wanyu/IteraTeR_v2 huggingface dataset:
Original: We investigate random search processes on complex networks and for the first time derive an exact expression for the partial cover time that quantifies the  time a walker needs to visit multiple targets.
Revised: We investigate random search processes on complex networks and derive an exact expression for the partial cover time that quantifies the time a walker needs to visit multiple targets.
Edit intent: clarity
Original: We investigate random search processes on complex networks and for the first time derive an exact expression for the partial cover time that quantifies the  time a walker needs to visit multiple targets.
Revised: We investigate random search processes on complex networks and for the first time derive an exact expression for the partial cover time that quantifies the expected time a walker needs to visit multiple targets.
Edit intent: clarity
Original:  Interestingly , we observe the slow, logarithmic increase of the global partial cover time with the target number across various real networks .
Revised:  Interestingly , we observe the logarithmic increase of the global partial cover time with the target number across various real networks .
Edit intent: clarity
Original: We prove that the set of all solutions for twisted word equations with regular constraints is an EDT0L language and  can be computed in PSPACE.
Revised: We prove that the set of all solutions of such a twisted word equation is an EDT0L language and can be computed in PSPACE.
Edit intent: clarity
Original:  It follows that the set of solutions to equations with rational constraints in a context-free group (= finitely generated virtually free group) in reduced normal forms is EDT0L.
Revised:  It follows that the set of solutions to equations with rational constraints in finitely generated virtually free group) in reduced normal forms is EDT0L.
Edit intent: clarity
Original:  Our results generalize the work by Lohrey and S \'e%DIFDELCMD < }%%% nizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to complexity and with respect to expressive power.
Revised:  Our results generalize the work by Lohrey and \'e%DIFDELCMD < }%%% nizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to complexity and with respect to expressive power.
Edit intent: clarity
Original:  Our results generalize the work by Lohrey and S \'e%DIFDELCMD < }%%% nizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to complexity and with respect to expressive power.
Revised:  Our results generalize the work by Lohrey and S %DIFDELCMD < }%%% nizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to complexity and with respect to expressive power.
Edit intent: fluency
Original:  Our results generalize the work by Lohrey and S \'e%DIFDELCMD < }%%% nizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to complexity and with respect to expressive power.
Revised:  Our results generalize the work by Lohrey and S \'e%DIFDELCMD < }%%% nizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to both complexity and expressive power.
Edit intent: clarity
Original:  Neither paper gave any concrete complexity bound and both rely on the exponent of periodicity, so the result in these papers concern only subsets of solutions  , whereas our results concern all solutions.
Revised:  Neither paper gave any concrete complexity bound and the results in these papers concern only subsets of solutions , whereas our results concern all solutions.
Edit intent: coherence
Original:  Neither paper gave any concrete complexity bound and both rely on the exponent of periodicity, so the result in these papers concern only subsets of solutions  , whereas our results concern all solutions.
Revised:  Neither paper gave any concrete complexity bound and both rely on the exponent of periodicity, so the result in these papers are stated subsets of solutions , whereas our results concern all solutions.
Edit intent: clarity
Original:  We do more , we give , in some sense, the "optimal" formal language characterization of the full solution set  .
Revised:  Moreover , we give , in some sense, the "optimal" formal language characterization of the full solution set .
Edit intent: coherence
Original:  We do more , we give , in some sense, the "optimal" formal language characterization of the full solution set  .
Revised:  We do more , we give a formal language characterization of the full solution set .
Edit intent: clarity
Original: It is well-known that the problem to solve equations in virtually free groups can be reduced to the problem to solve twisted word equations with regular constraints over free monoids with involution.
Revised: It is well-known that the problem solving equations in virtually free groups can be reduced to the problem to solve twisted word equations with regular constraints over free monoids with involution.
Edit intent: fluency
Original: It is well-known that the problem to solve equations in virtually free groups can be reduced to the problem to solve twisted word equations with regular constraints over free monoids with involution.
Revised: It is well-known that the problem to solve equations in virtually free groups can be reduced to the problem of solving twisted word equations with regular constraints over free monoids with involution.
Edit intent: fluency
Original:  In a first part of the paper we prove that the set of all solutions of such a twisted word equation is an EDT0L language and that the specification of that EDT0L language can be computed in PSPACE. (We give a more precise bound in the paper.)
Revised:  In this paper we prove that the set of all solutions of such a twisted word equation is an EDT0L language and that the specification of that EDT0L language can be computed in PSPACE. (We give a more precise bound in the paper.)
Edit intent: clarity
Original:  In a first part of the paper we prove that the set of all solutions of such a twisted word equation is an EDT0L language and that the specification of that EDT0L language can be computed in PSPACE. (We give a more precise bound in the paper.)
Revised:  In a first part of the paper we prove that the set of all solutions of a twisted word equation is an EDT0L language and that the specification of that EDT0L language can be computed in PSPACE. (We give a more precise bound in the paper.)
Edit intent: clarity
Original:  In a first part of the paper we prove that the set of all solutions of such a twisted word equation is an EDT0L language and that the specification of that EDT0L language can be computed in PSPACE. (We give a more precise bound in the paper.)
Revised:  In a first part of the paper we prove that the set of all solutions of such a twisted word equation is an EDT0L language whose specification can be computed in PSPACE. (We give a more precise bound in the paper.)
Edit intent: clarity
Original:  In the second part  we apply the results to the solution set of equations with rational constraints in finitely generated virtually free groups .
Revised:  In the second part of the paper we apply the results to the solution set of equations with rational constraints in finitely generated virtually free groups .
Edit intent: clarity
Original:  In the second part  we apply the results to the solution set of equations with rational constraints in finitely generated virtually free groups .
Revised:  In the second part we apply the results to the solution set of equations with rational constraints for finitely generated virtually free groups .
Edit intent: fluency
Original:  For each such group we obtain the same results as above for the set of solutions in standard normal forms with respect to some natural set of generators.
Revised:  For each such group we obtain the same results as above for the set of solutions in standard normal forms with respect to a natural set of generators.
Edit intent: clarity
Original:  Neither paper gave any concrete complexity bound and the results in these papers are stated  subsets of solutions only, whereas our results concern all solutions .
Revised:  Neither paper gave any concrete complexity bound and the results in these papers are stated for subsets of solutions only, whereas our results concern all solutions .
Edit intent: fluency
Original:  In this paper we prove that the set of all solutions of a twisted word equation is an EDT0L language whose specification can be computed in \mathsf{PSPACE .
Revised:  In this paper we prove that the set of all solutions of a twisted word equation is an EDT0L language whose specification can be computed in PSPACE .
Edit intent: coherence
Original:  In the second part of the paper we apply the results for twisted equations to obtain in \mathsf{PSPACE an EDT0L description of the solution set of equations with rational constraints for finitely generated virtually free groups in standard normal forms with respect to a natural set of generators.
Revised:  In the second part of the paper we apply the results for twisted equations to obtain in PSPACE an EDT0L description of the solution set of equations with rational constraints for finitely generated virtually free groups in standard normal forms with respect to a natural set of generators.
Edit intent: fluency
Original:  If the rational constraints are given by a homomorphism into a fixed (or "small enough") finite monoid, then our algorithms can be implemented in \mathsf{NSPACE (n^2\log n), that is, in quasi-quadratic nondeterministic space.
Revised:  If the rational constraints are given by a homomorphism into a fixed (or "small enough") finite monoid, then our algorithms can be implemented in NSPACE (n^2\log n), that is, in quasi-quadratic nondeterministic space.
Edit intent: coherence
Original: It is well-known that the problem solving equations in virtually free groups can be reduced to the problem of solving twisted word equations with regular constraints over free monoids with involution.
Revised: It is well known that the problem solving equations in virtually free groups can be reduced to the problem of solving twisted word equations with regular constraints over free monoids with involution.
Edit intent: fluency
Original: We introduce the dynamic conflict-free coloring problem for a set S of intervals in R^1 with respect to points, where the goal is to maintain a conflict-free coloring for S under insertions and deletions  .
Revised: We introduce the dynamic conflict-free coloring problem for a set S of intervals in R^1 with respect to points, where the goal is to maintain a conflict-free coloring forS under insertions and deletions .
Edit intent: fluency
Original:  we call this graph class {\em split-matching-extended graphs} and characterize them by forbidden subgraphs .
Revised:  we call this graph class {\em split-matching-extended graphs} (which can be characterized by forbidden induced subgraphs) .
Edit intent: clarity
Original: A vertex set D in a finite undirected graph G is an %DIFDELCMD < {\em %%% efficient dominating set (e.d.s. \ for short) of G if every vertex of G is dominated by exactly one vertex of D.
Revised: A vertex set D in a finite undirected graph G is an %DIFDELCMD < {\em %%% efficient dominating set e.d.s. \ for short) of G if every vertex of G is dominated by exactly one vertex of D.
Edit intent: fluency
Original:  The Efficient Domination (ED) problem, which asks for the existence of an e.d.s.\ in G, is known to be \NP-complete even for very restricted graph classes such as for 2P_3-free chordal graphs while it is solvable in polynomial time for P_6-free chordal graphs (and even for P_6-free graphs).
Revised:  The Efficient Domination (ED) problem, which asks for the existence of an e.d.s.\ in G, is known to be \NP-complete even for very restricted graph classes such as for 2P_3-free chordal graphs while it is solvable in polynomial time for P_6-free chordal graphs (and even for P_6-free graphs).
Edit intent: fluency
Original:  we call this graph class%DIFDELCMD < {\em %%% split-matching-extended graphs (which can be characterized by forbidden induced subgraphs) .
Revised:  we call this graph class%DIFDELCMD < {\em %%% (which can be characterized by forbidden induced subgraphs) .
Edit intent: clarity
Original:  we call this graph class%DIFDELCMD < {\em %%% split-matching-extended graphs (which can be characterized by forbidden induced subgraphs) .
Revised:  we call this graph class%DIFDELCMD < {\em %%% split-matching-extended graphs .
Edit intent: coherence
Original:  We show that our self-triggered coordination algorithm guarantees that the system asymptotically reaches the set of desired states.
Revised:  We prove that our self-triggered coordination algorithm guarantees that the system asymptotically reaches the set of desired states.
Edit intent: clarity
Original: In this paper we consider programmable matter that consists of computationally limited devices (which we call particles) that are able to self-organize in order to achieve a desired collective goal without the need for central control or external intervention.
Revised: We consider programmable matter that consists of computationally limited devices (which we call particles) that are able to self-organize in order to achieve a desired collective goal without the need for central control or external intervention.
Edit intent: coherence
Original: In this paper we consider programmable matter that consists of computationally limited devices (which we call particles) that are able to self-organize in order to achieve a desired collective goal without the need for central control or external intervention.
Revised: In this paper we consider programmable matter that consists of computationally limited devices (which we call particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention.
Edit intent: clarity
Original:  We investigate the feasibility of solving fundamental problems relevant for programmable matter.
Revised:  We investigate the feasibility of solving fundamental problems relevant to programmable matter.
Edit intent: fluency
Original:  We present an efficient local-control algorithm for leader election , that elects a leader particle in O(n)  rounds with high probability, where n is the number of particles in the system.
Revised:  We present an efficient local-control algorithm which solves the leader election problem in O(n) rounds with high probability, where n is the number of particles in the system.
Edit intent: clarity
Original:  Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.
Revised:  Our algorithm relies only on local information (e.g., particles do not have unique identifiers, any knowledge of n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.
Edit intent: clarity
Original:  Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.
Revised:  Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or any sort of global coordinate system), and requires only a constant-size memory per particle.
Edit intent: fluency
Original:  Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.
Revised:  Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only constant memory per particle.
Edit intent: clarity
Original: We consider programmable matter that consists of computationally limited devices ( which we call particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention.
Revised: We consider programmable matter that consists of computationally limited devices ( called particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention.
Edit intent: fluency
Original:  We use the geometric amoebot model to describe such self-organizing particle systems, which defines how particles can actively move and establish or release bonds with one another.
Revised:  We use the geometric amoebot model to describe such self-organizing particle systems, which defines how particles can actively move and communicate with one another.
Edit intent: clarity
Original:  Under this model, we investigate the feasibility of solving fundamental problems relevant to programmable matter.
Edit intent: coherence
Original:  Our algorithm relies only on local information (e.g., particles do not have unique identifiers, any knowledge of n, or any sort of global coordinate system ), and requires only constant memory per particle.
Revised:  Our algorithm relies only on local information --- particles do not have unique identifiers, any knowledge of n, or any sort of global coordinate system ), and requires only constant memory per particle.
Edit intent: coherence
Original:  Our algorithm relies only on local information (e.g., particles do not have unique identifiers, any knowledge of n, or any sort of global coordinate system ), and requires only constant memory per particle.
Revised:  Our algorithm relies only on local information (e.g., particles do not have unique identifiers, any knowledge of n, or any sort of global coordinate system --- and requires only constant memory per particle.
Edit intent: fluency
Original: We are concerned with finite element modeling of geometrically non-linear laminated glass beams consisting of stiff elastic glass layers connected with compliant polymeric interlayer of temperature-sensitive viscoelastic behavior.
Revised: Laminated glass elements, which consist of stiff elastic glass layers connected with compliant polymeric interlayer of temperature-sensitive viscoelastic behavior.
Edit intent: clarity
Original:  In particular, four layerwise theories are introduced in this paper, which differ in the non-linear beam formulation used at the layer level (von K\'{a}rm\'{a}n/Reissner) and in constitutive assumptions used for interlayer ( viscoelastic solid with  time-independent bulk modulus/Poisson ratio).
Revised:  In particular, four layerwise theories are introduced in this paper, which differ in the non-linear beam formulation at the layer level (von K\'{a}rm\'{a}n/Reissner) and in constitutive assumptions used for interlayer ( viscoelastic solid with time-independent bulk modulus/Poisson ratio).
Edit intent: fluency
Original:  In particular, four layerwise theories are introduced in this paper, which differ in the non-linear beam formulation used at the layer level (von K\'{a}rm\'{a}n/Reissner) and in constitutive assumptions used for interlayer ( viscoelastic solid with  time-independent bulk modulus/Poisson ratio).
Revised:  In particular, four layerwise theories are introduced in this paper, which differ in the non-linear beam formulation used at the layer level (von K\'{a}rm\'{a}n/Reissner) and in constitutive assumptions for the interlayer (a viscoelastic solid with time-independent bulk modulus/Poisson ratio).
Edit intent: fluency
Original:  In particular, four layerwise theories are introduced in this paper, which differ in the non-linear beam formulation used at the layer level (von K\'{a}rm\'{a}n/Reissner) and in constitutive assumptions used for interlayer ( viscoelastic solid with  time-independent bulk modulus/Poisson ratio).
Revised:  In particular, four layerwise theories are introduced in this paper, which differ in the non-linear beam formulation used at the layer level (von K\'{a}rm\'{a}n/Reissner) and in constitutive assumptions used for interlayer ( viscoelastic solid with the time-independent bulk modulus/Poisson ratio).
Edit intent: fluency
Original:  For the most straightforward formulation , combining the von K\'{a}rm\'{a}n model with the assumption of time-independent Poisson ratio , we perform detailed verification and validation studies at different temperatures and compare its accuracy with simplified elastic solutions mostly used in practice.
Revised:  For the most straightforward formulation that combines the von K\'{a}rm\'{a}n model with the assumption of time-independent Poisson ratio , we perform detailed verification and validation studies at different temperatures and compare its accuracy with simplified elastic solutions mostly used in practice.
Edit intent: coherence
Original:  These findings provide a suitable basis for extensions towards laminated plates and /or glass layer fracture, owing to the modular format of layerwise theories.
Revised:  These findings provide a suitable basis for extensions towards laminated plates and glass layer fracture, owing to the modular format of layerwise theories.
Edit intent: fluency
Original:  Carried out using both numerical and analytical approach , our results show that the invasion proceeds following preferentially a hierarchical order in the nodes from those with higher degree to those with lower degree.
Revised:  Carried out using both numerical and analytical approaches , our results show that the invasion proceeds following preferentially a hierarchical order in the nodes from those with higher degree to those with lower degree.
Edit intent: fluency
Original:  These findings have potential real-world applications, as they suggest that, in order to promote cooperative behavior on complex networks, one should infect with cooperators high but not too high degree nodes.
Revised:  These findings have potential applications, as they suggest that, in order to promote cooperative behavior on complex networks, one should infect with cooperators high but not too high degree nodes.
Edit intent: clarity
Original:  These findings have potential real-world applications, as they suggest that, in order to promote cooperative behavior on complex networks, one should infect with cooperators high but not too high degree nodes.
Revised:  These findings have potential real-world applications, as they suggest that, in order to promote cooperative behavior on complex networks, one should infect with cooperators high but not too high degree nodes.
Edit intent: fluency
Original:  Edward builds on two compositional representations---random variables and inference.
Revised:  Edward defines two compositional representations---random variables and inference.
Edit intent: clarity
Original:  For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation , to variational inference , to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks.
Revised:  For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation to variational inference , to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks.
Edit intent: fluency
Original:  For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation , to variational inference , to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks.
Revised:  For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation , to variational inference to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks.
Edit intent: fluency