wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We present an approximation algorithm with  time complexity O(n \log n) and approximation factor 1/4 for orthogonal trajectories, in which the entity moves in a direction parallel either to the x or to the y-axis  .
Revised:  We present an approximation algorithm with time complexity O(n \log n) and approximation factor 1/4 for orthogonal trajectories, in which the entity moves in a direction parallel either to the x or to the y-axis . We also present a 1/4-approximation algorithm for finding axis-parallel cube hotspots of fixed side length for orthogonal three-dimensional trajectories .
Edit intent: meaning-changed
Original:  The fastest optimal algorithm, due to Gudmundsson, van Kreveld, and Staals (2013) , finds an axis-parallel square hotspot of fixed side length in O(n^2).
Revised:  The fastest optimal algorithm, due to Gudmundsson, van Kreveld, and Staals (2013) finds an axis-parallel square hotspot of fixed side length in O(n^2).
Edit intent: fluency
Original:  We present an approximation algorithm with the time complexity O(n \log n) and approximation factor 1/4 for orthogonal trajectories, in which the entity moves in a direction parallel either to the x or to the y-axis .
Revised:  We present an approximation algorithm with the time complexity O(n \log n) and approximation factor 1/4 for orthogonal trajectories, in which the entity moves in a direction parallel either to the x or the y-axis .
Edit intent: fluency
Original:  We present an approximation algorithm with the time complexity O(n \log n) and approximation factor 1/4 for orthogonal trajectories, in which the entity moves in a direction parallel either to the x or to the y-axis . We also present a 1/ 4-approximation algorithm for finding axis-parallel cube hotspots of fixed side length for orthogonal three-dimensional trajectories.
Revised:  We present an approximation algorithm with the time complexity O(n \log n) and approximation factor 1/4 for orthogonal trajectories, in which the entity moves in a direction parallel either to the x or to the y-axis , We present an approximation algorithm with the time complexity O(n \log^3 n) and approximation factor 1/ 4-approximation algorithm for finding axis-parallel cube hotspots of fixed side length for orthogonal three-dimensional trajectories.
Edit intent: meaning-changed
Original:  Our analysis conforms to  current understanding of light-harvesting antennae in that we can explain known properties of the complex. a functional role of the notch at the light harvestor, the functional role of the special pair,
Revised:  Our analysis conforms to current understanding of light-harvesting antennae in that we can explain known properties of the complex. a functional role of the notch at the light harvester, a functional role of the polypeptide called PufX or W at the opening, a functional role of the special pair,
Edit intent: meaning-changed
Original:  a mechanism to prevent damage from excess sunlight, an advantage of the dimeric form, a reason that the cross section of the light harvestor must not be circular, a reason for the modular design of nature , a function of the non-heme iron at the reaction center, and a reason that the light harvestor must not be spherical . Based upon our analysis we provide a mechanism for dimerization and propose an experiment .
Revised:  a mechanism to prevent damage from excess sunlight, an advantage of the dimeric form, and reasons for the modular design of nature , a function of the non-heme iron at the reaction center, and a reason that the light harvestor must not be spherical . Based upon our analysis we provide a mechanism for dimerization and propose an experiment .
Edit intent: clarity
Original:  a mechanism to prevent damage from excess sunlight, an advantage of the dimeric form, a reason that the cross section of the light harvestor must not be circular, a reason for the modular design of nature , a function of the non-heme iron at the reaction center, and a reason that the light harvestor must not be spherical . Based upon our analysis we provide a mechanism for dimerization and propose an experiment .
Revised:  a mechanism to prevent damage from excess sunlight, an advantage of the dimeric form, a reason that the cross section of the light harvestor must not be circular, a reason for the modular design of nature . Based upon our analysis we provide a mechanism for dimerization and propose an experiment .
Edit intent: coherence
Original:  a mechanism to prevent damage from excess sunlight, an advantage of the dimeric form, a reason that the cross section of the light harvestor must not be circular, a reason for the modular design of nature , a function of the non-heme iron at the reaction center, and a reason that the light harvestor must not be spherical . Based upon our analysis we provide a mechanism for dimerization and propose an experiment .
Revised:  a mechanism to prevent damage from excess sunlight, an advantage of the dimeric form, a reason that the cross section of the light harvestor must not be circular, a reason for the modular design of nature , a function of the non-heme iron at the reaction center, and a reason that the light harvestor must not be spherical . Based upon our analysis we provide a mechanism for dimerization .
Edit intent: coherence
Original:  Several authors have investigated the effects of including anticipation into models of this type . Key findings include that anticipation inhibits polarized collective motion in alignment based models and promotes milling and swarming in the one attraction-repulsion model studied.
Revised:  Several authors have investigated the effects of including anticipation into models of this type , and have found that anticipation inhibits polarized collective motion in alignment based models and promotes milling and swarming in the one attraction-repulsion model studied.
Edit intent: clarity
Original:  Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation , or motion restricted to a lattice are not necessary requirements for polarized collective motion to emerge in models with anticipation .
Revised:  This establishes that neither asynchrony, mutual anticipation , or motion restricted to a lattice are not necessary requirements for polarized collective motion to emerge in models with anticipation .
Edit intent: clarity
Original:  Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation , or motion restricted to a lattice are not necessary requirements for polarized collective motion to emerge in models with anticipation .
Revised:  Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation nor motion restricted to a lattice are not necessary requirements for polarized collective motion to emerge in models with anticipation .
Edit intent: clarity
Original:  Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation , or motion restricted to a lattice are not necessary requirements for polarized collective motion to emerge in models with anticipation .
Revised:  Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation , or motion restricted to a lattice environment are strict requirements for anticipation to promote polarized collective motion to emerge in models with anticipation .
Edit intent: clarity
Original:  Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation , or motion restricted to a lattice are not necessary requirements for polarized collective motion to emerge in models with anticipation .
Revised:  Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation , or motion restricted to a lattice are not necessary requirements for polarized collective motion .
Edit intent: clarity
Original:  So here anticipation is a direct polarization inducing mechanism and we believe that utilizing anticipation instead of frequently used alternatives such as explicit alignment terms, asynchronous updates and asymmetric interactions to generate polarized collective motion may be advantageous in some cases.
Revised:  Here anticipation is a direct polarization inducing mechanism and we believe that utilizing anticipation instead of frequently used alternatives such as explicit alignment terms, asynchronous updates and asymmetric interactions to generate polarized collective motion may be advantageous in some cases.
Edit intent: coherence
Original:  So here anticipation is a direct polarization inducing mechanism and we believe that utilizing anticipation instead of frequently used alternatives such as explicit alignment terms, asynchronous updates and asymmetric interactions to generate polarized collective motion may be advantageous in some cases.
Revised:  So here anticipation is a direct polarization inducing mechanism . We believe that utilizing anticipation instead of frequently used alternatives such as explicit alignment terms, asynchronous updates and asymmetric interactions to generate polarized collective motion may be advantageous in some cases.
Edit intent: coherence
Original: We develop a method for incorporating relevant non-Euclidean geometric information into a broad range of classical filtering and statistical or machine learning algorithms. We apply these techniques to approximate the solution of the non-Euclidean filtering problem to arbitrary precision. We then extend the particle filtering algorithm to compute our asymptotic solution to arbitrary precision. Moreover, we find explicit error bounds measuring the discrepancy between our locally triangulated filter and the true theoretical non-Euclidean filter. Our methods are motivated by certain fundamental problems in mathematical finance. In particular we apply these filtering techniques to incorporate the non-Euclidean geometry present in stochastic volatility models and optimal Markowitz portfolios. We also extend Euclidean statistical or machine learning algorithms to non-Euclidean problems by using the local triangulation technique, which we show improves the accuracy of the original algorithm. We apply the local triangulation method to obtain improvements of the (sparse) principal component analysis and the principal geodesic analysis algorithms and show how these improved algorithms can be used to parsimoniously estimate the evolution of the shape of forward-rate curves. While focused on financial applications, the non-Euclidean geometric techniques presented in this paper can be employed to provide improvements to a range of other statistical or machine learning algorithms and may be useful in other areas of application .
Revised: We develop a method for incorporating relevant non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. This gives computationally tractable filtering equations for the dynamics of the intrinsic conditional expectation of a manifold-valued signal and is used to obtain accurate numerical forecasts of efficient portfolios by incorporating their geometric structure into the estimates .
Edit intent: meaning-changed
Original:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{%DIFAUXCMD Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{%DIFAUXCMD GustafssonSakai:1999hr . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Revised:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{%DIFAUXCMD GustafssonSakai:1999hr . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Edit intent: coherence
Original:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{%DIFAUXCMD Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{%DIFAUXCMD GustafssonSakai:1999hr . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Revised:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{%DIFAUXCMD Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Edit intent: coherence
Original:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{%DIFAUXCMD Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{%DIFAUXCMD GustafssonSakai:1999hr . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them. In addiction, we apply the mother body method to Electrostatics to compute the potentials of electric fields.
Revised:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{%DIFAUXCMD Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{%DIFAUXCMD GustafssonSakai:1999hr . In this paper, we attempt to apply the brilliant idea of mother body to Electrostatics to compute the potentials of electric fields.
Edit intent: clarity
Original:  We illustrate the technique and its implications using Bergman's model with different lending and borrowing rates  and a class of quadratic-growth BSDEs  .
Revised:  We illustrate the technique and its implications using Bergman's model with different lending and borrowing rates and a class of quadratic-growth BSDEs . We also present an extension of the deep BSDE solver for reflected BSDEs using an American basket option as an example .
Edit intent: meaning-changed
Original:  A key research challenge in designing large (in number of input/output ports N) input-queued crossbar switches is to develop crossbar scheduling algorithms that can compute "high quality" matchings - i.e.  those that result in high switch throughput (ideally 100\\%DIF < ) and low queueing delays for packets - at line rates.
Revised:  A key research challenge in designing large (in number of input/output ports N) input-queued crossbar switches is to develop crossbar scheduling algorithms that can compute "high quality" matchings -- i.e. those that result in high switch throughput (ideally 100\\%DIF < ) and low queueing delays for packets - at line rates.
Edit intent: fluency
Original:  A key research challenge in designing large (in number of input/output ports N) input-queued crossbar switches is to develop crossbar scheduling algorithms that can compute "high quality" matchings - i.e.  those that result in high switch throughput (ideally 100\\%DIF < ) and low queueing delays for packets - at line rates.
Revised:  A key research challenge in designing large (in number of input/output ports N) input-queued crossbar switches is to develop crossbar scheduling algorithms that can compute "high quality" matchings - i.e. , those that result in high switch throughput (ideally 100\\%DIF < ) and low queueing delays for packets - at line rates.
Edit intent: fluency
Original: In this article we consider a number of models for the statistical data generation in different areas of insurance, including life , pension and non-life insurance . Insurance statistics are usually truncated and censored, and often are multidimensional.
Revised: In this article we consider a number of models for the statistical data generation in different areas of insurance, including life insurance, pensions, and general insurance have been considered. It is shown that the insurance statistics data, as a rule, are truncated and censored, and often are multidimensional.
Edit intent: meaning-changed
Original:  We propose a nonparametric estimation of the distribution function for multidimensional truncated-censored data in the form of  quasi-empirical distribution and a simple iterative algorithm for it is calculating.
Revised:  We propose a non-parametric estimation of the distribution function for multidimensional truncated-censored data in the form of quasi-empirical distribution and a simple iterative algorithm for it is calculating.
Edit intent: fluency
Original:  We propose a nonparametric estimation of the distribution function for multidimensional truncated-censored data in the form of  quasi-empirical distribution and a simple iterative algorithm for it is calculating.
Revised:  We propose a nonparametric estimation of the distribution function for multidimensional truncated-censored data in the form of a quasi-empirical distribution and a simple iterative algorithm for it is calculating.
Edit intent: fluency
Original:  We propose a nonparametric estimation of the distribution function for multidimensional truncated-censored data in the form of  quasi-empirical distribution and a simple iterative algorithm for it is calculating. The accuracy of estimating the distribution function was verified by the Monte Carlo method. A comparative analysis of the quasi-empirical distribution with alternative estimates showed that in the one-dimensional case the proposed estimate almost coincides with the estimates calculated using the HPSEVERITY procedure, which is a part of SAS ETS. We did not make the comparative analysis in the multidimensional case due to the lack of analogues of such algorithms. But our algorithm has passed years of testing in the valuation of employees liabilities in accordance with IAS 19 (Employee benefits).
Revised:  We propose a nonparametric estimation of the distribution function for multidimensional truncated-censored data in the form of quasi-empirical distribution and a simple iterative algorithm for its construction. To check the accuracy of the proposed evaluation of the distribution function for truncated-censored data, simulation studies have been conducted, which showed its high efficiency. The proposed estimates have been tested for many years by the IAAC Group of Companies in the actuarial valuation of corporate social liabilities according to IAS 19 (Employee benefits).
Edit intent: clarity
Original:  But our algorithm has passed years of testing in the valuation of employees liabilities in accordance with IAS 19 (Employee benefits). As an example, the article provides an assessment of the joint function of distribution of workers age and seniority of a large Russian energy enterprise. The proposed estimates can also be usedin other areas, such as medicine, biology, demography,  reliability, etc.
Revised:  But our algorithm has passed years of testing in the valuation of employees liabilities in accordance with IAS 19 Employee Benefits. Apart from insurance, some results of the work can be used, for example in medicine, biology, demography, reliability, etc.
Edit intent: clarity
Original: In a Planar 3-SAT problem, we are given a 3-SAT formula together with its incidence graph, which is planar, and are asked whether this formula is satisfiable.
Revised: In the Planar 3-SAT problem, we are given a 3-SAT formula together with its incidence graph, which is planar, and are asked whether this formula is satisfiable.
Edit intent: fluency
Original:  In this paper, we investigate the restriction in which we require that the incidence graph can be augmented by the edges of a Hamiltonian cycle that first passes through all variables and then through all clauses, in a way that the resulting graph is still planar.
Revised:  In this paper, we investigate the restriction in which we require that the incidence graph is augmented by the edges of a Hamiltonian cycle that first passes through all variables and then through all clauses, in a way that the resulting graph is still planar.
Edit intent: clarity
Original:  In this paper, we investigate the restriction in which we require that the incidence graph is augmented by the edges of a Hamiltonian cycle that first passes through all variables and then through all clauses, in a way that the resulting graph is still planar.
Revised:  In this paper, we investigate the restriction in which we require that the incidence graph can be augmented by the edges of a Hamiltonian cycle that first passes through all variables and then through all clauses, in a way that the resulting graph is still planar.
Edit intent: clarity
Original:  In the course of this investigation, we show that monotone instances of Planar 3-SAT with  three distinct variables per clause are always satisfiable, thus settling the question by Darmann, D\"ocker, and Dorn on the complexity of this problem variant in a surprising way.
Revised:  In the course of this investigation, we show that monotone instances of Planar 3-SAT with exactly three distinct variables per clause are always satisfiable, thus settling the question by Darmann, D\"ocker, and Dorn on the complexity of this problem variant in a surprising way.
Edit intent: meaning-changed
Original:  Finally, we find that the interplay of non-normality and zero dynamics of the system is important in determining the pulse characteristics in response to an input. These results should be useful in analysis, to screen for pulsed dynamics in biomolecular circuits, and in design, by highlighting tunable system properties .
Revised:  Finally, we illustrate how these methods can be used to provide analytical support to numerical screens for pulsing dynamics as well as provide guidelines for design .
Edit intent: clarity
Original: While there exist a number of mathematical approaches to modeling the spread of disease on a network, analyzing such systems in the presence of uncertainty introduces significant complexity. In scenarios where system parameters must be inferred from limited observations, general approaches to uncertainty quantification can generate approximate distributions of the unknown parameters, but these methods often become computationally expensive if the underlying disease model is complex. In this paper, we apply the recent massively parallelizable Bayesian uncertainty quantification framework %DIFDELCMD < \Pi4U %%% to a model of a disease spreading on a network of communities , showing that the method can accurately and tractably recover system parameters and select optimal models in this setting .
Revised: Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework %DIFDELCMD < \Pi4U %%% to a model of a disease spreading on a network of communities , showing that the method can accurately and tractably recover system parameters and select optimal models in this setting .
Edit intent: clarity
Original:  In this paper, we apply the recent massively parallelizable Bayesian uncertainty quantification framework %DIFDELCMD < \Pi4U %%% to a model of a disease spreading on a network of communities , showing that the method can accurately and tractably recover system parameters and select optimal models in this setting .
Revised:  In this paper, we apply the recent massively parallelizable Bayesian uncertainty quantification framework %DIFDELCMD < \Pi4U %%% to infer model parameters for a disease spreading on a network of communities , showing that the method can accurately and tractably recover system parameters and select optimal models in this setting .
Edit intent: clarity