wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Using the theoretical estimate (\proptoN where N is  number of nucleotides) for folding free energy barrier, k_F data for both the RNAs are quantitatively fit using one dimensional Kramers' theory with two parameters specifying the curvatures in the unfolded basin and the barrier top.
Revised:  Using the theoretical estimate (\proptoN where N is the number of nucleotides) for folding free energy barrier, k_F data for both the RNAs are quantitatively fit using one dimensional Kramers' theory with two parameters specifying the curvatures in the unfolded basin and the barrier top.
Edit intent: fluency
Original:  Using the theoretical estimate (\proptoN where N is  number of nucleotides) for folding free energy barrier, k_F data for both the RNAs are quantitatively fit using one dimensional Kramers' theory with two parameters specifying the curvatures in the unfolded basin and the barrier top.
Revised:  Using the theoretical estimate (\proptoN where N is number of nucleotides) for folding free energy barrier, k_F data for both the RNAs are quantitatively fit using one-dimensional Kramers' theory with two parameters specifying the curvatures in the unfolded basin and the barrier top.
Edit intent: fluency
Original:  In the high-friction regime (\eta\gtrsim10^{-5}\,Pa \ensuremath{\cdot s}), for both HP and PK, k_Fs decrease as 1/\eta whereas in the low friction regime k_\mathrm{F increase as \eta increases, leading to a maximum folding rate at a moderate viscosity (\sim10^{-6}\,Pa \ensuremath{\cdot s}), which is the Kramers turnover.
Revised:  In the high-friction regime (\eta\gtrsim10^{-5}\,Pa \ensuremath{\cdot s}), for both HP and PK, k_Fs decrease as 1/\eta whereas in the low friction regime , k_\mathrm{F increase as \eta increases, leading to a maximum folding rate at a moderate viscosity (\sim10^{-6}\,Pa \ensuremath{\cdot s}), which is the Kramers turnover.
Edit intent: fluency
Original:  From the fits, we find that the speed limit to RNA folding at water viscosity is between (1-4) \mathrm{\mu s}, which is in accord with our previous theoretical prediction as well as results from several single molecule experiments.
Revised:  From the fits, we find that the speed limit to RNA folding at water viscosity is between 1 and 4 \mathrm{\mu s}, which is in accord with our previous theoretical prediction as well as results from several single molecule experiments.
Edit intent: coherence
Original: Since Bachelier  in 1900 , when mathematical finance began, attempts at understanding the nature of stock market prices and at predicting them have not succeeded. Statistical models have only found minor regularities and anomalies.
Revised: Since Bachelier in 1900 , when mathematical finance began, attempts at understanding the nature of stock market prices and at predicting them have failed. Statistical methods have only found minor regularities and anomalies.
Edit intent: clarity
Original:  Statistical models have only found minor regularities and anomalies. Other approaches have failed or are illusory. To this day, the physicists and mathematicians working in economy consider that the evolution of security prices is basically random, and, thus,  not predictable.
Revised:  Statistical models have only found minor regularities /anomalies, and other mathematical and physical approaches do not work. This leads researchers to consider that the evolution of security prices is basically random, and, thus, not predictable.
Edit intent: clarity
Original:  The law takes the form of a physicomathematical theory centered around a purely mathematical function (not a model and unrelated to statistical methods). The function can be described as an "isodense" network of "moving " regression curves of an order greater than or equal to 1.
Revised:  The law takes the form of a physicomathematical theory centered around a purely mathematical function , unrelated to models and statistical methods. It can be described as an "isodense" network of "moving " regression curves of an order greater than or equal to 1.
Edit intent: coherence
Original:  What is central to the function is that these cords have the unique property of attracting and repelling the price , so that the price bounces from one cord to another. The direct consequence is that prices are driven by the cords in a semi-deterministic manner (leaning towards deterministic).
Revised:  The attraction and repulsion of the price by the cords results in the price bouncing from cord to cord. Thus, the price has to be considered as driven by the cords in a semi-deterministic manner (leaning towards deterministic).
Edit intent: clarity
Original:  It is well known from the typical example, the superhedging risk measure in markets with transaction costs (expressed in the cash asset) as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied.
Revised:  It is well known from the superhedging risk measure in markets with transaction costs (expressed in the cash asset) as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied.
Edit intent: clarity
Original:  It is well known from the typical example, the superhedging risk measure in markets with transaction costs (expressed in the cash asset) as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied.
Revised:  It is well known from the typical example, the superhedging risk measure in markets with transaction costs , as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied.
Edit intent: clarity
Original:  More generally, when it comes to scalarizing a multivariate risk measure with the same scalarization weight at each time (as this is the case in this paper as the risk measures are expressed in the cash asset), one cannot expect these scalar risk measures to be time consistent. This aligns with recent research on scalarizations of multivariate problems as in Karnam et al. (2017) and Kovacova and Rudloff (2018). Surprisingly, we will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process.
Revised:  We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process.
Edit intent: coherence
Original:  We systematically characterize the phenotype dynamics including occurrence probability, dwell time, transition flux, and also obtain the invasion characteristicsof each phenotype . Using a URLanoid model, we show that the distinct invasion potentials of each phenotype modulate the phenotype homeostasis.
Revised:  We systematically characterize the phenotype evolutions including occurrence probability, dwell time, transition flux, and also obtain the invasion characteristicsof each phenotype . Using a URLanoid model, we show that the distinct invasion potentials of each phenotype modulate the phenotype homeostasis.
Edit intent: clarity
Original:  We systematically characterize the phenotype dynamics including occurrence probability, dwell time, transition flux, and also obtain the invasion characteristicsof each phenotype . Using a URLanoid model, we show that the distinct invasion potentials of each phenotype modulate the phenotype homeostasis.
Revised:  We systematically characterize the phenotype dynamics including occurrence probability, dwell time, transition flux, and 3D migrational characteristics. We find that manipulating Rho-signaling enhances the morphodynamics and phenotype transitions . Using a URLanoid model, we show that the distinct invasion potentials of each phenotype modulate the phenotype homeostasis.
Edit intent: meaning-changed
Original: A k-hole in a point set S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
Revised: Given a set of points S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
Edit intent: clarity
Original: A k-hole in a point set S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
Revised: A k-hole in a point set S \subseteq R^2 , a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
Edit intent: clarity
Original: A k-hole in a point set S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
Revised: A k-hole in a point set S \subseteq R^2 is a subset X \subseteq S, |X|=k, is called k-gon if all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
Edit intent: meaning-changed
Original: A k-hole in a point set S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) and no point of S \setminus X lies in conv (X).
Revised: A k-hole in a point set S \subseteq R^2 is a subset X \subseteq S, |X|=k, such that all points of X lie on the boundary of the convex hull conv (X) , and k-hole if, in addition, no point of S \setminus X lies in conv (X).
Edit intent: meaning-changed
Original:  Moreover, we provide new bounds for three and more pairwise disjoint holes  .
Revised:  Moreover, we provide new bounds for three and more pairwise disjoint holes . In a recent article, Hosono and Urabe (2018) present new results on interior-disjoint holes -- a variant, which also has been investigated in the last two decades. Using our program, we show that every set of 14 points contains two interior-disjoint 5-holes. Moreover, our program can be used to verify that every set of 17 points contains a 6-gon within significantly smaller computation time than the original program by Szekeres and Peters (2006) .
Edit intent: meaning-changed
Original: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
Revised: Given a set of points S \subseteq R^2, a subset X \subseteq S with |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
Edit intent: clarity
Original: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
Revised: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
Edit intent: fluency
Original: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
Revised: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull of X , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
Edit intent: clarity
Original: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in \mathrm{conv .
Revised: Given a set of points S \subseteq R^2, a subset X \subseteq S , |X|=k , is called k-gon if all points of X lie on the boundary of the convex hull \mathrm{conv , and k-hole if, in addition, no point of S \setminus X lies in the convex hull of X .
Edit intent: clarity
Original:  Moreover, our program can be used to verify that every set of 17 points contains a 6-gon within significantly smaller computation time than the original program by Szekeres and Peters (2006  ).
Revised:  Moreover, our program can be used to verify that every set of 17 points contains a 6-gon within significantly smaller computation time than the original program by Szekeres and Peters (2006 ). Another independent verification of this result was done by Mari\'c (2019 ).
Edit intent: meaning-changed
Original:  In this paper I show that, under certain assumptions , stochastic dominance reasoning can capture many of the plausible implications of expectational reasoning while avoiding its implausible implications. More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of her optionsrepresentable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter , many expectation-maximizing gambles that would not stochastically dominate their alternatives "in a vacuum" turn out to do so in virtue of that background uncertainty.
Revised:  In this paper I show that, under certain assumptions , stochastic dominance reasoning can capture many of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty about the choiceworthiness of her optionsrepresentable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter , many expectation-maximizing gambles that would not stochastically dominate their alternatives "in a vacuum" turn out to do so in virtue of that background uncertainty.
Edit intent: clarity
Original:  More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of her optionsrepresentable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter , many expectation-maximizing gambles that would not stochastically dominate their alternatives "in a vacuum" turn out to do so in virtue of that background uncertainty.
Revised:  More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of one's options , many expectation-maximizing gambles that would not stochastically dominate their alternatives "in a vacuum" turn out to do so in virtue of that background uncertainty.
Edit intent: clarity
Original:  More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of her optionsrepresentable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter , many expectation-maximizing gambles that would not stochastically dominate their alternatives "in a vacuum" turn out to do so in virtue of that background uncertainty.
Revised:  More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of her optionsrepresentable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter , many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" turn out to do so in virtue of that background uncertainty.
Edit intent: clarity
Original:  More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of her optionsrepresentable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter , many expectation-maximizing gambles that would not stochastically dominate their alternatives "in a vacuum" turn out to do so in virtue of that background uncertainty.
Revised:  More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of her optionsrepresentable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter , many expectation-maximizing gambles that would not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty.
Edit intent: clarity
Original:  Petersburg Lottery. I argue that the sort of background uncertainty on which these results depend is appropriate for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of an option in part by the total amount of value in the resulting world.
Revised:  Petersburg game. The sort of background uncertainty on which these results depend is appropriate for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of an option in part by the total amount of value in the resulting world.
Edit intent: clarity
Original:  I argue that the sort of background uncertainty on which these results depend is appropriate for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of an option in part by the total amount of value in the resulting world.
Revised:  I argue that the sort of background uncertainty on which these results depend looks unavoidable for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of an option in part by the total amount of value in the resulting world.
Edit intent: clarity
Original:  I argue that the sort of background uncertainty on which these results depend is appropriate for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of an option in part by the total amount of value in the resulting world.
Revised:  I argue that the sort of background uncertainty on which these results depend is appropriate for any agent who measures the choiceworthiness of an option in part by the total amount of value in the resulting world.
Edit intent: clarity
Original:  I argue that the sort of background uncertainty on which these results depend is appropriate for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of an option in part by the total amount of value in the resulting world.
Revised:  I argue that the sort of background uncertainty on which these results depend is appropriate for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of her options in part by the total amount of value in the resulting world.
Edit intent: clarity
Original: Let S be a set of  points in the plane, CH be the convex hull of S, \wp(S) be the set of all simple polygons crossing S, \gamma_P be the maximum angle of polygon P \in \wp(S) and \theta =min_{P\in\wp(S)} \gamma_P.
Revised: Let S be a set of n points in the plane, CH be the convex hull of S, \wp(S) be the set of all simple polygons crossing S, \gamma_P be the maximum angle of polygon P \in \wp(S) and \theta =min_{P\in\wp(S)} \gamma_P.
Edit intent: meaning-changed
Original: Let S be a set of  points in the plane, CH be the convex hull of S, \wp(S) be the set of all simple polygons crossing S, \gamma_P be the maximum angle of polygon P \in \wp(S) and \theta =min_{P\in\wp(S)} \gamma_P.
Revised: Let S be a set of points in the plane, \wp(S) be the set of all simple polygons crossing S, \gamma_P be the maximum angle of polygon P \in \wp(S) and \theta =min_{P\in\wp(S)} \gamma_P.
Edit intent: clarity
Original:  In this paper, we prove that \theta\leq 2\pi-2\pi{r.m} such that m and r are the number of edges and internal points of CH , respectively.
Revised:  In this paper, we prove that \theta\leq 2\pi-2\pi{r.m} such that m and r are the number of edges and inner points of the convex hull of S , respectively.
Edit intent: meaning-changed
Original: An L-shaped embedding of a tree in a point set is a planar drawing of the tree where the vertices are mapped to distinct points of the set and every edge is drawn as a sequence of two axis-aligned line segments.
Revised: An L-shaped embedding of a tree in a point set is a planar drawing of the tree where the vertices are mapped to distinct points and every edge is drawn as a sequence of two axis-aligned line segments.
Edit intent: clarity
Original:  Let f_d(n) denote the minimum number N of points such that every n-vertex tree with maximum degree d\in\{3,4\ admits an L-shaped embedding in every point set of size N, where no two points have the same abscissa or ordinate.
Revised:  There has been considerable work on establishing upper bounds on the minimum cardinality such that any point set of that size admits an L-shaped embedding in every point set of size N, where no two points have the same abscissa or ordinate.
Edit intent: clarity
Original:  Let f_d(n) denote the minimum number N of points such that every n-vertex tree with maximum degree d\in\{3,4\ admits an L-shaped embedding in every point set of size N, where no two points have the same abscissa or ordinate. The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date .
Revised:  Let f_d(n) denote the minimum number N of points such that every n-vertex tree with maximum degree d\in\{3,4\ admits an L-shaped embedding of any n-vertex tree with maximum degree 4. However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date .
Edit intent: clarity
Original:  The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date .
Revised:  The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no non-trivial lower bound is known to this date .
Edit intent: clarity
Original:  The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date .
Revised:  The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date , i.e., no known n-vertex tree requires more than n points to be embedded.
Edit intent: meaning-changed
Original:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Revised:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
Edit intent: clarity