wanyu/IteraTeR_v2 huggingface dataset:
Original:  This is done via an algorithmic translation of a chemical reaction network into a target expanded one where each discrete state is represented as a further distinct chemical species.
Revised:  An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct chemical species.
Edit intent: clarity
Original: Let \rho and \pi be two probability measures on [-1,1]^d with positive and analytic Lebesgue densities.
Revised: For two probability measures on [-1,1]^d with positive and analytic Lebesgue densities.
Edit intent: coherence
Original:  We investigate the approximation of the unique triangular monotone ( Knothe-Rosenblatt ) transport T:[-1,1]^d\to [-1,1]^d, such that the pushforward T_\sharp\rho equals \pi.
Revised:  We investigate the approximation of the unique triangular monotone Knothe-Rosenblatt ) transport T:[-1,1]^d\to [-1,1]^d, such that the pushforward T_\sharp\rho equals \pi.
Edit intent: clarity
Original:  We investigate the approximation of the unique triangular monotone ( Knothe-Rosenblatt ) transport T:[-1,1]^d\to [-1,1]^d, such that the pushforward T_\sharp\rho equals \pi.
Revised:  We investigate the approximation of the unique triangular monotone ( Knothe-Rosenblatt transport T:[-1,1]^d\to [-1,1]^d, such that the pushforward T_\sharp\rho equals \pi.
Edit intent: fluency
Original:  It is shown that for d\inN there exist approximations \tilde T of T  based on either sparse polynomial expansions or ReLU networks, such that the distance between \tilde T_\sharp\rho and \pi decreases exponentially.
Revised:  It is shown that for d\inN there exist approximations \tilde T of T , based on either sparse polynomial expansions or ReLU networks, such that the distance between \tilde T_\sharp\rho and \pi decreases exponentially.
Edit intent: fluency
Original:  More precisely, we show error bounds of the type \exp(-\beta N^{1/d}) (or \exp(-\beta N^{1/(d+1)}) for neural networks), where N refers to the dimension of the ansatz space (or the size of the network) containing \tilde T;
Revised:  More precisely, we prove error bounds of the type \exp(-\beta N^{1/d}) (or \exp(-\beta N^{1/(d+1)}) for neural networks), where N refers to the dimension of the ansatz space (or the size of the network) containing \tilde T;
Edit intent: clarity
Original:  (ii) the size of the training data;
Revised:  (ii) the amount of training data;
Edit intent: clarity
Original:  With this study, we aim to follow-up a discussion of publication patterns in SSH by providing complex data on recent developments primarily in CEE countries with similar cultural and political heritage (  Czech Republic, Slovakia  and Poland) and comparing the patterns with Flanders (Belgium) and Norway representing Western and Nordic countries.
Revised:  With this study, we aim to follow-up a discussion of publication patterns in SSH by providing complex data on recent developments primarily in CEE countries with similar cultural and political heritage ( the Czech Republic, Slovakia and Poland) and comparing the patterns with Flanders (Belgium) and Norway representing Western and Nordic countries.
Edit intent: fluency
Original:  With this study, we aim to follow-up a discussion of publication patterns in SSH by providing complex data on recent developments primarily in CEE countries with similar cultural and political heritage (  Czech Republic, Slovakia  and Poland) and comparing the patterns with Flanders (Belgium) and Norway representing Western and Nordic countries.
Revised:  With this study, we aim to follow-up a discussion of publication patterns in SSH by providing complex data on recent developments primarily in CEE countries with similar cultural and political heritage ( Czech Republic, Slovakia , and Poland) and comparing the patterns with Flanders (Belgium) and Norway representing Western and Nordic countries.
Edit intent: fluency
Original:  With this study, we aim to follow-up a discussion of publication patterns in SSH by providing complex data on recent developments primarily in CEE countries with similar cultural and political heritage (  Czech Republic, Slovakia  and Poland) and comparing the patterns with Flanders (Belgium) and Norway representing Western and Nordic countries.
Revised:  With this study, we aim to follow-up a discussion of publication patterns in SSH by providing complex data on recent developments primarily in CEE countries with similar cultural and political heritage ( Czech Republic, Slovakia and Poland) . The other two are Flanders (Belgium) and Norway representing Western and Nordic countries.
Edit intent: coherence
Original:  and the algorithm needs a large amount of labeled data .
Revised:  and the algorithm often needs precise labels of many data points .
Edit intent: clarity
Original:  It is motivated by the information bottleneck principle (extended with kernel methods), in which networks learn to squeeze as much information as possible out of the input without sacrificing prediction of the output.
Revised:  It is motivated by the information bottleneck principle (extended with kernel methods), in which networks learn to compress the input as much as possible without sacrificing prediction of the output.
Edit intent: clarity
Original:  instead, they rely on the similarity between the desired outputs.
Revised:  instead, they rely on the similarity between pairs of desired outputs.
Edit intent: clarity
Original:  They thus solve all three implausibility issues of backpropagation.
Edit intent: coherence
Original:  Moreover, to obtain good performance on hard problems and retain biologically plausible learning rules , our rules need divisive normalization - a known feature of biological networks.
Revised:  Moreover, to obtain good performance on hard problems and retain biological plausibility , our rules need divisive normalization - a known feature of biological networks.
Edit intent: clarity
Original:  Finally, simulations show that our rule performs nearly as well as backpropagation on image classification tasks.
Revised:  Finally, simulations show that our rules perform nearly as well as backpropagation on image classification tasks.
Edit intent: clarity
Original:  The finite-difference discretization of the SKT equation in space results in a system of linear-quadratic ordinary differential equations (ODEs).
Revised:  The finite-difference discretization of the SKT equation in space results in a system of linear--quadratic ordinary differential equations (ODEs).
Edit intent: fluency
Original:  The results are implemented to empirical S \& P 500 dataset.
Revised:  The results are implemented to empirical S P 500 dataset.
Edit intent: fluency
Original:  Several standard compliant compilers have since been developed of which at least five remain available and at least three are being actively maintained . Meanwhile, various deficiencies of the standard have become apparent but since its publication, no revision and no maintenance has been carried out.
Revised:  Several conforming compilers have since been developed of which at least five remain available and at least three are being actively maintained . Meanwhile, various deficiencies of the standard have become apparent but since its publication, no revision and no maintenance has been carried out.
Edit intent: clarity
Original:  Several standard compliant compilers have since been developed of which at least five remain available and at least three are being actively maintained . Meanwhile, various deficiencies of the standard have become apparent but since its publication, no revision and no maintenance has been carried out.
Revised:  Several standard compliant compilers have since been developed . At least five remain available and at least three are being actively maintained . Meanwhile, various deficiencies of the standard have become apparent but since its publication, no revision and no maintenance has been carried out.
Edit intent: coherence
Original:  Several standard compliant compilers have since been developed of which at least five remain available and at least three are being actively maintained . Meanwhile, various deficiencies of the standard have become apparent but since its publication, no revision and no maintenance has been carried out.
Revised:  Several standard compliant compilers have since been developed of which at least five remain available of which at least three are being actively maintained . Meanwhile, various deficiencies of the standard have become apparent but since its publication, no revision and no maintenance has been carried out.
Edit intent: coherence
Original:  Negative circular masks are employed to perform dual work , i.e., to decide material states of each element and also, to generate rigid contact surfaces.
Revised:  Negative circular masks are employed to perform dual task , i.e., to decide material states of each element and also, to generate rigid contact surfaces.
Edit intent: clarity
Original:  Each mask is characterized by five design variables, which are mutated by a zero-order based hill-climber optimizer.
Revised:  Each mask is characterized by five design variables, which are mutated by a zero-order based hill-climbing optimizer.
Edit intent: fluency
Original:  The nonlinear mechanical equilibrium equations are solved using the Newton-Raphson method.
Revised:  Nonlinear mechanical equilibrium equations are solved using the Newton-Raphson method.
Edit intent: clarity
Original:  The performance of the deformed profiles is verified using a commercial software.
Revised:  Performance of the deformed profiles is verified using a commercial software.
Edit intent: clarity
Original:  The effect of frictional contact surface on the actual profile is also studied .
Revised:  The effect of frictional contact surface on the actual profile is also studied 
Edit intent: fluency
Original:  The effects of later interventions remain unclear . Liberalizations of measures did not induce a re-increase of infections.
Revised:  The effects of later interventions cannot be detected clearly . Liberalizations of measures did not induce a re-increase of infections.
Edit intent: clarity
Original:  The study also exhibits three methodological challenges with respect to assessing of interventions : a) the estimation of true infection dates , b) the usage of several indicators and c) the influence of test volume .
Revised:  The study also exhibits three methodological challenges with respect to assessing of interventions is impeded by the estimation of true infection dates , b) the usage of several indicators and c) the influence of test volume .
Edit intent: coherence
Original:  The study also exhibits three methodological challenges with respect to assessing of interventions : a) the estimation of true infection dates , b) the usage of several indicators and c) the influence of test volume .
Revised:  The study also exhibits three methodological challenges with respect to assessing of interventions : a) the estimation of true infection dates and the influence of test volume .
Edit intent: clarity
Original:  Numerical examples are also presented to illustrate some theoretical conclusions and financial insights.
Revised:  Numerical examples are also presented to illustrate some theoretical results and financial insights.
Edit intent: clarity
Original: This paper studies an infinite horizon optimal consumption problem under exponential utility, together with non-negativity constraint on consumption rate and a reference point to the past consumption peak .
Revised: This paper studies the infinite horizon optimal consumption problem under exponential utility, together with non-negativity constraint on consumption rate and a reference point to the past consumption peak .
Edit intent: fluency
Original: This paper studies an infinite horizon optimal consumption problem under exponential utility, together with non-negativity constraint on consumption rate and a reference point to the past consumption peak .
Revised: This paper studies an infinite horizon optimal consumption with a path-dependent reference under the exponential utility .
Edit intent: clarity
Original:  To overcome its path-dependent nature, the consumption running maximum process is chosen as an auxiliary state process that renders the value function two dimensional depending on the wealth variable x and the reference variable h.
Revised:  The consumption running maximum process is chosen as an auxiliary state process that renders the value function two dimensional depending on the wealth variable x and the reference variable h.
Edit intent: coherence
Original:  The associated Hamilton-Jacobi-Bellman (HJB) equation is expressed in the piecewise manner across different regions to take into account  constraints.
Revised:  The associated Hamilton-Jacobi-Bellman (HJB) equation is expressed in the piecewise manner across different regions to take into account all constraints.
Edit intent: clarity
Original:  By employing the dual transform and smooth-fit principle,  the classical solution of the HJB equation is obtained in an analytical form, which in turn provides the feedback optimal investment and consumption .
Revised:  By employing the dual transform and smooth-fit principle, the HJB equation is obtained in an analytical form, which in turn provides the feedback optimal investment and consumption .
Edit intent: clarity
Original:  By employing the dual transform and smooth-fit principle,  the classical solution of the HJB equation is obtained in an analytical form, which in turn provides the feedback optimal investment and consumption .
Revised:  By employing the dual transform and smooth-fit principle, the classical solution of the HJB equation and the feedback optimal investment and consumption .
Edit intent: clarity
Original:  Numerical examples are also presented to illustrate some theoretical results and financial insights .
Revised:  Numerical examples are also presented to illustrate some financial implications .
Edit intent: clarity
Original: Spiking neural networks are nature's solution for parallel information processing with high temporal precision at a low metabolic energy cost.
Revised: To rapidly process temporal information at a low metabolic energy cost.
Edit intent: clarity
Original:  To that end , biological neurons integrate inputs as an analog sum and communicate their outputs digitally as spikes, i.e., sparse binary events in time.
Revised:  To that end , biological neurons integrate inputs as an analog sum but communicate with spikes, binary events in time.
Edit intent: clarity
Original:  Nevertheless, emulating high-performing spiking networks on such hardware remains a significant challenge due to device-mismatch and the lack of efficient training algorithms.
Revised:  However, instantiating high-performing spiking networks on such hardware remains a significant challenge due to device-mismatch and the lack of efficient training algorithms.
Edit intent: clarity
Original:  Nevertheless, emulating high-performing spiking networks on such hardware remains a significant challenge due to device-mismatch and the lack of efficient training algorithms.
Revised:  Nevertheless, emulating high-performing spiking networks on such hardware remains a significant challenge due to device mismatch and the lack of efficient training algorithms.
Edit intent: fluency
Original:  In summary, our work sets several new benchmarks for low-energy spiking network processing on analog neuromorphic substrates and constitutes an important step toward on-chip learning  .
Revised:  In summary, our work sets several new benchmarks for low-energy spiking network processing on analog neuromorphic hardware and paves the way for future on-chip learning .
Edit intent: clarity
Original:  In summary, our work sets several new benchmarks for low-energy spiking network processing on analog neuromorphic substrates and constitutes an important step toward on-chip learning  .
Revised:  In summary, our work sets several new benchmarks for low-energy spiking network processing on analog neuromorphic substrates and constitutes an important step toward on-chip learning algorithms .
Edit intent: clarity
Original:  We give novel formulas based on Markov Chain analysis to compute the distribution of opinions at any time and speed of convergence to stationary equilibrium  .
Revised:  We give novel formulas based on Markov Chain analysis to compute the distribution of opinions over time and speed of convergence to stationary equilibrium .
Edit intent: clarity
Original: We address the phenomenon of sedimentation of opinions in networks and investigate how stubborn agents who never change their minds ("zealots") can influence the opinion of a social group.
Revised: We explore a method to influence or even control the diversity of opinions within a polarised social group.
Edit intent: clarity
Original:  This is done via the voter model in which users are divided in two camps and repeatedly update their opinions based on others they connect with.
Revised:  We leverage the voter model in which users are divided in two camps and repeatedly update their opinions based on others they connect with.
Edit intent: clarity
Original:  This is done via the voter model in which users are divided in two camps and repeatedly update their opinions based on others they connect with.
Revised:  This is done via the voter model in which users hold binary opinions and repeatedly update their opinions based on others they connect with.
Edit intent: clarity
Original:  This is done via the voter model in which users are divided in two camps and repeatedly update their opinions based on others they connect with.
Revised:  This is done via the voter model in which users are divided in two camps and repeatedly update their beliefs based on others they connect with.
Edit intent: clarity
Original:  As an example of application we discuss a strategy to mitigate the polarisation of opinions in the presence of a backfire effect .
Revised:  As an example of application we discuss a strategy to inject zealots into a polarised network in order to shift the average opinion towards any target value. We account for the possible presence of a backfire effect .
Edit intent: clarity
Original: In this work, we present an extension of the genetic algorithm (GA) which exploits the  active subspaces (AS) property to evolve the individuals on a lower dimensional space.
Revised: In this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) to evolve the individuals on a lower dimensional space.
Edit intent: clarity
Original:  Thus, complex and high-dimensional functions may result intractable with the standard algorithm.
Revised:  Thus, complex and high-dimensional functions may result extremely demanding (from computational viewpoint) to optimize with the standard algorithm.
Edit intent: clarity
Original: Public sentiment (the opinion, attitude or feeling that the publicexpresses ) is a factor of interest for government, as it directly influences the implementation of policies.
Revised: Public sentiment (the opinions, attitudes or feelings expressed by the public ) is a factor of interest for government, as it directly influences the implementation of policies.
Edit intent: clarity
Original:  In this paper , we collect streaming data using the Twitter API starting from the COVID-19 outbreak in the Netherlands in February 2020, and track Dutch general public reactions on governmental measures and announcements.
Revised:  In this context , we collect streaming data using the Twitter API starting from the COVID-19 outbreak in the Netherlands in February 2020, and track Dutch general public reactions on governmental measures and announcements.
Edit intent: clarity
Original:  We also identify public attitudes towards the Dutch policy on wearing face masks in a case study .
Revised:  We also identify public attitudes towards the Dutch policy on wearing face masks .
Edit intent: clarity
Original: Collaborative multi-agent reinforcement learning (MARL) as a specific category of reinforcement learning provides effective results with agents learning from their observations, received rewards, and internal interactions between agents.
Revised: Reinforcement learning provides effective results with agents learning from their observations, received rewards, and internal interactions between agents.
Edit intent: clarity
Original:  However, centralized learning methods with a joint global policy in a highly dynamic environment present unique challenges in dealing with large amounts of information.
Edit intent: coherence
Original:  The first innovation is the introduction of a new open-source MARL framework, called COGMENT, to unite humans and agents in real-time complex dynamic systems and efficiently leverage their interactions as a source of learning.
Revised:  The first innovation is the introduction of a new open-source MARL framework, called COGMENT, to efficiently leverage human and agent interactions as a source of learning.
Edit intent: clarity
Original:  For the first time, we show a physics-based virtual character performing highly agile ballet dance moves such as pirouette, arabesque and jet\'e.
Revised:  Notably, we showcase a physics-based virtual character performing highly agile ballet dance moves such as pirouette, arabesque and jet\'e.
Edit intent: coherence
Original:  We demonstrate the validity of the approach on several synthetic datasets and on calcium recordings from the ellipsoid body of Drosophila melanogaster .
Revised:  We demonstrate the validity of the approach on several synthetic datasets , as well as on calcium recordings from the ellipsoid body of Drosophila melanogaster .
Edit intent: clarity
Original:  This circuit is known to encode head direction, and mGPLVM correctly recovers the ring topology expected from a neural population representing a single angular variable.
Revised:  This circuit is known to encode head direction, and mGPLVM correctly recovers the ring topology expected from neural populations representing a single angular variable.
Edit intent: fluency
Original:  Experiments show that our algorithm is able to quickly compute very close approximations of Nash equilibrium strategies for this game.
Revised:  Experiments show that our algorithm is able to quickly compute close approximations of Nash equilibrium strategies for this game.
Edit intent: clarity
Original:  However, solving continuous games---in which the pure strategy space is (potentially uncountably) infinite---is far more challenging.
Revised:  However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite---is far more challenging.
Edit intent: fluency
Original:  However, solving continuous games---in which the pure strategy space is (potentially uncountably) infinite---is far more challenging.
Revised:  However, solving continuous games---in which the pure strategy space is (potentially uncountably) infinite -- is far more challenging.
Edit intent: fluency
Original:  We present a new algorithm for computing Nash equilibrium strategies in continuous games.
Revised:  We present a new algorithm for approximating Nash equilibrium strategies in continuous games.
Edit intent: clarity
Original:  We present a new algorithm for approximating Nash equilibrium strategies in continuous games.
Revised:  We present a new algorithm for approximating Nash equilibrium strategies in continuous games.
Edit intent: fluency
Original:  In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games of imperfect information.
Revised:  In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games with imperfect information.
Edit intent: clarity