wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The subset of tetrahedra of triangulating each potential hexahedron is determined once its eight vertices are computed. The new algorithm computes around 3 millions potential hexahedra in 10 seconds and ensures that each potential hexahedron is computed only once.
Revised:  The subset of tetrahedra of triangulating each potential hexahedron is then determined. Quality checks allow to early discard poor quality hexahedra and to dramatically improve the efficiency of the method. Each potential hexahedron is computed only once.
Edit intent: meaning-changed
Original: Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra that may be combined to form hexahedra. In this paper we introduce an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh into hexahedra .
Revised: Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh into hexahedra .
Edit intent: clarity
Original: We ]  provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Revised: Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While ] provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Edit intent: meaning-changed
Original: We ]  provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Revised: We 1] provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Edit intent: meaning-changed
Original: We ]  provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Revised: We ] showed that no two-factor Cox-Ingersoll-Ross (CIR) model can exhibit USV, it has been unknown to date whether CIR models with more than two factors can exhibit USV or not. We formally review USV and relate it to bond market incompleteness. We provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Edit intent: meaning-changed
Original: We ]  provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Revised: We ] provide necessary and sufficient conditions for a multi-factor CIR model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Edit intent: meaning-changed
Original: We ]  provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
Revised: We ] provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit USV . We then construct a class of three-factor CIR models that exhibit USV.
Edit intent: clarity
Original:  For a frictionless market consisting of d risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of an upper semicontinuous path dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures.
Revised:  For a frictionless market consisting of d risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures.
Edit intent: clarity
Original:  The superhedging problem is formulated with simple trading strategies  and superhedging is required in the pathwise sense on a \sigma-compact sample space of price trajectories.
Revised:  The superhedging problem is formulated with simple trading strategies , the claim is the limit inferior of continuous functions, which allows for upper and lower semi-continuous claims, and superhedging is required in the pathwise sense on a \sigma-compact sample space of price trajectories.
Edit intent: meaning-changed
Original:  We make publicly available normalized representations of high frequency data for five stocks extracted from the NASDAQ Nordic stock market . Furthermore, we define an experimental protocol that can be used in order to evaluate the performance of related research methods.
Revised:  We make publicly available normalized representations of high frequency data for five stocks extracted from the NASDAQ Nordic stock market for a time period of ten consecutive days, leading to a dataset of ~4,000,000 time series samples in total. A day-based anchored cross-validation experimental protocol is also provided that can be used in order to evaluate the performance of related research methods.
Edit intent: meaning-changed
Original:  Furthermore, we define an experimental protocol that can be used in order to evaluate the performance of related research methods. Baseline results based on linear and nonlinear regression models are also provided and show the potential that these methods have for mid-price prediction .
Revised:  Furthermore, we define an experimental protocol that can be used in order to evaluate the performance of state-of-the-art methodologies. Performance of baseline approaches are also provided and show the potential that these methods have for mid-price prediction .
Edit intent: clarity
Original:  This is clearly a tremendous improvementfor the description of gene expression, but it is also a new challenge because a stochasticity dimension has now to be integrated to properly infer gene regulatory networks - mRNA synthesis is now acknowledged to occur in a highly bursty manner.
Revised:  Despite this considerable precision improvement, inferring regulatory networks remains challenging because stochasticity now proves to play a fundamental role in gene expression. In particular, mRNA synthesis is now acknowledged to occur in a highly bursty manner.
Edit intent: clarity
Original:  In the case of a simple toggle-switch, the output of this approximation was almost indistinguishable from the theoretical distribution. Our approach was finally applied to a number of simple two-gene networks simulated in silico from the mechanistic model and satisfactorily recovered an accurate version of the original networks.
Revised:  In the case of a simple toggle-switch, and we show that it can indeed fit real single-cell data. As a first step toward inference, our approach was applied to a number of simple two-gene networks simulated in silico from the mechanistic model and satisfactorily recovered an accurate version of the original networks.
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Original:  Most importantly, our results demonstrate that functional , dynamic interactions between genes can be identified even from the stationary distribution . This method stands as a promising tool in relation to the current explosion of single-cell expression data.
Revised:  Most importantly, our results demonstrate that functional , dynamic interactions between genes can be inferred from the distribution of a mechanistic, dynamical stochastic model that is able to describe gene expression in individual cells. This approach seems promising in relation to the current explosion of single-cell expression data.
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Original: The extension of DNA during confinement in a nanochannel has attracted substantial attention for next-generation genomics and as a fundamental problem in polymer physics. But recent experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA.
Revised: Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA.
Edit intent: clarity
Original:  We posit that this discrepancy arises because the experimental systems do not satisfy the strong inequalities underlying existing scaling approximations. We develop a new theory , based on the properties of a  weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space  .
Revised:  We show that a weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space .
Edit intent: clarity
Original:  We develop a new theory , based on the properties of a  weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space  .
Revised:  We develop a new theory , based on the properties of a theory based on a weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space .
Edit intent: meaning-changed
Original:  We develop a new theory , based on the properties of a  weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space  .
Revised:  We develop a new theory , based on the properties of a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space .
Edit intent: coherence
Original:  We develop a new theory , based on the properties of a  weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space  .
Revised:  We develop a new theory , based on the properties of a weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space .
Edit intent: clarity
Original:  We develop a new theory , based on the properties of a  weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space  .
Revised:  We develop a new theory , based on the properties of a weakly self-avoiding, one-dimensional "telegraph" process , that collapses both experimental data and computer-simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play .
Edit intent: clarity
Original:  In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50 \%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes deviations from random assignment of treatment, and one which indexes deviations from rank invariance. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of robustness of conclusions to deviations in the point identifying assumptions. We derive \sqrt{N \\%DIF > ).
Revised:  In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50 \\%DIF > ).
Edit intent: meaning-changed
Original:  In Appendices, we present applications of \v{Z 's technical approach to measurement of complex dynamical (chemical and biological) systems at the Institute of Complex Systems, University of South Bohemia in \v{Cesk\'e Budejovice}  .
Revised:  In Appendices, we present applications of Zampa 's technical approach to measurement of complex dynamical (chemical and biological) systems at the Institute of Complex Systems, University of South Bohemia in \v{Cesk\'e Budejovice} .
Edit intent: meaning-changed
Original:  In Appendices, we present applications of \v{Z 's technical approach to measurement of complex dynamical (chemical and biological) systems at the Institute of Complex Systems, University of South Bohemia in \v{Cesk\'e Budejovice}  .
Revised:  In Appendices, we present applications of \v{Z 's technical approach to measurement of complex dynamical (chemical and biological) systems at the Institute of Complex Systems, University of South Bohemia in esk\'e Budejovice} .
Edit intent: fluency
Original:  In Appendices, we present applications of \v{Z 's technical approach to measurement of complex dynamical (chemical and biological) systems at the Institute of Complex Systems, University of South Bohemia in \v{Cesk\'e Budejovice}  .
Revised:  In Appendices, we present applications of \v{Z 's technical approach to measurement of complex dynamical (chemical and biological) systems at the Institute of Complex Systems, University of South Bohemia in \v{Cesk\'e Budejovice} Ceske Budejovice .
Edit intent: meaning-changed
Original: We resolve in the affirmative conjectures of A. Skopenkov and Repov\v{s (1998), and M. Skopenkov (2003) generalizing the classical Hanani--Tutte  theorem to the setting of approximating maps of graphs in the plane by embeddings.
Revised: We resolve in the affirmative conjectures of A. Skopenkov and Repovs (1998), and M. Skopenkov (2003) generalizing the classical Hanani--Tutte theorem to the setting of approximating maps of graphs in the plane by embeddings.
Edit intent: fluency
Original: We resolve in the affirmative conjectures of A. Skopenkov and Repov\v{s (1998), and M. Skopenkov (2003) generalizing the classical Hanani--Tutte  theorem to the setting of approximating maps of graphs in the plane by embeddings.
Revised: We resolve in the affirmative conjectures of A. Skopenkov and Repov\v{s (1998), and M. Skopenkov (2003) generalizing the classical Hanani theorem to the setting of approximating maps of graphs in the plane by embeddings.
Edit intent: meaning-changed
Original: We resolve in the affirmative conjectures of A. Skopenkov and Repov\v{s (1998), and M. Skopenkov (2003) generalizing the classical Hanani--Tutte  theorem to the setting of approximating maps of graphs in the plane by embeddings.
Revised: We resolve in the affirmative conjectures of A. Skopenkov and Repov\v{s (1998), and M. Skopenkov (2003) generalizing the classical Hanani--Tutte Tutte theorem to the setting of approximating maps of graphs in the plane by embeddings.
Edit intent: meaning-changed
Original: We resolve in the affirmative conjectures of A. Skopenkov and Repov\v{s (1998), and M. Skopenkov (2003) generalizing the classical Hanani--Tutte  theorem to the setting of approximating maps of graphs in the plane by embeddings.
Revised: We resolve in the affirmative conjectures of A. Skopenkov and Repov\v{s (1998), and M. Skopenkov (2003) generalizing the classical Hanani--Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings.
Edit intent: meaning-changed
Original:  More precisely, an instance of this problem consists of (i) a planar graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of the plane given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise non-intersecting "pipes" corresponding to the bundles, connecting certain pairs of these discs.
Revised:  More precisely, an instance of this problem consists of (i) a graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of the plane given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise non-intersecting "pipes" corresponding to the bundles, connecting certain pairs of these discs.
Edit intent: clarity
Original:  More precisely, an instance of this problem consists of (i) a planar graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of the plane given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise non-intersecting "pipes" corresponding to the bundles, connecting certain pairs of these discs.
Revised:  More precisely, an instance of this problem consists of (i) a planar graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact surface M given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise non-intersecting "pipes" corresponding to the bundles, connecting certain pairs of these discs.
Edit intent: meaning-changed
Original:  We are to decide whether G can be embedded inside R so that the vertices in every cluster are drawn in the corresponding disc, the edges in every bundle pass only through its corresponding pipe, and every edge crosses the boundary of each disc at most once.
Revised:  We are to decide whether G can be embedded inside M so that the vertices in every cluster are drawn in the corresponding disc, the edges in every bundle pass only through its corresponding pipe, and every edge crosses the boundary of each disc at most once.
Edit intent: meaning-changed
Original: We resolve in the affirmative conjectures of  A. Skopenkov and Repovs (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings.
Revised: We resolve in the affirmative conjectures of Repovs and A. Skopenkov and Repovs (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings.
Edit intent: meaning-changed
Original: We resolve in the affirmative conjectures of  A. Skopenkov and Repovs (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings.
Revised: We resolve in the affirmative conjectures of A. Skopenkov (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings.
Edit intent: meaning-changed
Original:  Finally, we adopt an ecological perspective and show that the so-called 'neutral model ' of evolution , despite its simplicity, reproduces a number of key empirical observations . We anticipate that our results will be of interest to researchers interested in the study and modelling of the structural properties of the cryptocurrency market  .
Revised:  Finally, we adopt an ecological perspective and show that the so-called 'neutral model ' of evolution , despite its simplicity, reproduces a number of key empirical observations , despite its simplicity and the assumption of no selective advantage of one cryptocurrency over another. Our results shed light on the properties of the cryptocurrency market .
Edit intent: meaning-changed
Original: Visualization of large graphs has become increasingly important due to the growing size of data available around us. Traditional data visualization systems render the graph in full detail on a single screen. This approach sometimes requires to render many objects on the screen, which overwhelms the user. A GraphMaps system tries to overcome this problem by visualizing the graph using zoom levels, which is similar to a geographic map visualization.
Revised: A GraphMaps is a system that visualizes a graph using zoom levels, which is similar to a geographic map visualization.
Edit intent: clarity
Original:  The available implementation of GraphMaps system is based on an incremental mesh generation technique that does not control the number of zoom levels and the way the nodes appear on different levels .
Revised:  The available implementation of GraphMaps system is based on an incremental mesh generation technique that does not control the number of zoom levels may be large, nodes may be unevenly distributed to different levels, shared edges may create ambiguity due to the selection of multiple nodes .
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Original:  Finally, we give an algorithm for assigning nodes to zoom levels that minimizes the  number of nodes appearing while the user zooms in to a lower level. Keeping the number of such nodes low helps avoiding abrupt changes when zooming in and out between the levels  .
Revised:  Finally, we give an algorithm for assigning nodes to zoom levels that minimizes the number of nodes appearing while the user zooms in and out between the levels .
Edit intent: clarity
Original:  The relevance of R\'enyi entropy in portfolio selection applications is illustrated with an empirical study: minimizing this cost function yields portfolios that outperform standard risk optimal portfolios along most performance indicators .
Revised:  A portfolio selection application illustrates that minimizing R\'enyi entropy in portfolio selection applications is illustrated with an empirical study: minimizing this cost function yields portfolios that outperform standard risk optimal portfolios along most performance indicators .
Edit intent: clarity
Original:  The relevance of R\'enyi entropy in portfolio selection applications is illustrated with an empirical study: minimizing this cost function yields portfolios that outperform standard risk optimal portfolios along most performance indicators .
Revised:  The relevance of R\'enyi entropy in portfolio selection applications is illustrated with an empirical study: minimizing this cost function yields portfolios that outperform state-of-the-art minimum variance portfolios in terms of risk-return-turnover trade-off .
Edit intent: meaning-changed
Original:  RAE contains 72 days of 1Hz data from a residential house 's mains and 24 sub-meters resulting in 6.2 million samples for each sub-meter .
Revised:  RAE contains 72 days of 1Hz data (mains and sub-meters) from two a residential house 's mains and 24 sub-meters resulting in 6.2 million samples for each sub-meter .
Edit intent: meaning-changed