wanyu/IteraTeR_v2 huggingface dataset:
Original: We present a novel orbital-free density functional theory (OFDFT) implementation using the projector augmented-wave method (PAW) that simultaneously preserves the linear scaling characteristic of OFDFT and provides access to all-electron values .
Revised: We present a computational scheme for orbital-free density functional theory (OFDFT) implementation using the projector augmented-wave method (PAW) that simultaneously preserves the linear scaling characteristic of OFDFT and provides access to all-electron values .
Edit intent: clarity
Original: We present a novel orbital-free density functional theory (OFDFT) implementation using the projector augmented-wave method (PAW) that simultaneously preserves the linear scaling characteristic of OFDFT and provides access to all-electron values .
Revised: We present a novel orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values .
Edit intent: clarity
Original:  Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham (KS) codes.
Revised:  Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham codes.
Edit intent: clarity
Original:  Because computed bulk modulus and lattice constant are extremely different from reported pseudopotential values, we conclude that in order to assess the performance of OFDFT functionals it is necessary to use  all-electron methods .
Revised:  Because computed bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use all-electron methods .
Edit intent: clarity
Original:  Because computed bulk modulus and lattice constant are extremely different from reported pseudopotential values, we conclude that in order to assess the performance of OFDFT functionals it is necessary to use  all-electron methods .
Revised:  Because computed bulk modulus and lattice constant are extremely different from reported pseudopotential values, we conclude that in order to assess the performance of OFDFT functionals it is necessary to use all-electron values .
Edit intent: clarity
Original:  We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained at the PBE level , exemplified with the case of diamond.
Revised:  We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method , exemplified with the case of diamond.
Edit intent: clarity
Original:  From a coding theory point of view,  this model is approximately dual of the well-studied index coding problem.
Revised:  From a coding theory point of view, we show that this model is approximately dual of the well-studied index coding problem.
Edit intent: coherence
Original:  The well-known upper bounds on the distance of locally recoverable codes follow from our result.
Revised:  The well-known impossibility bounds on the distance of locally recoverable codes follow from our result.
Edit intent: clarity
Original: This paper studies the joint user association and resource allocation in heterogeneous networks (HetNets) from a novel perspective, motivated by and generating the idea of fractional frequency reuse.
Revised: This paper studies the joint user association and resource allocation in heterogeneous networks (HetNets) from a novel perspective, motivated by and generalizing the idea of fractional frequency reuse.
Edit intent: clarity
Original:  By treating the multi-cell multi-user resource allocation as resource partitioning among multiple reuse patterns, we propose a unified framework to analyze and compare a wide range of user association and resource allocation strategies for HetNets, and provide a benchmark of ultimate limit on network performance.
Revised:  By treating the multi-cell multi-user resource allocation as resource partitioning among multiple reuse patterns, we propose a unified framework to analyze and compare a wide range of user association and resource allocation strategies for HetNets, and provide an optimal benchmark for network performance.
Edit intent: clarity
Original:  The enabling mechanisms are a novel formulation to consider all possible  patterns or any pre-defined subset of patterns and an efficient sparsity-pursuit algorithm.
Revised:  The enabling mechanisms are a novel formulation to consider all possible patterns or any pre-defined subset of patterns , and efficient sparsity-pursuit algorithm.
Edit intent: fluency
Original:  Relying on the sparsity-pursuit capability of the proposed algorithm , we develop  practical guideline to identify the feature patterns in the given HetNet.
Revised:  Relying on the sparsity-pursuit capability of the proposed algorithms , we develop practical guideline to identify the feature patterns in the given HetNet.
Edit intent: fluency
Original:  Relying on the sparsity-pursuit capability of the proposed algorithm , we develop  practical guideline to identify the feature patterns in the given HetNet.
Revised:  Relying on the sparsity-pursuit capability of the proposed algorithm , we develop a practical guideline to identify the feature patterns in the given HetNet.
Edit intent: fluency
Original: Press and Dyson has recently revealed a new set of "zero-determinant " (ZD) strategies for repeated games, which grant a player with power of manipulation on the game's payoffs .
Revised: Press and Dyson has recently revealed a new set of "zero-determinant (ZD) strategies for repeated games, which grant a player with power of manipulation on the game's payoffs .
Edit intent: fluency
Original: Press and Dyson has recently revealed a new set of "zero-determinant " (ZD) strategies for repeated games, which grant a player with power of manipulation on the game's payoffs .
Revised: Press and Dyson has recently revealed a new set of "zero-determinant " (ZD) " strategies, which is an important advance in repeated games .
Edit intent: clarity
Original:  A ZD strategy player can unilaterally enforce a fixed linear relationship between his payoff and that of his opponent .
Revised:  A ZD strategy player can exert a unilaterally control on two players' payoffs .
Edit intent: clarity
Original:  In particular it can (i) deterministically set his opponent's payoff to a fixed value, regardless of how the opponent responds;
Revised:  In particular he can deterministically set the opponent's payoff to a fixed value, regardless of how the opponent responds;
Edit intent: clarity
Original:  In this work, we derive the generalized form of ZD strategies for noisy repeated games, and also study the conditions, feasible regions and corresponding payoffs for two specifications of ZD strategies , which are called the pinning strategies and extortion strategies.
Revised:  In this paper, we propose a general model of ZD strategies for noisy repeated games, and also study the conditions, feasible regions and corresponding payoffs for two specifications of ZD strategies , which are called the pinning strategies and extortion strategies.
Edit intent: clarity
Original: The famous Cern\'y conjecture , a 50-year-old mathematical problem, states that every n-state synchronizing automaton has a reset word of length at most (n-1)^2.
Revised: The Cern\'y conjecture , a 50-year-old mathematical problem, states that every n-state synchronizing automaton has a reset word of length at most (n-1)^2.
Edit intent: clarity
Original: The famous Cern\'y conjecture , a 50-year-old mathematical problem, states that every n-state synchronizing automaton has a reset word of length at most (n-1)^2.
Revised: The famous Cern\'y conjecture states that every n-state synchronizing automaton has a reset word of length at most (n-1)^2.
Edit intent: clarity
Original:  We consider the question of finding short reset words.
Revised:  We study the hardness of finding short reset words.
Edit intent: clarity
Original:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Revised:  i.e., finding the shortest reset word, is NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Edit intent: clarity
Original:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Revised:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and complete for the DP class, and that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Edit intent: coherence
Original:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Revised:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a factor of O(\log n) is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Edit intent: clarity
Original:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Revised:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary , even for the binary alphabet[ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Edit intent: coherence
Original:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is not possible to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Revised:  i.e., finding the shortest reset word, is both NP-hard and coNP-hard, and actually complete for a class known as DP . It is also known that approximating the length of the shortest reset word within a logarithmic factor is NP-hard , even if the alphabet is binary [ . We significantly improve on these results by showing that, unless P=NP , it is NP-hard to approximate the length of the shortest reset word within a factor of n^{ 0.0095 } in polynomial time .
Edit intent: clarity
Original:  The stability of rabbit prion protein is due to its highly ordered beta2-alpha2 loop {  PLoS One 5(10) e13273 (2010);
Revised:  The stability of rabbit prion protein is due to its highly ordered beta2-alpha2 loop {\alpha PLoS One 5(10) e13273 (2010);
Edit intent: fluency
Original:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Revised:  A spanning subgraph of Q_d is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Edit intent: clarity
Original:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Revised:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( Q_d,Q_m )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Edit intent: clarity
Original:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Revised:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( Q_d )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Edit intent: fluency
Original:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Revised:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each added edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Edit intent: fluency
Original:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Revised:  Given graphs F and H, a spanning subgraph G of F is said to be weakly ( F,H )-saturated if the edges of E( F )\setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of Q_m . Answering another question of Johnson and Pinto, we determine the minimum number of edges in a weakly (Q_d,Q_m)-saturated graph for all d\geq m\geq1.
Edit intent: fluency
Original:  We develop a high quality SVD software on top of the state-of-the-art eigensolver PRIMME that can take advantage of preconditioning , and of PRIMME's nearly-optimal methods and full functionality to compute both largest and smallest singular triplets.
Revised:  We develop a high quality SVD software on top of the state-of-the-art eigensolver PRIMME that can take advantage of preconditioning and of any well designed eigensolver to compute both largest and smallest singular triplets.
Edit intent: clarity
Original:  Accuracy and efficiency is achieved through a hybrid, two-stage meta-method, primme_svds .
Revised:  Accuracy and efficiency is achieved through a hybrid, two-stage meta-method, PHSVDS .
Edit intent: clarity
Original:  In the first stage, primme_svds solves the normal equations problem up to the best achievable accuracy.
Revised:  In the first stage, primme_svds solves the normal equations up to the best achievable accuracy.
Edit intent: clarity
Original:  We also discuss how to precondition primme_svds and to cope with some issues that arise .
Revised:  We also discuss how to precondition PHSVDS and to cope with some issues that arise .
Edit intent: clarity
Original: Hierarchical analysis is considered and a novel, multilevel model is presented in order to explore causality, chance and complexity in financial economics.
Revised: Hierarchical analysis is considered and a multilevel model is presented in order to explore causality, chance and complexity in financial economics.
Edit intent: clarity
Original:  Here, we studied stochastic tunneling in a Moran model.
Revised:  Here, we study stochastic tunneling in a Moran model.
Edit intent: fluency
Original:  Our analysis also reveals fitness landscapes and mutation rates for which finite populations have long-lived metastable states.
Revised:  Our analysis also reveals fitness landscapes and mutation rates for which finite populations are found in long-lived metastable states.
Edit intent: clarity
Original:  We first show that a simple CNN with little hyperparameter tuning and static vectors achieves excellent results on multiple benchmarks.
Revised:  We show that a simple CNN with little hyperparameter tuning and static vectors achieves excellent results on multiple benchmarks.
Edit intent: coherence
Original:  We additionally propose a simple modification to the architecture to allow for the use of both task-specific and static word vectors.
Revised:  We additionally propose a simple modification to the architecture to allow for the use of both task-specific and static vectors.
Edit intent: clarity
Original:  The CNN models discussed herein improve upon the state-of-the-art on 4 out of 7 tasks, which include sentiment analysis and question classification.
Revised:  The CNN models discussed herein improve upon the state of the art on 4 out of 7 tasks, which include sentiment analysis and question classification.
Edit intent: fluency
Original:   This leads us to think of ways to relax the notion of exactly satisfying a tolerance value , in a hopefully profitable way.
Revised:  This leads us to think of approaches to relax the notion of exactly satisfying a tolerance value , in a hopefully profitable way.
Edit intent: clarity
Original:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Revised:  We consider range expansion radii that grow with an arbitrary power-law in time: R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Edit intent: clarity
Original:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Revised:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Edit intent: clarity
Original:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Revised:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Edit intent: fluency
Original:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Revised:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Edit intent: fluency