wanyu/IteraTeR_v2 huggingface dataset:
Original: This article presents a fast solver for the dense "frontal" matrices that arise from the multi-frontal sparse elimination process of 2D and 3D elliptic PDEs.
Revised: This article presents a fast solver for the dense "frontal" matrices that arise from the multifrontal sparse elimination process of 2D and 3D elliptic PDEs.
Edit intent: fluency
Original: This article presents a fast solver for the dense "frontal" matrices that arise from the multi-frontal sparse elimination process of 2D and 3D elliptic PDEs.
Revised: This article presents a fast solver for the dense "frontal" matrices that arise from the multi-frontal sparse elimination process of 3D elliptic PDEs.
Edit intent: clarity
Original:  We also explore a variety of other low-rank approximation methods such as the adaptive cross approximation (ACA) and Chebyshev interpolation for the low-rank approximation of the off-diagonal blocks . Using the HODLR direct solver as a preconditioner (with a low tolerance)  , we can reach machine accuracy with a simple fixed point iterative scheme much faster than a conventional LU solver.
Revised:  We compare this new low-rank approximation methods such as the adaptive cross approximation (ACA) and Chebyshev interpolation for the low-rank approximation of the off-diagonal blocks . Using the HODLR direct solver as a preconditioner (with a low tolerance) , we can reach machine accuracy with a simple fixed point iterative scheme much faster than a conventional LU solver.
Edit intent: coherence
Original:  We also explore a variety of other low-rank approximation methods such as the adaptive cross approximation (ACA) and Chebyshev interpolation for the low-rank approximation of the off-diagonal blocks . Using the HODLR direct solver as a preconditioner (with a low tolerance)  , we can reach machine accuracy with a simple fixed point iterative scheme much faster than a conventional LU solver.
Revised:  We also explore a variety of other low-rank approximation method to the adaptive cross approximation (ACA) and Chebyshev interpolation for the low-rank approximation of the off-diagonal blocks . Using the HODLR direct solver as a preconditioner (with a low tolerance) , we can reach machine accuracy with a simple fixed point iterative scheme much faster than a conventional LU solver.
Edit intent: clarity
Original:  We also explore a variety of other low-rank approximation methods such as the adaptive cross approximation (ACA) and Chebyshev interpolation for the low-rank approximation of the off-diagonal blocks . Using the HODLR direct solver as a preconditioner (with a low tolerance)  , we can reach machine accuracy with a simple fixed point iterative scheme much faster than a conventional LU solver.
Revised:  We also explore a variety of other low-rank approximation methods such as the adaptive cross approximation (ACA) and Chebyshev interpolation for the low-rank approximation of the off-diagonal blocks . Using the HODLR direct solver as a preconditioner (with a low tolerance) , we can reach machine accuracy much faster than a conventional LU solver.
Edit intent: coherence
Original:  Numerical benchmarks are provided for 2D and 3D finite element matrices that arise from a wide range of applications.
Revised:  Numerical benchmarks are provided for frontal matrices arising from 3D finite element matrices that arise from a wide range of applications.
Edit intent: clarity
Original:  Numerical benchmarks are provided for 2D and 3D finite element matrices that arise from a wide range of applications.
Revised:  Numerical benchmarks are provided for 2D and 3D finite element problems corresponding to a wide range of applications.
Edit intent: clarity
Original: Let (f _1 ,\dots, f _s ) \in Q _p [X _1 ,\dots, X _n ]^s be a sequence of homogeneous polynomials with p-adic coefficients.
Revised: Let (f _1 ,\dots, f _s ) \in Q \_p [X _1 ,\dots, X _n ]^s be a sequence of homogeneous polynomials with p-adic coefficients.
Edit intent: fluency
Original:  Yet, since Q _p is not an effective field, classical algorithm does not apply.
Revised:  Yet, since Q \_p is not an effective field, classical algorithm does not apply.
Edit intent: fluency
Original:  We design a strategy to compute such a basis, when precision is enough and under the assumption that the input sequence is regular and the ideals \langle f _1 ,\dots,f _i \rangle are weakly-w-ideals.
Revised:  We design a strategy to compute such a basis, when precision is enough and under the assumption that the input sequence is regular and the ideals \langle f \_1 ,\dots,f _i \rangle are weakly-w-ideals.
Edit intent: fluency
Original:  We design a strategy to compute such a basis, when precision is enough and under the assumption that the input sequence is regular and the ideals \langle f _1 ,\dots,f _i \rangle are weakly-w-ideals.
Revised:  We design a strategy to compute such a basis, when precision is enough and under the assumption that the input sequence is regular and the ideals \langle f _1 ,\dots,f \_i \rangle are weakly-w-ideals.
Edit intent: fluency
Original:  by extending the so-called ``Che approximation'' , we then compute the performance of a LRU cache fed with such a request process, expressed by its hit ratio.
Revised:  by extending the so-called "Che approximation" , we then compute the performance of a LRU cache fed with such a request process, expressed by its hit ratio.
Edit intent: fluency
Original:  While FRET is often referred to and used as a `` molecular ruler" for distances around R_F, for dye pairs that have minimal rotational freedom, FRET can also be used to observe changes in structure for which there is no significant change in distance between the dyes.
Revised:  While FRET is often referred to and used as a " molecular ruler" for distances around R_F, for dye pairs that have minimal rotational freedom, FRET can also be used to observe changes in structure for which there is no significant change in distance between the dyes.
Edit intent: fluency
Original:  RNA II is a primer for replication of the ColE1 plasmid ;
Revised:  RNA II is a primer for replication of the ColE1 plasmid ,
Edit intent: fluency
Original:  The paper shows this to be a natural requirement by proving that a large class of practical trading strategies, defi?ned by means of trajectory based stopping times, give rise to locally continuous functionals.
Revised:  The paper shows this to be a natural requirement by proving that a large class of practical trading strategies, defined by means of trajectory based stopping times, give rise to locally continuous functionals.
Edit intent: fluency
Original:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of nodes all interacting with each other . Even if the initial and final configurations are correct, naively updating individual nodes can easily cause the network to exhibit incorrect behaviors such as forwarding loops, black holes, and security vulnerabilities .
Revised:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of interacting nodes . Even if the initial and final configurations are correct, naively updating individual nodes can easily cause the network to exhibit incorrect behaviors such as forwarding loops, black holes, and security vulnerabilities .
Edit intent: clarity
Original:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of nodes all interacting with each other . Even if the initial and final configurations are correct, naively updating individual nodes can easily cause the network to exhibit incorrect behaviors such as forwarding loops, black holes, and security vulnerabilities .
Revised:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of nodes all interacting with each other . Even if initial and final configurations are correct, naively updating individual nodes can easily cause the network to exhibit incorrect behaviors such as forwarding loops, black holes, and security vulnerabilities .
Edit intent: fluency
Original:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of nodes all interacting with each other . Even if the initial and final configurations are correct, naively updating individual nodes can easily cause the network to exhibit incorrect behaviors such as forwarding loops, black holes, and security vulnerabilities .
Revised:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of nodes all interacting with each other . Even if the initial and final configurations are correct, naively updating individual nodes can lead to incorrect transient behaviors, including loops, black holes, and security vulnerabilities .
Edit intent: clarity
Original:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of nodes all interacting with each other . Even if the initial and final configurations are correct, naively updating individual nodes can easily cause the network to exhibit incorrect behaviors such as forwarding loops, black holes, and security vulnerabilities .
Revised:  A key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or thousands of nodes all interacting with each other . Even if the initial and final configurations are correct, naively updating individual nodes can easily cause the network to exhibit incorrect behaviors such as forwarding loops, black holes, access control violations, and others .
Edit intent: clarity
Original:  This paper presents a new approach to the network update problem: we automatically generate updates that are guaranteed to preserve important correctness properties.
Revised:  This paper presents an approach for automatically synthesizing updates that are guaranteed to preserve important correctness properties.
Edit intent: clarity
Original:  We describe a prototype implementationof our system in OCaml , and present experimental results showing that it efficiently generates updates for real-world topologies with thousands of nodes  .
Revised:  We describe our prototype implementation , and present experimental results showing that it efficiently generates updates for real-world topologies with thousands of nodes .
Edit intent: clarity
Original:  We describe a prototype implementationof our system in OCaml , and present experimental results showing that it efficiently generates updates for real-world topologies with thousands of nodes  .
Revised:  We describe a prototype implementationof our system in OCaml , and present results from experiments on real-world topologies with thousands of nodes .
Edit intent: clarity
Original:  Even if initial and final configurations are correct, naively updating individual nodes can lead to incorrect transient behaviors, including loops, black holes,  access control violations , and others .
Revised:  Even if initial and final configurations are correct, naively updating individual nodes can lead to incorrect transient behaviors, including loops, black holes, and access control violations , and others .
Edit intent: coherence
Original:  Even if initial and final configurations are correct, naively updating individual nodes can lead to incorrect transient behaviors, including loops, black holes,  access control violations , and others .
Revised:  Even if initial and final configurations are correct, naively updating individual nodes can lead to incorrect transient behaviors, including loops, black holes, access control violations .
Edit intent: clarity
Original:  We formalize network updates as a distributed programming problem and develop a synthesis algorithm that uses counterexample-guided search and incremental model checking to dramatically improve performance .
Revised:  We formalize network updates as a distributed programming problem and develop a synthesis algorithm based on counterexample-guided search and incremental model checking to dramatically improve performance .
Edit intent: clarity
Original:  We formalize network updates as a distributed programming problem and develop a synthesis algorithm that uses counterexample-guided search and incremental model checking to dramatically improve performance .
Revised:  We formalize network updates as a distributed programming problem and develop a synthesis algorithm that uses counterexample-guided search and incremental model checking .
Edit intent: clarity
Original:  We describe our prototype implementation, and present results from experiments on real-world topologies and properties demonstrating that our tool scales to updates involving thousands of nodesin a few seconds .
Revised:  We describe a prototype implementation, and present results from experiments on real-world topologies and properties demonstrating that our tool scales to updates involving thousands of nodesin a few seconds .
Edit intent: fluency
Original: By extending large deviation theory to sub-exponential contributions , we determine the fine structure in the probability distribution of the observable displacement of a bead coupled to a molecular motor.
Revised: By considering subexponential contributions in large deviation theory to sub-exponential contributions , we determine the fine structure in the probability distribution of the observable displacement of a bead coupled to a molecular motor.
Edit intent: clarity
Original: By extending large deviation theory to sub-exponential contributions , we determine the fine structure in the probability distribution of the observable displacement of a bead coupled to a molecular motor.
Revised: By extending large deviation theory , we determine the fine structure in the probability distribution of the observable displacement of a bead coupled to a molecular motor.
Edit intent: clarity
Original:  The proposed software is entirely open source and is designed to be generic and applicable to a variety of data sets .
Revised:  The proposed software is entirely open source and is designed to be generic and applicable to a variety of datasets .
Edit intent: clarity
Original:  It provides access to full precision floating point data at terabyte scales, with the ability to precisely adjust image settings in real-time.
Revised:  It provides access to floating point data at terabyte scales, with the ability to precisely adjust image settings in real-time.
Edit intent: clarity
Original:  The proposed clients are light-weight, platform-independent web applications built on standard HTML5 web technologies and compatible with both touch-based and mouse-based devices.
Revised:  The proposed clients are light-weight, platform-independent web applications built on standard HTML5 web technologies and compatible with both touch and mouse-based devices.
Edit intent: fluency
Original:  This implies that energy-efficient systems can operate in high signal-to-noise-ratio regimes in which interference-suppressing signal processing is mandatory.
Revised:  This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory.
Edit intent: fluency
Original:  This subject is a topic of practical relevance to diverse Fields , ranging from neuroscience to engineering.
Revised:  This subject is a topic of practical relevance to diverse fields , ranging from neuroscience to engineering.
Edit intent: fluency
Original:  Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e is crossed by two independent edges and the other  where e is crossed by incident edges with the common endpoint on different sides of e.
Revised:  Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e is crossed by two independent edges and the other two where e is crossed by incident edges with the common endpoint on different sides of e.
Edit intent: clarity
Original:  Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e is crossed by two independent edges and the other  where e is crossed by incident edges with the common endpoint on different sides of e.
Revised:  Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e is crossed by two independent edges and the other where e is crossed by two incident edges in a way that encloses some endpoint of e.
Edit intent: clarity
Original:  In particular every edge of a fan-planar graph is crossed only by the edges of a star.
Edit intent: coherence
Original:  The class of fan-planar graphs is a natural variant of other classes defined by forbidden intersection patterns in a topological drawing of the graph.
Revised:  Fan-planar graphs are a new member in the ever-growing list of topological graphs defined by forbidden intersection patterns in a topological drawing of the graph.
Edit intent: clarity
Original:  So every 1-planar graph is also fan-planar , and every fan-planar graph is also quasiplanar, where both inclusions are strict.
Revised:  So every 1-planar graph is fan-planar , and every fan-planar graph is also quasiplanar, where both inclusions are strict.
Edit intent: fluency
Original:  So every 1-planar graph is also fan-planar , and every fan-planar graph is also quasiplanar, where both inclusions are strict.
Revised:  So every 1-planar graph is also fan-planar and every fan-planar graph is also quasiplanar, where both inclusions are strict.
Edit intent: fluency
Original:  We prove that every n-vertex graph without loops and parallel edges that admits a simple fan-planar drawig has at most 5n-10 edges and that this bound is tight for every n >= 20.
Revised:  We prove that every n-vertex graph without loops and parallel edges that admits a simple fan-planar graph on n vertices has at most 5n-10 edges and that this bound is tight for every n >= 20.
Edit intent: clarity
Original: As the total number of molecules in a system decreases, transitions in the qualitative behavior of autocatalytic chemical reaction dynamics may appear.
Revised: Transitions in the qualitative behavior of autocatalytic chemical reaction dynamics may appear.
Edit intent: clarity
Original: As the total number of molecules in a system decreases, transitions in the qualitative behavior of autocatalytic chemical reaction dynamics may appear.
Revised: As the total number of molecules in a system decreases, transitions in the qualitative behavior of chemical reaction dynamics may appear.
Edit intent: clarity
Original:  Bistability induced by the small-number effect in a two-component model is analyzed and excellent agreement with the simulated mean switching time is demonstrated.
Revised:  Bistability induced by the small-number effect and the mean switching time is demonstrated.
Edit intent: clarity
Original:  We prove a stronger variant of pumping lemma and an analogue of Ogden lemma for the class of tree-adjoining languages .
Revised:  We prove a stronger variant of pumping lemma and an analogue of Ogden lemma for this language family .
Edit intent: clarity
Original:  At early times  an advantage of recombination through the Fisher-Muller effect is generally observed , but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks.
Revised:  At early times , an advantage of recombination through the Fisher-Muller effect is generally observed , but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks.
Edit intent: fluency
Original:  In this paper, we present a content-aware synthesis method to enhance content-aware image retargeting.
Revised:  In this paper, we present a content-aware synthesis to enhance content-aware image retargeting.
Edit intent: clarity
Original:  By detecting the textural regions in an image, the  image content can be synthesized rather than simply distorted or cropped.
Revised:  By detecting the textural regions in an image, the textural image content can be synthesized rather than simply distorted or cropped.
Edit intent: fluency
Original:  We propose to resize the textural regions by content-aware synthesis and non-textural regions by fast multi-operators.
Revised:  We propose to retarget the textural regions by content-aware synthesis and non-textural regions by fast multi-operators.
Edit intent: clarity
Original:  To achieve practical resizing applications for general images, we develop an automatic and fast texture detection method that can detect multiple disjoint textural regions.
Revised:  To achieve practical retargeting applications for general images, we develop an automatic and fast texture detection method that can detect multiple disjoint textural regions.
Edit intent: clarity
Original:  The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with an overwhelming probability.
Revised:  The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high probability.
Edit intent: clarity
Original: In this paper, we consider the problem of dynamic spectrum allocation in cognitive radio (CR) networks and propose a new sealed-bid auction framework to address the spectrum allocation problem when the spectrum is not available with certainty.
Revised: In this paper, we consider the problem of dynamic spectrum allocation in cognitive radio (CR) networks and propose a novel sealed-bid auction framework to address the spectrum allocation problem when the spectrum is not available with certainty.
Edit intent: clarity
Original: In this paper, we consider the problem of dynamic spectrum allocation in cognitive radio (CR) networks and propose a novel sealed-bid auction framework to address the spectrum allocation problem when the spectrum is not available with certainty.
Revised: In this paper, we propose a novel sealed-bid auction framework to address the problem of dynamic spectrum allocation in cognitive radio (CR) networks and propose a novel sealed-bid auction framework to address the spectrum allocation problem when the spectrum is not available with certainty.
Edit intent: clarity
Original:  In our model, we assume that the moderator plays the dual role of being a fusion center (FC) for spectrum sensing and an auctioneer for spectrum allocation where it attempts to maximize its utility.
Revised:  We assume that the moderator plays the dual role of being a fusion center (FC) for spectrum sensing and an auctioneer for spectrum allocation where it attempts to maximize its utility.
Edit intent: clarity
Original:  Source code and binaries (Windows, OSX and Linux) are available at URL 
Revised:  Source code and binaries (Windows, OSX and Linux) are available at URL .
Edit intent: fluency
Original:  Source code and binaries (Windows, OSX and Linux) are available at URL .
Revised:  Source code and binaries (Windows, OSX and Linux) are available at URL 
Edit intent: fluency
Original:  It calculates iHS on chromosome 22 (22,147 loci) across 204 CEU haplotypes in 502s on one thread ( 77s on 16 threads) and calculates XPEHH for the same data relative to 210 YRI haplotypes in 907s on one thread ( 107s on 16 threads).
Revised:  It calculates iHS on chromosome 22 (22,147 loci) across 204 CEU haplotypes in 502s on one thread ( 33s on 16 threads) and calculates XPEHH for the same data relative to 210 YRI haplotypes in 907s on one thread ( 107s on 16 threads).
Edit intent: style
Original:  Even greater speedups are obtained when the algorithm is extended to the Python and MATLAB/OCTAVE programing environments.
Revised:  Even greater speedups are obtained when the algorithm is extended to the Python and MATLAB/OCTAVE programming environments.
Edit intent: fluency