wanyu/IteraTeR_v2 huggingface dataset:
Original:  We then go beyond the worst-case and provide--for a large range of parameters  instance-optimal algorithms (w.r.t. to the query complexity )-i. e., answering the question how important knowledge of the instance is.
Revised:  We then go beyond the worst-case and provide--for a large range of parameters , instance-optimal algorithms (w.r.t. to the query complexity )-i. e., answering the question how important knowledge of the instance is.
Edit intent: fluency
Original:  We then go beyond the worst-case and provide--for a large range of parameters  instance-optimal algorithms (w.r.t. to the query complexity )-i. e., answering the question how important knowledge of the instance is.
Revised:  We then go beyond the worst-case and provide--for a large range of parameters instance-optimal algorithms with respect to the query complexity )-i. e., answering the question how important knowledge of the instance is.
Edit intent: clarity
Original:  on the other side, the value model is strictly easier than the comparison model in the case where the papers are totally ordered .
Revised:  on the other side, the value model is strictly easier than the comparison model .
Edit intent: clarity
Original: We propose an efficient  graph-based divisive cluster analysis approach called sampling clustering .
Revised: We propose an efficient graph-based divisive cluster analysis approach called Sampling Clustering .
Edit intent: fluency
Original:  Experimental results show that they outperform state-of-the-art clustering algorithms with significantly less computing resources requirements.
Revised:  Experimental results show that they outperform state-of-the-art clustering algorithms with significantly less computing resource requirements.
Edit intent: fluency
Original: International football results are interpreted as a directed network  to give each team a rank.
Revised: We explore the advantages of representing international football results as a directed network to give each team a rank.
Edit intent: clarity
Original: International football results are interpreted as a directed network  to give each team a rank.
Revised: International football results are interpreted as a directed network in order to give each team a rank.
Edit intent: clarity
Original:  Two network-based models --- Static and Dynamic --- are constructed and compared with the current FIFA Rankings.
Revised:  Two network-based models --- Static and Dynamic --- are constructed and compared with the FIFA Rankings.
Edit intent: clarity
Original: This article reports proof-of-concept web apps that use commodity  open-source technologies for augmented and virtual reality to tackle real-world problems from chemistryand structural biology .
Revised: This article reports prototype web apps that use commodity open-source technologies for augmented and virtual reality to tackle real-world problems from chemistryand structural biology .
Edit intent: clarity
Original: This article reports proof-of-concept web apps that use commodity  open-source technologies for augmented and virtual reality to tackle real-world problems from chemistryand structural biology .
Revised: This article reports proof-of-concept web apps that use commodity , open-source technologies for augmented and virtual reality to tackle real-world problems from chemistryand structural biology .
Edit intent: fluency
Original:  Along the results and in the discussion section , future perspectives are depicted based on recent works in the areas of machine learning for chemistry , transcompilation of programs into JavaScript, and advanced APIs and libraries supported by major web browsers .
Revised:  From this bases , future perspectives are depicted based on recent works in the areas of machine learning for chemistry , transcompilation of programs into JavaScript, and advanced APIs and libraries supported by major web browsers .
Edit intent: coherence
Original:  Together, all these technologies that are today available in web browsers will likely lead to the next generation of tools for truly interactive  molecular modeling that can streamline human thought and intent with the numerical processing power of computers.
Revised:  Together, all these technologies that are today maturing in web browsers- to deliver the next generation of tools for truly interactive molecular modeling that can streamline human thought and intent with the numerical processing power of computers.
Edit intent: clarity
Original:  By directly mapping a molecular-level biophysical fitness function to the system-level dynamics of the population we show that both low and very high, but not intermediate, levels of stress  result in a disproportionate effect of hypermutation on resistance fixation and that traditional definitions of the selection coefficient are insufficient to account for this effect .
Revised:  By directly mapping a biophysical fitness function to the system-level dynamics of the population we show that both low and very high, but not intermediate, levels of stress result in a disproportionate effect of hypermutation on resistance fixation and that traditional definitions of the selection coefficient are insufficient to account for this effect .
Edit intent: clarity
Original:  By directly mapping a molecular-level biophysical fitness function to the system-level dynamics of the population we show that both low and very high, but not intermediate, levels of stress  result in a disproportionate effect of hypermutation on resistance fixation and that traditional definitions of the selection coefficient are insufficient to account for this effect .
Revised:  By directly mapping a molecular-level biophysical fitness function to the system-level dynamics of the population we show that both low and very high, but not intermediate, levels of stress result in a disproportionate effect of hypermutation on resistance fixation .
Edit intent: coherence
Original:  Over The Top (OTT) service providers provide video streaming services by creating a large distributed network cloud on top of  infrastructure owned by multiple entities.
Revised:  Over The Top (OTT) service providers offer video streaming services by creating a large distributed network cloud on top of infrastructure owned by multiple entities.
Edit intent: fluency
Original:  Over The Top (OTT) service providers provide video streaming services by creating a large distributed network cloud on top of  infrastructure owned by multiple entities.
Revised:  Over The Top (OTT) service providers provide video streaming services by creating a large distributed cloud network on top of infrastructure owned by multiple entities.
Edit intent: fluency
Original:  Our analysis of nationwide data shows interesting characteristics of video streaming such as viewing patterns (early leaving viewer vs.steady viewer) , viewing habits of users (when do the users watch? which contents ?), correlation between user profile information (e. g., age, sex)and viewing habits , etc.
Revised:  Our analysis of nationwide data shows interesting characteristics of video streaming such as correlation between user profile information (e.g., age, sex) and viewing habits , viewing habits of users (when do the users watch? which contents ?), correlation between user profile information (e. g., age, sex)and viewing habits , etc.
Edit intent: clarity
Original:  Our analysis of nationwide data shows interesting characteristics of video streaming such as viewing patterns (early leaving viewer vs.steady viewer) , viewing habits of users (when do the users watch? which contents ?), correlation between user profile information (e. g., age, sex)and viewing habits , etc.
Revised:  Our analysis of nationwide data shows interesting characteristics of video streaming such as viewing patterns (early leaving viewer vs.steady viewer) , viewing habits of users (when do the users watch? using which devices ?), correlation between user profile information (e. g., age, sex)and viewing habits , etc.
Edit intent: clarity
Original:  Our analysis of nationwide data shows interesting characteristics of video streaming such as viewing patterns (early leaving viewer vs.steady viewer) , viewing habits of users (when do the users watch? which contents ?), correlation between user profile information (e. g., age, sex)and viewing habits , etc.
Revised:  Our analysis of nationwide data shows interesting characteristics of video streaming such as viewing patterns (early leaving viewer vs.steady viewer) , viewing habits of users (when do the users watch? which contents ?), viewing patterns (early leaving viewer vs. steady viewer) , etc.
Edit intent: coherence
Original:  We discuss how understanding such user behaviors and patterns helps to better manage contents and network resources (number of active users inside the network for a given time, variations in popularity of contents for a given time and population set, change in preferred device type, hence, content type and quality).
Edit intent: coherence
Original:  for diploids, haplotypes associated with a pair of chromosomes may  conveniently represented by means of complementary binary sequences.
Revised:  for diploids, haplotypes associated with a pair of chromosomes may be conveniently represented by means of complementary binary sequences.
Edit intent: fluency
Original: Timed Automata (TA) are used to represent systems when the interest is the analysis of their behaviour as time progresses.
Revised: Timed Automata (TA) is de facto a standard modelling formalism to represent systems when the interest is the analysis of their behaviour as time progresses.
Edit intent: clarity
Original:  2. they rely on a precise semantics for the logic in which the property of interest is expressed which cannot be easily modified and customized ;
Revised:  2. they rely on a precise semantics for the logic in which the property of interest is specified which cannot be easily modified and customized ;
Edit intent: clarity
Original:  It relies on the translation of both the TA and the MITL formula into an intermediate Constraint LTL over clocks (CLTLoc) formula which is verified through an available decision procedure.
Revised:  The technique relies on the translation of both the TA and the MITL formula into an intermediate Constraint LTL over clocks (CLTLoc) formula which is verified through an available decision procedure.
Edit intent: clarity
Original:  The technique is flexible since the intermediate logic allows the encoding of new TA constructs, as well as new semantics for the logic in which the property of interest is expressed , by just adding new CLTLoc formulae.
Revised:  The technique is flexible since the intermediate logic allows the encoding of new semantics as well as new semantics for the logic in which the property of interest is expressed , by just adding new CLTLoc formulae.
Edit intent: clarity
Original:  The technique is flexible since the intermediate logic allows the encoding of new TA constructs, as well as new semantics for the logic in which the property of interest is expressed , by just adding new CLTLoc formulae.
Revised:  The technique is flexible since the intermediate logic allows the encoding of new TA constructs, as well as new TA constructs , by just adding new CLTLoc formulae.
Edit intent: clarity
Original: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \mathbb{R ^d, a point a \in \mathrm{conv \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \mathrm{conv \conv Q is less then diam\diam P/\sqrt {2r}.
Revised: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \Re ^d, a point a \in \mathrm{conv \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \mathrm{conv \conv Q is less then diam\diam P/\sqrt {2r}.
Edit intent: clarity
Original: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \mathbb{R ^d, a point a \in \mathrm{conv \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \mathrm{conv \conv Q is less then diam\diam P/\sqrt {2r}.
Revised: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \mathbb{R ^d, a point a \in \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \mathrm{conv \conv Q is less then diam\diam P/\sqrt {2r}.
Edit intent: fluency
Original: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \mathbb{R ^d, a point a \in \mathrm{conv \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \mathrm{conv \conv Q is less then diam\diam P/\sqrt {2r}.
Revised: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \mathbb{R ^d, a point a \in \mathrm{conv \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \conv Q is less then diam\diam P/\sqrt {2r}.
Edit intent: fluency
Original: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \mathbb{R ^d, a point a \in \mathrm{conv \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \mathrm{conv \conv Q is less then diam\diam P/\sqrt {2r}.
Revised: We prove a no-dimensional version of Carath\'edory's theorem: given an n-element set P\subset \mathbb{R ^d, a point a \in \mathrm{conv \conv P, and an integer r\le d, r \le n, there is a subset Q\subset P of r elements such that the distance between a and \mathrm{conv \conv Q is less than\diam P/\sqrt {2r}.
Edit intent: fluency
Original:  Similar versions of Tverberg's theorem , and some of their extensions are also established.
Revised:  Similar versions of Tverberg's theorem and some of their extensions are also established.
Edit intent: fluency
Original:  Insights into set theory using information theory and a universal hypercomputer are possible, and it is argued that the Generalised Continuum Hypothesis can be regarded as a information-theoretic principle, which follows from an information minimization principle.
Revised:  Insights into set theory using information theory and a universal hypercomputer are possible, and it is argued that the Generalised Continuum Hypothesis can be regarded as a information-theoretic principle, which follows from an information minimisation principle.
Edit intent: fluency
Original:  For example, a common slight variant of Young has a hard winner problem for dichotomous preferences, and natural versions of Dodgson and Kemeny for dichotomous preferences have easy score and winner problems .
Revised:  The easiness of the winner problem for dichotomous preferences, and natural versions of Dodgson and Kemeny for dichotomous preferences have easy score and winner problems .
Edit intent: clarity
Original: The estimation of the probability of the data under a given evolutionary model has been an important computational challenge in Bayesian phylogenetic inference .
Revised: We describe an "embarrassingly parallel" method for Bayesian phylogenetic inference .
Edit intent: clarity
Original:  The proposed annealed SMC algorithm provides an  unbiased estimator for the probability of the data .
Revised:  The proposed annealed SMC algorithm provides an unbiased estimator for the marginal likelihood .
Edit intent: clarity
Original:  Unlike the previous SMC methods in phylogenetics, the annealed SMC has the same state space for all the intermediate distributions, which allows standard Markov chain Monte Carlo (MCMC) tree moves to be utilized as the basis for SMC proposal distributions . Consequently, the annealed SMC should be relatively easy to incorporate into existing phylogenetic software packages based on MCMC algorithms.
Revised:  Unlike the previous SMC methods in phylogenetics, our annealed method can utilize standard Markov chain Monte Carlo (MCMC) tree moves to be utilized as the basis for SMC proposal distributions . Consequently, the annealed SMC should be relatively easy to incorporate into existing phylogenetic software packages based on MCMC algorithms.
Edit intent: clarity
Original:  Unlike the previous SMC methods in phylogenetics, the annealed SMC has the same state space for all the intermediate distributions, which allows standard Markov chain Monte Carlo (MCMC) tree moves to be utilized as the basis for SMC proposal distributions . Consequently, the annealed SMC should be relatively easy to incorporate into existing phylogenetic software packages based on MCMC algorithms.
Revised:  Unlike the previous SMC methods in phylogenetics, the annealed SMC has the same state space for all the intermediate distributions, which allows standard Markov chain Monte Carlo (MCMC) tree moves to be utilized as the basis for SMC proposal distributions . Consequently, the annealed SMC should be relatively easy to incorporate into existing phylogenetic software packages based on Markov chain Monte Carlo algorithms.
Edit intent: fluency
Original: The Fujitsu Digital Annealer  is designed to solve fully-connected quadratic unconstrained binary optimization (QUBO) problems.
Revised: The Fujitsu Digital Annealer is designed to solve fully connected quadratic unconstrained binary optimization (QUBO) problems.
Edit intent: fluency
Original:  The Digital Annealer 's algorithm is currently based on simulated annealing , however it differs from it in its utilization of an efficient parallel-trial scheme and a dynamic escape mechanism.
Revised:  The DA 's algorithm is currently based on simulated annealing , however it differs from it in its utilization of an efficient parallel-trial scheme and a dynamic escape mechanism.
Edit intent: clarity
Original:  The Digital Annealer 's algorithm is currently based on simulated annealing , however it differs from it in its utilization of an efficient parallel-trial scheme and a dynamic escape mechanism.
Revised:  The Digital Annealer 's algorithm is currently based on simulated annealing ; however, it differs from it in its utilization of an efficient parallel-trial scheme and a dynamic escape mechanism.
Edit intent: fluency
Original:  In addition, the Digital Annealer exploits the massive parallelization that custom application-specific CMOS hardware allows.
Revised:  In addition, the DA exploits the massive parallelization that custom application-specific CMOS hardware allows.
Edit intent: clarity
Original:  We compare the performance of the Digital Annealer to simulated annealing and parallel tempering with isoenergetic cluster moves on two-dimensional and fully-connected spin-glass problems with bimodal and Gaussian couplings.
Revised:  We compare the performance of the DA to simulated annealing and parallel tempering with isoenergetic cluster moves on two-dimensional and fully-connected spin-glass problems with bimodal and Gaussian couplings.
Edit intent: clarity
Original:  We compare the performance of the Digital Annealer to simulated annealing and parallel tempering with isoenergetic cluster moves on two-dimensional and fully-connected spin-glass problems with bimodal and Gaussian couplings.
Revised:  We compare the performance of the Digital Annealer to simulated annealing and parallel tempering with isoenergetic cluster moves on two-dimensional and fully connected spin-glass problems with bimodal and Gaussian couplings.
Edit intent: fluency
Original:  Our results show that the Digital Annealer currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully-connected spin-glass problems with bimodal or Gaussian couplings, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study.
Revised:  Our results show that the DA currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully-connected spin-glass problems with bimodal or Gaussian couplings, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study.
Edit intent: clarity
Original:  Our results show that the Digital Annealer currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully-connected spin-glass problems with bimodal or Gaussian couplings, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study.
Revised:  Our results show that the Digital Annealer currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully connected spin-glass problems with bimodal or Gaussian couplings, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study.
Edit intent: fluency
Original:  The Digital Annealer does not appear to exhibit a speedup for sparse two-dimensional spin-glass problems, which we explain on theoretical grounds.
Revised:  The DA does not appear to exhibit a speedup for sparse two-dimensional spin-glass problems, which we explain on theoretical grounds.
Edit intent: clarity
Original:  The next generation of the Digital Annealer is expected to be able to solve fully-connected problems up to a size of 8192 variables  .
Revised:  The next generation of the DA is expected to be able to solve fully-connected problems up to a size of 8192 variables .
Edit intent: clarity
Original:  The next generation of the Digital Annealer is expected to be able to solve fully-connected problems up to a size of 8192 variables  .
Revised:  The next generation of the Digital Annealer is expected to be able to solve fully connected problems up to a size of 8192 variables .
Edit intent: fluency
Original:  The next generation of the Digital Annealer is expected to be able to solve fully-connected problems up to a size of 8192 variables  .
Revised:  The next generation of the Digital Annealer is expected to be able to solve fully-connected problems up to 8192 variables .
Edit intent: clarity
Original: Some microfluidic lab-on-chip devices contain modules whose function is to mix two fluids, called reactant and buffer, in some desired proportions.
Revised: Some microfluidic lab-on-chip devices contain modules whose function is to mix two fluids, called reactant and buffer, in desired proportions.
Edit intent: clarity
Original:  A micro-mixer has two input channels and two output channels , it receives two fluid droplets, one from each input, mixes them perfectly, and produces two droplets of the mixed fluid on its output channels.
Revised:  A micro-mixer has two input channels and two output channels ; it receives two fluid droplets, one from each input, mixes them perfectly, and produces two droplets of the mixed fluid on its output channels.
Edit intent: fluency
Original:  A set T of droplets is called producible if it can be produced from a set I of pure reactant and buffer droplets by some mixing graph.
Edit intent: coherence
Original: In this paper, we study the coexistence and synergy between edge and central cloud computing in heterogeneous cellular networks (HetNets), in which multi-antenna  small base stations (SBSs) empowered by clouds at the edge offer computing services for user equipments (UEs), whereas a macro base station (MBS ) provides computing services from a central cloud via a high-speed backhaul .
Revised: In this paper, we study the coexistence and synergy between edge and central cloud computing in heterogeneous cellular networks (HetNets), in which multi-antenna small base stations (SBSs) empowered by clouds at the edge offer computing services for UEs, whereas the MBS provides high-performance central cloud computing services to UEs via a restricted multiple-input multiple-output (MIMO) backhaul to their associated SBSs .
Edit intent: clarity