wanyu/IteraTeR_v2 huggingface dataset:
Original:  The proposed method renders versatile information by constructing from the MCMC samples, e.g., posterior distributions, uncertainties, credible intervals and posterior of the operating conditions,  predictive check and Pareto fronts between each pair of the performance indicators.
Revised:  The proposed method renders versatile information by constructing from the MCMC samples, e.g., posterior distributions, uncertainties, credible intervals of the operating conditions, predictive check and Pareto fronts between each pair of the performance indicators.
Edit intent: clarity
Original:  The proposed method renders versatile information by constructing from the MCMC samples, e.g., posterior distributions, uncertainties, credible intervals and posterior of the operating conditions,  predictive check and Pareto fronts between each pair of the performance indicators.
Revised:  The proposed method renders versatile information by constructing from the MCMC samples, e.g., posterior distributions, uncertainties, credible intervals and posterior of the operating conditions, and posterior predictive check and Pareto fronts between each pair of the performance indicators.
Edit intent: coherence
Original:  It states roughly that any vector field can be L^2 -orthogonaly decomposed into a curl-free, divergence-free, and a harmonic field.
Revised:  It states roughly that any vector field can be L^2 -orthogonally decomposed into a curl-free, divergence-free, and a harmonic field.
Edit intent: fluency
Original:  The correctness and convergence of such model depends strongly on the choice of ansatz spaces defined on the surface or volumetric mesh to approximate infinite dimensional subspaces.
Revised:  The correctness and convergence of such a discretization depends strongly on the choice of ansatz spaces defined on the surface or volumetric mesh to approximate infinite dimensional subspaces.
Edit intent: clarity
Original:  This paper presents a consistent discretisation of Hodge-type decompositions for piecewise constant vector fields on volumetric meshes.
Revised:  This paper presents a consistent discretization of Hodge-type decompositions for piecewise constant vector fields on volumetric meshes.
Edit intent: fluency
Original:  This paper presents a consistent discretisation of Hodge-type decompositions for piecewise constant vector fields on volumetric meshes.
Revised:  This paper presents a consistent discretisation of Hodge-type decomposition for piecewise constant vector fields on volumetric meshes.
Edit intent: fluency
Original:  The method is stable under noisy vector field and mesh resolution, and  good performance for large sized models.
Revised:  The method is stable under noisy vector field and mesh resolution, and has a good performance for large sized models.
Edit intent: coherence
Original:  We give a detailed pseudocodes of a possible implementation of the method together with some insights on how the Hodge decomposition could answer some central question in computational fluid dynamic .
Revised:  We give pseudocodes for a possible implementation of the method together with some insights on how the Hodge decomposition could answer some central question in computational fluid dynamic .
Edit intent: clarity
Original:  We give a detailed pseudocodes of a possible implementation of the method together with some insights on how the Hodge decomposition could answer some central question in computational fluid dynamic .
Revised:  We give a detailed pseudocodes of a possible implementation of the method together with some insights on how the Hodge decomposition could answer some central question in computational fluid .
Edit intent: clarity
Original:  We design fully distributed continuous-time controllers, based on consensus and primal-dual gradient dynamics, to drive the agents to a generalized Nash equilibrium  .
Revised:  We start by designing continuous-time fully distributed feedback controllers, based on consensus and primal-dual gradient dynamics, to drive the agents to a generalized Nash equilibrium .
Edit intent: clarity
Original:  We design fully distributed continuous-time controllers, based on consensus and primal-dual gradient dynamics, to drive the agents to a generalized Nash equilibrium  .
Revised:  We design fully distributed continuous-time controllers, based on consensus and primal-dual gradient dynamics, to seek a generalized Nash equilibrium .
Edit intent: clarity
Original:  Our first solution adopts fixed gains , whose choice requires the knowledge of some global parameters of the game.
Revised:  Our first solution adopts a fixed gain , whose choice requires the knowledge of some global parameters of the game.
Edit intent: fluency
Original:  Therefore, to adapt the procedure to setups where the agents do not have any global information, we introduce a controller that can be tuned in a completely decentralized fashion, thanks to the use of  integral adaptive weights.
Revised:  To relax this requirement, we conceive a controller that can be tuned in a completely decentralized fashion, thanks to the use of integral adaptive weights.
Edit intent: clarity
Original:  Therefore, to adapt the procedure to setups where the agents do not have any global information, we introduce a controller that can be tuned in a completely decentralized fashion, thanks to the use of  integral adaptive weights.
Revised:  Therefore, to adapt the procedure to setups where the agents do not have any global information, we introduce a controller that can be tuned in a completely decentralized fashion, thanks to the use of uncoordinated integral adaptive weights.
Edit intent: clarity
Original:  We further introduce algorithms , both with constant and dynamic gains, specifically devised for generalized aggregative games.
Revised:  We further introduce algorithms specifically devised for generalized aggregative games.
Edit intent: clarity
Original:   For all the proposed control schemes , we show convergence to a variational equilibrium , under Lipschitz continuity and strong monotonicity of the game mapping , by leveraging monotonicity properties and stability theory for projected dynamical systems.
Revised:  For all the proposed dynamics , we show convergence to a variational equilibrium , under Lipschitz continuity and strong monotonicity of the game mapping , by leveraging monotonicity properties and stability theory for projected dynamical systems.
Edit intent: clarity
Original:   For all the proposed control schemes , we show convergence to a variational equilibrium , under Lipschitz continuity and strong monotonicity of the game mapping , by leveraging monotonicity properties and stability theory for projected dynamical systems.
Revised:  For all the proposed control schemes , we show convergence to a variational equilibrium , by leveraging monotonicity properties and stability theory for projected dynamical systems.
Edit intent: clarity
Original:  In this work we study the two different aspects  (i) the energy-efficiency trade-off for a specific nonequilibrium linear dynamics of two variables with feedback, and (ii) the cost of effective parameters  given by the  hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics.
Revised:  In this work we study the two different aspects , (i) the energy-efficiency trade-off for a specific nonequilibrium linear dynamics of two variables with feedback, and (ii) the cost of effective parameters given by the hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics.
Edit intent: fluency
Original:  In this work we study the two different aspects  (i) the energy-efficiency trade-off for a specific nonequilibrium linear dynamics of two variables with feedback, and (ii) the cost of effective parameters  given by the  hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics.
Revised:  In this work we study the two different aspects (i) the energy-efficiency tradeoff for a specific nonequilibrium linear dynamics of two variables with feedback, and (ii) the cost of effective parameters given by the hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics.
Edit intent: fluency
Original:  In this work we study the two different aspects  (i) the energy-efficiency trade-off for a specific nonequilibrium linear dynamics of two variables with feedback, and (ii) the cost of effective parameters  given by the  hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics.
Revised:  In this work we study the two different aspects (i) the energy-efficiency trade-off for a specific nonequilibrium linear dynamics of two variables with feedback, and (ii) the cost of effective parameters given by the " hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics.
Edit intent: fluency
Original:  To meaningfully discuss the trade-off between the energy consumption and the efficiency of the desired function  a one-to-one mapping between function(s) and energy input is required.
Revised:  To meaningfully discuss the tradeoff between energy consumption and the efficiency of the desired function a one-to-one mapping between function(s) and energy input is required.
Edit intent: fluency
Original:  To meaningfully discuss the trade-off between the energy consumption and the efficiency of the desired function  a one-to-one mapping between function(s) and energy input is required.
Revised:  To meaningfully discuss the trade-off between the energy consumption and the efficiency of the desired function , a one-to-one mapping between function(s) and energy input is required.
Edit intent: fluency
Original:  The function considered  is the variance .
Revised:  The function considered in this work is the variance .
Edit intent: clarity
Original:  A one-to-one mapping between is obtained by calculating the minimum variance achieved under the constraint of fixed entropy production rate and vice-versa.
Revised:  A one-to-one mapping by considering the minimum variance achieved under the constraint of fixed entropy production rate and vice-versa.
Edit intent: clarity
Original:  A one-to-one mapping between is obtained by calculating the minimum variance achieved under the constraint of fixed entropy production rate and vice-versa.
Revised:  A one-to-one mapping between is obtained by calculating the minimum variance obtained for a fixed entropy production rate and vice-versa.
Edit intent: clarity
Original:  We find that this minimum variance (entropy production rate) is a monotonically decreasing (increasing) function of the given entropy production rate (variance) .
Revised:  We find that this minimum achievable variance is a monotonically decreasing (increasing) function of the given entropy production rate (variance) .
Edit intent: clarity
Original:  We find that this minimum variance (entropy production rate) is a monotonically decreasing (increasing) function of the given entropy production rate (variance) .
Revised:  We find that this minimum variance (entropy production rate) is a monotonically decreasing function of the given entropy production rate (variance) .
Edit intent: clarity
Original:  We find that this minimum variance (entropy production rate) is a monotonically decreasing (increasing) function of the given entropy production rate (variance) .
Revised:  We find that this minimum variance (entropy production rate) is a monotonically decreasing (increasing) function of the given entropy production rate .
Edit intent: clarity
Original:  When there is a timescale separation, in the effective equilibrium limit, the cost of the effective potential and temperature is the associated "hidden" entropy production rate which depends on the parameters of the fast variables and can be optimized the same way as the full nonequilibrium dynamics .
Revised:  When there is a timescale separation, in the effective equilibrium limit, the cost of the effective potential and temperature is the associated "hidden" entropy production rate .
Edit intent: coherence
Original:  However, previous detection methods of the viscous and gravitational fingers are based on density thresholding, which is sensitive to the user-specified threshold value.
Revised:  However, previous detection methods of the viscous and gravitational fingers are based on density thresholding, which is susceptible to the user-specified threshold value.
Edit intent: clarity
Original:  In this work, we explore the topological and geometric detection and evolution of the fingers in detail to elucidate the dynamics of the instability.
Revised:  In this work, we explore the geometric detection and evolution of the fingers in detail to elucidate the dynamics of the instability.
Edit intent: clarity
Original:  We first detect finger cores in three-dimensional (3D) scalar fields to capture the central structures of fingers guided by a ridge voxel detection method ;
Revised:  Guided by a new ridge voxel detection method ;
Edit intent: clarity
Original:  From the identified finger skeletons, we design a spanning contour tree-based method to capture how fingers branch in 3D space .
Revised:  From the identified finger skeletons, we design a spanning tree based approach to capture how fingers branch in 3D space .
Edit intent: clarity
Original:  The geometric-glyph augmented tracking graph allows us to study how the fingers  grow, merge, and split over time.
Revised:  The geometric-glyph augmented tracking graph to study how the fingers grow, merge, and split over time.
Edit intent: clarity
Original:  Feedbacks from earth scientists demonstrate the usefulness of our approach to analyze the evolution of fingers.
Revised:  Feedback from earth scientists demonstrate the usefulness of our approach to analyze the evolution of fingers.
Edit intent: fluency
Original:  Feedbacks from earth scientists demonstrate the usefulness of our approach to analyze the evolution of fingers.
Revised:  Feedbacks from earth scientists demonstrates the usefulness of our approach to analyze the evolution of fingers.
Edit intent: fluency
Original:  Feedbacks from earth scientists demonstrate the usefulness of our approach to analyze the evolution of fingers.
Revised:  Feedbacks from earth scientists demonstrate the usefulness of our approach to analyzing the evolution of fingers.
Edit intent: fluency
Original:  Also, the geometric structures of fingers and their evolution are little studied .
Revised:  Also, the geometric structures of fingers and their evolution are important yet little studied in the literature .
Edit intent: coherence
Original:  Guided by a new ridge voxel detection method , we first extract finger cores from three-dimensional (3D) scalar fields.
Revised:  We propose a ridge voxel detection method , we first extract finger cores from three-dimensional (3D) scalar fields.
Edit intent: clarity
Original:  Guided by a new ridge voxel detection method , we first extract finger cores from three-dimensional (3D) scalar fields.
Revised:  Guided by a new ridge voxel detection method to guide the extraction of finger cores from three-dimensional (3D) scalar fields.
Edit intent: clarity
Original:  After skeletonizing finger cores into skeletons, we design a spanning tree based approach to capture how fingers branch in 3D space from the finger skeletons.
Revised:  After skeletonizing finger cores into skeletons, we design a spanning tree based approach to capture how fingers branch spatially from the finger skeletons.
Edit intent: clarity
Original: In this paper, we study the stablizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient.
Revised: In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient.
Edit intent: fluency
Original:  Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected spanners .
Revised:  Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected graphs .
Edit intent: fluency
Original:  For a directed graph with real edge weights in [1,W], we first propose a new deterministic algorithm that constructs a roundtrip spanner with (2k-1) stretch and O(k n^{1+1/k}\log (nW)) edges for every integer k %DIFDELCMD < \ge %%%  1, then remove the dependence of size on W to give a roundtrip spanner with (2k-1 +o(1) ) stretch and O(k n^{1+1/k}\log n) edges.
Revised:  For a directed graph with real edge weights in [1,W], we first propose a new deterministic algorithm that constructs a roundtrip spanner with (2k-1) stretch and O(k n^{1+1/k}\log (nW)) edges for every integer k %DIFDELCMD < \ge %%% > 1, then remove the dependence of size on W to give a roundtrip spanner with (2k-1 +o(1) ) stretch and O(k n^{1+1/k}\log n) edges.
Edit intent: fluency
Original:  Zhu, Lam'18], and almost match the undirected (2k-1)-spanner with O( k n^{1+1/k}) edges [Alth\"ofer et al. '93]  which is optimal under Erd\"os conjecture.
Revised:  Zhu, Lam'18], and almost matches the undirected (2k-1)-spanner with O( k n^{1+1/k}) edges [Alth\"ofer et al. '93] which is optimal under Erd\"os conjecture.
Edit intent: fluency
Original:  Zhu, Lam'18], and almost match the undirected (2k-1)-spanner with O( k n^{1+1/k}) edges [Alth\"ofer et al. '93]  which is optimal under Erd\"os conjecture.
Revised:  Zhu, Lam'18], and almost match the undirected (2k-1)-spanner with O( n^{1+1/k}) edges [Alth\"ofer et al. '93] which is optimal under Erd\"os conjecture.
Edit intent: clarity
Original:  In this paper, several criteria and an algorithm are introduced to analyze the influence of the initial guess on the evolution of Newton-Raphson's algorithm , and to identify which initial guesses need to be improved in case of convergence failure.
Revised:  In this paper, several criteria are introduced to analyze the influence of the initial guess on the evolution of Newton-Raphson's algorithm , and to identify which initial guesses need to be improved in case of convergence failure.
Edit intent: clarity
Original:  In this paper, several criteria and an algorithm are introduced to analyze the influence of the initial guess on the evolution of Newton-Raphson's algorithm , and to identify which initial guesses need to be improved in case of convergence failure.
Revised:  In this paper, several criteria and an algorithm are introduced to analyze the influence of the initial guess on the evolution of Newton-Raphson's algorithm and to identify which initial guesses need to be improved in case of convergence failure.
Edit intent: fluency
Original:  The use of the criteriaand algorithm , which are based on rigorously proven results, is successfully demonstrated in two exemplary test cases.
Revised:  The use of such criteria , which are based on rigorously proven results, is successfully demonstrated in two exemplary test cases.
Edit intent: clarity
Original: With the rapid evolution of wireless mobile devices, it emerges stronger incentive to design proper collaboration mechanisms among the intelligent agents.
Revised: With the rapid evolution of wireless mobile devices, there is a stronger need to design proper collaboration mechanisms among the intelligent agents.
Edit intent: clarity
Original:  In that regard, independent reinforcement learning (IRL) is often deployed within the multi-agent collaboration to alleviate the dilemma of non-stationary learning environment.
Revised:  In that regard, Independent Reinforcement Learning (IRL) is often deployed within the multi-agent collaboration to alleviate the dilemma of non-stationary learning environment.
Edit intent: fluency
Original:  Besides, we also present a federal training method to effectively optimize the neural networks within each agent in a decentralized manner.
Revised:  Besides, we also present a federal training method to effectively optimize the neural network within each agent in a decentralized manner.
Edit intent: fluency
Original: With the rapid evolution of wireless mobile devices, there is a stronger need to design proper collaboration mechanisms among the intelligent agents.
Revised: With the rapid evolution of wireless mobile devices, there emerges an increased need to design proper collaboration mechanisms among the intelligent agents.
Edit intent: clarity
Original:  In that regard, Independent Reinforcement Learning (IRL) is often deployed within the multi-agent collaboration to alleviate the dilemma of non-stationary learning environment.
Revised:  In that regard, Independent Reinforcement Learning (IRL) is often deployed in multi-agent collaboration to alleviate the dilemma of non-stationary learning environment.
Edit intent: clarity
Original:  In that regard, Independent Reinforcement Learning (IRL) is often deployed within the multi-agent collaboration to alleviate the dilemma of non-stationary learning environment.
Revised:  In that regard, Independent Reinforcement Learning (IRL) is often deployed within the multi-agent collaboration to alleviate the problem of a non-stationary learning environment.
Edit intent: clarity
Original:  However, behavioral strategies of the intelligent agents in IRL could only be formulated upon their local individual observations of the global environment, and appropriate communication mechanisms must be introduced to reduce their behavioral localities.
Revised:  However, behavioral strategies of intelligent agents in IRL could only be formulated upon their local individual observations of the global environment, and appropriate communication mechanisms must be introduced to reduce their behavioral localities.
Edit intent: fluency
Original:  However, behavioral strategies of the intelligent agents in IRL could only be formulated upon their local individual observations of the global environment, and appropriate communication mechanisms must be introduced to reduce their behavioral localities.
Revised:  However, behavioral strategies of the intelligent agents in IRL can only be formulated upon their local individual observations of the global environment, and appropriate communication mechanisms must be introduced to reduce their behavioral localities.
Edit intent: fluency
Original:  In this paper, we tackle the communication problem among the intelligent agents in IRL by jointly adopting two mechanisms with different scales.
Revised:  In this paper, we address the problem of communication between intelligent agents in IRL by jointly adopting two mechanisms with different scales.
Edit intent: clarity
Original:  In this paper, we tackle the communication problem among the intelligent agents in IRL by jointly adopting two mechanisms with different scales.
Revised:  In this paper, we tackle the communication problem among the intelligent agents in IRL by jointly adopting mechanisms with two different scales.
Edit intent: fluency
Original:  For the large scale, we introduce the stigmergy mechanism as an indirect communication bridge among the independent learning agents  and carefully design a mathematical representation to indicate the impact of digital pheromone.
Revised:  For the large scale, we introduce the stigmergy mechanism as an indirect communication bridge between independent learning agents and carefully design a mathematical representation to indicate the impact of digital pheromone.
Edit intent: fluency
Original:  For the large scale, we introduce the stigmergy mechanism as an indirect communication bridge among the independent learning agents  and carefully design a mathematical representation to indicate the impact of digital pheromone.
Revised:  For the large scale, we introduce the stigmergy mechanism as an indirect communication bridge among the independent learning agents , and carefully design a mathematical representation to indicate the impact of digital pheromone.
Edit intent: fluency