wanyu/IteraTeR_v2 huggingface dataset:
Original:  Fifth, we study the parallelizability of APA and establish lower and upper bounds: (i) in general, the problem is P-complete and hence not parallelizable, whereas (ii) under mild restrictions, the problem is in NC and hence parallelizable .
Revised:  Fifth, we study the parallelizability of APA and establish lower and upper bounds: (i) in general, the problem is P-complete and hence unlikely parallelizable, whereas (ii) under mild restrictions, the problem is in NC and hence parallelizable .
Edit intent: coherence
Original:  The update rule for the simplest version is x_{n+1}=x_n-w_n where w_n=pr_{A_n,+}(v_n)-pr_{A_n,-}(v_n), with A_n=\nabla ^2f(x_n)+\delta _n||\nabla f(x_n)||^2.
Revised:  The update rule is very simple conceptually, for example x_{n+1}=x_n-w_n where w_n=pr_{A_n,+}(v_n)-pr_{A_n,-}(v_n), with A_n=\nabla ^2f(x_n)+\delta _n||\nabla f(x_n)||^2.
Edit intent: clarity
Original:  We test the good performance of New Q-Newton 's method against algorithms such as Newton's method, BFGS , Adaptive Cubic Regularization , Random damping Newton's method and Inertial Newton's method, as well as Unbounded Two-way Backtracking Gradient Descent.
Revised:  We test the good performance of New Q-Newton 's method against algorithms such as BFGS and Adaptive Cubic Regularization , Random damping Newton's method and Inertial Newton's method, as well as Unbounded Two-way Backtracking Gradient Descent.
Edit intent: coherence
Original: Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived  by applying van der Corput type lemmas  for functions of logarithmatic singularities, which leads to the optimal convergence rates on the Jacobi, Gegenbauer and Chebyshev orthogonal projections.
Revised: Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived , by applying van der Corput type lemmas for functions of logarithmatic singularities, which leads to the optimal convergence rates on the Jacobi, Gegenbauer and Chebyshev orthogonal projections.
Edit intent: fluency
Original: Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived  by applying van der Corput type lemmas  for functions of logarithmatic singularities, which leads to the optimal convergence rates on the Jacobi, Gegenbauer and Chebyshev orthogonal projections.
Revised: Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived by applying van der Corput type lemmas , for functions of logarithmatic singularities, which leads to the optimal convergence rates on the Jacobi, Gegenbauer and Chebyshev orthogonal projections.
Edit intent: fluency
Original: We propose the concept of neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration for solving integral equations .
Revised: We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration for solving integral equations .
Edit intent: clarity
Original: We propose the concept of neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration for solving integral equations .
Revised: We propose the concept of neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration .
Edit intent: clarity
Original:  Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of insignificant visible bias.
Revised:  Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
Edit intent: fluency
Original: Reinforced elastic sheets surround us in daily life, from concrete shell buildings over cars and airplane fuselages to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves.
Revised: Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves.
Edit intent: clarity
Original:  Inspired by the hierarchically organized scaffolding networks found in plant leaves, here we model networks of bending beams that capture the discrete and non-uniform nature of biologically evolved mechanical structures . Using the principle of maximal rigidity under natural resource constraints, we show that optimal discrete beam networks reproduce the structural features of real leaf venation.
Revised:  Inspired by the hierarchically organized scaffolding networks found in plant leaves, here we model networks of bending beams that capture the discrete and non-uniform nature of natural materials . Using the principle of maximal rigidity under natural resource constraints, we show that optimal discrete beam networks reproduce the structural features of real leaf venation.
Edit intent: clarity
Original:  Thus, in addition to its ability to efficiently transport water and nutrients, the venation network optimizes leaf mechanical properties using practically the same hierarchical reticulated network topology.
Revised:  Thus, in addition to its ability to efficiently transport water and nutrients, the venation network also optimizes leaf rigidity using the same hierarchical reticulated network topology.
Edit intent: clarity
Original:  We finally implement these natural design rules by fabricating efficient, biologically inspired metamaterials.
Revised:  We implement these natural design rules by fabricating efficient, biologically inspired metamaterials.
Edit intent: coherence
Original:  Moreover, we deduce that our methodology extends to models with more generic drift and diffusions for the volatility process.
Revised:  Moreover, we deduce that our methodology extends to models with more general drift and diffusion coefficients for the volatility process.
Edit intent: clarity
Original:  The presented methods are used to simulate the de-pressurization of a pipe containing pure CO2 liquid and vapour under the one-dimensional approximation.
Revised:  The presented methods are used to simulate the de-pressurization of a pipe containing pure CO_2 liquid and vapour under the one-dimensional approximation.
Edit intent: fluency
Original:  This is achieved by internally using complex weights without requiring a conversion of the remaining network to complex numbers.
Revised:  We achieve this by using complex arithmetic without requiring a conversion of the remaining network to complex numbers.
Edit intent: clarity
Original:  This is achieved by internally using complex weights without requiring a conversion of the remaining network to complex numbers.
Revised:  This is achieved by internally using complex weights without requiring a conversion of the network to complex numbers.
Edit intent: clarity
Original:  Additionally, we demonstrate how the NPU can be used as a highly interpretable model to discover the generating equation of a dynamical system purely from data.
Revised:  Additionally, we demonstrate how the NPU can be used as a highly interpretable model to discover the generating equation of a dynamical systems only from data.
Edit intent: clarity
Original:  A simplification of the unit to the RealNPU yields a highly interpretable model.
Revised:  A simplification of the unit to the RealNPU yields a highly transparent model.
Edit intent: clarity
Original:  We show that the NPUs outperform their competitors in terms of accuracy and sparsity on artificial arithmetic datasets, and that the RealNPU can discover the governing equations of a dynamical systems only from data.
Revised:  We show that the NPUs outperform their competitors in terms of accuracy and sparsity on artificial arithmetic datasets, and that the RealNPU can discover the governing equations of a dynamical system only from data.
Edit intent: fluency
Original:  ALADIN-\alpha is a MATLAB implementation of  the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm , which is tailored towards rapid prototyping for non-convex distributed optimization  .
Revised:  ALADIN-\alpha is a MATLAB implementation of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm . Its user interface is convenient for rapid prototyping of non-convex distributed optimization .
Edit intent: clarity
Original:  ALADIN-\alpha is a MATLAB implementation of  the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm , which is tailored towards rapid prototyping for non-convex distributed optimization  .
Revised:  ALADIN-\alpha is a MATLAB implementation of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm , which is tailored towards rapid prototyping for non-convex distributed optimization algorithms .
Edit intent: fluency
Original:  A collection of application examples from different applications fields including chemical engineering, robotics, and power systems underpins the application potential of ALADIN-\alpha.
Revised:  A collection of examples from different applications fields including chemical engineering, robotics, and power systems underpins the application potential of ALADIN-\alpha.
Edit intent: fluency
Original:  A collection of application examples from different applications fields including chemical engineering, robotics, and power systems underpins the application potential of ALADIN-\alpha.
Revised:  A collection of application examples from different applications fields including chemical engineering, robotics, and power systems underpins the potential of ALADIN-\alpha.
Edit intent: fluency
Original: We price European-style options written on forward contracts in a commodity market, which we model with a state-dependent infinite-dimensional Heath-Jarrow-Morton (HJM) approach.
Revised: We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach.
Edit intent: clarity
Original:  We introduce a new class of volatility operators which map the square integrable noise into the Filipovi \'{c space of forward curves , and we specify a deterministic parametrized version of it.
Revised:  We introduce a new class of volatility operators which map the square integrable noise into the Filipovi \'{c space of forward curves , and we specify a deterministic parametrized version of it.
Edit intent: fluency
Original:  For calibration purposes, we train a neural network to approximate the  option price as a function of the model parameters.
Revised:  For calibration purposes, we train a neural network to approximate the true option price as a function of the model parameters.
Edit intent: clarity
Original:  This reveals that the original meaning of the parameters gets somehow lost in the approximation  .
Revised:  This reveals that the original meaning of the model parameters is partly lost in the approximation .
Edit intent: clarity
Original:  This reveals that the original meaning of the parameters gets somehow lost in the approximation  .
Revised:  This reveals that the original meaning of the parameters gets somehow lost in the approximation step .
Edit intent: clarity
Original:  For this purpose we introduce a new class of state-dependent volatility operators that map the square integrable noise into the Filipovi \'{c space of forward curves.
Revised:  For this purpose we introduce a new class of state-dependent volatility operators that map the square integrable noise into the Filipovi \'{c space of forward curves.
Edit intent: fluency
Original: Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control the disease transmission.
Revised: Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission.
Edit intent: fluency
Original:  We find that increasing the rate of rumor propagation reduces the disease prevalence, as one may expect.
Revised:  We find that increasing the rate of information dissemination reduces the disease prevalence, as one may expect.
Edit intent: clarity
Original:  However, increasing the speed of the rumor process as compare to the epidemic process has the counter intuitive result of increasing the  prevalence.
Revised:  However, increasing the speed of the information process as compared to that of the epidemic process has the counter intuitive result of increasing the prevalence.
Edit intent: clarity
Original:  However, increasing the speed of the rumor process as compare to the epidemic process has the counter intuitive result of increasing the  prevalence.
Revised:  However, increasing the speed of the rumor process as compare to the epidemic process has the counter intuitive effect of increasing the prevalence.
Edit intent: fluency
Original:  However, increasing the speed of the rumor process as compare to the epidemic process has the counter intuitive result of increasing the  prevalence.
Revised:  However, increasing the speed of the rumor process as compare to the epidemic process has the counter intuitive result of increasing the disease prevalence.
Edit intent: clarity
Original:  Taking a genome-scale, systems-level view of virus-host interactions, we adapt and specialize network label propagation methods to prioritize drug targets based on their probability to inhibit host-pathogen interactions or their downstream signaling targets.
Revised:  Taking a genome-scale, systems-level computational approach to prioritize drug targets based on their probability to inhibit host-pathogen interactions or their downstream signaling targets.
Edit intent: clarity
Original:  Moreover, the top-ranking proteins scored by our methods are enriched in  biological processes that are relevant to the virus.
Revised:  The top-ranked proteins that we identify are enriched in biological processes that are relevant to the virus.
Edit intent: clarity
Original:  Moreover, the top-ranking proteins scored by our methods are enriched in  biological processes that are relevant to the virus.
Revised:  Moreover, the top-ranking proteins scored by our methods are enriched in biological processes that are potentially coopted by the virus.
Edit intent: clarity
Original:  Several drugs that we discuss are already undergoing clinical trials to test their efficacy against COVID-19.
Revised:  Drugs that we discuss are already undergoing clinical trials to test their efficacy against COVID-19.
Edit intent: clarity
Original:  We make the prioritized list of human proteins and drug targets broadly available as a general resource for repositioning of existing and approved drugs  as anti-COVID-19 agents or for novel drug development .
Revised:  Our prioritized list of human proteins and drug targets broadly available as a general resource for repositioning of existing and approved drugs as anti-COVID-19 agents or for novel drug development .
Edit intent: coherence
Original:  We make the prioritized list of human proteins and drug targets broadly available as a general resource for repositioning of existing and approved drugs  as anti-COVID-19 agents or for novel drug development .
Revised:  We make the prioritized list of human proteins and drug targets is available as a general resource for repositioning of existing and approved drugs as anti-COVID-19 agents or for novel drug development .
Edit intent: clarity
Original:  We make the prioritized list of human proteins and drug targets broadly available as a general resource for repositioning of existing and approved drugs  as anti-COVID-19 agents or for novel drug development .
Revised:  We make the prioritized list of human proteins and drug targets broadly available as a general resource for repositioning of existing and approved drugs or developing novel therapeutics as anti-COVID-19 agents or for novel drug development .
Edit intent: clarity
Original:  We make the prioritized list of human proteins and drug targets broadly available as a general resource for repositioning of existing and approved drugs  as anti-COVID-19 agents or for novel drug development .
Revised:  We make the prioritized list of human proteins and drug targets broadly available as a general resource for repositioning of existing and approved drugs as anti-COVID-19 agents .
Edit intent: clarity
Original:  We also present applications of our algorithms for computing minimal unique palindromic substrings (MUPS) and for computing minimal absent palindromic words (MAPW) for a sliding window.
Revised:  We also show how our algorithms can be applied to efficient computation of minimal unique palindromic substrings (MUPS) and for computing minimal absent palindromic words (MAPW) for a sliding window.
Edit intent: clarity
Original:  We also present applications of our algorithms for computing minimal unique palindromic substrings (MUPS) and for computing minimal absent palindromic words (MAPW) for a sliding window.
Revised:  We also present applications of our algorithms for computing minimal unique palindromic substrings (MUPS) and minimal absent palindromic words (MAPW) for a sliding window.
Edit intent: fluency
Original: Research regarding design automation that integrates artificial intelligence (AI) into computer-aided design (CAD) and computer-aided engineering (CAE) is actively being conducted.
Revised: Engineering design research integrating artificial intelligence (AI) into computer-aided design (CAD) and computer-aided engineering (CAE) is actively being conducted.
Edit intent: clarity
Original:  This study proposes a deep learning-based CAD/CAE framework  that automatically generates three-dimensional ( 3D ) CAD models, predicts CAE results immediately, explains the results, and verifies the reliability .
Revised:  This study proposes a deep learning-based CAD/CAE framework that automatically generates 3D ) CAD models, predicts CAE results immediately, explains the results, and verifies the reliability .
Edit intent: clarity
Original:  This study proposes a deep learning-based CAD/CAE framework  that automatically generates three-dimensional ( 3D ) CAD models, predicts CAE results immediately, explains the results, and verifies the reliability .
Revised:  This study proposes a deep learning-based CAD/CAE framework that automatically generates three-dimensional ( 3D CAD designs and evaluates their engineering performance .
Edit intent: clarity
Original:  The proposed framework comprises seven stages: (1) two-dimensional ( 2D ) generative design, (2) dimensionality reduction, (3) design of experiment in latent space, (4) CAD automation, (5) CAE automation, (6) transfer learning, and (7) visualization and analysis.
Revised:  The proposed framework comprises seven stages: (1) 2D ) generative design, (2) dimensionality reduction, (3) design of experiment in latent space, (4) CAD automation, (5) CAE automation, (6) transfer learning, and (7) visualization and analysis.
Edit intent: fluency
Original:  The proposed framework comprises seven stages: (1) two-dimensional ( 2D ) generative design, (2) dimensionality reduction, (3) design of experiment in latent space, (4) CAD automation, (5) CAE automation, (6) transfer learning, and (7) visualization and analysis.
Revised:  The proposed framework comprises seven stages: (1) two-dimensional ( 2D generative design, (2) dimensionality reduction, (3) design of experiment in latent space, (4) CAD automation, (5) CAE automation, (6) transfer learning, and (7) visualization and analysis.
Edit intent: fluency
Original:  The proposed framework is demonstrated through a road wheel design case study and indicates that AI can be practically incorporated into  end-use product design . Using this framework, it is expected that industrial designers and engineers can jointly review feasible engineering 3D CAD models created by AI and select the best design for the market in the early stages of product development.
Revised:  The proposed framework is demonstrated through a road wheel design case study and indicates that AI can be practically incorporated into an end-use product design . Using this framework, it is expected that industrial designers and engineers can jointly review feasible engineering 3D CAD models created by AI and select the best design for the market in the early stages of product development.
Edit intent: fluency
Original:  The proposed framework is demonstrated through a road wheel design case study and indicates that AI can be practically incorporated into  end-use product design . Using this framework, it is expected that industrial designers and engineers can jointly review feasible engineering 3D CAD models created by AI and select the best design for the market in the early stages of product development.
Revised:  The proposed framework is demonstrated through a road wheel design case study and indicates that AI can be practically incorporated into end-use product design project. Engineers and industrial designers can jointly review feasible engineering 3D CAD models created by AI and select the best design for the market in the early stages of product development.
Edit intent: clarity
Original: Photoconductive devices (PCDs) enhanced with nanostructures have shown a significantly improved optical-to-terahertz conversion efficiency.
Revised: Photoconductive devices (PCDs) enhanced with nanostructures have a significantly improved optical-to-terahertz conversion efficiency.
Edit intent: clarity
Original:  The unit-cell model composed of these coupled equations and boundary conditions is discretized and solved using DG methods.
Revised:  The unit-cell model described by these coupled equations and boundary conditions is discretized and solved using DG methods.
Edit intent: clarity
Original:  The unit-cell model composed of these coupled equations and boundary conditions is discretized and solved using DG methods.
Revised:  The unit-cell model composed of these coupled equations and boundary conditions is discretized using DG methods.
Edit intent: clarity
Original:  The boundary conditions are enforced weakly through the numerical flux of DG. Numerical results show that the proposed DG-based unit-cell scheme models the device accurately but is significantly faster than the DG scheme that takes into account the whole device  .
Revised:  The resulting DG-based unit-cell scheme models the device accurately but is significantly faster than the DG scheme that takes into account the whole device .
Edit intent: coherence
Original: Photoconductive devices (PCDs) enhanced with nanostructures have a significantly improved optical-to-terahertz conversion efficiency.
Revised: Incorporation of plasmonic nanostructures in the design of photoconductive devices (PCDs) enhanced with nanostructures have a significantly improved optical-to-terahertz conversion efficiency.
Edit intent: clarity
Original: Photoconductive devices (PCDs) enhanced with nanostructures have a significantly improved optical-to-terahertz conversion efficiency.
Revised: Photoconductive devices (PCDs) has significantly improved their optical-to-terahertz conversion efficiency.
Edit intent: clarity
Original:  While the experimental research on the development of these devices has progressed remarkably, their simulation is still challenging due to the need for accurate and efficient modeling of multiphysics processes and intricate device geometries  .
Revised:  While the experimental research on the development of these devices . Indeed, accurate and efficient modeling of multiphysics processes and intricate device geometries .
Edit intent: coherence