wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations  .
Revised:  The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations .The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters .
Edit intent: meaning-changed
Original:  GeneSurrounder integrates transcriptomic data and pathway network information in a novel two--step procedure to detect genes that (i) appear to influence the expression of other genes local to it in the network and (ii) are part of a subnetwork of differentially expressed genes.
Revised:  GeneSurrounder integrates transcriptomic data and pathway network information in a novel two-step procedure to detect genes that (i) appear to influence the expression of other genes local to it in the network and (ii) are part of a subnetwork of differentially expressed genes.
Edit intent: fluency
Original:  Using tools from stochastic geometry, we derive approximations for the Signal-to-Interference-plus-Noise ratio (SINR) outage probability, as well as the probability that a user achieves a target communication rate (rate coverage probability).
Revised:  Using tools from stochastic geometry, we derive approximations for the Signal-to-Interference-plus-Noise Ratio (SINR) outage probability, as well as the probability that a user achieves a target communication rate (rate coverage probability).
Edit intent: fluency
Original:  In particular , we show that smaller antenna beamwidths and, unlike bi-dimensional mmWave cellular networks, smaller BS densities do not necessarily have a disruptive impact on improving the SINR outage probability , and consequently the rate coverage probability .
Revised:  In considered highway scenarios , we show that smaller antenna beamwidths and, unlike bi-dimensional mmWave cellular networks, smaller BS densities do not necessarily have a disruptive impact on improving the SINR outage probability , and consequently the rate coverage probability .
Edit intent: meaning-changed
Original:  In particular , we show that smaller antenna beamwidths and, unlike bi-dimensional mmWave cellular networks, smaller BS densities do not necessarily have a disruptive impact on improving the SINR outage probability , and consequently the rate coverage probability .
Revised:  In particular , we show that reducing the horizontal beamwidth from 90^\circ to 30^\circ determines a minimal reduction in the SINR outage probability (namely, 4 \cdot 10^{-2 unlike bi-dimensional mmWave cellular networks, smaller BS densities do not necessarily have a disruptive impact on improving the SINR outage probability , and consequently the rate coverage probability .
Edit intent: meaning-changed
Original:  In particular , we show that smaller antenna beamwidths and, unlike bi-dimensional mmWave cellular networks, smaller BS densities do not necessarily have a disruptive impact on improving the SINR outage probability , and consequently the rate coverage probability .
Revised:  In particular , we show that smaller antenna beamwidths and, unlike bi-dimensional mmWave cellular networks, for small BS densities (namely, one BS every 500 m) it is still possible to achieve an SINR outage probability , and consequently the rate coverage probability .
Edit intent: meaning-changed
Original:  In particular , we show that smaller antenna beamwidths and, unlike bi-dimensional mmWave cellular networks, smaller BS densities do not necessarily have a disruptive impact on improving the SINR outage probability , and consequently the rate coverage probability .
Revised:  In particular , we show that smaller antenna beamwidths and, unlike bi-dimensional mmWave cellular networks, smaller BS densities do not necessarily have a disruptive impact on improving the SINR outage probability smaller than 0.2 .
Edit intent: meaning-changed
Original:  On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with \pi_1(X) trivial), compute the higher homotopy group \pi_d(X) for any given d\geq 2. \%The first such algorithm was given by Brown, and more recently, Cadek et al.
Revised:  On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with \pi_1(X) trivial), compute the higher homotopy group \pi_d(X) for any given d\geq 2. \%The first such algorithm was given by Brown, and more recently, Cadek et al.
Edit intent: fluency
Original: Cross fields are auxiliary in the generation of quadrangular meshes. A method to generate cross fields on surface manifolds is presented in this paper . Algebraic topology constraints on quadrangular meshes are first discussed.
Revised: This paper proposes a method to compute crossfields based on the Ginzburg-Landau theory. The Ginzburg-Landau functional has two terms: the Dirichlet energy of the distribution and a term penalizing the mismatch between the fixed and actual norm of the distribution. Directional fields on surfaces are known to have a number of critical points, which are properly identified with the Ginzburg-Landau approach: the asymptotic behavior of Ginzburg-Landau problem provides well-distributed critical points over the 2-manifold, whose indices are as low as possible. The central idea in this paper . Algebraic topology constraints on quadrangular meshes are first discussed.
Edit intent: meaning-changed
Original:  A method to generate cross fields on surface manifolds is presented in this paper . Algebraic topology constraints on quadrangular meshes are first discussed. The duality between quadrangular meshes and cross fields is then outlined, and a generalization to cross fields of the Poincar\'e-Hopf theorem is proposed, which highlights some fundamental and important topological constraints on cross fields.
Revised:  A method to generate cross fields on surface manifolds is presented in this paper is to exploit this theoretical background for crossfield computation on arbitrary surfaces. Such crossfields are instrumental in the generation of meshes with quadrangular elements. The relation between the topological properties of quadrangular meshes and cross fields is then outlined, and a generalization to cross fields of the Poincar\'e-Hopf theorem is proposed, which highlights some fundamental and important topological constraints on cross fields.
Edit intent: meaning-changed
Original:  The duality between quadrangular meshes and cross fields is then outlined, and a generalization to cross fields of the Poincar\'e-Hopf theorem is proposed, which highlights some fundamental and important topological constraints on cross fields.A finite element formulation for the computation of cross fields is then presented, which is based on Ginzburg-Landau equations and makes use of edge-based Crouzeix-Raviart interpolation functions.
Revised:  The duality between quadrangular meshes and crossfields are hence first recalled. It is then shown that a crossfield on a surface can be represented by a complex function of unit norm with a number of critical points, i.e., a nearly everywhere smooth function taking its values in the unit circle of the complex plane. As maximal smoothness of the crossfield is equivalent with minimal energy, the crossfield problem is equivalent to an optimization problem based on Ginzburg-Landau equations and makes use of edge-based Crouzeix-Raviart interpolation functions.
Edit intent: meaning-changed
Original: A finite element formulation for the computation of cross fields is then presented, which is based on Ginzburg-Landau equations and makes use of edge-based Crouzeix-Raviart interpolation functions.
Revised: A finite element formulation for the computation of cross fields is then presented, which is based on Ginzburg-Landau functional. A discretization scheme with Crouzeix-Raviart interpolation functions.
Edit intent: meaning-changed
Original: A finite element formulation for the computation of cross fields is then presented, which is based on Ginzburg-Landau equations and makes use of edge-based Crouzeix-Raviart interpolation functions. It is first presented in the planar case, and then extended to a general surface manifold. Finally, application examples are solved and discussed .
Revised: A finite element formulation for the computation of cross fields is then presented, which is based on Ginzburg-Landau equations and makes use of edge-based Crouzeix-Raviart elements is applied and the correctness of the resulting finite element formulation is validated on the unit disk by comparison with an analytical solution. The method is also applied to the 2-sphere where, surprisingly but rightly, the computed critical points are not located at the vertices of a cube, but at those of an anticube .
Edit intent: meaning-changed
Original:  For this we compare backbone geometry-based (extrinsic) and structure-based (intrinsic) coordinate systems, and as an example we inspect the %DIFDELCMD < {\it %%% trans and%DIFDELCMD < {\it %%% cis peptide planes.
Revised:  For this we compare backbone geometry-based (extrinsic) and structure-based (intrinsic) coordinate systems, and as an example we inspect the %DIFDELCMD < {\it %%% and%DIFDELCMD < {\it %%% cis peptide planes.
Edit intent: fluency
Original:  For this we compare backbone geometry-based (extrinsic) and structure-based (intrinsic) coordinate systems, and as an example we inspect the %DIFDELCMD < {\it %%% trans and%DIFDELCMD < {\it %%% cis peptide planes.
Revised:  For this we compare backbone geometry-based (extrinsic) and structure-based (intrinsic) coordinate systems, and as an example we inspect the %DIFDELCMD < {\it %%% trans %DIFDELCMD < {\it %%% cis peptide planes.
Edit intent: coherence
Original:  For this we compare backbone geometry-based (extrinsic) and structure-based (intrinsic) coordinate systems, and as an example we inspect the %DIFDELCMD < {\it %%% trans and%DIFDELCMD < {\it %%% cis peptide planes.
Revised:  For this we compare backbone geometry-based (extrinsic) and structure-based (intrinsic) coordinate systems, and as an example we inspect the %DIFDELCMD < {\it %%% trans and%DIFDELCMD < {\it %%% trans and cis peptide planes.
Edit intent: coherence
Original:  We reveal systematics in the way how a %DIFDELCMD < {\it %%% cis peptide plane deforms the neighbouring atomic geometry, and we develop a virtual reality based visual methodology that can identify the presence of a %DIFDELCMD < {\it %%% cis peptide plane from the arrangement of atoms in its vicinity.
Revised:  We reveal systematics in the way how a %DIFDELCMD < {\it %%% cis peptide plane deforms the neighbouring atomic geometry, and we develop a virtual reality based visual methodology that can identify the presence of a %DIFDELCMD < {\it %%% cis peptide plane from the arrangement of atoms in its vicinity.
Edit intent: fluency
Original:  As concrete examples we identify a number of crystallographic protein structures in Protein Data Bank (PDB) that display exceptional atomic positions around their %DIFDELCMD < {\it %%% cis peptide planes.
Revised:  As concrete examples we identify a number of crystallographic protein structures in Protein Data Bank (PDB) that display exceptional atomic positions around their %DIFDELCMD < {\it %%% cis peptide planes.
Edit intent: fluency
Original: We present SimDex, a new technique for serving exact top-K recommendations on matrix factorization models that measures and optimizes for the similarity between users in the model.
Revised: We present SimDex, a new technique for serving exact top-K predictions for state-of-the-art Matrix Factorization models requires solving the Maximum Inner Product Search problem. Solving MIPS can be computationally expensive, thus spurring the recent development of several indexing techniques for this task. These techniques generally exploit similarity between user or item weights in the similarity between users in the model.
Edit intent: meaning-changed
Original: We present SimDex, a new technique for serving exact top-K recommendations on matrix factorization models that measures and optimizes for the similarity between users in the model. Previous serving techniques presume a high degree of similarity (e.g., L2 or cosine distance) among users and/or items in MF models; however, as we demonstrate, the most accurate models are not guaranteed to exhibit high similarity. As a result, brute-force matrix multiply outperforms recent proposals for top-K serving on several collaborative filtering tasks.
Revised: We present SimDex, a new technique for serving exact top-K recommendations on matrix factorization models that measures and optimizes for the models to accelerate predictions. In this paper, we show that the current state of the art does not always outperform brute-force matrix multiply outperforms recent proposals for top-K serving on several collaborative filtering tasks.
Edit intent: clarity
Original:  As a result, brute-force matrix multiply outperforms recent proposals for top-K serving on several collaborative filtering tasks. Based on this observation, we develop SimDex, a new technique for serving matrix factorization models that automatically optimizes serving based on the degree of similarity between users, and outperforms existing methods in both the high-similarity and low-similarity regimes.
Revised:  As a result, brute-force matrix multiplication: these models may have significantly less similarity than can be exploited by these techniques. To address this problem, we propose RecOpt, a system that uses an efficient, sampling-based estimation technique to automatically choose between indexing or brute force. In addition, we propose a new baseline indexing scheme, RecDex, that can leverage blocked linear algebra to improve indexing-based serving performance. Together, RecOpt and RecDex outperform state-of-the-art indexes by 3.2\times on average, and low-similarity regimes.
Edit intent: meaning-changed
Original:  Based on this observation, we develop SimDex, a new technique for serving matrix factorization models that automatically optimizes serving based on the degree of similarity between users, and outperforms existing methods in both the high-similarity and low-similarity regimes. SimDexfirst measures the degree of similarity among users via clustering and uses a cost-based optimizer to either construct an index on the model or defer to blocked matrix multiply. It leverages highly efficient linear algebra primitives in both cases to deliver predictions either from its index or from brute-force multiply. Overall, SimDex runs an averageof 2x and up to 6x faster than highly optimized baselines for the most accurate models on several popular collaborative filtering datasets .
Revised:  Based on this observation, we develop SimDex, a new technique for serving matrix factorization models that automatically optimizes serving based on the degree of similarity between users, and outperforms existing methods in both the high-similarity and up to 6x faster than highly optimized baselines for the most accurate models on several popular collaborative filtering datasets .
Edit intent: clarity
Original: Making top-K predictions for state-of-the-art Matrix Factorization models requires solving the Maximum Inner Product Search problem. Solving MIPS can be computationally expensive, thus spurring the recent development of several indexing techniques for this task.
Revised: Making top-K predictions for state-of-the-art Matrix Factorization models requires solving the Maximum Inner Product Search (MIPS) is an important task that is widely pertinent to recommender systems and high-dimensional similarity search. The brute-force approach to solving exact MIPS is computationally expensive, thus spurring the recent development of several indexing techniques for this task.
Edit intent: meaning-changed
Original:  In this paper, we show that the current state of the art does not always outperform brute-force matrix multiplication: these models may have significantly less similarity than can be exploited by these techniques. To address this problem, we propose RecOpt, a system that uses an efficient, sampling-based estimation technique to automatically choose between indexing or brute force. In addition, we propose a new baseline indexing scheme, RecDex, that can leverage blocked linear algebra to improve indexing-based serving performance .
Revised:  In this paper, we show that the current state of the art does not always outperform brute-force approach, blocked matrix multiply (BMM), can outperform the state-of-the-art MIPS solvers by over an order of magnitude, for some -- but not all -- inputs. In this paper, we also present a novel MIPS solution, MAXIMUS, that takes advantage of hardware efficiency and pruning of the search space. Like BMM, MAXIMUS is faster than other solvers by up to an order of magnitude, but again only for some inputs. Since no single solution offers the best runtime performance for all inputs, we introduce a new data-dependent optimizer, OPTIMUS, that selects online with minimal overhead the best MIPS solver for a given input .
Edit intent: meaning-changed
Original:  Together, RecOpt and RecDex outperform state-of-the-art indexes by 3.2\times on average, and up to 10.9\times, on widely studied models for recommendations and MIPS .
Revised:  Together, OPTIMUS and MAXIMUS outperform state-of-the-art indexes by 3.2\times on average, and up to 10.9\times, on widely studied models for recommendations and MIPS .
Edit intent: meaning-changed
Original:  Together, RecOpt and RecDex outperform state-of-the-art indexes by 3.2\times on average, and up to 10.9\times, on widely studied models for recommendations and MIPS .
Revised:  Together, RecOpt and RecDex outperform state-of-the-art MIPS solvers by 3.2\times on average, and up to 10.9\times, on widely studied models for recommendations and MIPS .
Edit intent: clarity
Original:  Together, RecOpt and RecDex outperform state-of-the-art indexes by 3.2\times on average, and up to 10.9\times, on widely studied models for recommendations and MIPS .
Revised:  Together, RecOpt and RecDex outperform state-of-the-art indexes by 3.2\times on average, and up to 10.9\times, on widely studied MIPS datasets .
Edit intent: clarity
Original:  Due to their minimal twist,  these frames are preferable over the usual Frenet one in many contexts , such as in motion design, sweep surface modeling, computer visualization, and in geometric considerations as well.
Revised:  Due to their minimal twist, in many contexts these frames are preferable over the usual Frenet one in many contexts , such as in motion design, sweep surface modeling, computer visualization, and in geometric considerations as well.
Edit intent: coherence
Original:  This is done by first solving the problem for spherical curves and then using the concept of osculating spheres to solve the general case. Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion , respectively, we discuss the behavior of the angle between the principal normal and a rotation minimizing vectornear these zeros.
Revised:  This is done by conveniently writing the curvature and torsion for a curve on a sphere. Later, we extend these expressions for the curvature and torsion , respectively, we discuss the behavior of the angle between the principal normal and a rotation minimizing vectornear these zeros.
Edit intent: clarity
Original:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion , respectively, we discuss the behavior of the angle between the principal normal and a rotation minimizing vectornear these zeros.
Revised:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion of a generic curve by studying its behavior near an osculating sphere, i.e., we describe them in terms of spherical analogs. Finally, we also address in this work the problem of characterizing those curves whose position vector, up to a translation, lies on a (moving) plane spanned by the angle between the principal normal and a rotation minimizing vectornear these zeros.
Edit intent: meaning-changed
Original:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion , respectively, we discuss the behavior of the angle between the principal normal and a rotation minimizing vectornear these zeros. For a curve whose torsion vanishes on intervals or isolated points only, we show that a rotation minimizing frame can be globally defined using our procedure by conveniently choosing some arbitrary constants. On the other hand, we mention that rotation minimizing frames can be well defined via their Frenet frames for analytic curves. Certainly, our approach will be of great importance in those contexts where rotation minimizing frames play a role .
Revised:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion , respectively, we discuss the behavior of the unit tangent and a rotation minimizing vector field and prove that they are precisely the plane curves .
Edit intent: meaning-changed
Original: In this work we furnish characterizations of spherical and plane curves using rotation minimizing frames. Due to their minimal twist, in many contexts these frames are preferable over the usual Frenet one, such as in motion design, sweep surface modeling, computer visualization, and in geometric considerations as well. Here, we first furnish an alternative proof for the characterization of spherical curves by using osculating spheres described in terms of a rotation minimizing frame. In addition , we show how to find the angle between the principal normal and a rotation minimizing vector for a spherical curve.
Revised: In this work , we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature and torsion for a curve on a sphere , we show how to find the angle between the principal normal and a rotation minimizing vector for a spherical curve.
Edit intent: meaning-changed
Original:  Later, we extend these expressions for the curvature and torsion of a generic curve by studying its behavior near an osculating sphere, i.e., we describe them in terms of spherical analogs. Finally, we also address in this work the problem of characterizing those curves whose position vector  , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Revised:  Later, we characterize plane and spherical curves as curves whose position vector , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Edit intent: clarity
Original:  Finally, we also address in this work the problem of characterizing those curves whose position vector  , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Revised:  Finally, we also address in this work the problem of characterizing those curves whose position vector lies , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Edit intent: meaning-changed