wanyu/IteraTeR_v2 huggingface dataset:
Original:  We present a characterization of a well-centered n-simplex and introduce a cost function that quantifies well-centeredness of a simplicial mesh.
Revised:  We prove that well-centered n-simplex and introduce a cost function that quantifies well-centeredness of a simplicial mesh.
Edit intent: clarity
Original:   We show the results of applying our algorithm to small , large, and graded two-dimensional meshes as well as one tiny three-dimensional mesh and a small tetrahedralization of the cube.
Revised:  We show the results of applying our algorithm to small and large two-dimensional meshes as well as one tiny three-dimensional mesh and a small tetrahedralization of the cube.
Edit intent: coherence
Original:  We present an iterative algorithm for transforming a given triangulation in two or three dimensions into a well-centered one .
Revised:  We present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well-centered one .
Edit intent: clarity
Original:  Ours is the first optimization-based algorithm for well-centeredness, and the first one that works in both two and three dimensions.
Revised:  Ours is the first optimization-based heuristic for well-centeredness, and the first one that works in both two and three dimensions.
Edit intent: clarity
Original:  Ours is the first optimization-based algorithm for well-centeredness, and the first one that works in both two and three dimensions.
Revised:  Ours is the first optimization-based algorithm for well-centeredness, and the first one that applies in both two and three dimensions.
Edit intent: clarity
Original:  We show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and show the first known well-centered tetrahedralization of the cube.
Revised:  We show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and obtain a well-centered tetrahedralization of the cube.
Edit intent: clarity
Original:  The effect of this perturbation on the partition function (Z_{L, \alpha(N), L is the length of the polymer chain, N is the size of the matrix and \alpha(}  = v/w) is the ratio of the strengths of the original and perturbed term in the action) and the Genus Distributions (%DIFDELCMD < \cal %%% N and a _{L, g, \alpha, where g is the genus ) is studied.
Revised:  The effect of this perturbation on the partition function (N), L is the length of the polymer chain, N is the size of the matrix and \alpha(} = v/w) is the ratio of the strengths of the original and perturbed term in the action) and the Genus Distributions (%DIFDELCMD < \cal %%% N and a _{L, g, \alpha, where g is the genus ) is studied.
Edit intent: coherence
Original:  The effect of this perturbation on the partition function (Z_{L, \alpha(N), L is the length of the polymer chain, N is the size of the matrix and \alpha(}  = v/w) is the ratio of the strengths of the original and perturbed term in the action) and the Genus Distributions (%DIFDELCMD < \cal %%% N and a _{L, g, \alpha, where g is the genus ) is studied.
Revised:  The effect of this perturbation on the partition function (Z_{L, \alpha(N), L is the length of the polymer chain, N is the size of the matrix and \alpha(} = v/w) is the ratio of the strengths of the original and perturbed term in the action) %DIFDELCMD < \cal %%% N and a _{L, g, \alpha, where g is the genus ) is studied.
Edit intent: coherence
Original:  We compare the results of the extended  model with the original RNA model of H. Orland and A. Zee , Nuclear Physics B620 FS%DIFDELCMD < ]%%% , 456 (2002 ).
Revised:  We compare the results of the extended RNA model with the original RNA model of H. Orland and A. Zee , Nuclear Physics B620 FS%DIFDELCMD < ]%%% , 456 (2002 ).
Edit intent: fluency
Original:  We compare the results of the extended  model with the original RNA model of H. Orland and A. Zee , Nuclear Physics B620 FS%DIFDELCMD < ]%%% , 456 (2002 ).
Revised:  We compare the results of the extended model with the original RNA model of H. Orland and A. Zee FS%DIFDELCMD < ]%%% , 456 (2002 ).
Edit intent: coherence
Original:  We compare the results of the extended  model with the original RNA model of H. Orland and A. Zee , Nuclear Physics B620 FS%DIFDELCMD < ]%%% , 456 (2002 ).
Revised:  We compare the results of the extended model with the original RNA model of H. Orland and A. Zee , Nuclear Physics B620 %DIFDELCMD < ]%%% , 456 (2002 ).
Edit intent: fluency
Original:  However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbor .
Revised:  However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbors .
Edit intent: coherence
Original:  In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient.
Revised:  In such cases, local clustering has traditionally been set to zero and this value influenced the global clustering coefficient.
Edit intent: clarity
Original:  Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks.
Revised:  Such a procedure leads to underestimation of the neighborhood clustering in sparse networks.
Edit intent: clarity
Original: A scaling analysis is presented of the statistics of long DNA confined in nanochannel and nanoslits.
Revised: A scaling analysis is presented of the statistics of long DNA confined in nanochannels and nanoslits.
Edit intent: fluency
Original:  We furthemore give an explicit formula for a higher order approximation and we test both approximations numerically for a class of one-factor interest rate models.
Revised:  We furthermore give an explicit formula for a higher order approximation and we test both approximations numerically for a class of one-factor interest rate models.
Edit intent: coherence
Original:  Which of these outcomes will occur crucially depends on the 'competition kernel' , which reflects the shape of the resource utilization pattern of the competing species.
Revised:  Which of these outcomes will occur crucially depends on the competition kernel , which reflects the shape of the resource utilization pattern of the competing species.
Edit intent: fluency
Original:  Most models considered in the literature assume a Gaussian (bell-shaped) competition kernel.
Revised:  Most models considered in the literature assume a Gaussian competition kernel.
Edit intent: clarity
Original:  In fact, Gaussian kernels are a border case scenario of ecologically relevant kernels , and slight deviations from the Gaussian assumption can lead to either uniform or lumped species distributions.
Revised:  In fact, Gaussian kernels are a border case scenario , and slight deviations from the Gaussian assumption can lead to either uniform or lumped species distributions.
Edit intent: clarity
Original:  In fact, Gaussian kernels are a border case scenario of ecologically relevant kernels , and slight deviations from the Gaussian assumption can lead to either uniform or lumped species distributions.
Revised:  In fact, Gaussian kernels are a border case scenario of ecologically relevant kernels , and slight deviations from this function can lead to either uniform or lumped species distributions.
Edit intent: clarity
Original:  Here we illustrate the non-robustness of the Gaussian assumption by simulations of the standard competition model with constant carrying capacity and different competition kernels .
Revised:  Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity and different competition kernels .
Edit intent: clarity
Original:  Here we illustrate the non-robustness of the Gaussian assumption by simulations of the standard competition model with constant carrying capacity and different competition kernels .
Revised:  Here we illustrate the non-robustness of the Gaussian assumption by simulations of the standard competition model with constant carrying capacity .
Edit intent: clarity
Original:  In this scenario, lumped species distributions can come about by  details of the numerical implementation of the model or by secondary ecological or evolutionary mechanisms .
Revised:  In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model or by secondary ecological or evolutionary mechanisms .
Edit intent: fluency
Original:  We show also that cobweb tiling problem is a particular case of clique problem in a certain graph .
Revised:  We show also that cobweb tiling problem into a clique problem of a graph specially invented for that purpose - is proposed here too .
Edit intent: coherence
Original:  To this end we illustrate the area of our reconnaissance by means of the Venn type map of various cobweb sequences families according to definitions from 3,4 .
Revised:  To this end we illustrate the area of our reconnaissance by means of the Venn type map of various cobweb sequences families 3,4 .
Edit intent: clarity
Original:  To this end we illustrate the area of our reconnaissance by means of the Venn type map of various cobweb sequences families according to definitions from 3,4 .
Revised:  To this end we illustrate the area of our reconnaissance by means of the Venn type map of various cobweb sequences families according to definitions from .
Edit intent: coherence
Original: The Resource Description Framework (RDF) is a standard semantic network data model that is used to create machine-understandable descriptions of the world and is the basis of the Semantic Web ;
Revised: The Resource Description Framework (RDF) is a semantic network data model that is used to create machine-understandable descriptions of the world and is the basis of the Semantic Web ;
Edit intent: clarity
Original:  The model minimizes implied volatility bias (for 2004-2007 S& P100 index options) and theoretically yields skews correspondent to practical term structure for interest rate derivatives.
Revised:  The model minimizes implied volatility bias (for 2004-2007 S& P 100 index data. The model theoretically yields skews correspondent to practical term structure for interest rate derivatives.
Edit intent: clarity
Original:  It allows increasing the number of stock price distribution parameters.
Revised:  The method allows increasing the number of stock price distribution parameters.
Edit intent: clarity
Original:  It allows increasing the number of stock price distribution parameters.
Revised:  It allows increasing the number of asset price probability distribution parameters.
Edit intent: clarity
Original: We show that a simple modification to the Yao-Yao structure for Unit Disk Graphs yields a spanner YY_k of maximum degree 2k and stretch factor t%DIFDELCMD < \ge %DIFDELCMD < %%% 1/(cos 4pi/k - 2 sin 4pi/k), for any k%DIFDELCMD < \ge %%% 28. Our algorithm has the same time and communication complexity as the original Yao-Yao algorithm .
Revised: It is a standing open question to decide whether the Yao-Yao structure for Unit Disk Graphs yields a spanner YY_k of maximum degree 2k and stretch factor t%DIFDELCMD < \ge %DIFDELCMD < %%% 1/(cos 4pi/k - 2 sin 4pi/k), for any k%DIFDELCMD < \ge %%% 28. Our algorithm has the same time and communication complexity as the original Yao-Yao algorithm .
Edit intent: clarity
Original: We show that a simple modification to the Yao-Yao structure for Unit Disk Graphs yields a spanner YY_k of maximum degree 2k and stretch factor t%DIFDELCMD < \ge %DIFDELCMD < %%% 1/(cos 4pi/k - 2 sin 4pi/k), for any k%DIFDELCMD < \ge %%% 28. Our algorithm has the same time and communication complexity as the original Yao-Yao algorithm .
Revised: We show that a simple modification to the Yao-Yao structure for %DIFDELCMD < \ge %DIFDELCMD < %%% 1/(cos 4pi/k - 2 sin 4pi/k), for any k%DIFDELCMD < \ge %%% 28. Our algorithm has the same time and communication complexity as the original Yao-Yao algorithm .
Edit intent: clarity
Original: We show that a simple modification to the Yao-Yao structure for Unit Disk Graphs yields a spanner YY_k of maximum degree 2k and stretch factor t%DIFDELCMD < \ge %DIFDELCMD < %%% 1/(cos 4pi/k - 2 sin 4pi/k), for any k%DIFDELCMD < \ge %%% 28. Our algorithm has the same time and communication complexity as the original Yao-Yao algorithm .
Revised: We show that a simple modification to the Yao-Yao structure for Unit Disk Graphs yields a spanner YY_k of maximum degree 2k and stretch factor t%DIFDELCMD < \ge %DIFDELCMD < %%% %DIFDELCMD < \ge %%% 28. Our algorithm has the same time and communication complexity as the original Yao-Yao algorithm .
Edit intent: coherence
Original:  Here, we get exact and asymptotic enumeration results on hypergraphs by mean of exponential generating functions.
Revised:  Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions.
Edit intent: fluency
Original: Here we show that correlated interactions of the indirect reciprocity type together with affective behavior and evolutionary selection rules changing with time are necessary  for the emergence of significant information exchange.
Revised: Here we show that correlated interactions of the indirect reciprocity type together with affective behavior and selection rules changing with time are necessary for the emergence of significant information exchange.
Edit intent: clarity
Original: Here we show that correlated interactions of the indirect reciprocity type together with affective behavior and evolutionary selection rules changing with time are necessary  for the emergence of significant information exchange.
Revised: Here we show that correlated interactions of the indirect reciprocity type together with affective behavior and evolutionary selection rules changing with time are necessary conditions for the emergence of significant information exchange.
Edit intent: clarity
Original:  They indicate as well new pathways for artificial evolution of information based phenomena, like complexity, modularity and intelligence .
Revised:  They indicate as well new pathways for evolution of information based phenomena, like complexity, modularity and intelligence .
Edit intent: clarity
Original:  They indicate as well new pathways for artificial evolution of information based phenomena, like complexity, modularity and intelligence .
Revised:  They indicate as well new pathways for artificial evolution of information based phenomena, such as intelligence and complexity .
Edit intent: clarity
Original: We investigate how a catastrophic event affects the extinction probability of an isolated  population whose dynamics is governed by a stochastic birth-death process.
Revised: We investigate how a catastrophic event increases the extinction probability of an isolated population whose dynamics is governed by a stochastic birth-death process.
Edit intent: clarity
Original:  Using the simple Verhulst logistic model as an example, we combine the probability generating function technique with an eikonal approximation to calculate, with exponential accuracy, the extinction probability caused by the catastrophe.
Revised:  Using the simple Verhulst logistic model as an example, we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction probability caused by the catastrophe.
Edit intent: clarity
Original:  This quantity is given by the  action computed over `` the optimal path"  of an effective classical Hamiltonian system with a time-dependent Hamiltonian.
Revised:  This quantity is given by the action computed over " the optimal path" of an effective classical Hamiltonian system with a time-dependent Hamiltonian.
Edit intent: fluency
Original:  It is predicted that transport properties of such channels are dramatically different from the neutral wild type \alpha-hemolysin channel.
Revised:  It is predicted that transport properties of such channels are dramatically different from neutral wild type \alpha-hemolysin channel.
Edit intent: fluency
Original: We propose a new algorithm, termed subspace pursuit, for signal reconstruction of sparse and compressible signals with and without noisy perturbations  .
Revised: We propose a new method for reconstruction of sparse and compressible signals with and without noisy perturbations .
Edit intent: clarity
Original: We propose a new algorithm, termed subspace pursuit, for signal reconstruction of sparse and compressible signals with and without noisy perturbations  .
Revised: We propose a new algorithm, termed subspace pursuit, for signal reconstruction of sparse signals with and without noisy perturbations .
Edit intent: clarity
Original:  The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques, and reconstruction capability of the same order as that of l_{1 optimization methods.
Revised:  The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques, and reconstruction accuracy of the same order as that of l_{1 optimization methods.
Edit intent: clarity
Original:  The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques, and reconstruction capability of the same order as that of l_{1 optimization methods.
Revised:  The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques, and reconstruction capability of the same order as that of LP optimization methods.
Edit intent: clarity
Original:  The presented analysis shows that in the noiseless setting, the proposed algorithm is capable of exactly reconstructing an arbitrary sparse signals , provided that the linear measurements satisfy the restricted isometry property with a constant parameter which can be described in a closed form .
Revised:  The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals , provided that the linear measurements satisfy the restricted isometry property with a constant parameter which can be described in a closed form .
Edit intent: clarity
Original:  The presented analysis shows that in the noiseless setting, the proposed algorithm is capable of exactly reconstructing an arbitrary sparse signals , provided that the linear measurements satisfy the restricted isometry property with a constant parameter which can be described in a closed form .
Revised:  The presented analysis shows that in the noiseless setting, the proposed algorithm is capable of exactly reconstructing an arbitrary sparse signals provided that the linear measurements satisfy the restricted isometry property with a constant parameter which can be described in a closed form .
Edit intent: fluency
Original:  The presented analysis shows that in the noiseless setting, the proposed algorithm is capable of exactly reconstructing an arbitrary sparse signals , provided that the linear measurements satisfy the restricted isometry property with a constant parameter which can be described in a closed form .
Revised:  The presented analysis shows that in the noiseless setting, the proposed algorithm is capable of exactly reconstructing an arbitrary sparse signals , provided that the sensing matrix satisfies the restricted isometry property with a constant parameter which can be described in a closed form .
Edit intent: clarity
Original:  The presented analysis shows that in the noiseless setting, the proposed algorithm is capable of exactly reconstructing an arbitrary sparse signals , provided that the linear measurements satisfy the restricted isometry property with a constant parameter which can be described in a closed form .
Revised:  The presented analysis shows that in the noiseless setting, the proposed algorithm is capable of exactly reconstructing an arbitrary sparse signals , provided that the linear measurements satisfy the restricted isometry property with a constant parameter .
Edit intent: clarity
Original:  In the noisy setting and  the case where the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by a constant multiple of the measurement and signal pertubation energy .
Revised:  In the noisy setting and in the case that the case where the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by a constant multiple of the measurement and signal pertubation energy .
Edit intent: fluency
Original:  In the noisy setting and  the case where the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by a constant multiple of the measurement and signal pertubation energy .
Revised:  In the noisy setting and the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by a constant multiple of the measurement and signal pertubation energy .
Edit intent: clarity
Original:  In the noisy setting and  the case where the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by a constant multiple of the measurement and signal pertubation energy .
Revised:  In the noisy setting and the case where the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by constant multiples of the measurement and signal pertubation energy .
Edit intent: fluency
Original:  In the noisy setting and  the case where the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by a constant multiple of the measurement and signal pertubation energy .
Revised:  In the noisy setting and the case where the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by a constant multiple of the measurement and signal perturbation energies .
Edit intent: fluency
Original:  Furthermore , the generated time series are long-range correlated  .
Revised:  Moreover , the generated time series are long-range correlated .
Edit intent: fluency
Original: The method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations.
Revised: A method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations.
Edit intent: fluency
Original: Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life datasets .
Revised: Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets .
Edit intent: clarity
Original:  More precisely, we investigate learning algorithms that satisfy differential privacy, a recent notion that provides meaningful confidentiality guarantees in the presence of arbitrary side information .
Revised:  More precisely, we investigate learning algorithms that satisfy differential privacy, a notion that provides meaningful confidentiality guarantees in the presence of arbitrary side information .
Edit intent: clarity
Original:  More precisely, we investigate learning algorithms that satisfy differential privacy, a recent notion that provides meaningful confidentiality guarantees in the presence of arbitrary side information .
Revised:  More precisely, we investigate learning algorithms that satisfy differential privacy, a recent notion that provides strong confidentiality guarantees in the presence of arbitrary side information .
Edit intent: clarity