wanyu/IteraTeR_v2 huggingface dataset:
Original:  We hypothesize that this diversity supports efficient exploration and robustness of solutions , also reflected in our observation  that the variance of the fitness values is maximal in critical network populations.
Revised:  We hypothesize that this diversity supports efficient exploration and robustness of solutions . Also reflected in our observation that the variance of the fitness values is maximal in critical network populations.
Edit intent: fluency
Original:  We hypothesize that this diversity supports efficient exploration and robustness of solutions , also reflected in our observation  that the variance of the fitness values is maximal in critical network populations.
Revised:  We hypothesize that this diversity supports efficient exploration and robustness of solutions , also reflected in our observation is that the variance of the fitness values is maximal in critical network populations.
Edit intent: clarity
Original:  We hypothesize that this diversity supports efficient exploration and robustness of solutions , also reflected in our observation  that the variance of the fitness values is maximal in critical network populations.
Revised:  We hypothesize that this diversity supports efficient exploration and robustness of solutions , also reflected in our observation that the variance of the values is maximal in critical network populations.
Edit intent: clarity
Original: Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges , so that every pair of vertices is connected by at least one path in which no two edges are colored the same  .
Revised: Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same .
Edit intent: fluency
Original:  In this paper we study the rainbow connection number with respect to three important graph product operations (  cartesian product, lexicographic product and strong product) and the operation of graph powering.
Revised:  In this paper we study the rainbow connection number with respect to three important graph product operations ( namely cartesian product, lexicographic product and strong product) and the operation of graph powering.
Edit intent: coherence
Original:  More specifically we show the following: (Here, r(G) denotes the radius of G, an obvious lower bound for rc(G)) (1.) For a connected graphG, let G^{k be the k-th power of G. We show that for k }%DIFDELCMD < \ge %%% 2, r(G^{k) }%DIFDELCMD < \le %%% rc(G^{k) }%DIFDELCMD < \le %%% 2r(G^{k non-trivial graphs G and H, let G \Box H be the Cartesian Product of G and H. We show that r(G \Box H)%DIFDELCMD < \le %%% rc(G \Box H)%DIFDELCMD < \le %%% 2r(G \Box H).
Revised:  More specifically we show the following: (Here, r(G) denotes the radius of G, an obvious lower bound for rc(G)) (1.) For a connected graphG, let G^{k be the k-th power of G. We show that for k }%DIFDELCMD < \ge %%% 2, r(G^{k) }%DIFDELCMD < \le %%% ) }%DIFDELCMD < \le %%% 2r(G^{k non-trivial graphs G and H, let G \Box H be the Cartesian Product of G and H. We show that r(G \Box H)%DIFDELCMD < \le %%% rc(G \Box H)%DIFDELCMD < \le %%% 2r(G \Box H).
Edit intent: clarity
Original:  More specifically we show the following: (Here, r(G) denotes the radius of G, an obvious lower bound for rc(G)) (1.) For a connected graphG, let G^{k be the k-th power of G. We show that for k }%DIFDELCMD < \ge %%% 2, r(G^{k) }%DIFDELCMD < \le %%% rc(G^{k) }%DIFDELCMD < \le %%% 2r(G^{k non-trivial graphs G and H, let G \Box H be the Cartesian Product of G and H. We show that r(G \Box H)%DIFDELCMD < \le %%% rc(G \Box H)%DIFDELCMD < \le %%% 2r(G \Box H).
Revised:  More specifically we show the following: (Here, r(G) denotes the radius of G, an obvious lower bound for rc(G)) (1.) For a connected graphG, let G^{k be the k-th power of G. We show that for k }%DIFDELCMD < \ge %%% 2, r(G^{k) }%DIFDELCMD < \le %%% rc(G^{k) }%DIFDELCMD < \le %%% 2r(G^{k non-trivial graphs G and H, let G \Box H be the Cartesian Product of G and H. We show that r(G \Box H)%DIFDELCMD < \le %%% %DIFDELCMD < \le %%% 2r(G \Box H).
Edit intent: fluency
Original:  For two graphs G and H such that G is a connected, non-trivial graph and H is any non-trivial graph, let G \circ H be the Lexicographic Product of G and H. We show that when r(G \circ H)%DIFDELCMD < \ge %%% 2 we have r(G \circ H)%DIFDELCMD < \le %%%  rc(G \circ H)%DIFDELCMD < \le %%%  2r(G \circ H)and when r(G \circ H) = 1 we have 1%DIFDELCMD < \le %%% rc(G \circ H)%DIFDELCMD < \le %%% 3. The bounds are tight. (4.)
Revised:  For two graphs G and H such that G is a connected, non-trivial graph and H is any non-trivial graph, let G \circ H be the Lexicographic Product of G and H. We show that when r(G \circ H)%DIFDELCMD < \ge %%% 2 we have r(G \circ H)%DIFDELCMD < \le %%% rc(G %DIFDELCMD < \le %%% 2r(G \circ H)and when r(G \circ H) = 1 we have 1%DIFDELCMD < \le %%% rc(G \circ H)%DIFDELCMD < \le %%% 3. The bounds are tight. (4.)
Edit intent: fluency
Original:  For two graphs G and H such that G is a connected, non-trivial graph and H is any non-trivial graph, let G \circ H be the Lexicographic Product of G and H. We show that when r(G \circ H)%DIFDELCMD < \ge %%% 2 we have r(G \circ H)%DIFDELCMD < \le %%%  rc(G \circ H)%DIFDELCMD < \le %%%  2r(G \circ H)and when r(G \circ H) = 1 we have 1%DIFDELCMD < \le %%% rc(G \circ H)%DIFDELCMD < \le %%% 3. The bounds are tight. (4.)
Revised:  For two graphs G and H such that G is a connected, non-trivial graph and H is any non-trivial graph, let G \circ H be the Lexicographic Product of G and H. We show that when r(G \circ H)%DIFDELCMD < \ge %%% 2 we have r(G \circ H)%DIFDELCMD < \le %%% rc(G \circ H)%DIFDELCMD < \le %%% ) <= 2r(G \circ H)and when r(G \circ H) = 1 we have 1%DIFDELCMD < \le %%% rc(G \circ H)%DIFDELCMD < \le %%% 3. The bounds are tight. (4.)
Edit intent: coherence
Original:  For two graphs G and H such that G is a connected, non-trivial graph and H is any non-trivial graph, let G \circ H be the Lexicographic Product of G and H. We show that when r(G \circ H)%DIFDELCMD < \ge %%% 2 we have r(G \circ H)%DIFDELCMD < \le %%%  rc(G \circ H)%DIFDELCMD < \le %%%  2r(G \circ H)and when r(G \circ H) = 1 we have 1%DIFDELCMD < \le %%% rc(G \circ H)%DIFDELCMD < \le %%% 3. The bounds are tight. (4.)
Revised:  For two graphs G and H such that G is a connected, non-trivial graph and H is any non-trivial graph, let G \circ H be the Lexicographic Product of G and H. We show that when r(G \circ H)%DIFDELCMD < \ge %%% 2 we have r(G \circ H)%DIFDELCMD < \le %%% rc(G \circ H)%DIFDELCMD < \le %%% 2r(G \circ H)and when r(G \circ H) = 1 we have 1%DIFDELCMD < \le %%% %DIFDELCMD < \le %%% 3. The bounds are tight. (4.)
Edit intent: fluency
Original:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a  graph can be independent of its radius .
Revised:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% ) denotes the radius of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a graph can be independent of its radius .
Edit intent: clarity
Original:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a  graph can be independent of its radius .
Revised:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and %DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a graph can be independent of its radius .
Edit intent: coherence
Original:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a  graph can be independent of its radius .
Revised:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% %DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a graph can be independent of its radius .
Edit intent: fluency
Original:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a  graph can be independent of its radius .
Revised:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% %DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a graph can be independent of its radius .
Edit intent: fluency
Original:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a  graph can be independent of its radius .
Revised:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% %DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a graph can be independent of its radius .
Edit intent: fluency
Original:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a  graph can be independent of its radius .
Revised:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in }. In general the rainbow connection number of a graph can be independent of its radius .
Edit intent: fluency
Original:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a  graph can be independent of its radius .
Revised:  For two-connected, non-trivial graphs G and H, let G%DIFDELCMD < \boxtimes %%% H be the Strong Product of G and H. We show that r(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% rc(G%DIFDELCMD < \boxtimes %%% H)%DIFDELCMD < \le %%% 2r(G%DIFDELCMD < \boxtimes %%% H) + 2. The upper bound is tight up to an additive constant of 2. Note that in } general the rainbow connection number of a graph can be as high as the square of its radius .
Edit intent: clarity
Original:  This implies that given an instance (G,k) of treewidth we can efficiently reduce its size to O( (l* )^4) vertices, where l* is the size of a minimum feedback vertex set in G. In contrast, we show that Treewidth parameterized by the vertex-deletion distance to a co-cluster graph and Weighted Treewidth parameterized by the size of a vertex cover do not have polynomial kernels unless NP \subseteq coNP/poly .
Revised:  This implies that given an instance (G,k) of treewidth we can efficiently reduce its size to O( (l* )^4) vertices, where l* is the size of a minimum feedback vertex set in G. In contrast, we show that Treewidth parameterized by the vertex-deletion distance to a single clique, and Weighted Treewidth parameterized by the size of a vertex cover do not have polynomial kernels unless NP \subseteq coNP/poly .
Edit intent: clarity
Original:  This implies that given an instance (G,k) of treewidth we can efficiently reduce its size to O( (l* )^4) vertices, where l* is the size of a minimum feedback vertex set in G. In contrast, we show that Treewidth parameterized by the vertex-deletion distance to a co-cluster graph and Weighted Treewidth parameterized by the size of a vertex cover do not have polynomial kernels unless NP \subseteq coNP/poly .
Revised:  This implies that given an instance (G,k) of treewidth we can efficiently reduce its size to O( (l* )^4) vertices, where l* is the size of a minimum feedback vertex set in G. In contrast, we show that Treewidth parameterized by the vertex-deletion distance to a co-cluster graph and Weighted Treewidth parameterized by the size of a vertex cover , do not admit polynomial kernelizations unless NP is in coNP/poly .
Edit intent: clarity
Original: This paper studies the kernelization complexity of graph coloring problems , with respect to certain structural parameterizations of the input instances.
Revised: This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances.
Edit intent: fluency
Original:  Acknowledging this gap, we propose a definition of "ecosystem viable yields" (EVY) as yields compatible i) with biological viability levels for all time and ii) with an ecosystem dynamics.
Revised:  Acknowledging this gap, we propose a definition of "ecosystem viable yields" (EVY) as yields compatible i) with guaranteed biological safety levels for all time and ii) with an ecosystem dynamics.
Edit intent: clarity
Original:  We apply our approach to the anchovy--hake couple in the Peruvian upwelling ecosystem between the years 1971 and 1981.
Revised:  We apply our approach to the anchovy--hake couple in the Peruvian upwelling ecosystem .
Edit intent: clarity
Original:  Based on these observations we employ the level set method to represent spatial behavior of remodeling.
Revised:  Based on these observations we employ the use of a level-set function to represent the spatial behavior of remodeling.
Edit intent: clarity
Original:  We use a temporal model for osteoclast and osteoblast population dynamics to determine the change in bone mass which influences how the interface between bone and marrow changes.
Revised:  We elaborate on a temporal model for osteoclast and osteoblast population dynamics to determine the change in bone mass which influences how the interface between bone and marrow changes.
Edit intent: clarity
Original:  The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo \emph{ . By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling.
Revised:  The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro \emph{ . By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling.
Edit intent: clarity
Original:  The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo \emph{ . By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling.
Revised:  The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo and\emph{ . By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling.
Edit intent: fluency
Original:  The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo \emph{ . By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling.
Revised:  The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo \emph{in vivo . By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling.
Edit intent: clarity
Original:  By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo  .
Revised:  By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro .
Edit intent: clarity
Original:  By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo  .
Revised:  By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo and .
Edit intent: coherence
Original:  By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo  .
Revised:  By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo in vivo .
Edit intent: clarity
Original:  This makes it possible to perform in silica experiments more closely resembling experimental observations 
Revised:  This makes it possible to perform in silica experiments more closely resembling experimental observations 
Edit intent: fluency
Original:  This makes it possible to perform in silica experiments more closely resembling experimental observations 
Revised:  This makes it possible to perform in silica experiments more closely resembling experimental observations .
Edit intent: fluency
Original: In a class of natural predator-prey models , two parameters are included.
Revised: In a class of predator-prey models , two parameters are included.
Edit intent: clarity
Original:  Broadly, our experiments show that over time the WTW moves to a "robust yet fragile" configuration where is it robust under random attacks but fragile under targeted attack.
Revised:  Broadly, our experiments show that over time the WTW moves to a "robust yet fragile" configuration where it is robust to random failures but fragile under targeted attack.
Edit intent: clarity
Original:  Moreover, there is evidence of  sharp change in the structure of the network in the 1960s and 1970s, where the most measures of robustness rapidly increase before resuming a declining trend.
Revised:  Moreover, there is evidence of sharp change in the structure of the network in the 1960s and 1970s, where most measures of robustness rapidly increase before resuming a declining trend.
Edit intent: clarity
Original:  This means that computing k copies of a function with less than k times the number of quantum queries needed to compute one copy of the function implies that the overall success probability will be exponentially small in k  . We do this by showing that the multiplicative adversary method, which inherently satisfies a strong direct product theorem, is always at least as large as the additive adversary method, which is known to characterize quantum query complexity.
Revised:  This means that computing k copies of a function with less than k times the quantum queries needed to compute one copy of the function implies that the overall success probability will be exponentially small in k . We do this by showing that the multiplicative adversary method, which inherently satisfies a strong direct product theorem, is always at least as large as the additive adversary method, which is known to characterize quantum query complexity.
Edit intent: clarity
Original:  Recently, the \beta2 -- \alpha2 loop has been reported to contribute to their protein structural stabilities.
Revised:  Recently, the \beta2 - \alpha2 loop has been reported to contribute to their protein structural stabilities.
Edit intent: fluency
Original:  Thus, the region of \beta2 -- \alpha2 loop should be a potential drug target region.
Revised:  Thus, the region of \beta2 - \alpha2 loop should be a potential drug target region.
Edit intent: fluency
Original:  Thus, the region of \beta2 -- \alpha2 loop should be a potential drug target region.
Revised:  Thus, the region of \beta2 -- \alpha2 loop might be a potential drug target region.
Edit intent: clarity
Original:  Moreover, it includes an mpirun wrapper allowing for portable thread-core affinity in MPI and hybrid MPI/threaded applications.
Revised:  Moreover, it includes a mpirun wrapper allowing for portable thread-core affinity in MPI and hybrid MPI/threaded applications.
Edit intent: fluency
Original:  The methods employed are similar to those introduced in some recent work, which showed that the Global Attractor Conjecture holds in the single linkage class case.
Edit intent: coherence
Original:  We show that r_3(n)=2^Theta(n  alpha(n  )) and for every s >= 4, we have almost tight upper and lower bounds of the form 2^{n poly(alpha(n))}.
Revised:  We show that r_3(n)=2^Theta(n alpha(n ) )) and for every s >= 4, we have almost tight upper and lower bounds of the form 2^{n poly(alpha(n))}.
Edit intent: fluency