wanyu/IteraTeR_full_sent huggingface dataset:
Original: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility results hold without the assumption of quasi-linear utility in  transfers.
Revised: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers.
Edit intent: fluency
Original: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility results hold without the assumption of quasi-linear utility in  transfers.
Revised: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility results hold without the assumption of quasi-linear utility in transfers. While our results are developed in a trading network model, they also imply analogous (and new) results for exchange economies with combinatorial demand and for two-sided matching markets with transfers.
Edit intent: meaning-changed
Original: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Revised: Several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Edit intent: clarity
Original: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Revised: We establish several structural results for the set of competitive equilibria in trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Edit intent: clarity
Original: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Revised: We establish several structural results for the set of competitive equilibria in bilateral trading networks with frictions are established : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Edit intent: clarity
Original: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Revised: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Edit intent: clarity
Original: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold without the assumption of quasi-linear utility in transfers .
Revised: We establish several structural results for the set of competitive equilibria in bilateral trading networks with transfers in the case of imperfectly transferable utility and frictions : The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, compactness of the set of equilibria and a group-incentive-compatibility result hold with imperfectly transferable utility and in the presence of frictions .
Edit intent: clarity
Original:  The algorithm is a sequential Monte Carlo algorithm that approximates numerically the posterior distribution with a set of weighted samples . Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios , correlated sources.
Revised:  Given the Fourier Transform of the data at one or multiple frequencies and/or trials, the algorithm approximates numerically the posterior distribution with a set of weighted samples . Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios , correlated sources.
Edit intent: meaning-changed
Original:  The algorithm is a sequential Monte Carlo algorithm that approximates numerically the posterior distribution with a set of weighted samples . Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios , correlated sources.
Revised:  The algorithm is a sequential Monte Carlo algorithm that approximates numerically the posterior distribution with Monte Carlo techniques . Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios , correlated sources.
Edit intent: clarity
Original:  The algorithm is a sequential Monte Carlo algorithm that approximates numerically the posterior distribution with a set of weighted samples . Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios , correlated sources.
Revised:  The algorithm is a sequential Monte Carlo algorithm that approximates numerically the posterior distribution with a set of weighted samples . Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios and correlated sources.
Edit intent: fluency
Original:  The two methods provide similar general pictures , however, the posterior distributions of the Bayesian approach contain richer information . Conclusions: The Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.
Revised:  The two methods provide similar general pictures ; the posterior distributions of the Bayesian approach contain richer information . Conclusions: The Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.
Edit intent: coherence
Original:  The two methods provide similar general pictures , however, the posterior distributions of the Bayesian approach contain richer information . Conclusions: The Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.
Revised:  The two methods provide similar general pictures , however, the posterior distributions of the Bayesian approach contain much richer information at the price of a higher computational cost . Conclusions: The Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.
Edit intent: meaning-changed
Original:  We tackle the challenge by introducing the so-called continuous-time Gaussian process dynamical model (GPDM) , based on Gaussian process framework that has gained popularity in nonlinear regression problems arising in machine learning.
Revised:  We tackle the challenge by introducing the so-called continuous-time Gaussian process dynamical model , based on Gaussian process framework that has gained popularity in nonlinear regression problems arising in machine learning.
Edit intent: clarity
Original: We present an accurate and computationally efficient method , based on Chebyshev Spectral Decomposition, to stochastically compute the Initial Margin of financial products within a Monte Carlo simulation , via sensitivities simulation.
Revised: We present two methods , based on Chebyshev Spectral Decomposition, to stochastically compute the Initial Margin of financial products within a Monte Carlo simulation , via sensitivities simulation.
Edit intent: meaning-changed
Original: We present an accurate and computationally efficient method , based on Chebyshev Spectral Decomposition, to stochastically compute the Initial Margin of financial products within a Monte Carlo simulation , via sensitivities simulation.
Revised: We present an accurate and computationally efficient method , based on Chebyshev tensors, to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation , via sensitivities simulation.
Edit intent: meaning-changed
Original: We present an accurate and computationally efficient method , based on Chebyshev Spectral Decomposition, to stochastically compute the Initial Margin of financial products within a Monte Carlo simulation , via sensitivities simulation. This methodology is compared in terms of accuracy, efficiency, and implementation /maintenance costs with common techniques used for the same purpose, such as amortisation-based, regression-based and Adjoint Algorithmic Differentiation.
Revised: We present an accurate and computationally efficient method , based on Chebyshev Spectral Decomposition, to stochastically compute the Initial Margin of financial products within a Monte Carlo simulation . These methods are implemented and run in a Monte Carlo engine to compute Dynamic Initial Margin as defined by ISDA (SIMM). We show that the levels of accuracy, efficiency, and implementation /maintenance costs with common techniques used for the same purpose, such as amortisation-based, regression-based and Adjoint Algorithmic Differentiation.
Edit intent: meaning-changed
Original:  This methodology is compared in terms of accuracy, efficiency, and implementation /maintenance costs with common techniques used for the same purpose, such as amortisation-based, regression-based and Adjoint Algorithmic Differentiation. Measured in terms of these criteria, the methodologies based on Chebyshev interpolants offer an optimal solution and set a new benchmark standard for the industry0pt%DIFAUXCMD ) and Deep Neural Nets (\mbox{%DIFAUXCMD DNNs IM}0pt%DIFAUXCMD )} .
Revised:  This methodology is compared in terms of accuracy, speed and implementation efforts obtained, compared to the benchmark (DIM obtained calling pricing functions such as are found in risk engines), are better than those obtained by alternative methods presented in the literature, such as regressions (\mbox{%DIFAUXCMD Zhu Chan0pt%DIFAUXCMD ) and Deep Neural Nets (\mbox{%DIFAUXCMD DNNs IM}0pt%DIFAUXCMD )} .
Edit intent: clarity
Original:  Using coarse-grained simulations and elasticity theory, we show that the potential for direction-dependent membrane curvature sensing is limited to asymmetric proteins, dimers, and tetramers  .
Revised:  Using coarse-grained simulations and elasticity theory, we show that the potential for direction-dependent membrane curvature sensing is limited to asymmetric proteins, dimers, and tetramers , and argue that one should expect this anisotropy to be strongest for dimers .
Edit intent: meaning-changed
Original:  Heart rate variability (HRV) derived from electrocardiogram (ECG) has been a powerful tool to identify alterations in ANS due to a plethora of pathophysiological conditions, including psychological ones such as depression. ECG-derived HRV thus carries a yet to be explored potential to be used as a diagnostic and follow-up biomarker of ASD. However, few studies have explored this potential.
Edit intent: coherence
Original:  In a cohort of boys (ages 8 - 11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Revised:  In a cohort of school-aged children with and without ASD (n=18), we tested a set of linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Edit intent: meaning-changed
Original:  11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Revised:  11 years) with (n=18) and without ASD , we test a set of linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Edit intent: coherence
Original:  11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Revised:  11 years) with (n=18) and without ASD (n=18), we tested a set of alternative linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Edit intent: clarity
Original:  11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Revised:  11 years) with (n=18) and without ASD (n=18), we tested a set of linear and nonlinear HRV measures, including phase rectified signal averaging , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Edit intent: clarity
Original:  11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Revised:  11 years) with (n=18) and without ASD (n=18), we tested a set of linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of resting ECG, for associations with ASD vs. other psychiatric conditions. Using machine learning, we identify HRV measures derived from time, frequency and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Edit intent: clarity
Original:  11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Revised:  11 years) with (n=18) and without ASD (n=18), we tested a set of linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency , and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Edit intent: fluency
Original:  11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Revised:  11 years) with (n=18) and without ASD (n=18), we tested a set of linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency and geometric signal-analytical domains that (1) identify children with ASD relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) .
Edit intent: meaning-changed
Original:  11 years) with (n=18) and without ASD (n=18), we tested a set of  linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency  and geometric signal-analytical domains which are changed in ASD children relative to peers without ASD and correlate to psychometric scores (p<0.05 for each) . Receiver operating curves area ranged between 0.71 - 0.74 for each HRV measure. Despite being a small cohort lacking external validation, these promising preliminary results warrant larger prospective validation studies.
Revised:  11 years) with (n=18) and without ASD (n=18), we tested a set of linear and nonlinear HRV measures, including phase rectified signal averaging (PRSA) , applied to a segment of ECG collected under resting conditions for their predictive properties of ASD . We identified HRV measures derived from time, frequency and geometric signal-analytical domains which are changed in ASD children relative to peers with receiver operating curve area of .89, and (2) differentiate such children from those with conduct problems or depression. Despite the small cohort and lack of prospective external validation, these promising preliminary results warrant larger prospective validation studies.
Edit intent: meaning-changed
Original:  There is C such that every 2-dimensional simplicial complex having n vertices and embeddable into \mathbb R^4 contains less than Cn^{ 5 /3} simplices of dimension 2.
Revised:  There is C such that every 2-dimensional simplicial complex having n vertices and embeddable into \mathbb R^4 contains less than Cn^{ 8 /3} simplices of dimension 2.
Edit intent: meaning-changed
Original:  The tax rate minimizes both the asymptotic mean and variance of the underlying posterior unemployment rate ; it also stimulates employment , boosts productivity, and mitigates income inequality. One could apply the  distribution rule and valuation approach to areas other than labor markets .
Revised:  The tax rate minimizes both the asymptotic mean and variance of the underlying posterior unemployment rate . The allocation rule stimulates employment and boosts productivity. Under some symmetry assumptions, we find that an unemployed person should also enjoy equivalent employment benefits, and the tax rate goes with this welfare equality. The tool employed is the cooperative game theory in which we assume a large number of players. The players are randomly bi-partitioned, and the payoff varies with the partition. Thus, one could apply the distribution rule and valuation approach to areas other than labor markets .
Edit intent: meaning-changed