wanyu/IteraTeR_v2 huggingface dataset:
Original: Traditionally, resource limitation in evolutionary game theory (EGT) is assumed just to impose a constant population size.
Revised: Traditionally, resource limitation in evolutionary game theory is assumed just to impose a constant population size.
Edit intent: clarity
Original:  Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma (PD) , and to allow for  stable coexistence between unconditional cooperators and defectors in well-mixed populations.
Revised:  Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma , and to allow for stable coexistence between unconditional cooperators and defectors in well-mixed populations.
Edit intent: clarity
Original:  Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma (PD) , and to allow for  stable coexistence between unconditional cooperators and defectors in well-mixed populations.
Revised:  Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma (PD) , and to allow for the stable coexistence between unconditional cooperators and defectors in well-mixed populations.
Edit intent: fluency
Original:  An asymptotic convergence rate is also achieved when the knocked-out barrier moves to infinity under suitable conditions.
Revised:  An asymptotic convergence rate is also studied when the knocked-out barrier moves to infinity under suitable conditions.
Edit intent: clarity
Original:  Among of them, a speci?c rebate option is also provided with a continuous rebate function, which corresponds to the unique classical solution of the associated parabolic PDE.
Revised:  Among of them, a specific rebate option is also provided with a continuous rebate function, which corresponds to the unique classical solution of the associated parabolic PDE.
Edit intent: fluency
Original:  An asymptotic convergence rate is also studied when the knocked-out barrier moves to in?nity under suitable conditions.
Revised:  An asymptotic convergence rate is also studied when the knocked-out barrier moves to infinity under suitable conditions.
Edit intent: clarity
Original:  Using the fact that our convergence result is unconditional, we show that it also applies to systems where the agent connectivity and interactions are random, or endogenous, that is, determined by the agent values.
Revised:  These results allow treating systems where the agent connectivity and interactions are random, or endogenous, that is, determined by the agent values.
Edit intent: clarity
Original:  Using the fact that our convergence result is unconditional, we show that it also applies to systems where the agent connectivity and interactions are random, or endogenous, that is, determined by the agent values.
Revised:  Using the fact that our convergence result is unconditional, we show that it also applies to systems where the agent interactions are a priori unknown, e.g., random or determined endogenously by the agent values.
Edit intent: clarity
Original: We discuss the "rate of averages" versus the "average of rates" in the case of the impact factor .
Revised: We show that as a consequence of basic properties of elementary arithmetic journal impact factors show a counterintuitive behaviour with respect to adding non-cited articles .
Edit intent: clarity
Original:  Our findings provide a rationale for not taking uncitable publications into account in impact factor calculations, at least if these items are truly uncitable , that is, are never cited .
Revised:  Our findings provide a rationale for not taking uncitable publications into account in impact factor calculations, at least if these items are truly uncitable .
Edit intent: clarity
Original:  Due to stringent QoS requirements of video streams and specific characterization of utility experienced by end-users, NUM formulation for these streams is nonconvex and even nonsmooth , hence making dual methods often incompetent to solve them.
Revised:  Due to stringent QoS requirements of video streams and specific characterization of utility experienced by end-users, one has to solve nonconvex and even nonsmooth , hence making dual methods often incompetent to solve them.
Edit intent: clarity
Original:  Due to stringent QoS requirements of video streams and specific characterization of utility experienced by end-users, NUM formulation for these streams is nonconvex and even nonsmooth , hence making dual methods often incompetent to solve them.
Revised:  Due to stringent QoS requirements of video streams and specific characterization of utility experienced by end-users, NUM formulation for these streams is nonconvex and even nonsmooth NUM formulation for such streams, where dual methods often incompetent to solve them.
Edit intent: coherence
Original:  Hence, to tackle the nonsmoothness and nonconvexity, we aim at reformulating the NUM problem by employing a series of approximation and transformation of the ideal discretely adaptive utility functions for scalable video streams.
Revised:  Hence, to tackle the nonsmoothness and nonconvexity, we aim at reformulating the NUM problem through approximation and transformation of the ideal discretely adaptive utility functions for scalable video streams.
Edit intent: clarity
Original:  Hence, to tackle the nonsmoothness and nonconvexity, we aim at reformulating the NUM problem by employing a series of approximation and transformation of the ideal discretely adaptive utility functions for scalable video streams.
Revised:  Hence, to tackle the nonsmoothness and nonconvexity, we aim at reformulating the NUM problem by employing a series of approximation and transformation of the ideal discretely adaptive utility function for scalable video streams.
Edit intent: fluency
Original:   Our experimental results show that the proposed rate control algorithm converges within a few iteration steps thereby admitting a low overhead .
Revised:  Our experimental results show that the proposed rate control algorithms converge with tractable convergence behavior .
Edit intent: clarity
Original: We give a new certificate-based characterization of \mathsf{NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by probabilistic finite automata (2pfa's) which have access to only a constant number of random bits .
Revised: We give a new characterization of NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by probabilistic finite automata (2pfa's) which have access to only a constant number of random bits .
Edit intent: clarity
Original: We give a new certificate-based characterization of \mathsf{NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by probabilistic finite automata (2pfa's) which have access to only a constant number of random bits .
Revised: We give a new certificate-based characterization of \mathsf{NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits .
Edit intent: clarity
Original:  A corollary of our main result is that the class of outcome problems corresponding to O( \log n)-space bounded games of incomplete information where the universal player is allowed a constant number of moves equals \mathsf{NL .
Revised:  A corollary of our main result is that the class of outcome problems corresponding to O( log n)-space bounded games of incomplete information where the universal player is allowed a constant number of moves equals \mathsf{NL .
Edit intent: fluency
Original:  In this paper  the localization problem is modelled as a cost function in terms of the source locations and the attenuation model parameters  .
Revised:  In this paper , the localization problem is modelled as a cost function in terms of the source locations and the attenuation model parameters .
Edit intent: fluency
Original:  In this paper  the localization problem is modelled as a cost function in terms of the source locations and the attenuation model parameters  .
Revised:  In this paper the localization problem is modeled as a cost function in terms of the source locations and the attenuation model parameters .
Edit intent: fluency
Original:  In this paper  the localization problem is modelled as a cost function in terms of the source locations and the attenuation model parameters  .
Revised:  In this paper the localization problem is modelled as a cost function in terms of the source locations , attenuation model parameters .
Edit intent: fluency
Original:  To globally perform the minimization  we propose a hybrid algorithm combining the differential evolution algorithm with the Levenberg-Marquardt algorithm.
Revised:  To globally perform the minimization , we propose a hybrid algorithm combining the differential evolution algorithm with the Levenberg-Marquardt algorithm.
Edit intent: fluency
Original:  Beside the proposed combination scheme, supporting technical details such as closed forms of cost function sensitivity matrices are provided.
Revised:  Besides the proposed combination scheme, supporting technical details such as closed forms of cost function sensitivity matrices are provided.
Edit intent: fluency
Original:  Beside the proposed combination scheme, supporting technical details such as closed forms of cost function sensitivity matrices are provided.
Revised:  Beside the proposed combination of optimization schemes, supporting the technical details such as closed forms of cost function sensitivity matrices are provided.
Edit intent: clarity
Original:  Finally  the validity of the proposed method is verified through various simulations .
Revised:  Finally , the validity of the proposed method is verified through various simulations .
Edit intent: coherence
Original:  A frequency permutation array (FPA) of minimum distance d is a subset of S_n^\lambda in which every two elements have distance  d.
Revised:  A frequency permutation array (FPA) of minimum distance d is a subset of S_n^\lambda in which every two elements have distance at least d.
Edit intent: clarity
Original:  The first one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%%  space.
Revised:  The first one runs in O %DIFDELCMD < \left(%%% ( {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%% time and O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%% space.
Edit intent: fluency
Original:  The first one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%%  space.
Revised:  The first one runs in O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%% ) time and O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%% space.
Edit intent: fluency
Original:  The first one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%%  space.
Revised:  The first one runs in O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%% time and O %DIFDELCMD < \left(%%% ( {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%% space.
Edit intent: fluency
Original:  The first one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%%  space.
Revised:  The first one runs in O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}^{2.376}\log n %DIFDELCMD < \right) %%% time and O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}^{2} %DIFDELCMD < \right) %%% ) space.
Edit intent: fluency
Original:  The second one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%%  space.
Revised:  The second one runs in O %DIFDELCMD < \left(%%% ( {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%% time and O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%% space.
Edit intent: fluency
Original:  The second one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%%  space.
Revised:  The second one runs in O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%% ) time and O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%% space.
Edit intent: fluency
Original:  The second one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%%  space.
Revised:  The second one runs in O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%% time and O %DIFDELCMD < \left(%%% ( {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%% space.
Edit intent: fluency
Original:  The second one runs in O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%%  time and O %DIFDELCMD < \left(%%%  {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%%  space.
Revised:  The second one runs in O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}n{\lambda} %DIFDELCMD < \right) %%% time and O %DIFDELCMD < \left(%%% {2d\lambda \choose d\lambda} %DIFDELCMD < \right) %%% ) space.
Edit intent: fluency
Original: The Nuclear Science References (NSR) database , and associated Web inter- face , is the world's only comprehensive source of easily accessible low- and intermediate-energy nuclear physics bibliographic information for more than 200,000 articles since the beginning of nuclear science.
Revised: The Nuclear Science References (NSR) database together with its associated Web interface , is the world's only comprehensive source of easily accessible low- and intermediate-energy nuclear physics bibliographic information for more than 200,000 articles since the beginning of nuclear science.
Edit intent: clarity
Original:  The weekly-updated NSR database provides essential support for nuclear data evaluation, com- pilation and research activities.
Revised:  The weekly-updated NSR database provides essential support for nuclear data evaluation, compilation and research activities.
Edit intent: fluency
Original:  We also extend and modify a graph-based technique by Zivny and Kolmogorov (originally introduced by Takhanov) for efficiently obtaining hardness results in our setting.
Revised:  We also extend and modify a graph-based technique by Kolmogorov and Zivny (originally introduced by Takhanov) for efficiently obtaining hardness results in our setting.
Edit intent: fluency
Original:  In this paper we provide a general framework for understanding the weak error of numerical approximation techniques in this setting.
Edit intent: coherence
Original:  Quantifying how different numerical approximation techniques behave in this settingtherefore requires that these scalings be taken into account in an appropriate manner .
Revised:  Quantifying how different numerical approximation techniques in the multi-scale setting .
Edit intent: clarity
Original:  We show that Euler's method, also called explicit tau-leaping, acts as an order one method, in that the error decreases linearly with the step-size, and that the approximate midpoint method acts as either an order one or two method, depending on the relation between the time-step and the scalings in the system.
Edit intent: coherence
Original:  In this paper  we provide a general framework for understanding the weak error of numerical approximation techniques in the multi-scale setting.
Revised:  In this paper , we provide a general framework for understanding the weak error of numerical approximation techniques in the multi-scale setting.
Edit intent: fluency
Original:  We quantify how the error of three different methods depends upon both the natural scalings within a given system , and with the step-size of the numerical method.
Revised:  We quantify how the error of three different methods depends upon both the natural scalings within a given system and the step-size of the numerical method.
Edit intent: fluency
Original:  However, when using ensemble averages to approximate expected values, the computational complexity can become prohibitive as the number of computations per path scales linearly with the number of jumps , or reactions, of the process.
Revised:  However, when using ensemble averages to approximate expected values, the computational complexity can become prohibitive as the number of computations per path scales linearly with the number of jumps of the process.
Edit intent: clarity
Original:  Further, the weak trapezoidal method is introduced in the current setting, and is proven to be second order accurate in a weak sense, making it the first higher order method in this setting.
Edit intent: coherence
Original:  Examples are provided demonstrating both the main analytical results , and the reduction in computational complexity achieved with the approximate methods.
Revised:  Examples are provided to demonstrate the main analytical results , and the reduction in computational complexity achieved with the approximate methods.
Edit intent: clarity
Original:  Examples are provided demonstrating both the main analytical results , and the reduction in computational complexity achieved with the approximate methods.
Revised:  Examples are provided demonstrating both the main analytical results as well as the reduction in computational complexity achieved with the approximate methods.
Edit intent: clarity
Original:  Examples are provided demonstrating both the main analytical results , and the reduction in computational complexity achieved with the approximate methods.
Revised:  Examples are provided demonstrating both the main analytical results , and the reduction in computational complexity achieved by the approximate methods.
Edit intent: fluency
Original:   We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus give the answer to a longstanding open problem posed by Nisan Nis1991 in algebraic complexity.
Revised:  We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus provide a strong solution to Nisan's question Nis1991 in algebraic complexity.
Edit intent: clarity
Original:  More specifically, we exhibit  a homogeneous algebraic function f of degree d (d even) on n variables with the monotone algebraic branching program (ABP) complexity \Omega( n^{d/2 ) and the non-monotone ABP complexity O(d^2).
Revised:  More specifically, we exhibit that there exists a homogeneous algebraic function f of degree d (d even) on n variables with the monotone algebraic branching program (ABP) complexity \Omega( n^{d/2 ) and the non-monotone ABP complexity O(d^2).
Edit intent: clarity
Original:  We propose a relaxed version of the famous Bell's theorem \mbox{ Bel19640pt \mbox{ CHSH1969}0pt . Bell's theorem basically states that } \hspace{0pt} , a basic assumption is that players have free will, and under such an assumption, } local hidden variable theory  cannot predict the correlations produced by quantum mechanics , and therefore is an impossibility result.
Revised:  In Bell's theorem \mbox{ Bel19640pt \mbox{ CHSH1969}0pt . Bell's theorem basically states that } \hspace{0pt} , a basic assumption is that players have free will, and under such an assumption, } local hidden variable theory cannot predict the correlations produced by quantum mechanics , and therefore is an impossibility result.
Edit intent: clarity
Original:  We propose a relaxed version of the famous Bell's theorem \mbox{ Bel19640pt \mbox{ CHSH1969}0pt . Bell's theorem basically states that } \hspace{0pt} , a basic assumption is that players have free will, and under such an assumption, } local hidden variable theory  cannot predict the correlations produced by quantum mechanics , and therefore is an impossibility result.
Revised:  We propose a relaxed version of the famous Bell's theorem \mbox{ Bel19640pt \mbox{ CHSH1969}0pt . Bell's theorem basically states that } \hspace{0pt} , a basic assumption is that players have free will, and under such an assumption, } local hidden variable theory still cannot predict the correlations produced by quantum mechanics , and therefore is an impossibility result.
Edit intent: clarity
Original:  This means that the log-rank conjecture does not hold in "high " dimensions.
Revised:  This means that the log-rank conjecture does not hold in high dimensions.
Edit intent: fluency
Original: Cells use genetic switches to shift between alternate gene expression states, e.g., to adapt to new environments or to follow a preprogrammed developmental pathway.
Revised: Cells use genetic switches to shift between alternate gene expression states, e.g., to adapt to new environments or to follow a developmental pathway.
Edit intent: clarity
Original:  Here, we investigate the dynamics of switching between metastable states of a feedback based on/off switch , by employing the WKB theory to treat the underlying master equations.
Revised:  Here, we study the dynamics of switching between metastable states of a feedback based on/off switch , by employing the WKB theory to treat the underlying master equations.
Edit intent: fluency
Original:  Here, we investigate the dynamics of switching between metastable states of a feedback based on/off switch , by employing the WKB theory to treat the underlying master equations.
Revised:  Here, we investigate the dynamics of switching in a generic-feedback on/off switch , by employing the WKB theory to treat the underlying master equations.
Edit intent: clarity
Original:  This technique, applicable for any generic feedback function, yields accurate results for the quasi-stationary distributions of mRNA and protein copy numbers and  mean switching time, starting from either state.
Revised:  This technique, applicable for any generic feedback function, yields accurate results for the quasi-stationary distributions of mRNA and protein copy numbers and for the mean switching time, starting from either state.
Edit intent: fluency
Original:  Our analytical results compare well with Monte Carlo simulations.
Revised:  Our analytical results agree well with Monte Carlo simulations.
Edit intent: clarity
Original:  Importantly, the approach may be used to study the effect of varying biological parameters on the stability of the switch states, and we use it to show that in some cases promoter kinetics, not just thermodynamic stability, can influence switching .
Revised:  Importantly, the approach may be used to study the effect of varying biological parameters on switch stability .
Edit intent: coherence
Original: Complementation of finite automata on infinite words is not only a fundamental problem in automata theory, but also serves as a cornerstone for solving numerous decision problems in mathematical logics , model-checking, program analysis and verification.
Revised: Complementation of finite automata on infinite words is not only a fundamental problem in automata theory, but also serves as a cornerstone for solving numerous decision problems in mathematical logic , model-checking, program analysis and verification.
Edit intent: fluency