wanyu/IteraTeR_v2 huggingface dataset:
Original:  Along the way, we establish  procedures to construct optimal confidence intervals for the eigenvalues of interest .
Revised:  Along the way, we establish procedures to construct optimal confidence intervals for the unknown eigenvalues .
Edit intent: clarity
Original:  We then consider the game played dynamically under stochastic interactions among individuals implementing best-response dynamics and analyze the nature of the converged networks.
Revised:  We then consider the game played dynamically under stochastic interactions among individuals implementing better-response dynamics and analyze the nature of the converged networks.
Edit intent: fluency
Original:  We transform the specification to a limit-deterministic  B\"uchi automaton ( LDBA ) with several accepting sets that accepts all infinite sequences satisfying the formula.
Revised:  We convert the specification to a limit-deterministic B\"uchi automaton ( LDBA ) with several accepting sets that accepts all infinite sequences satisfying the formula.
Edit intent: fluency
Original:  There exist many results for decentralized versions of the latter  but there is almost no result for a decentralized version of the former .
Revised:  There exist results for decentralized versions of the latter but there is almost no result for a decentralized version of the former .
Edit intent: clarity
Original:  In this paper, we propose a decentralized version of strong detectability called co-detectability which implies that once a system satisfies this property, for each generated infinite-length event sequence, at least one local observer can determine the current and subsequent states after a common  time delay.
Revised:  In this paper, we propose a decentralized version of strong detectability called co-detectability which implies that once a system satisfies this property, for each generated infinite-length event sequence, at least one local observer can determine the current and subsequent states after a common observation time delay.
Edit intent: clarity
Original:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability and ]  co-predictability are notions that have been widely studied in the literature, but most of their verification algorithms in the literature work under two widely-used assumptions of deadlock-freeness and having no unobservable reachable cycle, or after modifying the FSA under consideration by ]  adding at each deadlock state a self-loop.
Revised:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability is firstly studied by ] co-predictability are notions that have been widely studied in the literature, but most of their verification algorithms in the literature work under two widely-used assumptions of deadlock-freeness and having no unobservable reachable cycle, or after modifying the FSA under consideration by ] adding at each deadlock state a self-loop.
Edit intent: clarity
Original:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability and ]  co-predictability are notions that have been widely studied in the literature, but most of their verification algorithms in the literature work under two widely-used assumptions of deadlock-freeness and having no unobservable reachable cycle, or after modifying the FSA under consideration by ]  adding at each deadlock state a self-loop.
Revised:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability and ] under a liveness assumption, while co-predictability are notions that have been widely studied in the literature, but most of their verification algorithms in the literature work under two widely-used assumptions of deadlock-freeness and having no unobservable reachable cycle, or after modifying the FSA under consideration by ] adding at each deadlock state a self-loop.
Edit intent: clarity
Original:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability and ]  co-predictability are notions that have been widely studied in the literature, but most of their verification algorithms in the literature work under two widely-used assumptions of deadlock-freeness and having no unobservable reachable cycle, or after modifying the FSA under consideration by ]  adding at each deadlock state a self-loop.
Revised:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability and ] co-predictability is firstly studied by ] adding at each deadlock state a self-loop.
Edit intent: coherence
Original:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability and ]  co-predictability are notions that have been widely studied in the literature, but most of their verification algorithms in the literature work under two widely-used assumptions of deadlock-freeness and having no unobservable reachable cycle, or after modifying the FSA under consideration by ]  adding at each deadlock state a self-loop.
Revised:  co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability and ] co-predictability are notions that have been widely studied in the literature, but most of their verification algorithms in the literature work under two widely-used assumptions of deadlock-freeness and having no unobservable reachable cycle, or after modifying the FSA under consideration by ] by adding at each deadlock state a self-loop.
Edit intent: fluency
Original:  Under the unified framework used in the paper, &   one can see that in order to verify co-detectability, more technical difficulties will be met compared to verifying the other two properties, because in co-detectability, generated outputs are counted, but in the latter two properties, only occurrences of events are counted.
Revised:  Under the unified framework used in the paper, Kumar& one can see that in order to verify co-detectability, more technical difficulties will be met compared to verifying the other two properties, because in co-detectability, generated outputs are counted, but in the latter two properties, only occurrences of events are counted.
Edit intent: coherence
Original:  The PSPACE-hardness of verifying co-diagnosability is already known in the literature .
Revised:  The PSPACE-hardness of verifying co-diagnosability is already known .
Edit intent: clarity
Original:  We prove that the problem of verifying co-detectability of FSAs is NP-hard . Moreover, we use a unified concurrent-composition method to give PSPACE verification algorithms for co-detectability, co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability is firstly studied by [Wang, Yoo, \& Lafortune 2007]
Revised:  We prove that the problem of verifying co-detectability of FSAs is coNP-hard . Moreover, we use a unified concurrent-composition method to give PSPACE verification algorithms for co-detectability, co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability is firstly studied by [Wang, Yoo, \& Lafortune 2007]
Edit intent: clarity
Original:  Moreover, we use a unified concurrent-composition method to give PSPACE verification algorithms for co-detectability, co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability is firstly studied by [ Wang, Yoo, \& Lafortune 2007 &  ] under a liveness assumption , while co-predictability is firstly studied by [Kumar \& Takai 2010] by adding at each deadlock state an unbounded unobservable trace.
Revised:  Moreover, we use a unified concurrent-composition method to give PSPACE verification algorithms for co-detectability, co-diagnosability, and co-predictability of FSAs, without any assumption or modifying the FSAs under consideration, where co-diagnosability is firstly studied by [ Wang, Yoo, \& Lafortune 2007 & ] , while co-predictability is firstly studied by [Kumar \& Takai 2010] by adding at each deadlock state an unbounded unobservable trace.
Edit intent: coherence
Original:  This modification to FSAs used in Kumar%DIFDELCMD < & %%% Takai 2010 does not preserve co-diagnosability or co-predictability.
Revised:  This modification to FSAs used in %DIFDELCMD < & %%% Takai 2010 does not preserve co-diagnosability or co-predictability.
Edit intent: fluency
Original:  This modification to FSAs used in Kumar%DIFDELCMD < & %%% Takai 2010 does not preserve co-diagnosability or co-predictability.
Revised:  This modification to FSAs used in Kumar%DIFDELCMD < & %%% does not preserve co-diagnosability or co-predictability.
Edit intent: clarity
Original:  Specifically, we devise a new stationary threshold-based age-dependent random access (ADRA) protocol, in which each IoT device accesses the channel with a certain probability only  its instantaneous AoI exceeds a predetermined threshold.
Revised:  Specifically, we devise a new stationary threshold-based age-dependent random access (ADRA) protocol, in which each IoT device accesses the channel with a certain probability only when its instantaneous AoI exceeds a predetermined threshold.
Edit intent: clarity
Original:  We manage to evaluate the average AoI of the proposed ADRA protocol mathematically by decoupling the tangled AoI evolution of multiple IoT devices and modelling the decoupled AoI evolution of each device as a Discrete-Time Markov Chain.
Revised:  We manage to evaluate the average AoI of the proposed ADRA protocol mathematically by decoupling the tangled AoI evolution of multiple IoT devices and modeling the decoupled AoI evolution of each device as a Discrete-Time Markov Chain.
Edit intent: fluency
Original:  Simulation results validate our theoretical analysis and affirm the superior age performance of the proposed ADRA protocol over the conventional age-independent scheme .
Revised:  Simulation results validate our theoretical analysis and affirm the superior age performance of the proposed ADRA protocol over the state-of-the-art age-oriented random access schemes .
Edit intent: clarity
Original:  The boundary operator method is used to treat different types of boundary conditions, and the "reflux-free" method is introduced to efficiently and easily treat the coarse-fine boundaries that arise in BSAMR. Examples are presented that demonstrate the use of this method in a variety of cases relevant to materials science , including Eshelby inclusions, material discontinuities, and phase field fracture.
Revised:  The boundary operator method is used to treat different types of boundary conditions, and the "reflux-free" method is introduced to efficiently and easily treat the coarse-fine boundaries that arise in BSAMR. Examples are presented that demonstrate the use of this method in a variety of cases relevant to materials science : Eshelby inclusions, material discontinuities, and phase field fracture.
Edit intent: clarity
Original:  It is shown that the implementation scales very well to\sim4000  tens of millions of grid points and exhibits good AMR efficiency 
Revised:  It is shown that the implementation scales very well to\sim4000 tens of millions of grid points , and good AMR efficiency 
Edit intent: coherence
Original:  We introduce a parameter, called \alpha , that quantifies the amount of orientation.
Revised:  We introduce a parameter, called alpha , that quantifies the amount of orientation.
Edit intent: coherence
Original:  We show that the parameter \alpha can be tuned in order to increase the amount of quantum walk-based transport on oriented graphs.
Revised:  We show that the parameter alpha can be tuned in order to increase the amount of quantum walk-based transport on oriented graphs.
Edit intent: fluency
Original: Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology  among many others.
Revised: Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology , among many others.
Edit intent: fluency
Original:  However, the vast majority of microscopy techniques for evolving microstructure in a given material system deliver micrographs of pattern evolution wherein the domain at one instant does not spatially overlap with that at another time .
Revised:  However, the vast majority of microscopy techniques for evolving microstructure in a given material system deliver micrographs of pattern evolution over domains that bear no relation with each other at different time instants .
Edit intent: clarity
Original:  Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical samples . Against this backdrop of spatially non-overlapping , sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics.
Revised:  Furthermore, data for evolution of the same phenomenon in a material system may well be obtained from different physical samples . Against this backdrop of spatially non-overlapping , sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics.
Edit intent: coherence
Original:  Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical samples . Against this backdrop of spatially non-overlapping , sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics.
Revised:  Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical specimens . Against this backdrop of spatially non-overlapping , sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics.
Edit intent: fluency
Original:  Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical samples . Against this backdrop of spatially non-overlapping , sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics.
Revised:  Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical samples . Against this backdrop of spatially unrelated , sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics.
Edit intent: clarity
Original:  Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical samples . Against this backdrop of spatially non-overlapping , sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics.
Revised:  Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical samples . Against this backdrop of spatially non-overlapping , sparse and multi-source data, we exploit the variational framework to make judicious choices of weighting functions and identify PDE operators from the dynamics.
Edit intent: clarity
Original:  This step is preceded by an imposition of consistency to parsimoniously infer a minimal set of the spatial operators at steady state.
Revised:  A consistency condition arises for parsimonious inference of a minimal set of the spatial operators at steady state.
Edit intent: clarity
Original:  The framework is demonstrated on synthetic data that reflects the characteristics of the experimental material microscopy images.
Revised:  The framework is demonstrated on synthetic data that reflect the characteristics of the experimental material microscopy images.
Edit intent: fluency
Original: We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold M, one wants to recover information about the geometry of M. Minimax estimators which have been proposed so far all depend crucially on the a priori knowledge of some parameters quantifying the regularity of M (such as its reach ), whereas those quantities will be unknown in practice.
Revised: We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold M, one wants to recover information about the geometry of M. Minimax estimators which have been proposed so far all depend crucially on the a priori knowledge of some parameters quantifying the underlying distribution generating the sample (such as its reach ), whereas those quantities will be unknown in practice.
Edit intent: clarity
Original: We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold M, one wants to recover information about the geometry of M. Minimax estimators which have been proposed so far all depend crucially on the a priori knowledge of some parameters quantifying the regularity of M (such as its reach ), whereas those quantities will be unknown in practice.
Revised: We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold M, one wants to recover information about the geometry of M. Minimax estimators which have been proposed so far all depend crucially on the a priori knowledge of some parameters quantifying the regularity of M (such as bounds on its density ), whereas those quantities will be unknown in practice.
Edit intent: clarity
Original:  This selection procedure actually allows  to recover the sample rate of the set of observations  , and can therefore be used as an hyperparameter in other settings, such as tangent space estimation.
Revised:  This selection procedure actually allows us to recover the sample rate of the set of observations , and can therefore be used as an hyperparameter in other settings, such as tangent space estimation.
Edit intent: fluency
Original:  In this paper, we present an iteration-free mixed-stabilised finite element formulation for incompressible Navier-Stokes that preserves second-order temporal accuracy  for both velocity and pressure fields.
Revised:  In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier-Stokes that preserves second-order temporal accuracy for both velocity and pressure fields.
Edit intent: clarity
Original:  We prove the second-order temporal accuracy using  an example with a manufactured solution.
Revised:  First, we demonstrate the second-order temporal accuracy using an example with a manufactured solution.
Edit intent: coherence
Original:  We then illustrate the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder and then using two benchmark examples in fluid-flexible structure interaction.
Revised:  Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder and then using two benchmark examples in fluid-flexible structure interaction.
Edit intent: clarity
Original:  The size of such a graph can grow quadratically with the size of the trace making the analysis not scalable.
Revised:  The number of edges in such a graph can grow quadratically with the size of the trace making the analysis not scalable.
Edit intent: clarity
Original:  The size of such a graph can grow quadratically with the size of the trace making the analysis not scalable.
Revised:  The size of such a graph can grow quadratically with the length of the trace making the analysis not scalable.
Edit intent: clarity
Original: By growing the number of Internet users and the prevalence of web applications , we have to deal with very complex software and applications in the network.
Revised: The growing number of Internet users and the prevalence of web applications , we have to deal with very complex software and applications in the network.
Edit intent: clarity
Original: By growing the number of Internet users and the prevalence of web applications , we have to deal with very complex software and applications in the network.
Revised: By growing the number of Internet users and the prevalence of web applications make it necessary to deal with very complex software and applications in the network.
Edit intent: clarity
Original:  This results in an increasing number of new vulnerabilities in the systems, which consequently leads to an increase in the cyber and, in particular, zero-day attacks.
Revised:  This results in an increasing number of new vulnerabilities in the systems, and leading to an increase in the cyber and, in particular, zero-day attacks.
Edit intent: coherence
Original:  This results in an increasing number of new vulnerabilities in the systems, which consequently leads to an increase in the cyber and, in particular, zero-day attacks.
Revised:  This results in an increasing number of new vulnerabilities in the systems, which consequently leads to an increase in cyber threats and, in particular, zero-day attacks.
Edit intent: clarity
Original:  Although there exist many studies on the use of learning-based methods for attack detection, they generally use extracted features and overlook raw contents.
Revised:  Although there are many studies on the use of learning-based methods for attack detection, they generally use extracted features and overlook raw contents.
Edit intent: clarity
Original:  Although there exist many studies on the use of learning-based methods for attack detection, they generally use extracted features and overlook raw contents.
Revised:  Although there exist many studies on using learning-based methods for attack detection, they generally use extracted features and overlook raw contents.
Edit intent: fluency
Original:  As a new paradigm, in this work, we propose a scheme , called deep intrusion detection (DID) system  that uses the pure content of traffic flows in addition to traffic metadata in the learning and detection phases  .
Revised:  In this work, we propose a scheme , called deep intrusion detection (DID) system that uses the pure content of traffic flows in addition to traffic metadata in the learning and detection phases .
Edit intent: coherence
Original:  As a new paradigm, in this work, we propose a scheme , called deep intrusion detection (DID) system  that uses the pure content of traffic flows in addition to traffic metadata in the learning and detection phases  .
Revised:  As a new paradigm, in this work, we propose a framework , called deep intrusion detection (DID) system that uses the pure content of traffic flows in addition to traffic metadata in the learning and detection phases .
Edit intent: clarity
Original:  As a new paradigm, in this work, we propose a scheme , called deep intrusion detection (DID) system  that uses the pure content of traffic flows in addition to traffic metadata in the learning and detection phases  .
Revised:  As a new paradigm, in this work, we propose a scheme , called deep intrusion detection (DID) system , that uses the pure content of traffic flows in addition to traffic metadata in the learning and detection phases .
Edit intent: fluency
Original: A physical model called dressed photons , a composite system of photons and excitation of electrons in the nano-particles, is effectively used in the realm of near-field optics.
Revised: A physical model called dressed photon , a composite system of photons and excitation of electrons in the nano-particles, is effectively used in the realm of near-field optics.
Edit intent: fluency