wanyu/IteraTeR_v2 huggingface dataset:
Original:  The fit allows us to make best estimates of the preferences of individual nodes, define metrics to quantify individual variation in assortativity, perform sensitive community detection even in the absence of traditional assortative structure, and accurately predict missing data in unlabeled or partially labeled networks .
Revised:  We propose metrics to characterize the mean and variation of mixing patterns and show how to infer their values from the fitted model, either using maximum-likelihood estimates of model parameters or in a Bayesian framework that does not require fixing any parameters .
Edit intent: clarity
Original: Nonlinear dynamical systems are ubiquitous in science and engineering, yet many issues still exist related to the analysis and prediction of these systems . Koopman theory circumvents these issues by transforming the finite-dimensional nonlinear dynamics to a linear dynamical system of functions in an infinite-dimensional Hilbert space of observables.
Revised: Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems . Koopman theory circumvents these issues by transforming the finite-dimensional nonlinear dynamics to a linear dynamical system of functions in an infinite-dimensional Hilbert space of observables.
Edit intent: clarity
Original:  Physicians primarily diagnose Parkinson's disease by performing a clinical assessment of symptoms.
Revised:  Clinicians primarily diagnose Parkinson's disease by performing a clinical assessment of symptoms.
Edit intent: fluency
Original:   Our results confirm that smartphone data collected over extended periods of time could in the future potentially be used as additional evidence for the diagnosis of Parkinson's disease.
Revised:  Our results confirm that smartphone data collected over extended periods of time could in the future potentially be used as a digital biomarker for the diagnosis of Parkinson's disease.
Edit intent: clarity
Original: In this paper we analyze the computational cost of various operations performed symbolically in real algebraic number fields where the elements are represented as polynomials of a primitive element of the field.
Revised: In this paper we analyze the computational costs of various operations performed symbolically in real algebraic number fields where the elements are represented as polynomials of a primitive element of the field.
Edit intent: fluency
Original: In this paper we analyze the computational cost of various operations performed symbolically in real algebraic number fields where the elements are represented as polynomials of a primitive element of the field.
Revised: In this paper we analyze the computational cost of various operations and algorithms in algebraic number fields where the elements are represented as polynomials of a primitive element of the field.
Edit intent: clarity
Original:  Previously, such run time was known only for the case of p = 1 (\ell_1 distances) , by Gawrychowski and Uzna\'nski [ICALP 2018] and only with a randomized algorithm.
Revised:  Previously, such run time was known only for the case of \ell_1 distance , by Gawrychowski and Uzna\'nski [ICALP 2018] and only with a randomized algorithm.
Edit intent: coherence
Original:  For  0 \le p \le 1 we show a randomized algorithm for the (\ell_p)^p distance (the p-th power of the \ell_p distance) , thereby providing a smooth tradeoff between algorithms of Kopelowitz and Porat [FOCS~2015, SOSA~2018] for Hamming distance (case of p=0) and of Gawrychowski and Uzna\'nski for \ell_1 distance.
Revised:  For 0 \le p \le 1 we show a randomized algorithm for the \ell_p , thereby providing a smooth tradeoff between algorithms of Kopelowitz and Porat [FOCS~2015, SOSA~2018] for Hamming distance (case of p=0) and of Gawrychowski and Uzna\'nski for \ell_1 distance.
Edit intent: clarity
Original: We interpret uncertainty in the parameters of a model for seismic wave propagation by treating the  parameters as random variables, and we apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables.
Revised: We interpret uncertainty in a model for seismic wave propagation by treating the parameters as random variables, and we apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables.
Edit intent: clarity
Original: We interpret uncertainty in the parameters of a model for seismic wave propagation by treating the  parameters as random variables, and we apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables.
Revised: We interpret uncertainty in the parameters of a model for seismic wave propagation by treating the model parameters as random variables, and we apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables.
Edit intent: clarity
Original: We interpret uncertainty in the parameters of a model for seismic wave propagation by treating the  parameters as random variables, and we apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables.
Revised: We interpret uncertainty in the parameters of a model for seismic wave propagation by treating the parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables.
Edit intent: fluency
Original:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake  from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI   is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Revised:  Targeting source inversion problems, where we seek to infer the source of an earthquake from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Edit intent: clarity
Original:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake  from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI   is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Revised:  Aiming to solve source inversion problems, where the source of an earthquake from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Edit intent: clarity
Original:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake  from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI   is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Revised:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake is inferred from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Edit intent: clarity
Original:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake  from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI   is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Revised:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake from ground motion recordings on the Earth's surface, we consider two QoI that measure the discrepancies between computed seismic signals and given reference signals: one QoI is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Edit intent: fluency
Original:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake  from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI   is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Revised:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI , is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Edit intent: fluency
Original:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake  from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI   is defined in terms of the L2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Revised:  Aiming to solve source inversion problems, where we seek to infer the source of an earthquake from ground motion recordings on the Earth's surface, we consider two QoI which measure the discrepancy between computed seismic signals and given reference signals: one QoI is defined in terms of the L^2-misfit , which is directly related to maximum likelihood estimates of the source parameters;
Edit intent: clarity
Original:  the other   is based on the quadratic Wasserstein distance between probability distributions, and represents one possible choice in a class of such misfit functions which have become increasingly popular for seismic inversion .
Revised:  the other , is based on the quadratic Wasserstein distance between probability distributions, and represents one possible choice in a class of such misfit functions which have become increasingly popular for seismic inversion .
Edit intent: fluency
Original:  the other   is based on the quadratic Wasserstein distance between probability distributions, and represents one possible choice in a class of such misfit functions which have become increasingly popular for seismic inversion .
Revised:  the other is based on the quadratic Wasserstein distance between probability distributions, and represents one possible choice in a class of such misfit functions that have become increasingly popular for seismic inversion .
Edit intent: fluency
Original:  With this code, using random coefficients and deterministic initial and boundary data, we have performed benchmark numerical experiments with synthetic data in a two-dimensional physical domain with a one-dimensional velocity model where the assumed parameter uncertainty is motivated by realistic Earth models.
Revised:  With this code, using random coefficients and deterministic initial and boundary data, we present benchmark numerical experiments with synthetic data in a two-dimensional physical domain with a one-dimensional velocity model where the assumed parameter uncertainty is motivated by realistic Earth models.
Edit intent: clarity
Original:  With this code, using random coefficients and deterministic initial and boundary data, we have performed benchmark numerical experiments with synthetic data in a two-dimensional physical domain with a one-dimensional velocity model where the assumed parameter uncertainty is motivated by realistic Earth models.
Revised:  With this code, using random coefficients and deterministic initial and boundary data, we have performed benchmark numerical experiments with synthetic data in a two-dimensional physical domain and a one-dimensional velocity model where the assumed parameter uncertainty is motivated by realistic Earth models.
Edit intent: fluency
Original:  In this test case, the MLMC method reduced the computational cost of the standard Monte Carlo (MC) method by up to 97\% for the L2-based QoI \hbox{QoI} and up to 78\% for the QoI based on the quadratic Wasserstein distance, for \hbox{QoI} a relevant range of tolerances.
Revised:  Here, the computational cost of the standard Monte Carlo (MC) method by up to 97\% for the L2-based QoI \hbox{QoI} and up to 78\% for the QoI based on the quadratic Wasserstein distance, for \hbox{QoI} a relevant range of tolerances.
Edit intent: clarity
Original:  In this test case, the MLMC method reduced the computational cost of the standard Monte Carlo (MC) method by up to 97\% for the L2-based QoI \hbox{QoI} and up to 78\% for the QoI based on the quadratic Wasserstein distance, for \hbox{QoI} a relevant range of tolerances.
Revised:  In this test case, the MLMC method reduced the computational cost of the standard Monte Carlo method was reduced by up to 97\% for the L2-based QoI \hbox{QoI} and up to 78\% for the QoI based on the quadratic Wasserstein distance, for \hbox{QoI} a relevant range of tolerances.
Edit intent: clarity
Original:  Extending the method to three-dimensional domains is straight-forward and will further increase the relative computational work reduction , allowing the solution of source inversion problems which would be infeasible using standard MC .
Revised:  Shifting to three-dimensional domains is straight-forward and will further increase the relative computational work reduction , allowing the solution of source inversion problems which would be infeasible using standard MC .
Edit intent: clarity
Original:  Extending the method to three-dimensional domains is straight-forward and will further increase the relative computational work reduction , allowing the solution of source inversion problems which would be infeasible using standard MC .
Revised:  Extending the method to three-dimensional domains is straight-forward and will further increase the relative computational work reduction .
Edit intent: coherence
Original: There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of r- and (r,s)-robustness.
Revised: Convergence guarantees of many resilient consensus algorithms are based on the graph theoretic properties of r- and (r,s)-robustness.
Edit intent: clarity
Original:  We analyse a simple tessellation technique based on the regular icosahedron, which decreases the upper-bound for the online version of this problem to around 2.84.
Revised:  We analyse a simple tessellation technique based on the regular icosahedron, which improves the upper-bound for the online version of this problem to around 2.84.
Edit intent: clarity
Original:  We analyse a simple tessellation technique based on the regular icosahedron, which decreases the upper-bound for the online version of this problem to around 2.84.
Revised:  We analyse a simple tessellation technique based on the regular icosahedron, which decreases the upper-bound for the online version of this problem , decreasing it to approximately 2.84.
Edit intent: clarity
Original:  We estimate deposition of iron (another potential fertilizer) and find it also to be too small to be significant.
Revised:  We estimate deposition of iron (another potential fertilizer) and find it is also too small to be significant.
Edit intent: fluency
Original:  The recurrent nature of the model allows complex dependencies between  items to be captured directly in a flexible and scalable way.
Revised:  The recurrent nature of the model allows complex dependencies between the items to be captured directly in a flexible and scalable way.
Edit intent: fluency
Original: Cell-cell communication is often achieved by diffusible signaling molecules that bind membrane-bound receptors.
Revised: Cell-cell communication is often achieved by secreted signaling molecules that bind membrane-bound receptors.
Edit intent: clarity
Original: The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz [2001] is the most widely used method for pricing options with early exercise features .
Revised: The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz [2001] is widely used for pricing American options .
Edit intent: clarity
Original:  The LSM estimator contains  look-ahead bias, and the conventional technique of removing it necessitates an independent set of simulations.
Revised:  The LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates an independent set of simulations.
Edit intent: clarity
Original:  The leave-one-out LSM (LOOLSM) method is illustrated with examples, including  multi-asset options whose LSM price is biased high.
Revised:  The leave-one-out LSM (LOOLSM) method is illustrated with examples, including the multi-asset options whose LSM price is biased high.
Edit intent: fluency
Original:  The asymptotic behavior of look-ahead bias is also discussed with the LOOLSM approach .
Revised:  The asymptotic behavior of look-ahead bias by measuring it using the LOOLSM method. The analysis and computational evidence support our findings .
Edit intent: clarity
Original: The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz  2001  is widely used for pricing American options.
Revised: The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz ( 2001 is widely used for pricing American options.
Edit intent: fluency
Original: The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz  2001  is widely used for pricing American options.
Revised: The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz 2001 ) is widely used for pricing American options.
Edit intent: fluency
Original:  At present, there are several flavours of the method, including ` cell-centre ', `staggered', `vertex-centred', `periodic heterogenous microstructural', `Godunov-type', `matrix-free', `meshless', as well as others.
Revised:  At present, there are several flavours of the method, including ` cell-centred ', `staggered', `vertex-centred', `periodic heterogenous microstructural', `Godunov-type', `matrix-free', `meshless', as well as others.
Edit intent: fluency
Original:  This article gives an overview, historical perspective, comparison and critical analysis of the different approaches , including their relative strengths, weaknesses, similarities and dissimilarities, where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given.
Revised:  This article gives an overview, historical perspective, comparison and critical analysis of the different approaches where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given.
Edit intent: coherence
Original:  The article finishes with a look towards future research directions and steps required for finite volume solid mechanics to achieve  widespread acceptance.
Revised:  The article finishes with a look towards future research directions and steps required for finite volume solid mechanics to achieve more widespread acceptance.
Edit intent: clarity
Original: We consider unions of interior disjoint discs in the plane such that the graph whose vertices are disc centers and edges connect centers of mutually tangent discs is triangulated, called compact packings .
Revised: A compact packing is a set of non-overlapping discs where all the holes between discs are curvilinear triangles .
Edit intent: clarity
Original:  It has been proven that there are exactly 9 values of r which allow a compact packing with discs of radius 1 and r.
Revised:  It has been proven that there are exactly 9 values of r which allow a compact packing by discs of sizes 1 and r.
Edit intent: clarity
Original:  It has also been proven that at most 11462 pairs (r,s) allow a compact packing with discs of radius 1, r and s . This paper shows that there are exactly 164 such pairs (r,s) .
Revised:  It has also been proven that at most 11462 pairs (r,s) allowing a compact packing with discs of radius 1, r and s . This paper shows that there are exactly 164 such pairs (r,s) .
Edit intent: fluency
Original:  It has also been proven that at most 11462 pairs (r,s) allow a compact packing with discs of radius 1, r and s . This paper shows that there are exactly 164 such pairs (r,s) .
Revised:  It has also been proven that at most 11462 pairs (r,s) allow a compact packing by discs of sizes 1, r and s . This paper shows that there are exactly 164 such pairs (r,s) .
Edit intent: clarity
Original:  It has also been proven that at most 11462 pairs (r,s) allow a compact packing with discs of radius 1, r and s . This paper shows that there are exactly 164 such pairs (r,s) .
Revised:  It has also been proven that at most 11462 pairs (r,s) allow a compact packing with discs of radius 1, r and s .
Edit intent: coherence
Original: The kth-power of a given graph G=(V,E) is obtained from G by adding an edge between every two distinct vertices at a distance at most k in G. We call G a k-Steiner power if it is an induced subgraph of the kth-power of some tree.
Revised: The k^{th of a given graph G=(V,E) is obtained from G by adding an edge between every two distinct vertices at a distance at most k in G. We call G a k-Steiner power if it is an induced subgraph of the kth-power of some tree.
Edit intent: clarity
Original: The kth-power of a given graph G=(V,E) is obtained from G by adding an edge between every two distinct vertices at a distance at most k in G. We call G a k-Steiner power if it is an induced subgraph of the kth-power of some tree.
Revised: The kth-power of a given graph G=(V,E) is obtained from G by adding an edge between every two distinct vertices at a distance at most k in G. We call G a k-Steiner power if it is an induced subgraph of the k^{th of some tree.
Edit intent: clarity
Original:  A graph G is termed k-leaf power if there is some tree T such that: all vertices in V(G) are leaf-nodes of T, and G is an induced subgraph of the kth-power of T. As a byproduct of our main result, we give the first known polynomial-time recognition algorithm for 6-leaf powers.
Revised:  A graph G is termed k-leaf power if there is some tree T such that: all vertices in V(G) are leaf-nodes of T, and G is an induced subgraph of the k^{th of T. As a byproduct of our main result, we give the first known polynomial-time recognition algorithm for 6-leaf powers.
Edit intent: clarity
Original: For a market with m assets and T discrete trading sessions, Cover and Ordentlich (1998) found that the " Cost of Achieving the Best Rebalancing Rule in Hindsight " is p(T,m)=\sumn_1+\cdot\cdot\cdot+n_m=TT{n_1,...,n_m}(n_1/T)^{n_1}\cdot\cdot\cdot(n_m/T)^{n_m}.
Revised: For a market with m assets and T discrete trading sessions, Ordentlich and Cover (1998) found that the " Cost of Achieving the Best Rebalancing Rule in Hindsight " is p(T,m)=\sumn_1+\cdot\cdot\cdot+n_m=TT{n_1,...,n_m}(n_1/T)^{n_1}\cdot\cdot\cdot(n_m/T)^{n_m}.
Edit intent: fluency