wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this manuscript we investigate an implementation of Discrete local Sensitivity Analysis via Automatic Differentiation (DSAAD)  . A non-stiff Lotka-Volterra model, a discretization of the two dimensional (N \times N) Brusselator stiff reaction-diffusion PDE , a stiff non-linear air pollution and a non-stiff pharmacokinetic/pharmacodynamic (PK/PD) model were used as prototype models for this investigation.
Revised:  In this manuscript we investigate an implementation of Discrete local Sensitivity Analysis via Automatic Differentiation (DSAAD) . 
Edit intent: coherence
Original:  Our benchmarks show that on sufficiently small ( <100 parameters ) stiff and non-stiff systems of ODEs , forward-mode DSAAD is more efficient than both reverse-mode DSAAD and continuous forward/adjoint sensitivity analysis.
Revised:  Our benchmarks show that on small systems of ODEs (approximately <100 parameters ) stiff and non-stiff systems of ODEs , forward-mode DSAAD is more efficient than both reverse-mode DSAAD and continuous forward/adjoint sensitivity analysis.
Edit intent: clarity
Original:  Our benchmarks show that on sufficiently small ( <100 parameters ) stiff and non-stiff systems of ODEs , forward-mode DSAAD is more efficient than both reverse-mode DSAAD and continuous forward/adjoint sensitivity analysis.
Revised:  Our benchmarks show that on sufficiently small ( <100 parameters +ODEs) , forward-mode DSAAD is more efficient than both reverse-mode DSAAD and continuous forward/adjoint sensitivity analysis.
Edit intent: clarity
Original:  Our benchmarks show that on sufficiently small ( <100 parameters ) stiff and non-stiff systems of ODEs , forward-mode DSAAD is more efficient than both reverse-mode DSAAD and continuous forward/adjoint sensitivity analysis.
Revised:  Our benchmarks show that on sufficiently small ( <100 parameters ) stiff and non-stiff systems of ODEs , forward-mode DSAAD is more efficient than both reverse-mode and continuous forward/adjoint sensitivity analysis.
Edit intent: fluency
Original:  The robust upper and local lower bounds are derived with respect to an error notion which measures the error of the solution and of a suitable approximation of the constraining force in a \epsilon-dependent energy norm and its dual norm.
Revised:  Upper and lower bounds are derived with respect to an error notion which measures the error of the solution and of a suitable approximation of the constraining force in a \epsilon-dependent energy norm and its dual norm.
Edit intent: clarity
Original: In this article, global stabilization results for the two dimensional viscous Burgers' equation  that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law.
Revised: In this article, global stabilization results for the two dimensional viscous Burgers' equation , that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law.
Edit intent: fluency
Original:  Further, convergence result is derived for the boundary feedback control law  . All the results preserve exponential stabilization property.
Revised:  Further, convergence result is derived for the boundary feedback control law are derived . All the results preserve exponential stabilization property.
Edit intent: clarity
Original:  Finally, some numerical experiments are conducted to confirm our theoretical findings.
Revised:  Finally, several numerical experiments are conducted to confirm our theoretical findings.
Edit intent: clarity
Original: In this article, global stabilization results for the two dimensional  viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law.
Revised: In this article, global stabilization results for the two dimensional (2D) viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law.
Edit intent: clarity
Original:  Then, using C^0-conforming finite element method in spatial direction, global stabilization results for the semidiscrete solution are shown.
Revised:  Then, applying C^0-conforming finite element method in spatial direction, global stabilization results for the semidiscrete solution are shown.
Edit intent: fluency
Original:  Moreover, optimal error estimates in L^\infty(L^2) and in L^\infty(H^1) -norms for the state variable and convergence result for the boundary feedback control law are derived.
Revised:  Moreover, optimal error estimates in L^\infty(L^2) and in L^\infty(H^1) - norms for the state variable and convergence result for the boundary feedback control law are derived.
Edit intent: fluency
Original:  Therefore, linear-complexity approximation algorithms have been proposed to improve its scalability .
Revised:  Even though linear-complexity approximation algorithms have been proposed to improve its scalability .
Edit intent: coherence
Original:  All our algorithms are data parallel, and therefore, we can take advantage of massively parallel computing engines, such as Graphics Processing Units (GPUs).
Revised:  All our algorithms are data parallel, and thus, we take advantage of massively parallel computing engines, such as Graphics Processing Units (GPUs).
Edit intent: clarity
Original:  The experiments on MNIST images show that the new algorithms can perform a billion distance computations in less than a minute using a single GPU.
Edit intent: coherence
Original:  First, full-model solutions are approximated locally in time via local reduced spaces that are adapted with basis updates during time stepping.
Revised:  Full-model solutions are approximated locally in time via local reduced spaces that are adapted with basis updates during time stepping.
Edit intent: coherence
Original:  Second, the locality in space of the coherent structures is exploited via an adaptive sampling scheme that selects at which components to query the full model for computing the basis updates.
Revised:  A core contribution of this work is an adaptive sampling scheme that selects at which components to query the full model for computing the basis updates.
Edit intent: clarity
Original:  Second, the locality in space of the coherent structures is exploited via an adaptive sampling scheme that selects at which components to query the full model for computing the basis updates.
Revised:  Second, the locality in space of the coherent structures is exploited via an adaptive sampling scheme for selecting at which components to query the full model for computing the basis updates.
Edit intent: coherence
Original:  Second, the locality in space of the coherent structures is exploited via an adaptive sampling scheme that selects at which components to query the full model for computing the basis updates.
Revised:  Second, the locality in space of the coherent structures is exploited via an adaptive sampling scheme that selects at which components to query the full model to compute basis updates.
Edit intent: fluency
Original:  Our analysis shows that, in probability, the more local the coherent structure is in space, the fewer full-model samples are required to adapt the reduced basis with the proposed adaptive sampling scheme.
Revised:  The presented analysis shows that, in probability, the more local the coherent structure is in space, the fewer full-model samples are required to adapt the reduced basis with the proposed adaptive sampling scheme.
Edit intent: clarity
Original: The estimation of the mortality rate function for a stage-structured population is obtained starting from time-series field data on the abundance of the species.
Revised: Simulating the population dynamics of a stage-structured population is obtained starting from time-series field data on the abundance of the species.
Edit intent: clarity
Original:  A crucial role for this switch is played by a parameter \varepsilon=\varepsilon({\Delta t,\Delta x})>0 which goes to 0 as  (\Delta t,\Delta x) is going to 0 and does not depend on the time t_n  .
Revised:  A crucial role for this switch is played by a parameter \varepsilon=\varepsilon({\Delta t,\Delta x})>0 which goes to 0 as (\Delta t,\Delta x) are going to 0 and does not depend on the time t_n .
Edit intent: clarity
Original:  For a particular family of graphs, this process can be modeled using cellular automata.
Revised:  For a particular family of graphs, this process can be modelled using cellular automata.
Edit intent: fluency
Original:  We use this connection to show that such processes can exhibit arbitrarily-long periodicity .
Revised:  We use this connection to show that such processes can exhibit arbitrarily-long periods .
Edit intent: clarity
Original: Complex systems of the real world can be modeled as a network of connected components.
Revised: Complex systems in the real world can be modeled as a network of connected components.
Edit intent: clarity
Original:  The human brain, as a network of neurons among which the interactions cause perception, is most suited to be modeled as a complex network.
Revised:  The human brain, as a network of neurons among which the interactions cause perception, is a complex network.
Edit intent: clarity
Original:  Coherence level which is measured and utilized as the criteria to analyze synchronicity, experienced a sharp increase as the network changes into the small-world network and grows steadily by the end.
Revised:  Coherence level which is measured and utilized as the criteria to analyze synchronicity, experiencing a sharp increase as the network changes into the small-world network and grows steadily by the end.
Edit intent: fluency
Original:  Coherence level which is measured and utilized as the criteria to analyze synchronicity, experienced a sharp increase as the network changes into the small-world network and grows steadily by the end.
Revised:  Coherence level which is measured and utilized as the criteria to analyze synchronicity, experienced a sharp increase as the network changes into the small-world network and growing steadily by the end.
Edit intent: fluency
Original:  however, the number of synaptic connections of each neuron and their conductance have a positive effect on synchronization.
Revised:  however, the number of synaptic connections of each neuron and their conductance have a positive impact on synchronization.
Edit intent: clarity
Original:  By applying the model to a C-elegance neural network, not only the mentioned parameters but also the role of  degree distribution are highlighted.
Revised:  By applying the model to a C-elegance neural network, not only the mentioned parameters but also the role of the degree distribution are highlighted.
Edit intent: fluency
Original: Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is a problem often encountered in the logistics industry, where, on a daily basis, vehicles are required to pick up parcels from depots and deliver them to clients.
Edit intent: coherence
Original:  This paper introduces an approach to solve the Capacitated Vehicle Routing Problem with Time Windows  for a high number of nodes by splitting the problem into smaller sub-problems with lower number of nodes.
Revised:  This paper introduces a new approach to improve the performance of the Capacitated Vehicle Routing Problem with Time Windows for a high number of nodes by splitting the problem into smaller sub-problems with lower number of nodes.
Edit intent: clarity
Original:  It introduces an approach based on clustering nodes together using Recursive-DBSCAN - a method that recursively applies DBSCAN until clusters below the preset maximum number of nodes per cluster are obtained.
Revised:  It introduces an approach based on clustering nodes together using Recursive-DBSCAN - an algorithm that recursively applies DBSCAN until clusters below the preset maximum number of nodes per cluster are obtained.
Edit intent: clarity
Original:  It introduces an approach based on clustering nodes together using Recursive-DBSCAN - a method that recursively applies DBSCAN until clusters below the preset maximum number of nodes per cluster are obtained.
Revised:  It introduces an approach based on clustering nodes together using Recursive-DBSCAN - a method that recursively applies DBSCAN until clusters below the preset maximum number of nodes are obtained.
Edit intent: clarity
Original:  We introduce Continuous Learning Augmentation (CLA) which is based on an explicit memory structure and a feed forward neural network (FFNN) base model and used to drive long term financial investment decisions.
Revised:  We introduce Continual Learning Augmentation (CLA) which is based on an explicit memory structure and a feed forward neural network (FFNN) base model and used to drive long term financial investment decisions.
Edit intent: fluency
Original:  Connected vehicles will utilize IEEE 802.
Revised:  Connected vehicles can utilize IEEE 802.
Edit intent: clarity
Original:  However, a widespread deployment of connected vehicles and the introduction of connected automated driving applications will notably increase the bandwidth and scalability requirements of the vehicular network .
Revised:  However, a widespread deployment of connected vehicles and the introduction of connected automated driving applications will notably increase the bandwidth and scalability requirements of vehicular networks .
Edit intent: coherence
Original:  In particular, the paper proposes the first distributed (and decentralized) context-aware heterogeneous V2V communications algorithm that is technology and application agnostic, and that allows each vehicle to autonomously and dynamically select its communications technology taking into account its application requirements and the  context conditions.
Revised:  In particular, the paper proposes the first distributed (and decentralized) context-aware heterogeneous V2V communications algorithm that is technology and application agnostic, and that allows each vehicle to autonomously and dynamically select its communications technology taking into account its application requirements and the communication context conditions.
Edit intent: clarity
Original:  We also presents bounds on parameters measuring geometric quality (aspect ratios, minimum edge length, and maximum angle) of K in terms of the corresponding parameters of K (for d=2, 3).
Revised:  We also present bounds on parameters measuring geometric quality (aspect ratios, minimum edge length, and maximum angle) of K in terms of the corresponding parameters of K (for d=2, 3).
Edit intent: fluency
Original: We present a new formulation of the hyperbolic singular value decomposition (HSVD) for an arbitrary complex (or real) matrix without using the concept of hyperexchange matrices and using only the concept of pseudo-unitary (or pseudo-orthogonal) matrices.
Revised: We present a new formulation of the hyperbolic singular value decomposition (HSVD) for an arbitrary complex (or real) matrix without hyperexchange matrices and using only the concept of pseudo-unitary (or pseudo-orthogonal) matrices.
Edit intent: clarity
Original:  The new formulation allows us to present an algorithm for computing HSVD in the general case  .
Revised:  We show that computing the HSVD in the general case .
Edit intent: clarity
Original:  We introduce two bicriteria temporal min-cost path problems in which we are interested in the set of all efficient paths with low costs and short duration or early arrival times , respectively.
Revised:  We introduce two bicriteria temporal min-cost path problems in which we are interested in the set of all efficient paths with low cost and short duration or early arrival times , respectively.
Edit intent: fluency
Original:  We introduce two bicriteria temporal min-cost path problems in which we are interested in the set of all efficient paths with low costs and short duration or early arrival times , respectively.
Revised:  We introduce two bicriteria temporal min-cost path problems in which we are interested in the set of all efficient paths with low costs and short duration or early arrival time , respectively.
Edit intent: fluency
Original:  Unfortunately , the number of efficient paths can be exponential in the size of the input.
Revised:  However , the number of efficient paths can be exponential in the size of the input.
Edit intent: coherence
Original:  For the case of strictly positive edge costs , however, we are able to provide algorithms that enumerate the set of efficient paths with polynomial time delay and polynomial space.
Revised:  For the case of strictly positive edge costs we are able to provide algorithms that enumerate the set of efficient paths with polynomial time delay and polynomial space.
Edit intent: coherence
Original:  If we are only interested in the set of pareto-optimal solutions ( not in the paths itself), then we show that in the case of nonnegative edge costs these sets can be found in polynomial time  .
Revised:  If we are only interested in the set of Pareto-optimal solutions and not in the paths itself), then we show that in the case of nonnegative edge costs these sets can be found in polynomial time .
Edit intent: fluency
Original:  If we are only interested in the set of pareto-optimal solutions ( not in the paths itself), then we show that in the case of nonnegative edge costs these sets can be found in polynomial time  .
Revised:  If we are only interested in the set of pareto-optimal solutions ( not in the paths themselves, then these can be determined in polynomial time .
Edit intent: clarity
Original:  In addition, for each pareto-optimal solution, we are able to find an efficient path in polynomial time  .
Revised:  In addition, for each Pareto-optimal solution, we are able to find an efficient path in polynomial time .
Edit intent: fluency
Original:  It is difficult to provide theoretical proofs on the control stability of such neural control architectures in general, and G \& CNETs in particular, to perturbations, time delays or model uncertainties or to compute stability margins and trace them back to the network training process or to its architecture.
Revised:  It is difficult to provide theoretical proofs on the control stability of such neural control architectures in general, and G CNETs in particular, to perturbations, time delays or model uncertainties or to compute stability margins and trace them back to the network training process or to its architecture.
Edit intent: fluency
Original:  This lack of validation naturally leads to skepticism especially in cases where safety and validation are of paramount importance such as is the case, for example, in the automotive or space industry.
Revised:  This lack of validation naturally leads to scepticism especially in cases where safety and validation are of paramount importance such as is the case, for example, in the automotive or space industry.
Edit intent: fluency
Original:  In an attempt to narrow the gap between deep learning research and control theory, we propose a new methodology based on differntal algebra and automated differentiation to obtain formal guarantees on the behaviour of neural based control sysetems .
Revised:  In an attempt to narrow the gap between deep learning research and control theory, we propose a new methodology based on differential algebra and automated differentiation to obtain formal guarantees on the behaviour of neural based control sysetems .
Edit intent: fluency
Original:  In an attempt to narrow the gap between deep learning research and control theory, we propose a new methodology based on differntal algebra and automated differentiation to obtain formal guarantees on the behaviour of neural based control sysetems .
Revised:  In an attempt to narrow the gap between deep learning research and control theory, we propose a new methodology based on differntal algebra and automated differentiation to obtain formal guarantees on the behaviour of neural based control systems .
Edit intent: fluency
Original: Research has shown how the optimal feedback control of several non linear systems of interest in aerospace applications can be represented by deep neural architectures and trained using techniques including imitation learning, reinforcement learning and evolutionary algorithms.
Revised: Recent work have shown how the optimal feedback control of several non linear systems of interest in aerospace applications can be represented by deep neural architectures and trained using techniques including imitation learning, reinforcement learning and evolutionary algorithms.
Edit intent: clarity
Original:  We devise a neural network architecture and training procedure that allows predicting the MSE, SSIM or VGG16 image difference A-B from the distorted image A alone , when the reference B is not observed.
Revised:  We devise a neural network architecture and training procedure that allows predicting the MSE, SSIM or VGG16 image difference from the distorted image A alone , when the reference B is not observed.
Edit intent: clarity
Original:  We devise a neural network architecture and training procedure that allows predicting the MSE, SSIM or VGG16 image difference A-B from the distorted image A alone , when the reference B is not observed.
Revised:  We devise a neural network architecture and training procedure that allows predicting the MSE, SSIM or VGG16 image difference A-B from the distorted image alone while the reference is not observed.
Edit intent: clarity
Original:  This is enabled by two insights: The first is to inject sufficiently many un-distorted natural image patches, which can be had in arbitrary amounts and are known to have no perceivable difference to themselves.
Revised:  This is enabled by two insights: The first is to inject sufficiently many un-distorted natural image patches, which can be found in arbitrary amounts and are known to have no perceivable difference to themselves.
Edit intent: clarity
Original:  Surprisingly, we observe, that the resulting non-paired metric, subjectively, can even perform better than the paired one, as it had to become robust to misalignments.
Revised:  Surprisingly, we observe, that the resulting no-reference metric, subjectively, can even perform better than the paired one, as it had to become robust to misalignments.
Edit intent: clarity
Original:  We demonstrate the effectiveness of our approach quantitatively and in a user study, as well as qualitatively, in an image-based rendering application where we predict difference visibility maps .
Revised:  We demonstrate the effectiveness of our approach in an image-based rendering application where we predict difference visibility maps .
Edit intent: coherence
Original:  As to running time, depending on the particular shape of the problem , either method can excel.
Revised:  As to running time, depending on the particular problem instance , either method can excel.
Edit intent: clarity
Original:  When our method excels it may not just beat BooleanConvert but also SatisfiabilityCount by orders of magnitude .
Revised:  When our method wins it may not just beat BooleanConvert but also SatisfiabilityCount by orders of magnitude .
Edit intent: clarity
Original:  Our algorithm, coded in high-level Mathematica code, compares favorably to the hardwired Mathematica command BooleanConvert (=exclusive sums of products).
Revised:  Our algorithm, coded in high-level Mathematica code, compares favorably to both the Mathematica command BooleanConvert (=exclusive sums of products).
Edit intent: clarity
Original:  Motivated by our theoretical analysis, we propose the Max-Margin Adversarial (MMA) training to maximize the average margin .
Revised:  Motivated by our theoretical analysis, we propose Max-Margin Adversarial (MMA) training to maximize the average margin .
Edit intent: fluency