wanyu/IteraTeR_v2 huggingface dataset:
Original: Networks of model neurons with balanced recurrent excitation and inhibition produce chaotic spiking activity that is irregular and asynchronous  .
Revised: Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous .
Edit intent: clarity
Original: Networks of model neurons with balanced recurrent excitation and inhibition produce chaotic spiking activity that is irregular and asynchronous  .
Revised: Networks of model neurons with balanced recurrent excitation and inhibition produce chaotic spiking activity that is irregular and asynchronous spiking activity .
Edit intent: clarity
Original:  The chaotic spatiotemporal dynamics of balanced networks offer new challenges in the statistical mechanics of complex systems.
Revised:  The spatiotemporal dynamics of balanced networks offer new challenges in the statistical mechanics of complex systems.
Edit intent: clarity
Original:  Constrained problems with a relaxation of order two may contain up to a hundred variables.
Revised:  Constrained problems with a relaxation of order two may contain up to hundreds of variables.
Edit intent: fluency
Original:  We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of resulting relaxation . Constrained problems with a relaxation of order one may contain up to hundreds of variables.
Revised:  We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of the resulting relaxations . Constrained problems with a relaxation of order one may contain up to hundreds of variables.
Edit intent: fluency
Original:  We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of resulting relaxation . Constrained problems with a relaxation of order one may contain up to hundreds of variables.
Revised:  We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of resulting relaxation . Constrained problems with a relaxation of order one may contain up to a hundred variables.
Edit intent: fluency
Original:  The implementation is available in C++ and Python.
Revised:  The implementation is available in Python.
Edit intent: coherence
Original:  We apply a distributed string mining framework to efficiently extract all informative sequence k-mers from a pool of metagenomic samples , and use them to measure the dissimilarity between two samples.
Revised:  We apply a distributed string mining framework to efficiently extract all informative sequence k-mers from a pool of metagenomic samples and use them to measure the dissimilarity between two samples.
Edit intent: fluency
Original:  We evaluate the performance of the proposed approach on two human gut metagenome data sets and observe significant enrichment for diseased  samples in results of queries with another diseased sample .
Revised:  We evaluate the performance of the proposed approach on two human gut metagenome data sets and observe significant enrichment for diseased gut samples in results of queries with another diseased sample .
Edit intent: clarity
Original:  Based on a linear-noise approximation  we calculate the characteristic length scale of these patterns.
Revised:  Based on a linear-noise approximation , we calculate the characteristic length scale of these patterns.
Edit intent: fluency
Original:  We demonstrate the applicability of this approach in a simple model of opinion dynamics, a model in evolutionary game theory with a time-dependent fitness structure, and in a model of cell differentiation.
Revised:  We demonstrate the applicability of this approach in a simple model of opinion dynamics, a model in evolutionary game theory with a time-dependent fitness structure, and a model of cell differentiation.
Edit intent: fluency
Original:  In further numerical work  we observe a similar phenomenon when the symmetry-breaking bifurcation is triggered by population growth.
Revised:  In further numerical work , we observe a similar phenomenon when the symmetry-breaking bifurcation is triggered by population growth.
Edit intent: fluency
Original: The Partner Units Problem (PUP) is a graph theoretical problem with various industrial application fields like surveillance, electrical engineering, computer networks or railway safety .
Revised: The partner units problem (PUP) is a graph theoretical problem with various industrial application fields like surveillance, electrical engineering, computer networks or railway safety .
Edit intent: fluency
Original:  Furthermore  we present QuickPup, a heuristic search algorithm for PUP instances which outperforms all state-of-the-art solving approaches and is already used in industrial configuration environments.
Revised:  Furthermore , we present QuickPup, a heuristic search algorithm for PUP instances which outperforms all state-of-the-art solving approaches and is already used in industrial configuration environments.
Edit intent: fluency
Original:  Furthermore  we present QuickPup, a heuristic search algorithm for PUP instances which outperforms all state-of-the-art solving approaches and is already used in industrial configuration environments.
Revised:  Furthermore we present QuickPup, a heuristic search algorithm for PUP instances which outperforms all state-of-the-art solving approaches and which is already in use in real world industrial configuration environments.
Edit intent: clarity
Original: Using the growth of population in Australia over the past 10,000 years it is illustrated here how an illusion created by hyperbolic distributions may lead easily to incorrect conclusions.
Revised: Using the growth of population in Australia in the past 10,000 years it is illustrated here how an illusion created by hyperbolic distributions may lead easily to incorrect conclusions.
Edit intent: fluency
Original:  Contrary to the published claim, there was no change in the mechanism of growth of  ancient human population in Australia around 5000 years before present (BP).
Revised:  Contrary to the published claim, there was no change in the mechanism of growth of the ancient human population in Australia around 5000 years before present (BP).
Edit intent: fluency
Original: The target of this paper is consider to model the risky asset price in the Knightian uncertain financial market , and pricing the upper (bid) and lower (ask ) prices of the uncertain risk.
Revised: The target of this paper is to consider model the risky asset price in the Knightian uncertain financial market , and pricing the upper (bid) and lower (ask ) prices of the uncertain risk.
Edit intent: fluency
Original: The target of this paper is consider to model the risky asset price in the Knightian uncertain financial market , and pricing the upper (bid) and lower (ask ) prices of the uncertain risk.
Revised: The target of this paper is consider to model the risky asset price on the financial market under the Knightian uncertainty , and pricing the upper (bid) and lower (ask ) prices of the uncertain risk.
Edit intent: clarity
Original: The target of this paper is consider to model the risky asset price in the Knightian uncertain financial market , and pricing the upper (bid) and lower (ask ) prices of the uncertain risk.
Revised: The target of this paper is consider to model the risky asset price in the Knightian uncertain financial market , and pricing the ask and bid prices of the uncertain risk.
Edit intent: clarity
Original:  The ] basic risky asset price model  we construct here is  drift uncertain and volatility uncertain , we describe such model by using general G-Brownian motion and call it as G-asset price system.
Revised:  The ] basic risky asset price model we construct here is drift uncertain and volatility uncertain . We describe such model by using general G-Brownian motion and call it as G-asset price system.
Edit intent: fluency
Original:  We present the uncertain risk premium which is distributed with Max distributionN( \mu ,%DIFDELCMD < \mu]%%% ,\{0\ closed form of bid and ask prices of the European contingent claim against  risky asset with G-asset price system , and give the bid and ask prices are the viscosity solution to nonlinear HJB .
Revised:  We present the uncertain risk premium which is distributed with Max distributionN( ,%DIFDELCMD < \mu]%%% ,\{0\ closed form of bid and ask prices of the European contingent claim against risky asset with G-asset price system , and give the bid and ask prices are the viscosity solution to nonlinear HJB .
Edit intent: fluency
Original:  We present the uncertain risk premium which is distributed with Max distributionN( \mu ,%DIFDELCMD < \mu]%%% ,\{0\ closed form of bid and ask prices of the European contingent claim against  risky asset with G-asset price system , and give the bid and ask prices are the viscosity solution to nonlinear HJB .
Revised:  We present the uncertain risk premium which is distributed with Max distributionN( \mu %DIFDELCMD < \mu]%%% ,\{0\ closed form of bid and ask prices of the European contingent claim against risky asset with G-asset price system , and give the bid and ask prices are the viscosity solution to nonlinear HJB .
Edit intent: fluency
Original:  We present the uncertain risk premium which is distributed with Max distributionN( \mu ,%DIFDELCMD < \mu]%%% ,\{0\ closed form of bid and ask prices of the European contingent claim against  risky asset with G-asset price system , and give the bid and ask prices are the viscosity solution to nonlinear HJB .
Revised:  We present the uncertain risk premium which is distributed with Max distributionN( \mu ,%DIFDELCMD < \mu]%%% ,\{0\ closed form of bid-ask price of the European contingent claim against risky asset with G-asset price system , and give the bid and ask prices are the viscosity solution to nonlinear HJB .
Edit intent: fluency
Original:  We present the uncertain risk premium which is distributed with Max distributionN( \mu ,%DIFDELCMD < \mu]%%% ,\{0\ closed form of bid and ask prices of the European contingent claim against  risky asset with G-asset price system , and give the bid and ask prices are the viscosity solution to nonlinear HJB .
Revised:  We present the uncertain risk premium which is distributed with Max distributionN( \mu ,%DIFDELCMD < \mu]%%% ,\{0\ closed form of bid and ask prices of the European contingent claim against risky asset with G-asset price system , and give the bid and ask prices are the viscosity solutions to the nonlinear HJB equations .
Edit intent: clarity
Original: Furthermore, we consider the main part of this paper, i.e., consider the risky asset on  uncertain financial market with the price fluctuation as continuous path .
Revised: Furthermore, we consider the main part of this paper, i.e., consider the risky asset on uncertain financial market with the price fluctuation shows as continuous trajectories .
Edit intent: clarity
Original:  We give examples, such as G-Markovian processes and  fractional G-Brownian   , satisfying the G-conditional full support condition.
Revised:  We give examples, such as G-Markovian processes and fractional G-Brownian motion , satisfying the G-conditional full support condition.
Edit intent: clarity
Original:  For sufficiently large density and self-propulsion, the system is found to phase separate into a dilute and a dense phase  .
Revised:  Our simulations reveal a phase separation into a dilute and a dense phase .
Edit intent: clarity
Original:  The packing fraction of dense phase may approach random close packing at high activity, but nevertheless it remains a fluid.
Revised:  The packing fraction of the dense phase approaches random close packing at high activity, but nevertheless it remains a fluid.
Edit intent: clarity
Original:  The packing fraction of dense phase may approach random close packing at high activity, but nevertheless it remains a fluid.
Revised:  The packing fraction of dense phase may approach random close packing at high activity, yet the system remains fluid.
Edit intent: clarity
Original:  Although polar order is absent, long-lived cooperative motion with nearly scale-free correlations is detected for systems with a density close to or above the glass transition density in passive systems.
Revised:  Although no alignment mechanism exists in this model, we find long-lived cooperative motion with nearly scale-free correlations is detected for systems with a density close to or above the glass transition density in passive systems.
Edit intent: clarity
Original:  Although polar order is absent, long-lived cooperative motion with nearly scale-free correlations is detected for systems with a density close to or above the glass transition density in passive systems.
Revised:  Although polar order is absent, long-lived cooperative motion with nearly scale-free for systems with a density close to or above the glass transition density in passive systems.
Edit intent: clarity
Original:  Although polar order is absent, long-lived cooperative motion with nearly scale-free correlations is detected for systems with a density close to or above the glass transition density in passive systems.
Revised:  Although polar order is absent, long-lived cooperative motion with nearly scale-free correlations is detected for systems with densities close to or above the glass transition density in passive systems.
Edit intent: fluency
Original:  Although polar order is absent, long-lived cooperative motion with nearly scale-free correlations is detected for systems with a density close to or above the glass transition density in passive systems.
Revised:  Although polar order is absent, long-lived cooperative motion with nearly scale-free correlations is detected for systems with a density close to or above the glass transition density of passive systems.
Edit intent: clarity
Original: Most decision theories  including expected utility theory, rank dependent utility theory and the cumulative prospect theory  assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received.
Revised: Most decision theories including expected utility theory, rank dependent utility theory and cumulative prospect theory assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received.
Edit intent: fluency
Original: Most decision theories  including expected utility theory, rank dependent utility theory and the cumulative prospect theory  assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received.
Revised: Most decision theories including expected utility theory, rank dependent utility theory and the cumulative prospect theory assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received.
Edit intent: fluency
Original:  Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this  is often at odds with the needs of many investors.
Revised:  Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors.
Edit intent: clarity
Original:  We introduce a framework for portfolio selection that permits to deal with state-dependent preferences .
Revised:  We introduce a framework for portfolio selection within which state-dependent preferences .
Edit intent: clarity
Original:  Given a maximal node degree, \delta, and no access to external reference, we consider the problem of the existence of collision-free self-stabilizing TDMA algorithms that have constant communication delay of \tau .
Revised:  Given a maximal node degree, \delta, and no access to external reference, we consider the problem of collision-free self-stabilizing TDMA algorithms that have constant communication delay of \tau .
Edit intent: clarity
Original:  Given a maximal node degree, \delta, and no access to external reference, we consider the problem of the existence of collision-free self-stabilizing TDMA algorithms that have constant communication delay of \tau .
Revised:  Given a maximal node degree, \delta, and no access to external reference, we consider the problem of the existence of collision-free self-stabilizing TDMA algorithms that use constant frame size .
Edit intent: clarity
Original:  We observe the bound relevance to the bandwidth utilization when the network topology is a planar graph.
Edit intent: coherence
Original:  As a complement to this lower bound, we focus on proving the existence of probabilistic collision-free self-stabilizing TDMA algorithms that have constant communication delay of \tau.
Revised:  As a complement to this lower bound, we focus on proving the existence of collision-free self-stabilizing TDMA algorithms that have constant communication delay of \tau.
Edit intent: clarity
Original: Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been claimed that operating at criticality entails functional advantages, such as optimal computational capabilities, memory, and large dynamical ranges.
Revised: Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational capabilities, memory, and large dynamical ranges.
Edit intent: clarity
Original:  An apparent paradox is that criticality requires a high degree of fine tuning to emerge and hence, self-organizing mechanisms need to be invoked.
Revised:  As critical behavior requires a high degree of fine tuning to emerge and hence, self-organizing mechanisms need to be invoked.
Edit intent: clarity
Original:  An apparent paradox is that criticality requires a high degree of fine tuning to emerge and hence, self-organizing mechanisms need to be invoked.
Revised:  An apparent paradox is that criticality requires a high degree of fine tuning to emerge , some type of self-tuning mechanism needs to be invoked.
Edit intent: clarity
Original:  Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics -- to a Griffiths phase.
Revised:  Here we show that, taking into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics -- to a Griffiths phase.
Edit intent: clarity
Original:  Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics -- to a Griffiths phase.
Revised:  Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the singular critical point is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics -- to a Griffiths phase.
Edit intent: clarity
Original:  Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics -- to a Griffiths phase.
Revised:  Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds --in the jargon of statistical mechanics -- to a Griffiths phase.
Edit intent: fluency
Original:  Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics -- to a Griffiths phase.
Revised:  Here we show that, taking explicitly into account the complex hierarchical-modular architecture of cortical networks, the standard critical point picture is replaced by an extended critical-like region which corresponds -- in the jargon of statistical mechanics-- to a Griffiths phase.
Edit intent: fluency
Original:  Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical neural networks such as those of C. elegans and the human connectome  .
Revised:  Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical brain networks such as those of C. elegans and the human connectome .
Edit intent: clarity
Original:  Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical neural networks such as those of C. elegans and the human connectome  .
Revised:  Using computational and analytical approaches, we find Griffiths phases in synthetic hierarchical networks and also in empirical neural networks such as the human connectome .
Edit intent: clarity
Original:  Stretched critical regions, stemming from structural disorder, yield optimal functionality in a generic way, facilitating the task of self-organizing, adaptive  and evolutionary mechanisms selecting for criticality.
Revised:  Stretched critical regions, stemming from structural disorder, yield enhanced functionality in a generic way, facilitating the task of self-organizing, adaptive and evolutionary mechanisms selecting for criticality.
Edit intent: clarity
Original:  Stretched critical regions, stemming from structural disorder, yield optimal functionality in a generic way, facilitating the task of self-organizing, adaptive  and evolutionary mechanisms selecting for criticality.
Revised:  Stretched critical regions, stemming from structural disorder, yield optimal functionality in a generic way, facilitating the task of self-organizing, adaptive , and evolutionary mechanisms selecting for criticality.
Edit intent: fluency
Original: We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing {\Gamma} of G in the plane such that the edges of S are not crossed in \Gamma  ?
Revised: We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing {\Gamma} of G in the plane such that the edges of S are not crossed in \Gamma ?
Edit intent: fluency
Original: We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing {\Gamma} of G in the plane such that the edges of S are not crossed in \Gamma  ?
Revised: We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing {\Gamma} of G in the plane such that the edges of S are not crossed in \Gamma by any edge of G ?
Edit intent: clarity
Original:  in this setting  different trade-offs between  number of bends and drawing area are given .
Revised:  in this setting we discuss different trade-offs between number of bends and drawing area are given .
Edit intent: clarity
Original:  in this setting  different trade-offs between  number of bends and drawing area are given .
Revised:  in this setting different trade-offs between the number of bends and drawing area are given .
Edit intent: fluency
Original:  in this setting  different trade-offs between  number of bends and drawing area are given .
Revised:  in this setting different trade-offs between number of bends and the required drawing area .
Edit intent: clarity