wanyu/IteraTeR_v2 huggingface dataset:
Original:  We focus on an alternative generalized harmonic mean (GHM) estimator which, recycling MCMC simulations from the posterior, shares the computational simplicity of the original HM estimator, but, unlike it, overcomes the infinite variance issue.
Revised:  Our new implementation of the generalized harmonic mean (GHM) estimator which, recycling MCMC simulations from the posterior, shares the computational simplicity of the original HM estimator, but, unlike it, overcomes the infinite variance issue.
Edit intent: clarity
Original:  We focus on an alternative generalized harmonic mean (GHM) estimator which, recycling MCMC simulations from the posterior, shares the computational simplicity of the original HM estimator, but, unlike it, overcomes the infinite variance issue.
Revised:  We focus on an alternative generalized harmonic mean (GHM) idea recycles MCMC simulations from the posterior, shares the computational simplicity of the original HM estimator, but, unlike it, overcomes the infinite variance issue.
Edit intent: clarity
Original:  We show that the Inflated Density Ratio (IDR) estimator when applied to some standard phylogenetic benchmark data , produces fully satisfactory results outperforming those simple estimators currently provided by most of the publicly available software.
Revised:  The alternative estimator is applied to simulated phylogenetic data and produces fully satisfactory results outperforming those simple estimators currently provided by most of the publicly available software.
Edit intent: clarity
Original:  HepML tags contain an information enough to understand what kind of physics the simulated events describe and how the events have been prepared.
Revised:  HepML tags contain enough information to understand what kind of physics the simulated events describe and how the events have been prepared.
Edit intent: fluency
Original:  A HepML block is an additional part to the LHEF format of event files .
Revised:  A HepML block can be included into event files in the LHEF format of event files .
Edit intent: clarity
Original:  A HepML block is an additional part to the LHEF format of event files .
Revised:  A HepML block is an additional part to the LHEF format .
Edit intent: clarity
Original:  The library is an API for an external software.
Revised:  The library is an API for external software.
Edit intent: fluency
Original:  In turn, Showering and Hadronization event generators can parse the HepML header and get the information in the form of C++ classes. libhepml can be used in C++, C, and Fortran programs.
Revised:  In turn, Showering and Hadronization event generators can parse the HepML header and get the information in the form of C++ classes. Libhepml can be used in C++, C, and Fortran programs.
Edit intent: fluency
Original:  Libhepml can be used in C++, C, and Fortran programs.
Revised:  libhepml can be used in C++, C, and Fortran programs.
Edit intent: fluency
Original:  We show that for any p > 1, the p-norm of the matrix , which is defined to be\ge  |A| _p = Max_x | | Ax| |_p , where | | x| |_p =  1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Revised:  We show that for any p > p norm of a matrix A , which is defined to be\ge |A| _p = Max_x | | Ax| |_p , where | | x| |_p = 1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Edit intent: clarity
Original:  We show that for any p > 1, the p-norm of the matrix , which is defined to be\ge  |A| _p = Max_x | | Ax| |_p , where | | x| |_p =  1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Revised:  We show that for any p > 1, the p-norm of the matrix , which is defined to be\ge 1, as |A| _p = Max_x | | Ax| |_p , where | | x| |_p = 1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Edit intent: coherence
Original:  We show that for any p > 1, the p-norm of the matrix , which is defined to be\ge  |A| _p = Max_x | | Ax| |_p , where | | x| |_p =  1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Revised:  We show that for any p > 1, the p-norm of the matrix , which is defined to be\ge |A| _p = Max_x | Ax| |_p , where | | x| |_p = 1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Edit intent: fluency
Original:  We show that for any p > 1, the p-norm of the matrix , which is defined to be\ge  |A| _p = Max_x | | Ax| |_p , where | | x| |_p =  1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Revised:  We show that for any p > 1, the p-norm of the matrix , which is defined to be\ge |A| _p = Max_x | | Ax| |_p , where | x| |_p = 1 can be computed to a factor of (1+\delta) in time polynomial in \log(1/\delta), N and the dimension of the matrix n . However, in the case of general n-dimensional matrices, for\ge p >1,p != 2, we show that it is NP-hard to approximate the p-norm to within a factor if (1+n^{-c), for any constant c>0.
Edit intent: fluency
Original:  Recently, Englert and Racke } \ge  [ER] showed the existence of an O(log n)-competitive oblivious routing scheme when the aggregate function is an lp norm (p\le \le \le  > 1).
Revised:  Recently, Englert and Racke } \ge [ER] on O(log n)-competitive oblivious routing scheme when the aggregate function is an lp norm (p\le \le \le > 1).
Edit intent: clarity
Original: The problems studied in this paper arise out of how advertisers allocate their budget in internet advertising.
Revised: Internet advertising is a sophisticated game in which the many advertisers "play" to optimize their return on investment. There are many "targets" for the advertisements, and in each "target" is a collection of games with a potentially different set of players are involved. In this paper, we study the problem of how advertisers allocate their budget in internet advertising.
Edit intent: coherence
Original:  Advertisers have a set of keywords  and some stochastic information about the future, in our case, a probability distribution over scenarios of cost vs click combinations.
Revised:  Advertisers have a set of keywords and some stochastic information about the future, namely a probability distribution over scenarios of cost vs click combinations.
Edit intent: clarity
Original:  The stochastic budget optimization problems that the advertisers face then is to figure out how to spread a given budget across these keywords to maximize the expected number of clicks.
Revised:  The stochastic budget optimization problems to figure out how to spread a given budget across these keywords to maximize the expected number of clicks.
Edit intent: clarity
Original:  We present the first known nontrivial polylogarithmic approximation for these problems ;
Revised:  We present the first known non-trivial poly-logarithmic approximation for these problems ;
Edit intent: fluency
Original:  we also present first known hardness results of getting approximations better than logarithmic in various parameters involved.
Revised:  we also present first known hardness results of getting better than logarithmic in various parameters involved.
Edit intent: clarity
Original:  we also present first known hardness results of getting approximations better than logarithmic in various parameters involved.
Revised:  we also present first known hardness results of getting approximations better than logarithmic approximation ratios in the various parameters involved.
Edit intent: clarity
Original:  We also identify several special cases of these problems of practical interest, such as with fixed number of scenarios or with polynomial-sized parameters related to cost, which are solvable  in polynomial time or with good approximations.
Revised:  We also identify several special cases of these problems of practical interest, such as with fixed number of scenarios or with polynomial-sized parameters related to cost, which are solvable either in polynomial time or with good approximations.
Edit intent: coherence
Original:  Our approximation results as well as hardness results come from relating these problems to a special type of (0/1, bipartite) quadratic programs inherent in them  .
Revised:  Our approximation and hardness results come from relating these problems to a special type of (0/1, bipartite) quadratic programs inherent in them .
Edit intent: clarity
Original:  There are many "targets" for the advertisements, and in each "target" is a collection of games with a potentially different set of players are involved.
Revised:  There are many "targets" for the advertisements, and each "target" is a collection of games with a potentially different set of players are involved.
Edit intent: clarity
Original:  There are many "targets" for the advertisements, and in each "target" is a collection of games with a potentially different set of players are involved.
Revised:  There are many "targets" for the advertisements, and in each "target" has a collection of games with a potentially different set of players are involved.
Edit intent: clarity
Original:  There are many "targets" for the advertisements, and in each "target" is a collection of games with a potentially different set of players are involved.
Revised:  There are many "targets" for the advertisements, and in each "target" is a collection of games with a potentially different set of players involved.
Edit intent: clarity
Original: Bayesian methods are now one of the main tools for inferring phylogenetic trees from aligned sequence data.
Revised: Bayesian inference is now a leading technique for reconstructing phylogenetic trees from aligned sequence data.
Edit intent: clarity
Original:  We mathematically demonstrate that Bayesian methods for inferring resolved trees are statistically consistent over the entire parameter range of branch lengths,  under general conditions on priors , at least for simple models where the usual ' identifiability' conditions hold  .
Revised:  We mathematically demonstrate that Bayesian methods for inferring resolved trees are statistically consistent over the entire parameter range of branch lengths, and under general conditions on priors , at least for simple models where the usual ' identifiability' conditions hold .
Edit intent: coherence
Original:  We mathematically demonstrate that Bayesian methods for inferring resolved trees are statistically consistent over the entire parameter range of branch lengths,  under general conditions on priors , at least for simple models where the usual ' identifiability' conditions hold  .
Revised:  We mathematically demonstrate that Bayesian methods for inferring resolved trees are statistically consistent over the entire parameter range of branch lengths, under general conditions on priors in models where the usual ' identifiability' conditions hold .
Edit intent: clarity
Original:  We mathematically demonstrate that Bayesian methods for inferring resolved trees are statistically consistent over the entire parameter range of branch lengths,  under general conditions on priors , at least for simple models where the usual ' identifiability' conditions hold  .
Revised:  We mathematically demonstrate that Bayesian methods for inferring resolved trees are statistically consistent over the entire parameter range of branch lengths, under general conditions on priors , at least for simple models where the usual ` identifiability' conditions hold .
Edit intent: fluency
Original:  Our methods and results may prove useful beyond the Heston model: the entire quantitative analysis is based on affine principles ;
Revised:  Our methods and results may prove useful beyond the Heston model: the entire quantitative analysis is based on affine principles :
Edit intent: fluency
Original:  A minor-embedding of a graph G in a quantum hardware graph %DIFDELCMD < \uni %%%  is a subgraph of U such that G can be obtained from it by contracting edges.
Revised:  A minor-embedding of a graph G in a quantum hardware graph %DIFDELCMD < \uni %%% U is a subgraph of U such that G can be obtained from it by contracting edges.
Edit intent: fluency
Original:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{  } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Revised:  Given a family F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{ } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Edit intent: fluency
Original:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{  } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Revised:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{ } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Edit intent: fluency
Original:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{  } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Revised:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a -minor-universal hardware graph U_{ } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Edit intent: fluency
Original:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{  } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Revised:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F F-minor-universal hardware graph U_{ } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Edit intent: fluency
Original:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{  } in which \mathcal{F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Revised:  Given a family \mathcal{F of graphs, a (host) graph U is called \mathcal{F if for each graph G in \mathcal{F , U contains a minor-embedding of G. The problem for designing a \mathcal{F -minor-universal hardware graph U_{ } in which F consists of a family of sparse graphs (e.g., bounded degree graphs) is open.
Edit intent: fluency
Original: Modern Web services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers.
Revised: Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers.
Edit intent: clarity
Original:  Such services are modeled by networks of queues, where one queue models each of the individual computers in the system.
Revised:  Such services are modeled by networks of queues, where each queue models one of the computers in the system.
Edit intent: clarity
Original:  A key challenge is that the data is incomplete, because recording detailed information about every request to a heavily used system can require unacceptable overhead.
Revised:  A key challenge is that the data are incomplete, because recording detailed information about every request to a heavily used system can require unacceptable overhead.
Edit intent: fluency
Original: The growth in data traffic and the increased demand for quality of service has meant current network systems need to be more efficient.
Revised: The growth in data traffic and the increased demand for quality of service had generated a large demand for network systems to be more efficient.
Edit intent: clarity
Original:  The introduction of improved routing systems to meet the increasing demand and varied protocols to accommodate various scales of challenges in network efficiency has further complicated the operations.
Revised:  The introduction of improved routing systems to meet the increasing demand and varied protocols to accommodate various scales of challenges in network efficiency had further complicated the operations.
Edit intent: fluency
Original:  This means  a better mode of intelligence had to be infused into networking for smoother operations and better autonomic features.
Revised:  This means that a better mode of intelligence had to be infused into networking for smoother operations and better autonomic features.
Edit intent: fluency
Original:  This means  a better mode of intelligence had to be infused into networking for smoother operations and better autonomic features.
Revised:  This means a better mode of intelligence has to be infused into networking for smoother operations and better autonomic features.
Edit intent: fluency
Original:  The cognitive elements of  system like perception, learning, planning, reasoning and decision forming can enable the systems to be more aware of their environment and offer better services.
Revised:  The cognitive elements of a system like perception, learning, planning, reasoning and decision forming can enable the systems to be more aware of their environment and offer better services.
Edit intent: fluency
Original:  However, simulations demonstrating these methods' efficacy employed a continuum of rating values,  whereas in most practical rating systems only a limited range of discrete values (such as a 5-star system) is employed.
Revised:  However, simulations demonstrating these methods' efficacy assumed a continuum of rating values, whereas in most practical rating systems only a limited range of discrete values (such as a 5-star system) is employed.
Edit intent: clarity
Original:  However, simulations demonstrating these methods' efficacy employed a continuum of rating values,  whereas in most practical rating systems only a limited range of discrete values (such as a 5-star system) is employed.
Revised:  However, simulations demonstrating these methods' efficacy employed a continuum of rating values, whereas in most actual rating systems only a limited range of discrete values (such as a 5-star system) is employed.
Edit intent: clarity
Original:  The standard computer model in computability theory is the Turing machine, introduced by Alan Turing 38%DIFDELCMD < ] %%% in 1936 . Although the model was introduced before physical computers were built, it nevertheless continues to be accepted as the proper computer model for the purpose of defining the notion of computable function.
Revised:  The standard computer model in computability theory is the Turing machine, introduced by Alan Turing %DIFDELCMD < ] %%% in 1936 . Although the model was introduced before physical computers were built, it nevertheless continues to be accepted as the proper computer model for the purpose of defining the notion of computable function.
Edit intent: coherence
Original:  Under certain constraints on the parameters a mathematical analysis yields an eigenvalue spectrum for the linearised evolution operator, from which the stability properties of the steady state can be inferred .
Revised:  We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, from which the stability properties of the steady state can be inferred .
Edit intent: clarity
Original:  Under certain constraints on the parameters a mathematical analysis yields an eigenvalue spectrum for the linearised evolution operator, from which the stability properties of the steady state can be inferred .
Revised:  Under certain constraints on the parameters a mathematical analysis yields an eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the steady state can be inferred .
Edit intent: coherence
Original:  Under certain constraints on the parameters a mathematical analysis yields an eigenvalue spectrum for the linearised evolution operator, from which the stability properties of the steady state can be inferred .
Revised:  Under certain constraints on the parameters a mathematical analysis yields an eigenvalue spectrum for the linearised evolution operator, from which the stability properties of the power-law steady state .
Edit intent: clarity
Original: Solving multi-homogeneous systems, as a wide range of structured algebraic systems occurring frequently in practical problems, is of first importance.
Revised: Solving multihomogeneous systems, as a wide range of structured algebraic systems occurring frequently in practical problems, is of first importance.
Edit intent: fluency
Original:  Experimentally, solving these systems with Gr\"obner bases algorithms seems  easier than solving homogeneous systems of the same degree , but the reasons of this behaviour are not clear.
Revised:  Experimentally, solving these systems with Gr\"obner bases algorithms seems to be easier than solving homogeneous systems of the same degree , but the reasons of this behaviour are not clear.
Edit intent: fluency
Original:  Experimentally, solving these systems with Gr\"obner bases algorithms seems  easier than solving homogeneous systems of the same degree , but the reasons of this behaviour are not clear.
Revised:  Experimentally, solving these systems with Gr\"obner bases algorithms seems easier than solving homogeneous systems of the same degree . Nevertheless, the reasons of this behaviour are not clear.
Edit intent: coherence