wanyu/IteraTeR_v2 huggingface dataset:
Original:  We find that an asexual model with  strength of selection tuned to that of the linkage block provides an excellent description of genetic diversity and the site frequency spectra when compared to computer simulations of population dynamics.
Revised:  We find that an asexual model with the strength of selection tuned to that of the linkage block provides an excellent description of genetic diversity and the site frequency spectra when compared to computer simulations of population dynamics.
Edit intent: fluency
Original:  In particular a connected graph has linear rank-width 1 if and only if it is locally equivalent to a caterpillar if and only if it is a vertex-minor of a path [O-joung Kwon and Sang-il Oum, Graphs of small rank-width are pivot-minors of graphs of small tree-width, to appear in Discrete Applied Mathematics, arxiv:
Revised:  In particular a connected graph has linear rank-width 1 if and only if it is locally equivalent to a caterpillar if and only if it is a vertex-minor of a path [O-joung Kwon and Sang-il Oum, Graphs of small rank-width are pivot-minors of graphs of small tree-width, arxiv:
Edit intent: coherence
Original: 1203.3606] if and only if it does not contain the co-K_2 graph, the Net graph and the 5-cycle graph as vertex-minors [Isolde Adler, Arthur M. Farley and Andrzej Proskurowski, Obstructions for linear rank-width at most 1 , to appear in Discrete Applied Mathematics , arxiv:1106.2533].
Revised: 1203.3606] if and only if it does not contain the co-K_2 graph, the Net graph and the 5-cycle graph as vertex-minors [Isolde Adler, Arthur M. Farley and Andrzej Proskurowski, Obstructions for linear rank-width at most 1 , arxiv:1106.2533].
Edit intent: coherence
Original:  This model is for a system of ordinary differential equations.
Revised:  This model is written as a system of ordinary differential equations.
Edit intent: clarity
Original: In this case study, we apply the technique of pseudo-first order approximation to simplify the reaction rates.
Revised: In this case study, the technique of pseudo-first order approximation to simplify the reaction rates.
Edit intent: coherence
Original: In this case study, we apply the technique of pseudo-first order approximation to simplify the reaction rates.
Revised: In this case study, we apply the technique of Pseudo-first order approximation is applied to simplify the reaction rates.
Edit intent: clarity
Original: We study the complexity classes P and NP through a semigroup fP ( `` polynomial-time functions '' ), consisting of all polynomially balanced polynomial-time computable partial functions.
Revised: We study the complexity classes P and NP through a semigroup fP ( " polynomial-time functions '' ), consisting of all polynomially balanced polynomial-time computable partial functions.
Edit intent: fluency
Original: We study the complexity classes P and NP through a semigroup fP ( `` polynomial-time functions '' ), consisting of all polynomially balanced polynomial-time computable partial functions.
Revised: We study the complexity classes P and NP through a semigroup fP ( `` polynomial-time functions " ), consisting of all polynomially balanced polynomial-time computable partial functions.
Edit intent: fluency
Original:  We define reductions with respect to which certain functions, such as Levin's universal one-way function, are fP-complete.
Revised:  We define reductions with respect to which certain universal one-way function, are fP-complete.
Edit intent: clarity
Original:  We define reductions with respect to which certain functions, such as Levin's universal one-way function, are fP-complete.
Revised:  We define reductions with respect to which certain functions, such as Levin's universal one-way functions are fP-complete.
Edit intent: fluency
Original:  The joint outage probability is used to determine the diversity gain (as the SIR goes to infinity), and it turns out that there is no diversity gain in simple retransmission schemes, even with iid Rayleigh fading over all links.
Revised:  The joint outage probability is used to determine the diversity gain (as the SIR goes to infinity), and it turns out that there is no diversity gain in simple retransmission schemes, even with independent Rayleigh fading over all links.
Edit intent: fluency
Original: A recent result provides a combinatorial characterization of the generic rigidity for the majority of Computer Aided Design (CAD) structures.
Revised: Geometric constraint systems underly popular Computer Aided Design (CAD) structures.
Edit intent: clarity
Original:  The corresponding candidacy game, where candidates choose strategically to participate or not, has been studied in very few papers, mainly by Dutta et al., who showed that no non-dictatorial voting procedure satisfying unanimity is candidacy-strategyproof, or equivalently , is such that the joint action where all candidates enter the election is always a pure strategy Nash equilibrium.
Revised:  The corresponding candidacy game, where candidates choose strategically to participate or not, has been studied \%initially by Dutta et al., who showed that no non-dictatorial voting procedure satisfying unanimity is candidacy-strategyproof, or equivalently , is such that the joint action where all candidates enter the election is always a pure strategy Nash equilibrium.
Edit intent: clarity
Original:  The corresponding candidacy game, where candidates choose strategically to participate or not, has been studied in very few papers, mainly by Dutta et al., who showed that no non-dictatorial voting procedure satisfying unanimity is candidacy-strategyproof, or equivalently , is such that the joint action where all candidates enter the election is always a pure strategy Nash equilibrium.
Revised:  The corresponding candidacy game, where candidates choose strategically to participate or not, has been studied in very few papers, mainly by Dutta et al., who showed that no non-dictatorial voting procedure satisfying unanimity is candidacy-strategyproof, that is , is such that the joint action where all candidates enter the election is always a pure strategy Nash equilibrium.
Edit intent: coherence
Original:  They also showed that for voting trees , there are candidacy games with no pure strategy equilibria.
Revised:  They also showed that for some voting tree procedures , there are candidacy games with no pure strategy equilibria.
Edit intent: clarity
Original:  We focus our study into the simplest case in which vertices are spread in the one dimensional Euclidean metric space.
Revised:  We focus our study on the simplest case in which vertices are spread in the one dimensional Euclidean metric space.
Edit intent: fluency
Original:  We focus our study into the simplest case in which vertices are spread in the one dimensional Euclidean metric space.
Revised:  We focus our study into the simplest case in which vertices are spread in the one dimensional Euclidean space.
Edit intent: clarity
Original: In this document, we study the scope of the following graph representation: vertices are points spread in a metric space and each vertex is assigned to a box in the space .
Revised: In this document, we study the scope of the following graph model: each vertex is assigned to a box in the space .
Edit intent: clarity
Original:  Two vertices are connected by an edge if and only if its respective boxes contain the opposite vertex .
Revised:  Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element .
Edit intent: clarity
Original:  Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path , and interval bigraphs graphs ).
Revised:  Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path ).
Edit intent: coherence
Original:  We also study the particular case where each point is the center of its respective box.
Revised:  We also study the particular case where each representative element is the center of its respective box.
Edit intent: clarity
Original:  In this case we provide constructive representations for interval, block and outerplanar graphs.
Revised:  In this particular case, we provide constructive representations for interval, block and outerplanar graphs.
Edit intent: clarity
Original:  Finally, we present a family of graphs that separates the general and the particular case .
Revised:  Finally, we show that the general and the particular case .
Edit intent: clarity
Original: We use Markov chains and numerical linear algebra - and several CPU hours - to determine the most likely set of coins in your wallet under reasonable spending assumptions.
Revised: We use Markov chains and numerical linear algebra -- and several CPU hours - to determine the most likely set of coins in your wallet under reasonable spending assumptions.
Edit intent: fluency
Original: We use Markov chains and numerical linear algebra - and several CPU hours - to determine the most likely set of coins in your wallet under reasonable spending assumptions.
Revised: We use Markov chains and numerical linear algebra - and several CPU hours -- to determine the most likely set of coins in your wallet under reasonable spending assumptions.
Edit intent: fluency
Original: We use Markov chains and numerical linear algebra - and several CPU hours - to determine the most likely set of coins in your wallet under reasonable spending assumptions.
Revised: We use Markov chains and numerical linear algebra - and several CPU hours - to determine the expected number of coins in your wallet under reasonable spending assumptions.
Edit intent: clarity
Original:  We identify the spending strategy that results in the minimum possible expected number of coins, and we consider two other strategies which are more realistic.
Revised:  We identify the spending strategy that results in the minimum possible expected number of coins, and we consider two other strategies that are more realistic.
Edit intent: fluency
Original:  The well-known computational problem, called recognition, asks for an input graph G whether it can be represented by closed intervals, i.e., whether G is an interval graph.
Revised:  The well-known computational problem, called recognition, asks whether an input graph G whether it can be represented by closed intervals, i.e., whether G is an interval graph.
Edit intent: clarity
Original:  The well-known computational problem, called recognition, asks for an input graph G whether it can be represented by closed intervals, i.e., whether G is an interval graph.
Revised:  The well-known computational problem, called recognition, asks for an input graph G can be represented by closed intervals, i.e., whether G is an interval graph.
Edit intent: clarity
Original:  Input of this problem consists of a graph G with a partial representation \cal R' fixing  positions of some intervals.
Revised:  The input of this problem consists of a graph G with a partial representation \cal R' fixing positions of some intervals.
Edit intent: fluency
Original:  Input of this problem consists of a graph G with a partial representation \cal R' fixing  positions of some intervals.
Revised:  Input of this problem consists of a graph G with a partial representation \cal R' fixing the positions of some intervals.
Edit intent: fluency
Original:  We  ]  give a linear-time algorithm based on PQ-trees which solves this problem .
Revised:  We ] give a linear-time algorithm based on PQ-trees .
Edit intent: clarity
Original:  We construct a global optimization-based version of such a method for mixed volume meshes  .
Revised:  We construct a global optimization-based versions of such methods for mixed volume meshes .
Edit intent: fluency
Original: We consider the following activation process in d-regular undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors, where  1 <r\leq d is the activation threshold.
Revised: We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors, where 1 <r\leq d is the activation threshold.
Edit intent: clarity
Original: We consider the following activation process in d-regular undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors, where  1 <r\leq d is the activation threshold.
Revised: We consider the following activation process in d-regular undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors, where 1 is the activation threshold.
Edit intent: clarity
Original:  Such processes are studied in several fields such as fault tolerant distributed computing, epidemiology, \%social networks, probability theory, risk analysis, statistical physics and viral marketing.
Edit intent: coherence
Original:  In this work we present upper bounds on m(G,r) on d-regular graphs with expansion properties( \le  parameterized by the spectral gap and/or the girth of the graphs ).
Revised:  In this work we present upper bounds on m(G,r) \le parameterized by the spectral gap and/or the girth of the graphs ).
Edit intent: clarity
Original:  The general flavor of our results is that sufficiently strong expansion ( i.e. \lambda(G)=O(d) ) or sufficiently large girth (that is, girth \Omega(\log \log d)) implies that in n-vertex graphs, m(G,2) \le O(n{d^2}) .
Revised:  The general flavor of our results is that sufficiently strong expansion ( e.g., \lambda(G)=O(d) ) or sufficiently large girth (that is, girth \Omega(\log \log d)) implies that in n-vertex graphs, m(G,2) \le O(n{d^2}) .
Edit intent: clarity
Original:  The general flavor of our results is that sufficiently strong expansion ( i.e. \lambda(G)=O(d) ) or sufficiently large girth (that is, girth \Omega(\log \log d)) implies that in n-vertex graphs, m(G,2) \le O(n{d^2}) .
Revised:  The general flavor of our results is that sufficiently strong expansion ( i.e. \lambda(G)=O(d) , or girth \Omega(\log \log d)) implies that in n-vertex graphs, m(G,2) \le O(n{d^2}) .
Edit intent: clarity
Original:  For such graphs we prove that \Omega(\frac{n}{d^2 \log d}) }\le m(G,2) =O(\frac{n \log d{\epsilon^2 d^2}) } \le {d^2\log d}) almost surely} .
Revised:  For such graphs we prove that \Omega(\frac{n}{d^2 \log d}) }\le m(G,2) =O(\frac{n \log d{\epsilon^2 d^2}) } \le O(\frac{n\log\log d{d^2\log d}) almost surely} .
Edit intent: fluency
Original: Given a directed graph D = (V,A) we de?fine its intersection graph I(D) = (A,E) to be the graph having A as a node-set and two nodes of I(D) are adjacent if their corresponding arcs share a common node that is the tail of at least one of these arcs.
Revised: Given a directed graph D = (V,A) we define its intersection graph I(D) = (A,E) to be the graph having A as a node-set and two nodes of I(D) are adjacent if their corresponding arcs share a common node that is the tail of at least one of these arcs.
Edit intent: fluency
Original:  We find that full determination of observed cell-to-cell variations in protein abundances is not inherent in chemotaxis itself, but in fact appears to be jointly imposed by the chemotaxis program in conjunction with other factors, e.g., the protein synthesis machinery and/or additional non-chemotactic cell functions  .
Revised:  We find that full determination of observed cell-to-cell variations in protein abundances is not inherent in chemotaxis itself, but in fact appears to be jointly imposed by the chemotaxis program in conjunction with other factors, e.g., the protein synthesis machinery and/or additional non-chemotactic cell functions such as cell metabolism .
Edit intent: clarity
Original:  In this paper, we explore the edge coloring problem of cubic graphs by using the newly proposed complex coloring approach.
Revised:  In this paper, based on the complex coloring of cubic graphs by using the newly proposed complex coloring approach.
Edit intent: clarity
Original:  We introduce a new particle representation, which we call  labelled Moran model, and which has the same empirical type distribution as the original Moran model, provided the initial values are chosen appropriately.
Revised:  We introduce a new particle representation, which we call the labelled Moran model, and which has the same empirical type distribution as the original Moran model, provided the initial values are chosen appropriately.
Edit intent: fluency
Original:  We introduce a new particle representation, which we call  labelled Moran model, and which has the same empirical type distribution as the original Moran model, provided the initial values are chosen appropriately.
Revised:  We introduce a new particle representation, which we call labelled Moran model, and which has the same distribution of type frequencies as the original Moran model, provided the initial values are chosen appropriately.
Edit intent: clarity
Original:  With the help of elementary methods only, we do not only recover fixation probabilities, but  obtain detailed insight into the number and nature of the selective events that play a role in the fixation process forward in time.
Revised:  With the help of elementary methods only, we not only recover fixation probabilities, but obtain detailed insight into the number and nature of the selective events that play a role in the fixation process forward in time.
Edit intent: coherence
Original:  With the help of elementary methods only, we do not only recover fixation probabilities, but  obtain detailed insight into the number and nature of the selective events that play a role in the fixation process forward in time.
Revised:  With the help of elementary methods only, we do not only recover fixation probabilities, but also obtain detailed insight into the number and nature of the selective events that play a role in the fixation process forward in time.
Edit intent: coherence
Original:  In this model, the typical spacing between adjacent cortical orientation columns preferring the same orientation  arises via Moir\'{e}-Interference between hexagonal ON/OFF RGC mosaics.
Revised:  The typical spacing between adjacent cortical orientation columns preferring the same orientation arises via Moir\'{e}-Interference between hexagonal ON/OFF RGC mosaics.
Edit intent: clarity
Original:  This Moir\'{e}-Interference critically depends on long-range hexagonal order within the RGC mosaics .
Revised:  While this Moir\'{e}-Interference critically depends on long-range hexagonal order within the RGC mosaics .
Edit intent: coherence
Original:  We conclude , that the positioning of ON/OFF ganglion cell pairs lacks the spatial structure necessary to generate the OPMs periodicity found in the visual cortex.
Revised:  We conclude that the layout of ON/OFF ganglion cell pairs lacks the spatial structure necessary to generate the OPMs periodicity found in the visual cortex.
Edit intent: clarity
Original:  We conclude , that the positioning of ON/OFF ganglion cell pairs lacks the spatial structure necessary to generate the OPMs periodicity found in the visual cortex.
Revised:  We conclude , that the positioning of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to generate the OPMs periodicity found in the visual cortex.
Edit intent: clarity
Original: Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell-the capsid.
Revised: Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid.
Edit intent: fluency
Original:  Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to %DIFDELCMD < {\sl %%% maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.
Revised:  Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to %DIFDELCMD < {\sl %%% maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.
Edit intent: fluency
Original: In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where their network topologies change by continuous removal and addition of nodes.
Revised: In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where the network topologies change by continuous removal and addition of nodes.
Edit intent: clarity
Original:  Each of these removal and addition can be either random or intentional.
Revised:  Each removal and addition can be either random or intentional.
Edit intent: clarity
Original:  We find that cooperation clusters are the most fragile against TR, while they are the most robust against RP even in high temptation coefficients for defect .
Revised:  We find that cooperation clusters are most fragile against TR, while they are the most robust against RP even in high temptation coefficients for defect .
Edit intent: fluency
Original:  We find that cooperation clusters are the most fragile against TR, while they are the most robust against RP even in high temptation coefficients for defect .
Revised:  We find that cooperation clusters are the most fragile against TR, while they are most robust against RP even in high temptation coefficients for defect .
Edit intent: fluency
Original:  We find that cooperation clusters are the most fragile against TR, while they are the most robust against RP even in high temptation coefficients for defect .
Revised:  We find that cooperation clusters are the most fragile against TR, while they are the most robust against RP , even for large values of the temptation coefficient for defection .
Edit intent: clarity
Original:  The effect of the degree mixing pattern of the network is not the primary factor for the robustness of cooperation under continuous change in network topology due to consequential removal and addition of nodes , which is quite different from the cases observed in static networks.
Revised:  The effect of the degree mixing pattern of the network is not the primary factor for the robustness of cooperation under continuous change in network topology , which is quite different from the cases observed in static networks.
Edit intent: coherence
Original:  Cooperation clusters become more robust as the number of links of the hubs occupied by cooperators increase.
Revised:  Cooperation clusters become more robust as the number of links of hubs occupied by cooperators increase.
Edit intent: fluency
Original:  Our results indicate that a huge variety of individuals are needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.
Revised:  Our results might infer the fact that a huge variety of individuals are needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.
Edit intent: clarity
Original:  Our results indicate that a huge variety of individuals are needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.
Revised:  Our results indicate that a huge variety of individuals is needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.
Edit intent: fluency