wanyu/IteraTeR_v2 huggingface dataset:
Original:  We find that quantum fluctuations significantly modify the reaction mechanism with respect to a classical calculation .
Revised:  We find that the inclusion of quantum fluctuations can significantly modify the reaction mechanism with respect to a classical calculation .
Edit intent: clarity
Original:  We find that quantum fluctuations significantly modify the reaction mechanism with respect to a classical calculation .
Revised:  We find that quantum fluctuations significantly modify the reaction mechanism .
Edit intent: clarity
Original:  We first illustrate our approach with a simple toy model and then we apply it to study the C7 _{eq to C7 _{ax transition of alanine dipeptide.
Revised:  We first illustrate our approach with a simple toy model and then we apply it to study the C7 _eq to C7 _{ax transition of alanine dipeptide.
Edit intent: fluency
Original:  We first illustrate our approach with a simple toy model and then we apply it to study the C7 _{eq to C7 _{ax transition of alanine dipeptide.
Revised:  We first illustrate our approach with a simple toy model and then we apply it to study the C7 _{eq to C7 _ax transition of alanine dipeptide.
Edit intent: fluency
Original:  We prove that the minimal spanning tree, given a sufficiently dense sample set of a curve , correctly reconstructs the smooth arcs and further closed and simple curves in Riemannian manifolds.
Revised:  We prove that the minimal spanning tree, given a sufficiently dense sample , correctly reconstructs the smooth arcs and further closed and simple curves in Riemannian manifolds.
Edit intent: clarity
Original:  We also present examples of successfully reconstructed curves and show  applications of curve reconstruction to ordering motion frames.
Revised:  We also present examples of successfully reconstructed curves and show an applications of curve reconstruction to ordering motion frames.
Edit intent: fluency
Original:  A subset of users is called admissible {\it  when their simultaneous activity obeys the prevailing interference constraints .
Revised:  A subset of users is called {\it when their simultaneous activity obeys the prevailing interference constraints .
Edit intent: clarity
Original:  We give two natural example of deep sets, by showing that both the set of Levin-random strings and the set of Kolmogorov  strings are monotone poly deep.
Revised:  We give two natural examples of deep sets, by showing that both the set of Levin-random strings and the set of Kolmogorov strings are monotone poly deep.
Edit intent: fluency
Original:  We give two natural example of deep sets, by showing that both the set of Levin-random strings and the set of Kolmogorov  strings are monotone poly deep.
Revised:  We give two natural example of deep sets, by showing that both the set of Levin-random strings and the set of Kolmogorov random strings are monotone poly deep.
Edit intent: clarity
Original:  One early clustering algorithm that computes a hierarchy of approximate solutions to this problem  for all values of k  is the agglomerative clustering algorithm with the complete linkage strategy.
Revised:  One early clustering algorithm that computes a hierarchy of approximate solutions to this problem ( for all values of k is the agglomerative clustering algorithm with the complete linkage strategy.
Edit intent: fluency
Original:  One early clustering algorithm that computes a hierarchy of approximate solutions to this problem  for all values of k  is the agglomerative clustering algorithm with the complete linkage strategy.
Revised:  One early clustering algorithm that computes a hierarchy of approximate solutions to this problem for all values of k ) is the agglomerative clustering algorithm with the complete linkage strategy.
Edit intent: fluency
Original:  For decades  this algorithm has been widely used by practitioners.
Revised:  For decades , this algorithm has been widely used by practitioners.
Edit intent: fluency
Original:  In this paper  we analyze the agglomerative complete linkage clustering algorithm.
Revised:  In this paper , we analyze the agglomerative complete linkage clustering algorithm.
Edit intent: fluency
Original:  Moreover, our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm  .
Revised:  Our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm .
Edit intent: coherence
Original:  Furthermore, we adapt our analysis to the closely related k-center and discrete k-center problem.
Revised:  Furthermore, we analyze the closely related k-center and discrete k-center problem.
Edit intent: clarity
Original: An interface stabilised finite element method for the incompressible Navier-Stokes equations is presented.
Revised: An interface stabilised finite element method for the incompressible Navier--Stokes equations is presented.
Edit intent: fluency
Original:  The method inherits the attractive stabilising mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally.
Revised:  The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally.
Edit intent: fluency
Original:  In contrast with discontinuous Galerkin methods , the number of global degrees of freedom is the same as for a continuous  method on the same mesh.
Revised:  In contrast with discontinuous Galerkin methods , the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh.
Edit intent: fluency
Original:  Different from  earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries.
Revised:  Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries.
Edit intent: fluency
Original:  Different from  earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries.
Revised:  Different from earlier investigations on the approach for the Navier--Stokes equations, the pressure field in this work is discontinuous across cell boundaries.
Edit intent: fluency
Original:  It is shown that this leads to very good local mass conservation and, for the appropriate choice of finite element spaces, momentum conservation.
Revised:  It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation.
Edit intent: fluency
Original:  Also, in this work a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a point-wise solenoidal velocity field.
Revised:  Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a point-wise solenoidal velocity field.
Edit intent: clarity
Original:  The presented analysis results are supported by a number of numerical simulations.
Revised:  The presented analysis results are supported by a range of numerical simulations.
Edit intent: clarity
Original:  We discuss the consequences of this connection to topopatric speciation and the theory of neutral speciation and biodiversity.
Revised:  We discuss the consequences of this connection for topopatric speciation and the theory of neutral speciation and biodiversity.
Edit intent: fluency
Original:  The population breaks up into multiple species each of which satisfies the mating preference, while diversity across the population of species increases .
Revised:  We derive an explicit relation involving the parameters characterizing the population that indicates when speciation is possible .
Edit intent: clarity
Original:  As a supplemental result , squares of galled networks can also be recognized in polynomial time.
Revised:  As a consequence , squares of galled networks can also be recognized in polynomial time.
Edit intent: clarity
Original:  In particular in times of crises when assets tend to have high correlation, the understanding of this di?erence can be crucial in managing systemic risk of a portfolio.
Revised:  In particular in times of crises when assets tend to have high correlation, the understanding of this difference can be crucial in managing systemic risk of a portfolio.
Edit intent: fluency
Original:  In this paper we gen- eralize Merton's option formula in the presence jumps to the multi-asset case.
Revised:  In this paper we generalize Merton's option formula in the presence jumps to the multi-asset case.
Edit intent: fluency
Original:  Intensive research into the Vertex Cover problem has shown that there is a preprocessing algorithm which given an instance (G,k) of Vertex Cover outputs an equivalent instance (G',k') in polynomial time with the guarantee that G' has at most 2k' vertices (and thus O((k')^2) edges) with k' <= k. Using the terminology of parameterized complexity we say that k-Vertex Cover has a kernel with 2k vertices.
Revised:  Intensive research into the Vertex Cover problem has shown that there is an algorithm which given an instance (G,k) of Vertex Cover outputs an equivalent instance (G',k') in polynomial time with the guarantee that G' has at most 2k' vertices (and thus O((k')^2) edges) with k' <= k. Using the terminology of parameterized complexity we say that k-Vertex Cover has a kernel with 2k vertices.
Edit intent: clarity
Original:  There is complexity-theoretic evidence that both 2k vertices and \Theta (k^2) edges are optimal for the kernel size.
Revised:  There is complexity-theoretic evidence that both 2k vertices and Theta (k^2) edges are optimal for the kernel size.
Edit intent: fluency
Original:  In this paper we consider the Vertex Cover problem with a different parameter, the size FVS (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number VC (G) since FVS (G) <= VC (G) and the difference can be arbitrarily large.
Revised:  In this paper we consider the Vertex Cover problem with a different parameter, the size fvs (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number VC (G) since FVS (G) <= VC (G) and the difference can be arbitrarily large.
Edit intent: fluency
Original:  In this paper we consider the Vertex Cover problem with a different parameter, the size FVS (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number VC (G) since FVS (G) <= VC (G) and the difference can be arbitrarily large.
Revised:  In this paper we consider the Vertex Cover problem with a different parameter, the size FVS (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number vc (G) since FVS (G) <= VC (G) and the difference can be arbitrarily large.
Edit intent: fluency
Original:  In this paper we consider the Vertex Cover problem with a different parameter, the size FVS (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number VC (G) since FVS (G) <= VC (G) and the difference can be arbitrarily large.
Revised:  In this paper we consider the Vertex Cover problem with a different parameter, the size FVS (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number VC (G) since fvs (G) <= VC (G) and the difference can be arbitrarily large.
Edit intent: fluency
Original:  In this paper we consider the Vertex Cover problem with a different parameter, the size FVS (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number VC (G) since FVS (G) <= VC (G) and the difference can be arbitrarily large.
Revised:  In this paper we consider the Vertex Cover problem with a different parameter, the size FVS (G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number VC (G) since FVS (G) <= vc (G) and the difference can be arbitrarily large.
Edit intent: fluency
Original:  We give a kernel for Vertex Cover with a number of vertices that is cubic in FVS (G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that k' <= k, | X'| <= |X| and most importantly | V(G')| <= 2k and |V(G')| <= O(|X'|^3).
Revised:  We give a kernel for Vertex Cover with a number of vertices that is cubic in fvs (G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that k' <= k, | X'| <= |X| and most importantly | V(G')| <= 2k and |V(G')| <= O(|X'|^3).
Edit intent: fluency
Original:  We give a kernel for Vertex Cover with a number of vertices that is cubic in FVS (G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that k' <= k, | X'| <= |X| and most importantly | V(G')| <= 2k and |V(G')| <= O(|X'|^3).
Revised:  We give a kernel for Vertex Cover with a number of vertices that is cubic in FVS (G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that | X'| <= |X| and most importantly | V(G')| <= 2k and |V(G')| <= O(|X'|^3).
Edit intent: coherence
Original:  We give a kernel for Vertex Cover with a number of vertices that is cubic in FVS (G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that k' <= k, | X'| <= |X| and most importantly | V(G')| <= 2k and |V(G')| <= O(|X'|^3).
Revised:  We give a kernel for Vertex Cover with a number of vertices that is cubic in FVS (G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that k' <= k, | V(G')| <= 2k and |V(G')| <= O(|X'|^3).
Edit intent: coherence
Original:  This permits PoDA to reveal pathways in which a purely epistatic interaction drives risk.
Revised:  This permits PoDA to reveal pathways in which epistatic interactions drives risk.
Edit intent: clarity
Original:  To date , there is little molecular structural data available  on the AGAAAAGA palindrome in the hydrophobic region ( 113-120 ) of prion proteins .
Revised:  To date , there is little structural data available on the AGAAAAGA palindrome in the hydrophobic region ( 113-120 ) of prion proteins .
Edit intent: clarity
Original:  To date , there is little molecular structural data available  on the AGAAAAGA palindrome in the hydrophobic region ( 113-120 ) of prion proteins .
Revised:  To date , there is little molecular structural data available to date on the AGAAAAGA palindrome in the hydrophobic region ( 113-120 ) of prion proteins .
Edit intent: fluency
Original:  To date , there is little molecular structural data available  on the AGAAAAGA palindrome in the hydrophobic region ( 113-120 ) of prion proteins .
Revised:  To date , there is little molecular structural data available on the AGAAAAGA palindrome in the hydrophobic region ( 113--120 ) of prion proteins .
Edit intent: fluency
Original:  We make the rescaling factors available , for use by the readers.
Revised:  We make the rescaling factors available for use by the readers.
Edit intent: fluency
Original: We propose and analyse a quasirandom analogue of the classical push model for disseminating information in networks ("randomized rumor spreading").
Revised: We propose and analyze a quasirandom analogue of the classical push model for disseminating information in networks ("randomized rumor spreading").
Edit intent: fluency
Original:  In the classical model, in each round each informed vertex chooses a neighbor at random and informs it, if it was not  before.
Revised:  In the classical model, in each round each informed vertex chooses a neighbor at random and informs it, if it was not informed before.
Edit intent: fluency
Original:  Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list.
Revised:  Once informed, it starts at a random position on the list, but from then on informs its neighbors in the order of the list.
Edit intent: fluency
Original:  Surprisingly, irrespective of the orders of the lists, the above mentioned bounds still hold.
Revised:  Surprisingly, irrespective of the orders of the lists, the above-mentioned bounds still hold.
Edit intent: fluency
Original:  In some cases  even better bounds than for the classical model can be shown.
Revised:  In some cases , even better bounds than for the classical model can be shown.
Edit intent: fluency
Original:  We apply the method to various test problems and report on the observed convergence rate .
Revised:  We apply the method to various test problems and report on the observed convergence behavior .
Edit intent: clarity
Original:  Some of these regimes are characterized by heterogeneous, hierarchical interaction networks, where cooperation and network topology co-emerge from the dynamics.
Revised:  Some of these regimes are characterized by heterogeneous, hierarchical interaction networks, where cooperation and network topology coemerge from the dynamics.
Edit intent: fluency
Original: We give a protocol for an interactive proof for the recursive Fourier sampling problem .
Revised: We consider the recursive Fourier sampling problem .
Edit intent: clarity
Original: The goal of this report is to provide an introduction to the basic computational models used in quantum information theory.
Revised: The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory.
Edit intent: clarity
Original:  We various review models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts.
Revised:  We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts.
Edit intent: fluency
Original: Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce network congestion, amount of data stored in the network and offer increased resilience in the presence of node failures.
Revised: Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures.
Edit intent: coherence
Original:  Under this framework, the nodes are partitioned into two types and encoded using two codes in a manner that reduces the problem of node-repair to that of erasure-decoding of the constituent codes.
Revised:  Under this framework, the nodes are partitioned into two 'types' and encoded using two codes in a manner that reduces the problem of node-repair to that of erasure-decoding of the constituent codes.
Edit intent: clarity
Original: Future wireless networks are expected to operate in dense environments where the system capacity is fundamentally limited by severe co-channel interference among neighboring links.
Revised: Transmit power control in wireless networks has long been recognized as an effective mechanism to mitigate co-channel interference among neighboring links.
Edit intent: clarity
Original:  This problem had eluded researchers and remained open until our recent work 11%DIFDELCMD < ]%%% , where a centralized optimal power control algorithm, referred to as MAPEL, is developed based on a monotonic optimization framework.
Revised:  This problem had eluded researchers and remained open until our recent work %DIFDELCMD < ]%%% , where a centralized optimal power control algorithm, referred to as MAPEL, is developed based on a monotonic optimization framework.
Edit intent: clarity
Original:  However , there does not yet exist a distributed power control algorithm that achieves the global optimal solution for generic utilityfunctions, although the distributed implementation is crucial for the wireless infrastructureless networks such as ad hoc and sensor networks.
Revised:  However , there does not yet exist a distributed power control algorithm that maximizes any form of system utility, despite the importance of distributed implementation for the wireless infrastructureless networks such as ad hoc and sensor networks.
Edit intent: clarity
Original:  This paper fills this gap by developing a  distributed power control algorithm that converges to the global optimal solution for any forms of utility functions regardless of the concavity, continuity, differentiability and monotonicity .
Revised:  This paper fills this gap by developing a distributed power control algorithm that converges to the global optimal solution regardless of the concavity, continuity, differentiability and monotonicity .
Edit intent: clarity
Original:  Particularly, we investigate eigenvector localization properties of various model networks with varying correlations \tau among their entries.
Revised:  We investigate in particular eigenvector localization properties of various model networks with varying correlations \tau among their entries.
Edit intent: clarity
Original:  Particularly, we investigate eigenvector localization properties of various model networks with varying correlations \tau among their entries.
Revised:  Particularly, we investigate eigenvector localization properties of various model networks for different value of correlation among their entries.
Edit intent: clarity
Original:  As connections are made directed by making some nodes inhibitory, some of eigenstates start occurring in complex conjugate pairs .
Revised:  As connections are made directed , eigenstates start occurring in complex conjugate pairs .
Edit intent: clarity
Original:  For a very well distinguished community structure (rewiring probability p_r \sim 0) , the whole spectra is localized except some of eigenstates at boundary .
Revised:  For a very well distinguished community structure , the whole spectra is localized except some of eigenstates at boundary .
Edit intent: clarity
Original:  For a very well distinguished community structure (rewiring probability p_r \sim 0) , the whole spectra is localized except some of eigenstates at boundary .
Revised:  For a very well distinguished community structure (rewiring probability p_r \sim 0) , the whole spectrum is localized except some of eigenstates at boundary .
Edit intent: fluency
Original:  For a very well distinguished community structure (rewiring probability p_r \sim 0) , the whole spectra is localized except some of eigenstates at boundary .
Revised:  For a very well distinguished community structure (rewiring probability p_r \sim 0) , the whole spectra is localized except few eigenstates at boundary .
Edit intent: clarity
Original:  As p_r is increased and network deviates from  community structure there is a sudden change in the localization property for  very small value of deformation from the perfect community structure.
Revised:  As p_r is increased and network deviates from the community structure there is a sudden change in the localization property for very small value of deformation from the perfect community structure.
Edit intent: fluency