wanyu/IteraTeR_v2 huggingface dataset:
Original:  It is well-known that the vertex set of every graph without isolated vertices can be partitioned into two dominating sets \mbox{ \cite{ID3}\hspace{0pt} . Determining the computational complexity of deciding whether the vertices of a given connected cubic graph G can be partitioned into independent dominating sets remains unsolved.
Revised:  }\hspace{0pt} . Determining the computational complexity of deciding whether the vertices of a given connected cubic graph G can be partitioned into independent dominating sets remains unsolved.
Edit intent: coherence
Original:  The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it departs from realistic cognitive pressures (2) it does not require fine tuning of parameters and (3) it sheds light on the origins of other statistical laws of language and thus can lead to a compact theory of linguistic laws.
Revised:  The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts from realistic cognitive pressures (2) it does not require fine tuning of parameters and (3) it sheds light on the origins of other statistical laws of language and thus can lead to a compact theory of linguistic laws.
Edit intent: clarity
Original: Population structure and spatial heterogeneity are integral components of evolutionary dynamics and, in particular, of the evolution of cooperation in social dilemmas.
Revised: Population structure and spatial heterogeneity are integral components of evolutionary dynamics , in general, and of evolution of cooperation in social dilemmas.
Edit intent: clarity
Original:  Despite the fact that structure can promote the emergence of cooperation in some populations , it can suppress it in others.
Revised:  Despite the fact that structure can promote the emergence of cooperation in some populations and suppress it in others.
Edit intent: clarity
Original:  Thus, a detailed understanding of the influence of population structure is crucial for describing the features that allow cooperative behaviors to spread.
Edit intent: coherence
Original:  Here, we provide a complete description of when selection favors cooperation on regular graphs under birth-death and death-birth updating for any initial configuration.
Revised:  Here, we provide results for weak selection to favor cooperation on regular graphs under birth-death and death-birth updating for any initial configuration.
Edit intent: clarity
Original:  This formula elucidates two important features concerning the emergence of cooperation : (i) the takeover of cooperation can be enhanced by the strategic placement of cooperators , and (ii) adding more cooperators to the initial configuration can sometimes suppress the evolution of cooperation  .
Revised:  This formula elucidates two important features : (i) the takeover of cooperation can be enhanced by the strategic placement of cooperators , and (ii) adding more cooperators to the initial configuration can sometimes suppress the evolution of cooperation .
Edit intent: clarity
Original:  This formula elucidates two important features concerning the emergence of cooperation : (i) the takeover of cooperation can be enhanced by the strategic placement of cooperators , and (ii) adding more cooperators to the initial configuration can sometimes suppress the evolution of cooperation  .
Revised:  This formula elucidates two important features concerning the emergence of cooperation : (i) the takeover of cooperation can be enhanced by the strategic placement of cooperators and (ii) adding more cooperators to the initial configuration can sometimes suppress the evolution of cooperation .
Edit intent: fluency
Original:  This formula elucidates two important features concerning the emergence of cooperation : (i) the takeover of cooperation can be enhanced by the strategic placement of cooperators , and (ii) adding more cooperators to the initial configuration can sometimes suppress the evolution of cooperation  .
Revised:  This formula elucidates two important features concerning the emergence of cooperation : (i) the takeover of cooperation can be enhanced by the strategic placement of cooperators , and (ii) adding more cooperators to a configuration can sometimes suppress the evolution of cooperation .
Edit intent: clarity
Original:  This paper introduces SimInf, an efficient and general framework for stochastic spatio-temporal disease-spread modelling over a temporal network of connected nodes.
Revised:  This paper introduces SimInf, an efficient and general framework for stochastic spatio-temporal disease-spread modeling over a temporal network of connected nodes.
Edit intent: fluency
Original:  We provide a technical description of the framework, how to use a built-in model , demonstrate a case study and finally how to extend the framework with a user defined model.
Revised:  We provide a technical description of the framework, how to use a built-in model , demonstrate a case study , and finally show how to extend the framework with a user defined model.
Edit intent: coherence
Original:  We provide a technical description of the framework , how to use a predefined model in SimInf, demonstrate a case study, and finally show how to extend the framework with a user defined model .
Revised:  We provide a technical description of the framework and demonstrate its use on some basic examples. We also discuss how to specify and extend the framework with a user defined model .
Edit intent: clarity
Original:  We provide a technical description of the framework , how to use a predefined model in SimInf, demonstrate a case study, and finally show how to extend the framework with a user defined model .
Revised:  We provide a technical description of the framework , how to use a predefined model in SimInf, demonstrate a case study, and finally show how to extend the framework with user-defined models .
Edit intent: fluency
Original: In cognitive radio (CR) networks,  secondary users (SUs) sense the spectrum to identify and possibly transmit over temporarily unoccupied channels licensed to primary users (PUs).
Revised: In cognitive radio (CR) networks, the secondary users (SUs) sense the spectrum to identify and possibly transmit over temporarily unoccupied channels licensed to primary users (PUs).
Edit intent: fluency
Original: In cognitive radio (CR) networks,  secondary users (SUs) sense the spectrum to identify and possibly transmit over temporarily unoccupied channels licensed to primary users (PUs).
Revised: In cognitive radio (CR) networks, secondary users (SUs) sense the spectrum licensed to the primary users (PUs) to identify and possibly transmit over temporarily unoccupied channels licensed to primary users (PUs).
Edit intent: fluency
Original:  However, fair payoff (spectrum access) allocation has not been investigated for cooperative sensing in multichannel CR networks with heterogeneous PU signal quality at different SU sensorsalthough such scenarios are prevalent in practice .
Revised:  However, fair payoff (spectrum access) allocation has not been investigated for cooperative sensing in multichannel CR networks with heterogeneous PU signal quality at their sensors .
Edit intent: clarity
Original:  Moreover,  we propose a new physical-layer approach to distribute the network-level miss-detection (MD) constraints fairly among the interfering SUs for guaranteed PU protection .
Revised:  Moreover, we propose a new physical-layer approach to distributing the network-level miss-detection (MD) constraints fairly among the interfering SUs for guaranteed PU protection .
Edit intent: fluency
Original: We consider the Online Boolean Matrix-Vector Multiplication (OMV) problem studied by Henzinger et al.
Revised: We consider the Online Boolean Matrix-Vector Multiplication (OMV) problem studied by Henzinger et al.
Edit intent: fluency
Original: We prove that estimating the smallest eigenvalue of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D chain of quantum systems is QMAEXP-complete, even for systems of low dimension.
Revised: We prove that estimating the smallest eigenvalue of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low dimension.
Edit intent: clarity
Original:  This improves on the work by Gottesman and Irani (2009), where this dimension was several orders of magnitude larger, whereas our dimension is comparable to the best-known non-translationally-invariant result by Hallgren et al. (2013).
Revised:  This improves on the work by Gottesman and Irani (2009), where this dimension was several orders of magnitude larger, whereas our dimension is comparable to the smallest-known non-translationally-invariant result by Hallgren et al. (2013).
Edit intent: clarity
Original:  While previous constructions directly encoded one of the standard models , we introduce a new Turing-complete model of  quantum computation - a quantum ring machine.
Revised:  While previous constructions of quantum computation - a quantum ring machine.
Edit intent: clarity
Original:  This hybrid classical-quantum model is an extension of string rewriting systems and is specifically tailored to encoding quantum computation in a nearest-neighbour Hamiltonian with translationally-invariant interactions .
Revised:  This hybrid classical-quantum model is an extension of string rewriting systems and is specifically tailored to encoding quantum computation into the ground state of a translationally-invariant interactions .
Edit intent: clarity
Original:  This hybrid classical-quantum model is an extension of string rewriting systems and is specifically tailored to encoding quantum computation in a nearest-neighbour Hamiltonian with translationally-invariant interactions .
Revised:  This hybrid classical-quantum model is an extension of string rewriting systems and is specifically tailored to encoding quantum computation in a nearest-neighbour Hamiltonian with translationally-invariant system .
Edit intent: clarity
Original:  This allows us to shift the proof burden from simplifying the Hamiltonians used to encode a standard computational model, to proving universality of a very simplified model.
Revised:  This allows us to shift the proof burden from optimizing the Hamiltonian encoding a standard computational model, to proving universality of a very simplified model.
Edit intent: clarity
Original:  This requires more sophisticated techniques for analyzing the spectrum of the resulting Hamiltonian : we relate it to the Laplacian of a graph with unitary edge weights.
Revised:  This requires more sophisticated techniques for analysing the spectrum of the resulting Hamiltonian : we relate it to the Laplacian of a graph with unitary edge weights.
Edit intent: fluency
Original:  This requires more sophisticated techniques for analyzing the spectrum of the resulting Hamiltonian : we relate it to the Laplacian of a graph with unitary edge weights.
Revised:  This requires more sophisticated techniques for analyzing the spectrum of the resulting Hamiltonian . To address this, we introduce a framework of graphs with unitary edge weights.
Edit intent: coherence
Original:  This allows us to shift the proof burden from optimizing the Hamiltonian encoding a standard computational model , to proving universality of a very simple model.
Revised:  This allows us to shift the proof burden from optimizing the Hamiltonian encoding a standard computational model to proving universality of a very simple model.
Edit intent: fluency
Original:  This allows us to shift the proof burden from optimizing the Hamiltonian encoding a standard computational model , to proving universality of a very simple model.
Revised:  This allows us to shift the proof burden from optimizing the Hamiltonian encoding a standard computational model , to proving universality of a simple model.
Edit intent: clarity
Original:  We significantly extend these techniques by allowing much more general paths, including branching and cycles, thus enabling a highly efficient encoding of our computational model.
Revised:  We extend these techniques by allowing much more general paths, including branching and cycles, thus enabling a highly efficient encoding of our computational model.
Edit intent: clarity
Original:  We significantly extend these techniques by allowing much more general paths, including branching and cycles, thus enabling a highly efficient encoding of our computational model.
Revised:  We significantly extend these techniques by allowing significantly more general paths, including branching and cycles, thus enabling a highly efficient encoding of our computational model.
Edit intent: fluency
Original: This work is devoted to studying the dynamics of a population subject to the combined effects of stochastic environments , competition for resources, and spatio-temporal heterogeneity and dispersal.
Revised: This work is devoted to studying the dynamics of a population subject to the combined effects of environmental stochasticity , competition for resources, and spatio-temporal heterogeneity and dispersal.
Edit intent: clarity
Original: This work is devoted to studying the dynamics of a population subject to the combined effects of stochastic environments , competition for resources, and spatio-temporal heterogeneity and dispersal.
Revised: This work is devoted to studying the dynamics of a population subject to the combined effects of stochastic environments , competition for resources, spatio-temporal heterogeneity and dispersal.
Edit intent: fluency
Original:  The population is spread throughout n patches whose population abundances are modeled as the solutions of a system of nonlinear stochastic differential equations living on [0,\infty)^n.
Revised:  The population is spread throughout n patches whose population abundances are modelled as the solutions of a system of nonlinear stochastic differential equations living on [0,\infty)^n.
Edit intent: fluency
Original:  We prove that \lambda , the stochastic growth rate of the system in the absence of competition, determines the long-term behaviour of the population.
Revised:  We prove that \lambda , the stochastic growth rate of the total population in the absence of competition, determines the long-term behaviour of the population.
Edit intent: clarity
Original:  Detailed analysis shows that if \lambda >0, the population abundances converge polynomially fast to a unique invariant probability measure on (0,\infty)^n, while when \lambda <0, the  abundances of the patches converge almost surely to 0 exponentially fast.
Revised:  Detailed analysis shows that if r >0, the population abundances converge polynomially fast to a unique invariant probability measure on (0,\infty)^n, while when \lambda <0, the abundances of the patches converge almost surely to 0 exponentially fast.
Edit intent: clarity
Original:  Detailed analysis shows that if \lambda >0, the population abundances converge polynomially fast to a unique invariant probability measure on (0,\infty)^n, while when \lambda <0, the  abundances of the patches converge almost surely to 0 exponentially fast.
Revised:  Detailed analysis shows that if \lambda >0, the population abundances converge polynomially fast to a unique invariant probability measure on (0,\infty)^n, while when r <0, the abundances of the patches converge almost surely to 0 exponentially fast.
Edit intent: clarity
Original:  Detailed analysis shows that if \lambda >0, the population abundances converge polynomially fast to a unique invariant probability measure on (0,\infty)^n, while when \lambda <0, the  abundances of the patches converge almost surely to 0 exponentially fast.
Revised:  Detailed analysis shows that if \lambda >0, the population abundances converge polynomially fast to a unique invariant probability measure on (0,\infty)^n, while when \lambda <0, the population abundances of the patches converge almost surely to 0 exponentially fast.
Edit intent: fluency
Original:  This is more natural from a biological point of view since, for example, the environments of the different patches can be perfectly correlated  .
Revised:  This is relevant from a biological point of view since, for example, the environments of the different patches can be perfectly correlated .
Edit intent: clarity
Original:  Walklets uses the offsets between vertices observed in a random walk to learn a series of latent representations, each  which captures successively larger relationships .
Revised:  Walklets uses the offsets between vertices observed in a random walk to learn a series of latent representations, each of which captures successively larger relationships .
Edit intent: clarity
Original:  We demonstrate Walklets' latent representations on several multi-label network classification tasks for social networks such as BlogCatalog,  Flickr, and YouTube.
Revised:  We demonstrate the efficacy of Walklets's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, Flickr, and YouTube.
Edit intent: clarity
Original: We study the complexity of computing the simulation preorder of finite transition systems, a crucial problem in model checking of temporal logic , showing that it is strongly related to some variants of  matrix multiplication.
Revised: Computing the simulation preorder of finite transition systems, a crucial problem in model checking of temporal logic , showing that it is strongly related to some variants of matrix multiplication.
Edit intent: coherence
Original:  We first show that any O(n ^\alpha )-time algorithm for n-states transition systems can be used to compute the product of two n\times n boolean matrices in O(n ^\alpha ) time.
Revised:  We show that any O(n ^\alpha )-time algorithm for n-states transition systems can be used to compute the product of two n\times n boolean matrices in O(n ^\alpha ) time.
Edit intent: coherence
Original:  We first show that any O(n ^\alpha )-time algorithm for n-states transition systems can be used to compute the product of two n\times n boolean matrices in O(n ^\alpha ) time.
Revised:  We first show that any O(n ^{\alpha )-time algorithm for n-states transition systems can be used to compute the product of two n\times n boolean matrices in O(n ^\alpha ) time.
Edit intent: fluency
Original:  We first show that any O(n ^\alpha )-time algorithm for n-states transition systems can be used to compute the product of two n\times n boolean matrices in O(n ^\alpha ) time.
Revised:  We first show that any O(n ^\alpha )-time algorithm for n-states transition systems can be used to compute the product of two n\times n boolean matrices in O(n ^{\alpha ) time.
Edit intent: fluency
Original:  This reduction is the first evidence of the difficulty to get a truly subcubic combinatorial algorithm for the simulation preorder, and holds even restricting the problem to acyclic systems.
Revised:  This is the first evidence of the difficulty to get a truly subcubic combinatorial algorithm for the simulation preorder, and holds even restricting the problem to acyclic systems.
Edit intent: coherence
Original:  Moreover, we exhibit O(n ^2 )-size canonical certificates that can be checked by verifying a constant number of n\times n standard matrix multiplications over the integers, i.e., in O(n ^2) (randomized) time .
Revised:  Moreover, we exhibit O(n ^2 )-size certificates, that can be checked by verifying a constant number of n\times n standard matrix multiplications over the integers, i.e., in O(n ^2) (randomized) time .
Edit intent: clarity
Original:  Hence, for any \alpha%DIFDELCMD < \geq2%%% , if MSBMM can be verified in %DIFDELCMD < \tilde{O}%%% (n^\alpha) time, then the simulation preorder admits certificates that can be checked in%DIFDELCMD < \tilde{O}%%% (n^\alpha) time, otherwise the simulation preorder does not admit a%DIFDELCMD < \tilde{O}%%% (n^\alpha)-time algorithm .
Revised:  Hence, for any \alpha%DIFDELCMD < \geq2%%% , if MSBMM can be verified in %DIFDELCMD < \tilde{O}%%% %DIFDELCMD < \tilde{O}%%% (n^\alpha) time, otherwise the simulation preorder does not admit a%DIFDELCMD < \tilde{O}%%% (n^\alpha)-time algorithm .
Edit intent: clarity
Original:  Hence, for any \alpha%DIFDELCMD < \geq2%%% , if MSBMM can be verified in %DIFDELCMD < \tilde{O}%%% (n^\alpha) time, then the simulation preorder admits certificates that can be checked in%DIFDELCMD < \tilde{O}%%% (n^\alpha) time, otherwise the simulation preorder does not admit a%DIFDELCMD < \tilde{O}%%% (n^\alpha)-time algorithm .
Revised:  Hence, for any \alpha%DIFDELCMD < \geq2%%% , if MSBMM can be verified in %DIFDELCMD < \tilde{O}%%% (n^\alpha) time, then the simulation preorder admits certificates that can be checked in%DIFDELCMD < \tilde{O}%%% %DIFDELCMD < \tilde{O}%%% (n^\alpha)-time algorithm .
Edit intent: clarity
Original:  Hence, for any \alpha%DIFDELCMD < \geq2%%% , if MSBMM can be verified in %DIFDELCMD < \tilde{O}%%% (n^\alpha) time, then the simulation preorder admits certificates that can be checked in%DIFDELCMD < \tilde{O}%%% (n^\alpha) time, otherwise the simulation preorder does not admit a%DIFDELCMD < \tilde{O}%%% (n^\alpha)-time algorithm .
Revised:  Hence, for any \alpha%DIFDELCMD < \geq2%%% , if MSBMM can be verified in %DIFDELCMD < \tilde{O}%%% (n^\alpha) time, then the simulation preorder admits certificates that can be checked in%DIFDELCMD < \tilde{O}%%% (n^\alpha) time, otherwise the simulation preorder does not admit a%DIFDELCMD < \tilde{O}%%% n^{\omega+o(1) .
Edit intent: clarity
Original: Indirect reciprocity is a major mechanism in the maintenance of cooperation among unfamiliar individuals.
Revised: Indirect reciprocity is a major mechanism in the maintenance of cooperation among unrelated individuals.
Edit intent: clarity
Original:  Despite intensive research, however, there is no definitive consensus on what social norms best promote cooperation through indirect reciprocity, and it remains unclear even how those who refuse help to the bad should be assessed.
Revised:  Despite intensive research, however, there is no definitive consensus on what social norms best promote cooperation through indirect reciprocity, and it remains unclear even how those who refuse to help the bad should be assessed.
Edit intent: fluency
Original:  Here  we propose a new simple norm called 'Staying' that prescribes to abstain from assessment, with the focal individual's image remaining unchanged, if its opponent has a bad image.
Revised:  Here , we propose a new simple norm called 'Staying' that prescribes to abstain from assessment, with the focal individual's image remaining unchanged, if its opponent has a bad image.
Edit intent: fluency
Original:  We fully analyse the Staying norm in terms of evolutionary game theory and unveil that Staying is most effective in establishing cooperation , compared to the prevailing social norms  which rely on constant monitoring and unconditional assessment.
Revised:  We fully analyse the Staying norm in terms of evolutionary game theory and demonstrate that Staying is most effective in establishing cooperation , compared to the prevailing social norms which rely on constant monitoring and unconditional assessment.
Edit intent: clarity
Original:  We fully analyse the Staying norm in terms of evolutionary game theory and unveil that Staying is most effective in establishing cooperation , compared to the prevailing social norms  which rely on constant monitoring and unconditional assessment.
Revised:  We fully analyse the Staying norm in terms of evolutionary game theory and unveil that Staying is most effective in establishing cooperation compared to the prevailing social norms which rely on constant monitoring and unconditional assessment.
Edit intent: fluency