wanyu/IteraTeR_v2 huggingface dataset:
Original:  When the value distribution is uniform in%DIFDELCMD < [%%% 0,1 , there exists a threshold equilibrium with expected revenue at least \frac{4{3+22} \sim 69\% of the Myerson optimal revenue benchmark}  .
Revised:  When the value distribution is uniform in%DIFDELCMD < [%%% 0,1 {3+22} \sim 69\% of the Myerson optimal revenue benchmark} .
Edit intent: clarity
Original:  In the final part of the paper, we have constructed asymptotics which are different from the semiclassical ones and can describe the evolution of the solutions of the Fisher-Kolmogorov-Petrovskii-Piskunov equation at large times.
Revised:  In the final part of the paper, we have constructed asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-Kolmogorov-Petrovskii-Piskunov equation at large times.
Edit intent: fluency
Original:  These asymptotics represent small perturbations on the background of an exact quasi-stationary solution.
Edit intent: coherence
Original:  In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as pattern formation .
Revised:  In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure .
Edit intent: clarity
Original:  In this paper, we pursue this latter direction by introducing the physically well-motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from  stabilizer codes to quantum memories.
Revised:  In this paper, we take a new direction by introducing the physically well-motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from stabilizer codes to quantum memories.
Edit intent: clarity
Original:  In this paper, we pursue this latter direction by introducing the physically well-motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from  stabilizer codes to quantum memories.
Revised:  In this paper, we pursue this latter direction by introducing the physically motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from stabilizer codes to quantum memories.
Edit intent: clarity
Original:  In this paper, we pursue this latter direction by introducing the physically well-motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from  stabilizer codes to quantum memories.
Revised:  In this paper, we pursue this latter direction by introducing the physically well-motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from quantum stabilizer codes to quantum memories.
Edit intent: fluency
Original:  As a result, we obtain a natural QCMA-complete problem, a goal which has proven elusive since the conception of QCMA over a decade ago.
Revised:  As a result, we obtain a natural QCMA-complete problem, a goal which has generally proven difficult since the conception of QCMA over a decade ago.
Edit intent: clarity
Original:  Our proofs crucially rely on a new technical tool, the Traversal Lemma, which analyzes the Hilbert space a local unitary evolution must traverse under certain conditions , and which we believe may be of independent interest .
Revised:  Our proofs rely on a new technical tool, the Traversal Lemma, which analyzes the Hilbert space a local unitary evolution must traverse under certain conditions , and which we believe may be of independent interest .
Edit intent: coherence
Original:  We show that determining how " connected " the ground space } } of a local Hamiltonian is } } can range from QCMA-complete to  NEXP-complete  .
Revised:  Roughly, " connected " the ground space } } of a local Hamiltonian is } } can range from QCMA-complete to NEXP-complete .
Edit intent: coherence
Original:  We show that determining how " connected " the ground space } } of a local Hamiltonian is } } can range from QCMA-complete to  NEXP-complete  .
Revised:  We show that determining how " ground state connectivity " the ground space } } of a local Hamiltonian is } } can range from QCMA-complete to NEXP-complete .
Edit intent: clarity
Original:  We show that determining how " connected " the ground space } } of a local Hamiltonian is } } can range from QCMA-complete to  NEXP-complete  .
Revised:  We show that determining how " connected " the ground space } }> of a local Hamiltonian is } } can range from QCMA-complete to NEXP-complete .
Edit intent: coherence
Original:  We show that this lemma is tight up to a polynomial factor with respect to the length of the unitary evolution in question.
Revised:  We show that this lemma is essentially tight with respect to the length of the unitary evolution in question.
Edit intent: clarity
Original:  In this paper, we consider a general model where two arbitrarily connected subnetworks are connected by random external edges , which includes the stochastic block model as a special case . Using random matrix theory and concentration inequalities, we show that when one performs community detection via spectral clustering there exists an abrupt phase transition as a function of the random external edge connection probability.
Revised:  In this paper, we consider a general model where two arbitrarily connected subnetworks are connected by random external edges . Using random matrix theory and concentration inequalities, we show that when one performs community detection via spectral clustering there exists an abrupt phase transition as a function of the random external edge connection probability.
Edit intent: coherence
Original: Many phylogenetic tree reconstruction methods require appropriate modelling of data to infer an accurate evolutionary tree.
Revised: Phylogenetic methods typically rely on an appropriate model of how data evolved in order to infer an accurate evolutionary tree.
Edit intent: clarity
Original: Many phylogenetic tree reconstruction methods require appropriate modelling of data to infer an accurate evolutionary tree.
Revised: Many phylogenetic tree reconstruction methods require appropriate modelling of data to infer an accurate phylogenetic tree.
Edit intent: clarity
Original:  However, for other types of data (e.g. morphological data), some (or even many) character state changes are too in-decisive, homoplastic and/ or saturated to develop models that are effective at capturing the underlying process of change.
Revised:  However, for other types of data (e.g. morphological data), characters can be too ambiguous, homoplastic or saturated to develop models that are effective at capturing the underlying process of change.
Edit intent: clarity
Original:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae that show how maximum compatibility is able to clearly identify the homoplasy-free characters, when the number  of taxa is large  .
Revised:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae regarding the performance of maximum compatibility. We show that this method is able to clearly identify the homoplasy-free characters, when the number of taxa is large .
Edit intent: clarity
Original:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae that show how maximum compatibility is able to clearly identify the homoplasy-free characters, when the number  of taxa is large  .
Revised:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae that show how maximum compatibility is able to identify a set of non-trivial homoplasy-free characters, when the number of taxa is large .
Edit intent: clarity
Original:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae that show how maximum compatibility is able to clearly identify the homoplasy-free characters, when the number  of taxa is large  .
Revised:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae that show how maximum compatibility is able to clearly identify the homoplasy-free characters, when the number n of taxa is large .
Edit intent: fluency
Original:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae that show how maximum compatibility is able to clearly identify the homoplasy-free characters, when the number  of taxa is large  .
Revised:  By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae that show how maximum compatibility is able to clearly identify the homoplasy-free characters, when the number of taxa is large , even when the number of random characters is large .
Edit intent: coherence
Original:  By contrast, we show that a method that makes more uniform use of all the data --- maximum parsimony -- can provably fail to detect any of the{\em   homoplasy-free characters  .
Revised:  By contrast, we show that a method that makes more uniform use of all the data --- maximum parsimony --- can provably estimate trees in which{\em homoplasy-free characters .
Edit intent: clarity
Original:  By contrast, we show that a method that makes more uniform use of all the data --- maximum parsimony -- can provably fail to detect any of the{\em   homoplasy-free characters  .
Revised:  By contrast, we show that a method that makes more uniform use of all the data --- maximum parsimony -- can provably fail to detect any of the{\em none homoplasy-free characters .
Edit intent: fluency
Original: Food webs, the networks of predator-prey interactions in ecological systems, are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole.
Revised: The networks of predator-prey interactions in ecological systems, are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole.
Edit intent: clarity
Original:  In order to understand the mechanism driving the complexity and stability of  food webs, we developed an eco-evolutionary food web model in which new species emerge via evolution from existing ones and dynamic ecological interactions determine which species is viableand which goes extinct .
Revised:  In order to understand the mechanism driving the complexity and stability of such food webs, we developed an eco-evolutionary food web model in which new species emerge via evolution from existing ones and dynamic ecological interactions determine which species is viableand which goes extinct .
Edit intent: clarity
Original:  In order to understand the mechanism driving the complexity and stability of  food webs, we developed an eco-evolutionary food web model in which new species emerge via evolution from existing ones and dynamic ecological interactions determine which species is viableand which goes extinct .
Revised:  In order to understand the mechanism driving the complexity and stability of food webs, we developed an eco-evolutionary model in which new species emerge via evolution from existing ones and dynamic ecological interactions determine which species is viableand which goes extinct .
Edit intent: fluency
Original:  In order to understand the mechanism driving the complexity and stability of  food webs, we developed an eco-evolutionary food web model in which new species emerge via evolution from existing ones and dynamic ecological interactions determine which species is viableand which goes extinct .
Revised:  In order to understand the mechanism driving the complexity and stability of food webs, we developed an eco-evolutionary food web model in which new species emerge as modifications of existing ones and dynamic ecological interactions determine which species is viableand which goes extinct .
Edit intent: clarity
Original:  In order to understand the mechanism driving the complexity and stability of  food webs, we developed an eco-evolutionary food web model in which new species emerge via evolution from existing ones and dynamic ecological interactions determine which species is viableand which goes extinct .
Revised:  In order to understand the mechanism driving the complexity and stability of food webs, we developed an eco-evolutionary food web model in which new species emerge via evolution from existing ones and dynamic ecological interactions determine which species are viable .
Edit intent: clarity
Original:  The proposed model is less abstract than earlier models of this type in the sense that all three evolving traits have a clear biological meaning, namely the average body size of the individuals, the preferred prey body mass, and the width of their potential prey body mass spectrum.
Revised:  The proposed model is less abstract than earlier models of this type in the sense that all three evolving traits have a clear biological meaning, namely the average body mass of the individuals, the preferred prey body mass, and the width of their potential prey body mass spectrum.
Edit intent: clarity
Original:  The model networks exhibit a continuous species turnover, during which phases of increasing specialisation are interrupted by extinction avalanches.
Revised:  The model networks exhibit a continuous species turnover, during which phases of increasing specialization are interrupted by extinction avalanches.
Edit intent: fluency
Original:  After these avalanches also more generalised predators can again occur.
Edit intent: coherence
Original: The networks of predator-prey interactions in ecological systems , are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole.
Revised: The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole.
Edit intent: fluency
Original:  Massive extinction waves that affect more than 50 \ of the network are not observed, suggesting that corresponding events in earth's history had external causes.
Revised:  Massive extinction waves that affect more than 50 
Edit intent: clarity
Original:  One originality of our proof is that it draws new connections between the adversary bound, a modern  theoretical computer science technique , and early theorems of quantum mechanics.
Revised:  One originality of our proof is that it draws new connections between the adversary bound, a modern technique of theoretical computer science technique , and early theorems of quantum mechanics.
Edit intent: clarity
Original:  One originality of our proof is that it draws new connections between the adversary bound, a modern  theoretical computer science technique , and early theorems of quantum mechanics.
Revised:  One originality of our proof is that it draws new connections between the adversary bound, a modern theoretical computer science , and early theorems of quantum mechanics.
Edit intent: clarity
Original:  Indeed, the proof of the lower bound is based on Ehrenfest's theorem, while the upper bound relies on the Adiabatic theorem, as we construct an optimal adiabatic quantum query algorithm  .
Revised:  Indeed, the proof of the lower bound is based on Ehrenfest's theorem, while the upper bound relies on the adiabatic theorem, as we construct an optimal adiabatic quantum query algorithm .
Edit intent: fluency
Original:  However, we introduce a symbolic zone-based method for synthesising bounded integer parameters of parametric timed automata with an LTL specification.
Revised:  We propose an alternative symbolic zone-based method for synthesising bounded integer parameters of parametric timed automata with an LTL specification.
Edit intent: clarity
Original:  Our method extends the ideas of the standard automata-based approach to LTL model checking of timed automata.
Revised:  Our method extends the ideas of the automata-based approach to LTL model checking of timed automata.
Edit intent: clarity
Original:  Our solution employs constrained parametric difference bound matrices and a suitable notion of extrapolation .
Revised:  To justify the usefulness of our approach, we provide experimental evaluation and compare our method with explicit enumeration technique .
Edit intent: coherence
Original:  In this work, we consider a continuous  description of a population of ants and simulate numerically their foraging behavior using a system of PDEs of chemotaxis type.
Revised:  In this work, we consider a continuous description of a population of ants and simulate numerically their foraging behavior using a system of partial differential equations of chemotaxis type.
Edit intent: clarity
Original: We prove that for every sign matrix A there is a deterministic communication protocol that uses O(corr_{1/4(A)\log^2 rk(A)) bits of communication, where corr_{1/4}(A) is the corruption/rectangle boundwith error 1/4.
Revised: We prove (A)\log^2 rk(A)) bits of communication, where corr_{1/4}(A) is the corruption/rectangle boundwith error 1/4.
Edit intent: clarity
Original: A quantitative function for community detection called modularity density has been proposed by Li, Zhang, Wang, Zhang, and Chen in [Phys.
Revised: A "quantitative function" for community detection called modularity density has been proposed by Li, Zhang, Wang, Zhang, and Chen in [Phys.
Edit intent: fluency
Original:  Among the properties presented by the authors, some of them are not proved or need to be clarified, e. g., the NP-hardness of the problem, the fact that the modularity density of each community must be non-negative, and the fact that a clique is not divided into two or more parts when maximizing the modularity density.
Revised:  Among the properties presented by the authors, some of them are not proved or need to be clarified, e. g., the NP-hardness of the problem, the fact that the modularity density of each community must be non-negative, and the fact that a clique can be divided into two or more parts when maximizing the modularity density.
Edit intent: clarity
Original:  Finally, we show that the solution yielding the highest value of modularity density for the Zachary karate club network is found when the number of communities is 3, and not 4 as claimed by the authors .
Revised:  Finally, we show that the solution yielding the highest value of modularity density for the Zachary karate club network .
Edit intent: clarity
Original: Kolmogorov-Chaitin complexity has long been believed to be unapproachable when it comes to short sequences (e.g. of length 5-50).
Revised: Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50).
Edit intent: clarity
Original:  However, with the newly developed coding theorem method the complexity of strings of length 2-11 can now be numerically estimated.
Revised:  However, with the newly developed coding theorem method the complexity of strings of length 2-11 can now be numerically estimated.
Edit intent: fluency
Original:   Our method is based on previous work by Ross and Selinger on the optimal ancilla-free approximation of z-rotations using Clifford+T gates and on previous work by Bocharov, Gurevich, and Svore on the asymptotically optimal ancilla-free approximation of z-rotations using Pauli +V gates.
Revised:  Our method is based on previous work by the author and Selinger on the optimal ancilla-free approximation of z-rotations using Clifford+T gates and on previous work by Bocharov, Gurevich, and Svore on the asymptotically optimal ancilla-free approximation of z-rotations using Pauli +V gates.
Edit intent: clarity
Original: We prove that the model checking problem for the existential fragment of first order (FO) logic on partially ordered sets is fixed-parameter tractable (FPT) with respect to the formula and the width of a poset (the maximum size of an antichain).
Revised: We prove that the model checking problem for the existential fragment of first-order (FO) logic on partially ordered sets is fixed-parameter tractable (FPT) with respect to the formula and the width of a poset (the maximum size of an antichain).
Edit intent: fluency
Original:  We improve upon their result in two ways: (1) the runtime of our algorithm is O(f(|{\phi}|,w) \cdot n^2) on n-element posets of width w, compared to O(g(|{\phi}|) \cdot n^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow.
Revised:  We improve upon their result in two ways: (1) the runtime of our algorithm is O(f(|{\phi}|,w) \cdot n^2) on n-element posets of width w, compared to O(g(|{\phi}|) . n^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow.
Edit intent: fluency
Original: The whole body of experimental and empirical observations on cell metabolism cannot be understood  without their integration into a consistent systematic framework.
Revised: Experimental and empirical observations on cell metabolism cannot be understood without their integration into a consistent systematic framework.
Edit intent: clarity
Original:  However, the characterization of metabolic flux phenotypes under a certain environmental condition is typically reduced to the study of a single optimal state, like maximum biomass yield that is by far the most common assumption.
Revised:  However, the characterization of metabolic flux phenotypes is typically reduced to the study of a single optimal state, like maximum biomass yield that is by far the most common assumption.
Edit intent: clarity
Original:  Here we confront optimal growth solutions to the whole set of feasible flux phenotypes (FFP), which provides a bechmark to assess the likelihood of optimal and high-growth states and their agreement with experimental results.
Revised:  Here we confront optimal growth solutions to the whole set of feasible flux phenotypes (FFP), which provides a benchmark to assess the likelihood of optimal and high-growth states and their agreement with experimental results.
Edit intent: fluency
Original:  Two-month model forecasts show an increasingly severe epidemic with no sign of having reached a peak.
Revised:  Model forecasts until Dec. 31, 2014 show an increasingly severe epidemic with no sign of having reached a peak.
Edit intent: clarity
Original: Based on the ideas by Talal Rahman and Jan Valdman we propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB  for problems discretized by edge finite elements.
Revised: We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB for problems discretized by edge finite elements.
Edit intent: coherence
Original: Based on the ideas by Talal Rahman and Jan Valdman we propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB  for problems discretized by edge finite elements.
Revised: Based on the ideas by Talal Rahman and Jan Valdman we propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB . We apply this for problems discretized by edge finite elements.
Edit intent: coherence