wanyu/IteraTeR_v2 huggingface dataset:
Original:  A scalable alternative is to fuse estimates under unknown correlations, updating the local estimates and error covariance matrix as the solution of an optimisation problem.
Revised:  A scalable alternative is to fuse estimates under unknown correlations, doing the update by solving an optimisation problem.
Edit intent: clarity
Original:  Unfortunately, this problem is NP-hard, forcing relaxations that lose optimality guarantees over the original problem .
Revised:  Unfortunately, this problem is NP-hard, forcing relaxations that lose optimality guarantees .
Edit intent: clarity
Original:  This particular relaxation allows to certify  locally and in real time if the solution from the relaxed problem is the optimum of the original .
Revised:  This particular relaxation allows to certify , locally and in real time if the solution from the relaxed problem is the optimum of the original .
Edit intent: fluency
Original:  This particular relaxation allows to certify  locally and in real time if the solution from the relaxed problem is the optimum of the original .
Revised:  This particular relaxation allows to certify locally and in real time , if the relaxed solution is the actual optimum .
Edit intent: clarity
Original:  In that case, we prove that CO-DKF is optimal in the Mean Square Error (MSE) sense.
Revised:  In that case, we prove optimality in the Mean Square Error (MSE) sense.
Edit intent: clarity
Original: The reconfigurable intelligent surface (RIS) is an emerging promising candidate technology for the sixth-generation wireless networks, where the element spacing is usually of sub-wavelength.
Revised: The reconfigurable intelligent surface (RIS) is an emerging promising candidate technology for future wireless networks, where the element spacing is usually of sub-wavelength.
Edit intent: clarity
Original:  Only limited knowledge, however, has been gained about the spatial-temporal correlation behavior among the elements in an RIS. In this paper, we investigate the joint spatial-temporal correlation models for an RIS in a wireless communication system.
Revised:  Only limited knowledge, however, has been gained about the spatial-temporal correlation behavior among the elements in an RIS. In this paper, we investigate the spatial-temporal correlation models for an RIS in a wireless communication system.
Edit intent: clarity
Original:  Only limited knowledge, however, has been gained about the spatial-temporal correlation behavior among the elements in an RIS. In this paper, we investigate the joint spatial-temporal correlation models for an RIS in a wireless communication system.
Revised:  Only limited knowledge, however, has been gained about the spatial-temporal correlation behavior among the elements in an RIS. In this paper, we investigate the joint spatial-temporal correlation for an RIS-enabled wireless communication system.
Edit intent: clarity
Original:  Our methods also lead to efficient policy extragradient algorithms for solving  entropy-regularized  zero-sum Markov games at a linear rate .
Revised:  Our methods also lead to efficient policy extragradient algorithms for solving ( entropy-regularized zero-sum Markov games at a linear rate .
Edit intent: fluency
Original:  Our methods also lead to efficient policy extragradient algorithms for solving  entropy-regularized  zero-sum Markov games at a linear rate .
Revised:  Our methods also lead to efficient policy extragradient algorithms for solving entropy-regularized ) zero-sum Markov games at a linear rate .
Edit intent: fluency
Original:  Our methods also lead to efficient policy extragradient algorithms for solving  entropy-regularized  zero-sum Markov games at a linear rate .
Revised:  Our methods also lead to efficient policy extragradient algorithms for solving entropy-regularized zero-sum Markov games at similar rates .
Edit intent: clarity
Original: A novel second-order nonstandard finite difference  method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is constructed and analyzed.
Revised: In this work, a novel second-order nonstandard finite difference method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is constructed and analyzed.
Edit intent: clarity
Original: A novel second-order nonstandard finite difference  method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is constructed and analyzed.
Revised: A novel second-order nonstandard finite difference method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced and analyzed.
Edit intent: clarity
Original: We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and  facet size distribution, respectively.
Revised: We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively.
Edit intent: fluency
Original:  Rev. E 96, 032312 (2017)], we facilitate  efficient sampling of simplicial ensembles from arbitrary degree and size distributions.
Revised:  Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions.
Edit intent: fluency
Original:  We find that, contrary to expectations based on dyadic networks, increasing  nodes' degrees reduces the number of loops in simplicial complexes.
Revised:  We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes.
Edit intent: fluency
Original: The current public transportation system is unable to keep up with the growing passenger demand as the population grows in urban areas.
Revised: Many public transportation systems are unable to keep up with the growing passenger demand as the population grows in urban areas.
Edit intent: clarity
Original: The current public transportation system is unable to keep up with the growing passenger demand as the population grows in urban areas.
Revised: The current public transportation system is unable to keep up with growing passenger demand as the population grows in urban areas.
Edit intent: fluency
Original:  In this paper, we propose a centralized transit system that integrates public transit and ridesharing, which is capable of matching drivers and public transit riders such that the riders would result in shorter travel time  .
Revised:  In this paper, we describe a centralized transit system that integrates public transit and ridesharing, which is capable of matching drivers and public transit riders such that the riders would result in shorter travel time .
Edit intent: clarity
Original:  In this paper, we propose a centralized transit system that integrates public transit and ridesharing, which is capable of matching drivers and public transit riders such that the riders would result in shorter travel time  .
Revised:  In this paper, we propose a centralized transit system that integrates public transit and ridesharing, which matches drivers and transit riders such that the riders would result in shorter travel time .
Edit intent: clarity
Original:  We describe an exact approach and approximation algorithms to achieve the optimization goal.
Revised:  We give an exact approach and approximation algorithms to achieve the optimization goal.
Edit intent: clarity
Original:  Exact characterizations (for the log-loss) and bounds (for more general losses) are derived for the epistemic uncertainty - quantified by the minimum excess meta-risk (MEMR)- of optimal meta-learning rules.
Revised:  Exact characterizations (for the log-loss) and bounds (for more general losses) are derived for the epistemic uncertainty -quantified by the minimum excess meta-risk (MEMR)- of optimal meta-learning rules.
Edit intent: clarity
Original:  Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML) .
Revised:  Experiments are presented that use the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML) .
Edit intent: clarity
Original:  Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML) .
Revised:  Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, to compare the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML) .
Edit intent: coherence
Original:  Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML) .
Revised:  Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of conventional learning and meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML) .
Edit intent: clarity
Original:  Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML) .
Revised:  Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning as the number of meta-learning tasks increases .
Edit intent: clarity
Original:  Differences in processing intervals and other factors typically lead to a relative delay between measurement from two disparate sensors.
Revised:  Differences in processing intervals and other factors typically lead to a relative delay between measurement updates from disparate sensors.
Edit intent: clarity
Original:  There have been several recent proposals in the literature to determine the delay parameter using recursive, causal filters such as the extended Kalman filter (EKF).
Revised:  There have been several recent proposals in the literature to determine the delay using recursive, causal filters such as the extended Kalman filter (EKF).
Edit intent: clarity
Original:  We carefully review this formulation and show that there are fundamental issues with the structure of the EKF (and related algorithms) when the delay is included in the filter state vector as a value to be estimated.
Revised:  We carefully review this formulation and show that there are fundamental issues with the structure of the EKF (and related algorithms) when the delay is included in the filter state vector as a parameter to be estimated.
Edit intent: clarity
Original:  We offer brief suggestions for ways to maintain the computational efficiency of recursive filtering for temporal calibration while avoiding the drawbacks of the standard  algorithms.
Revised:  We offer brief suggestions for ways to maintain the computational efficiency of recursive filtering for temporal calibration while avoiding the drawbacks of the standard filtering algorithms.
Edit intent: clarity
Original: In the recent years, the problem of addressing fairness in Machine Learning (ML) and automatic decision-making has attracted a lot of attention in the scientific communities dealing with Artificial Intelligence.
Revised: In recent years, the problem of addressing fairness in Machine Learning (ML) and automatic decision-making has attracted a lot of attention in the scientific communities dealing with Artificial Intelligence.
Edit intent: fluency
Original:  We find that multi-taxel vibro-tactile sensing at sufficiently high sampling rate (above 2 kHz) led to the best performance across the various tasks and objects.
Revised:  We find that multi-taxel vibro-tactile sensing at sufficiently high sampling rate led to the best performance across the various tasks and objects.
Edit intent: clarity
Original: The paper introduces and analyzes N-player and common-noise mean-field games in It\^{o the context of both complete and incomplete financial markets .
Revised: In It\^{o N-player and common-noise mean-field games in It\^{o the context of both complete and incomplete financial markets .
Edit intent: clarity
Original: The paper introduces and analyzes N-player and common-noise mean-field games in It\^{o the context of both complete and incomplete financial markets .
Revised: The paper introduces and analyzes N-player and common-noise mean-field games in the context of both complete and incomplete financial markets .
Edit intent: fluency
Original: The paper introduces and analyzes N-player and common-noise mean-field games in It\^{o the context of both complete and incomplete financial markets .
Revised: The paper introduces and analyzes N-player and common-noise mean-field games in It\^{o the context of optimal portfolio choice in a common market .
Edit intent: clarity
Original:  In both kinds of market environments, the players have  individual risk tolerance coefficients .
Revised:  In both kinds of market environments, the players have constant individual risk tolerance coefficients .
Edit intent: clarity
Original:  For all these distinct models , we derive explicit or closed-form solutions for the optimal policies and optimal wealth processes, as well as for the related game values .
Revised:  For all cases , we derive explicit or closed-form solutions for the optimal policies and optimal wealth processes, as well as for the related game values .
Edit intent: clarity
Original:  For all these distinct models , we derive explicit or closed-form solutions for the optimal policies and optimal wealth processes, as well as for the related game values .
Revised:  For all these distinct models , we derive explicit or closed-form solutions for the equilibrium stochastic processes, the optimal state processes, and the values of the games .
Edit intent: clarity
Original:  However , we use a  more general class of polygons -- polygons that are horizontally or vertically convex -- which allows us to provide an arguably simpler analysis and already improve the approximation ratio .
Revised:  First , we use a more general class of polygons -- polygons that are horizontally or vertically convex -- which allows us to provide an arguably simpler analysis and already improve the approximation ratio .
Edit intent: fluency
Original:  His algorithm achieves an approximation ratio of 10 and it is based on a dynamic program that intuitively recursively partitions the input plane into special polygons called corner-clipped rectangles  , without intersecting certain special horizontal line segments called fences.
Revised:  His algorithm achieves an approximation ratio of 10 and it is based on a dynamic program that intuitively recursively partitions the input plane into special polygons called corner-clipped rectangles (CCRs) , without intersecting certain special horizontal line segments called fences.
Edit intent: clarity
Original:  In this paper, we present a 3-approximation algorithm for MISR which is  based on a similar recursive partitioning scheme.
Revised:  In this paper, we present a 3-approximation algorithm for MISR which is also based on a similar recursive partitioning scheme.
Edit intent: clarity
Original:  In this paper, we present a 3-approximation algorithm for MISR which is  based on a similar recursive partitioning scheme.
Revised:  In this paper, we present a 3-approximation algorithm for MISR which is based on a recursive partitioning scheme.
Edit intent: clarity
Original:  First, we use a partition into a more general class of axis-parallel polygons with constant complexity each , which allows us to provide an arguably simpler analysis and at the same time already improves the approximation ratio to 6.
Revised:  First, we use a partition into a class of axis-parallel polygons with constant complexity each , which allows us to provide an arguably simpler analysis and at the same time already improves the approximation ratio to 6.
Edit intent: clarity
Original:  In particular, our partitioning uses more general fences that can be sequences of up to O(1  ) line segments each.
Revised:  In particular, our partitioning uses more general fences which can be sequences of up to O(1 ) line segments each.
Edit intent: fluency
Original:  Many ofthese will contribute to the fundamental dynamical stability of the system.
Revised:  Many of these will contribute to the fundamental dynamical stability of the system.
Edit intent: fluency
Original:  By taking a complexitytheoretic perspective we derive a normal form for grid forming components in power grids.
Revised:  By taking a complexity theoretic perspective we derive a normal form for grid forming components in power grids.
Edit intent: fluency
Original:  Thisallows analyzing the grids systemic properties without the need for detailed technical models.
Revised:  This allows analyzing the grids systemic properties without the need for detailed technical models.
Edit intent: fluency
Original:  Our approach is based on the physics of the power flow in the grid on the one hand, and on thecommon symmetry that is inherited from the control objectives grid-forming power grid componentsare trying to achieve.
Revised:  Our approach is based on the physics of the power flow in the grid on the one hand, and on the common symmetry that is inherited from the control objectives grid-forming power grid componentsare trying to achieve.
Edit intent: fluency
Original:  Our approach is based on the physics of the power flow in the grid on the one hand, and on thecommon symmetry that is inherited from the control objectives grid-forming power grid componentsare trying to achieve.
Revised:  Our approach is based on the physics of the power flow in the grid on the one hand, and on thecommon symmetry that is inherited from the control objectives grid-forming power grid components are trying to achieve.
Edit intent: fluency
Original:  We provide a first experimental validation that this normal form can capturethe behavior of complex grid forming inverters without any knowledge of the underlying technology, and show that it can be used to make technology independent statements on the stability of futuregrids .
Revised:  We provide a first experimental validation that this normal form can capture the behavior of complex grid forming inverters without any knowledge of the underlying technology, and show that it can be used to make technology independent statements on the stability of futuregrids .
Edit intent: fluency
Original:  We provide a first experimental validation that this normal form can capturethe behavior of complex grid forming inverters without any knowledge of the underlying technology, and show that it can be used to make technology independent statements on the stability of futuregrids .
Revised:  We provide a first experimental validation that this normal form can capturethe behavior of complex grid forming inverters without any knowledge of the underlying technology, and show that it can be used to make technology independent statements on the stability of future grids .
Edit intent: fluency
Original: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment and only have access to the data and functionality that is either already on the blockchain or fed into the blockchain.
Revised: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment . Thus, they only have access to the data and functionality that is either already on the blockchain or fed into the blockchain.
Edit intent: coherence
Original: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment and only have access to the data and functionality that is either already on the blockchain or fed into the blockchain.
Revised: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment and only have access to data and functionality that is either already on the blockchain or fed into the blockchain.
Edit intent: fluency
Original: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment and only have access to the data and functionality that is either already on the blockchain or fed into the blockchain.
Revised: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment and only have access to the data and functionality that is already on the blockchain or fed into the blockchain.
Edit intent: coherence
Original: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment and only have access to the data and functionality that is either already on the blockchain or fed into the blockchain.
Revised: One fundamental limitation of blockchain-based smart contracts is that they execute in a closed environment and only have access to the data and functionality that is either already on the blockchain , or is fed into the blockchain.
Edit intent: coherence
Original:  Thus any interactions with the real world need to be mediated by a bridge service, which is called an oracle.
Revised:  Any interactions with the real world need to be mediated by a bridge service, which is called an oracle.
Edit intent: coherence
Original:  With their evolution comes more attacks, necessitating a greater attention to the trust modelof using oracles .
Revised:  With their evolution comes more attacks, necessitating greater attention to the trust modelof using oracles .
Edit intent: fluency
Original:  With their evolution comes more attacks, necessitating a greater attention to the trust modelof using oracles .
Revised:  With their evolution comes more attacks, necessitating a greater attention to their trust model .
Edit intent: clarity
Original:  In this SoK, we systemize the design alternatives for oracles, showcase attacks, and discuss attack mitigation strategies.
Revised:  In this systemization of knowledge paper (SoK), we dissect the design alternatives for oracles, showcase attacks, and discuss attack mitigation strategies.
Edit intent: clarity
Original: We provide a theory as to why the locus of a triangle center over Poncelet 3-periodics in an ellipse pair is an ellipse or not.
Revised: We propose a theory which predicts the ellipticity of a triangle center over Poncelet 3-periodics in an ellipse pair is an ellipse or not.
Edit intent: clarity
Original: We propose a theory which predicts the ellipticity of a triangle center 's locus over a Poncelet 3-periodic family .
Revised: We present a theory which predicts the ellipticity of a triangle center 's locus over a Poncelet 3-periodic family .
Edit intent: clarity
Original: We propose a theory which predicts the ellipticity of a triangle center 's locus over a Poncelet 3-periodic family .
Revised: We propose a theory which predicts when the locus of a triangle center 's locus over a Poncelet 3-periodic family .
Edit intent: clarity
Original:  We show that if the triangle center can be expressed as a fixed affine combination of barycenter, circumcenter, and a third , stationary point over some family, then its locus will be an ellipse.
Revised:  We show that if the triangle center is a fixed affine combination of barycenter, circumcenter, and a third , stationary point over some family, then its locus will be an ellipse.
Edit intent: clarity