original:  the P4-P6 domain of the Tetrahymena group I ribozyme ;
Revised:  the P4-P6 domain of the Tetrahymena group I ribozyme ,
Edit intent: fluency
Original:  SHAPE-directed modeling of these RNAs gave significant errors ( overall false negative rate  of 17\% ;
Revised:  SHAPE-directed modeling of these RNAs gave significant errors ( overall false negative rate of 17\% and a
Edit intent: coherence
Original:  false discovery rate  of 21\% ) , with at least one  error in five of the six cases.
Revised:  false discovery rate of 21\% , with at least one error in five of the six cases.
Edit intent: fluency
Original:  Variations of data processing or modeling do not mitigate these errors.
Revised:  Extensive variations of data processing or modeling do not mitigate these errors.
Edit intent: clarity
Original:  Instead, as evaluated by bootstrapping, the information content of SHAPE data appears insufficient to define these RNAs' structures.
Revised:  Instead, as evaluated by bootstrapping, the information content of these RNAs' structures.
Edit intent: clarity