wanyu/IteraTeR_full_sent huggingface dataset:
Original:  For the equal-weights case, the upper and lower bounds coincide, which implies the heavy-traffic insensitivity of the expectation of the total number of flows .
Revised:  Our approach is Lyapunov-drift based, which is different from the widely used diffusion approximation approach. A key technique we develop is to construct a novel inner product in the state space, which then allows us to obtain a multiplicative type of state-space collapse in steady state .
Edit intent: meaning-changed
Original:  Furthermore, our state-space collapse result implies an interchange of limits as a by-product for the diffusion approximation by Vlasiou, Zhang and Zwart (2014) .
Revised:  Furthermore, our state-space collapse result implies an interchange of limits as a by-product for the diffusion approximation of the equal-weight case under phase-type file-size distributions, demonstrating the heavy-traffic insensitivity of the stationary distribution .
Edit intent: meaning-changed
Original: We study the asymptotic behavior of the persistent homology of i.i.d. samples from a d-Ahlfors regular measure --- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots  x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Revised: We %DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Edit intent: coherence
Original: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots  x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Revised: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% prove that the fractal dimension of a metric space equipped with an Ahlfors regular measure can be recovered from the persistent homology of random samples . Our main result is that if x_1,\ldots x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Edit intent: meaning-changed
Original: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots  x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Revised: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots , x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Edit intent: fluency
Original: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots  x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Revised: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots x_n are i.i.d.~samples from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Edit intent: meaning-changed
Original: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots  x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Revised: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots x_n are sampled from a d-Ahlfors regular measure on a metric space, and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Edit intent: clarity
Original: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots  x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimal spanning tree on x_1,\ldots,x_n:
Revised: -- one that satisfies uniform bounds of the form%DIFDELCMD < equation* 1{c} r^d \leq \mu \big(B_r\left(x\right)\big) \leq c r^d equation* %%% for some c>0, all x in the support of \mu, and all sufficiently small r . Our main result is that if x_1,\ldots x_n are sampled from a d-Ahlfors regular measure on \mathbb{R and E_\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimum spanning tree on x_1,\ldots,x_n:
Edit intent: fluency
Original:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\] %%% then%DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right) \approx n^{d-\alpha{d}}\] %%% \[E_\alpha\left(x_1,\ldots,x_n\right)=\sum_{e\in T\left(x_1,\ldots,x_n\right)} |e|^\alpha\,,\] \[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{\frac{d-\alpha}{d}}\] with high probability as n\rightarrow \infty.
Revised:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\] %%% %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right) \approx n^{d-\alpha{d}}\] %%% \[E_\alpha\left(x_1,\ldots,x_n\right)=\sum_{e\in T\left(x_1,\ldots,x_n\right)} |e|^\alpha\,,\] \[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{\frac{d-\alpha}{d}}\] with high probability as n\rightarrow \infty.
Edit intent: fluency
Original:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\] %%% then%DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right) \approx n^{d-\alpha{d}}\] %%% \[E_\alpha\left(x_1,\ldots,x_n\right)=\sum_{e\in T\left(x_1,\ldots,x_n\right)} |e|^\alpha\,,\] \[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{\frac{d-\alpha}{d}}\] with high probability as n\rightarrow \infty.
Revised:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\] %%% then%DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right) \approx n^{d-\alpha{d}}\] %%% \[E_\alpha\left(x_1,\ldots,x_n\right)=\sum_{e\in T\left(x_1,\ldots,x_n\right)} |e|^\alpha\,,\] then\[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{\frac{d-\alpha}{d}}\] with high probability as n\rightarrow \infty.
Edit intent: fluency
Original:  \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\]  We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher-dimensional persistent homology.
Revised:  In particular,\[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher-dimensional persistent homology.
Edit intent: coherence
Original:  \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\]  We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher-dimensional persistent homology.
Revised:  \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting. We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher-dimensional persistent homology.
Edit intent: meaning-changed
Original:  \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\]  We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher-dimensional persistent homology.
Revised:  \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] We also prove analogous results for weighted sums defined in terms of higher-dimensional persistent homology.
Edit intent: clarity
Original:  \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\]  We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher-dimensional persistent homology. As an application, we exhibit hypotheses under which the fractal dimension of a measure can be computed from the persistent homology of i.i.d. samples from that space, in a manner similar to that proposed in the experimental work of Adams et al. (2018) .
Revised:  \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher dimensional persistent homology .
Edit intent: meaning-changed
Original:  Our main result is that if x_1,\ldots, x_n are i.i.d. ~ samples from a d-Ahlfors regular measure on a metric space, and E  _\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimum spanning tree on x_1,\ldots,x_n:
Revised:  Our main result is that if x_1,\ldots, x_n are i.i.d. samples from a d-Ahlfors regular measure on a metric space, and E _\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimum spanning tree on x_1,\ldots,x_n:
Edit intent: fluency
Original:  Our main result is that if x_1,\ldots, x_n are i.i.d. ~ samples from a d-Ahlfors regular measure on a metric space, and E  _\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimum spanning tree on x_1,\ldots,x_n:
Revised:  Our main result is that if x_1,\ldots, x_n are i.i.d. ~ samples from a d-Ahlfors regular measure on a metric space, and E ^0 _\alpha\left(x_1,\ldots,x_n\right) denotes the \alpha-weight of the minimum spanning tree on x_1,\ldots,x_n:
Edit intent: meaning-changed
Original:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] %%% then%DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{d-\alpha{d}}\] %%% \[E_\alpha^0\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] \[C_1\leq n^{-d-\alpha{d}} E^0_\alpha\left(x_1,\ldots,x_n\right)\leq C_2\,\] with high probability as n\rightarrow \infty.
Revised:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] %%% %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{d-\alpha{d}}\] %%% \[E_\alpha^0\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] \[C_1\leq n^{-d-\alpha{d}} E^0_\alpha\left(x_1,\ldots,x_n\right)\leq C_2\,\] with high probability as n\rightarrow \infty.
Edit intent: fluency
Original:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] %%% then%DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{d-\alpha{d}}\] %%% \[E_\alpha^0\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] \[C_1\leq n^{-d-\alpha{d}} E^0_\alpha\left(x_1,\ldots,x_n\right)\leq C_2\,\] with high probability as n\rightarrow \infty.
Revised:  %DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] %%% then%DIFDELCMD < \[E_\alpha\left(x_1,\ldots,x_n\right)\approx n^{d-\alpha{d}}\] %%% \[E_\alpha^0\left(x_1,\ldots,x_n\right)=e\in T\left(x_1,\ldots,x_n\right) |e|^\alpha\,,\] then there exist constants 0<C_1\leq C_2 so that\[C_1\leq n^{-d-\alpha{d}} E^0_\alpha\left(x_1,\ldots,x_n\right)\leq C_2\,\] with high probability as n\rightarrow \infty.
Edit intent: meaning-changed
Original:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting  n^{-d-\alpha{d}} E^0_\alpha}\left(\right)  .
Revised:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the non-singular case to the fractal setting n^{-d-\alpha{d}} E^0_\alpha}\left(\right) .
Edit intent: meaning-changed
Original:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting  n^{-d-\alpha{d}} E^0_\alpha}\left(\right)  .
Revised:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting . Our result is best possible, in the sense that there exist Ahlfors regular measures for which the limit \lim_{n\rightarrow\infty n^{-d-\alpha{d}} E^0_\alpha}\left(\right) .
Edit intent: meaning-changed
Original:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting  n^{-d-\alpha{d}} E^0_\alpha}\left(\right)  .
Revised:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting n^{-d-\alpha{d}} E^0_\alpha}\left(x_1,\ldots,x_n\right) .
Edit intent: fluency
Original:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting  n^{-d-\alpha{d}} E^0_\alpha}\left(\right)  .
Revised:  In particular, %DIFDELCMD < \[\log\big(E_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] %%% \[\log\big(E^0_\alpha(x_1,\ldots,x_n)\big)/\log(n)\longrightarrow (d-\alpha)/d\,.\] This is a generalization of a result of Steele (1988) from the absolutely continuous case to the fractal setting n^{-d-\alpha{d}} E^0_\alpha}\left(\right) does not exist with high probability .
Edit intent: meaning-changed
Original:  We show that by offering a generous refund policy the seller can significantly reduce this type of uncertainty and regain market power. A simple mechanism that utilizes a generous refund policy and random discountsachieves the best guaranteed-profit among all possible mechanisms .
Revised:  We show that the seller may use a simple mechanism to best take advantage of the buyer's post-purchase learning to maximize his guaranteed-profit. We show that this mechanism combines a generous refund policy and random discountsachieves the best guaranteed-profit among all possible mechanisms .
Edit intent: clarity
Original:   We employed this architecture on mRNA transcription profiles of 10787 clinical samples from 34 classes (one healthy and 33 different types of cancer) from 27 tissues.
Revised:  It encodes the whole transcription profile into a strikingly low-dimensional latent vector of size 8, and then recovers mRNA and miRNA expression profiles, tissue and disease type from this vector. This latent space is significantly better than the original gene expression profiles for discriminating samples based on their tissue and disease. We employed this architecture on mRNA transcription profiles of 10787 clinical samples from 34 classes (one healthy and 33 different types of cancer) from 27 tissues.
Edit intent: meaning-changed
Original: This paper develops estimation and inference tools for the structural parameter in the dynamic game with a high-dimensional state space under the assumption that the data are generated by a single Markov perfect equilibrium.
Revised: Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a high-dimensional state space under the assumption that the data are generated by a single Markov perfect equilibrium.
Edit intent: meaning-changed
Original: This paper develops estimation and inference tools for the structural parameter in the dynamic game with a high-dimensional state space under the assumption that the data are generated by a single Markov perfect equilibrium. The equilibrium assumption implies that the expected value function evaluated at the equilibrium strategy profile is not smaller than the expected value function evaluated at a feasible suboptimal alternative. The target identified set is defined as the set of parameters obeying this inequality restriction. I estimate the expected value function in the two-stage procedure. At the first stage, I estimate the  law of motion of the state variable and the equilibrium policy function using modern machine learning methods.
Revised: This paper develops estimation and inference tools for the structural parameter in the dynamic game with a high-dimensional state space into the dynamic model of imperfect competition. In the first stage, I estimate the law of motion of the state variable and the equilibrium policy function using modern machine learning methods.
Edit intent: clarity
Original:  At the first stage, I estimate the  law of motion of the state variable and the equilibrium policy function using modern machine learning methods. At the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .
Revised:  At the first stage, I estimate the law of motion of the state variable and the equilibrium policy function using machine learning tools. In the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .
Edit intent: clarity
Original:  At the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .
Revised:  At the second stage, I plug the first-stage estimates into a moment inequality and solve for the structural parameter. The moment function is presented as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .
Edit intent: meaning-changed
Original:  At the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .
Revised:  At the second stage, I construct the estimator of the expected value function as the sum of two components, where the first one expresses the equilibrium assumption and the second one is a bias correction term which removes the bias of the naive estimator .
Edit intent: meaning-changed
Original:  At the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .
Revised:  At the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term that makes the sum insensitive (i.e., orthogonal) to first-stage bias .
Edit intent: meaning-changed
Original:  The proposed estimator of the identified set converges at the root-N rate to the true identified set and can be used to construct its confidence regions .
Revised:  The proposed estimator of the identified set converges at the root-N rate and I use it to construct confidence regions. The results developed here can be used to incorporate high-dimensional state space into classic dynamic discrete choice models, for example, those considered in Rust (1987), Bajari et al. (2007), and Scott (2013) .
Edit intent: meaning-changed
Original:  Within this framework, it is shown how to characterize the whole term structurewithout admitting arbitrage. The pricing of zero-coupon bonds in such a setting differs substantially from traditional models, since the prices need to be chosen in a different way in order to exclude arbitrage .
Revised:  The main question in this setting is how to find an arbitrage-free term structure. This question is crucial, since we can show that the classical approach, martingale modeling, does not work in the presence of volatility uncertainty. Therefore, we need to adjust the model in order to find an arbitrage-free term structure. The resulting term structure is affine with respect to the short rate and the adjustment factor. Although the adjustment changes the structure of the model, it is still consistent with the traditional Hull-White model after fitting the yield curve. In addition, we extend the model and the results to a multifactor version, driven by multiple risk factors .
Edit intent: meaning-changed
Original:  The main advantage of the BooST  is that it estimates the derivatives (partial effects) of very general nonlinear models, providing more interpretation than other tree based models concerning the mapping between the covariates and the dependent variable  .
Revised:  The main advantage of the BooST model is that it estimates the derivatives (partial effects) of very general nonlinear models, providing more interpretation than other tree based models concerning the mapping between the covariates and the dependent variable .
Edit intent: fluency