wanyu/IteraTeR_v2 huggingface dataset:
Original:  The solver computes the unique  min-length solution to x \in \mathbb{R^n} \|A x - b\|_2, where A \in R^{m \times n} can be either full rank or rank-deficient, and where m \gg n or m \ll n . Since A is only involved in matrix-matrix and matrix-vector multiplications, A can be a dense matrix, a sparse matrix , or a linear operator ;
Revised:  The solver computes the unique min-length solution to x \in \mathbb{R^n} \|A x - b\|_2, where A \in R^{m \times n} can be either full rank or rank-deficient, and where m \gg n or m \ll n . Since A is only involved in matrix-matrix and matrix-vector multiplications, it can be a dense matrix, a sparse matrix , or a linear operator ;
Edit intent: fluency
Original:  The solver computes the unique  min-length solution to x \in \mathbb{R^n} \|A x - b\|_2, where A \in R^{m \times n} can be either full rank or rank-deficient, and where m \gg n or m \ll n . Since A is only involved in matrix-matrix and matrix-vector multiplications, A can be a dense matrix, a sparse matrix , or a linear operator ;
Revised:  The solver computes the unique min-length solution to x \in \mathbb{R^n} \|A x - b\|_2, where A \in R^{m \times n} can be either full rank or rank-deficient, and where m \gg n or m \ll n . Since A is only involved in matrix-matrix and matrix-vector multiplications, A can be a dense or sparse matrix or a linear operator ;
Edit intent: fluency
Original:  and, in addition, LSRN automatically speeds up on sparse matrices and with fast linear operators .
Revised:  and, in addition, LSRN automatically speeds up when A is sparse or a fast linear operator .
Edit intent: clarity
Original:  \rceil \times \min(m,n), where \gamma is moderately larger than 1, e.g., \gamma = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method to the preconditioned system .
Revised:  \rceil \times \min(m,n), where \gamma is moderately larger than 1, e.g., \gamma = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method .
Edit intent: clarity
Original:  As we will demonstrate, the latter method is particularly efficient for solving large-scale problems on distributed clusters with high communication cost.
Revised:  As we demonstrate, the latter method is particularly efficient for solving large-scale problems on distributed clusters with high communication cost.
Edit intent: clarity
Original:  As we will demonstrate, the latter method is particularly efficient for solving large-scale problems on distributed clusters with high communication cost.
Revised:  As we will demonstrate, the latter method is particularly efficient for solving large problems on clusters with high communication cost.
Edit intent: clarity
Original:  Numerical results demonstrate that , on a local shared memory machine, \texttt{LSRN} outperforms LAPACK's DGELSD on large-scale dense problems and MATLAB's backslash (SuiteSparseQR) on large-scale sparse problems;
Revised:  Numerical results demonstrate that on a shared-memory machine, \texttt{LSRN} outperforms LAPACK's DGELSD on large-scale dense problems and MATLAB's backslash (SuiteSparseQR) on large-scale sparse problems;
Edit intent: clarity
Original:  Numerical results demonstrate that , on a local shared memory machine, \texttt{LSRN} outperforms LAPACK's DGELSD on large-scale dense problems and MATLAB's backslash (SuiteSparseQR) on large-scale sparse problems;
Revised:  Numerical results demonstrate that , on a local shared memory machine, \texttt{LSRN} outperforms LAPACK's DGELSD on large dense problems, and MATLAB's backslash (SuiteSparseQR) on large-scale sparse problems;
Edit intent: fluency
Original:  and empirical results also demonstrate that \texttt{LSRN} scales well on  Amazon Elastic Compute Cloud (EC2) clusters .
Revised:  and empirical results also demonstrate that \texttt{LSRN} scales well on an Amazon Elastic Compute Cloud (EC2) clusters .
Edit intent: fluency
Original: Inspired by concepts from ergodic theory, we give new insight into coding sequence (CDS) density estimation for the human genome.
Revised: Inspired by concepts from ergodic theory, we give a new approach to coding sequence (CDS) density estimation for the human genome.
Edit intent: clarity
Original: Inspired by concepts from ergodic theory, we give new insight into coding sequence (CDS) density estimation for the human genome.
Revised: Inspired by concepts from ergodic theory, we give new insight into coding sequence (CDS) density estimation , focusing on the human genome.
Edit intent: clarity
Original:  Our approach is based on the introduction and study of topological pressure : a numerical quantity assigned to any finite sequence based on an appropriate notion of `weighted information content'.
Revised:  Our approach is based on the introduction and study of topological pressure , which assigns a real number to any finite sequence based on an appropriate notion of `weighted information content'.
Edit intent: clarity
Original:  Inspired again by ergodic theory, we use the weightings on the codons to define a probability measure on finite sequences .
Revised:  Inspired again by ergodic theory, we use the weightings on the codons to define a probability distribution on finite sequences .
Edit intent: clarity
Original: Inspired by concepts from ergodic theory, we give a new approach to coding sequence (CDS) density estimation , focusing on the human genome.
Revised: We give a new approach to coding sequence (CDS) density estimation , focusing on the human genome.
Edit intent: clarity
Original:  Our approach is based on the introduction and study of topological pressure, which assigns a real number to any finite sequence based on an appropriate notion of ` weighted information content '.
Revised:  Our approach is based on the topological pressure, which assigns a real number to any finite sequence based on an appropriate notion of ` weighted information content '.
Edit intent: clarity
Original:  We cross-validate our results to check that we are not overfitting, and use the parameters obtained by training on the human genome for ab initio estimation of CDS density  on the genomes of  Rhesus Macaque and Mus Musculus.
Revised:  We cross-validate our results to check that we are not overfitting, and use the parameters obtained by training on the human genome , and use this to give ab initio predictions of CDS density on the genomes of Rhesus Macaque and Mus Musculus.
Edit intent: clarity
Original:  We cross-validate our results to check that we are not overfitting, and use the parameters obtained by training on the human genome for ab initio estimation of CDS density  on the genomes of  Rhesus Macaque and Mus Musculus.
Revised:  We cross-validate our results to check that we are not overfitting, and use the parameters obtained by training on the human genome for ab initio estimation of CDS density on the genomes of Mus Musculus, Rhesus Macaque and Mus Musculus.
Edit intent: coherence
Original:  Inspired again by ergodic theory, we use the weightings on the codons to define a probability distribution on finite sequences, which we show to be effective in distinguishing between coding and non-coding human DNA sequences of lengths between 750bp and 5,000bp.
Revised:  Inspired again by ergodic theory, we use the weightings on the codons to define a probability distribution on finite sequences, which can be used to distinguish between intron and exon sequences from the human genome of lengths between 750bp and 5,000bp.
Edit intent: clarity
Original: An accessing set in a graph is a subset B of vertices such that %DIFDELCMD < \existsD %DIFDELCMD < %%% \subseteq B,%DIFDELCMD < \forallv %%% \in V\B ,|N(v)%DIFDELCMD < \capD%%% | = 0 mod2 .
Revised: An accessing set in a graph is a subset B of vertices such that %DIFDELCMD < \existsD %DIFDELCMD < %%% %DIFDELCMD < \forallv %%% \in V\B ,|N(v)%DIFDELCMD < \capD%%% | = 0 mod2 .
Edit intent: clarity
Original: An accessing set in a graph is a subset B of vertices such that %DIFDELCMD < \existsD %DIFDELCMD < %%% \subseteq B,%DIFDELCMD < \forallv %%% \in V\B ,|N(v)%DIFDELCMD < \capD%%% | = 0 mod2 .
Revised: An accessing set in a graph is a subset B of vertices such that %DIFDELCMD < \existsD %DIFDELCMD < %%% \subseteq B,%DIFDELCMD < \forallv %%% \in V\B %DIFDELCMD < \capD%%% | = 0 mod2 .
Edit intent: coherence
Original:  In this paper, we introduce new bounds on the minimal size \kappa '(G) of an accessing set, and on the maximal size \kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly \kappa (G) and \kappa '(G) for several families of graphs.
Revised:  In this paper, we introduce new bounds on the minimal size kappa '(G) of an accessing set, and on the maximal size \kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly \kappa (G) and \kappa '(G) for several families of graphs.
Edit intent: fluency
Original:  In this paper, we introduce new bounds on the minimal size \kappa '(G) of an accessing set, and on the maximal size \kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly \kappa (G) and \kappa '(G) for several families of graphs.
Revised:  In this paper, we introduce new bounds on the minimal size \kappa '(G) of an accessing set, and on the maximal size kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly \kappa (G) and \kappa '(G) for several families of graphs.
Edit intent: clarity
Original:  In this paper, we introduce new bounds on the minimal size \kappa '(G) of an accessing set, and on the maximal size \kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly \kappa (G) and \kappa '(G) for several families of graphs.
Revised:  In this paper, we introduce new bounds on the minimal size \kappa '(G) of an accessing set, and on the maximal size \kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly kappa (G) and \kappa '(G) for several families of graphs.
Edit intent: fluency
Original:  In this paper, we introduce new bounds on the minimal size \kappa '(G) of an accessing set, and on the maximal size \kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly \kappa (G) and \kappa '(G) for several families of graphs.
Revised:  In this paper, we introduce new bounds on the minimal size \kappa '(G) of an accessing set, and on the maximal size \kappa (G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly \kappa (G) and kappa '(G) for several families of graphs.
Edit intent: fluency
Original:  Here we examine a specific microscopic description, introduced by Yan and Marko, which allows for disruption of base pairing (i.e., "melting" ) and consequently enhanced local flexibility.
Revised:  Here we examine a class of microscopic models which allow for disruption of base pairing (i.e., "melting" ) and consequently enhanced local flexibility.
Edit intent: clarity
Original: This paper investigates the achievable rate of two-way  Orthogonal Frequency Division Multiplexing (OFDM) relay network, in which two terminal nodes exchange information via a single relay node.
Revised: This paper presents a novel two-way Orthogonal Frequency Division Multiplexing (OFDM) relay network, in which two terminal nodes exchange information via a single relay node.
Edit intent: clarity
Original:  A novel multi-carrier two-way decode-and-forward (DF ) scheme is proposed, which introduces cross-subcarrier channel coding to exploit frequency selective fading, and achieves higher data rate than individual channel coding for each subcarrier .
Revised:  A novel multi-carrier two-way decode-and-forward (DF ) scheme is proposed, which introduces cross-subcarrier channel coding to leverage frequency selective fading, and achieves higher data rate than individual channel coding for each subcarrier .
Edit intent: clarity
Original:  A novel multi-carrier two-way decode-and-forward (DF ) scheme is proposed, which introduces cross-subcarrier channel coding to exploit frequency selective fading, and achieves higher data rate than individual channel coding for each subcarrier .
Revised:  A novel multi-carrier two-way decode-and-forward (DF ) scheme is proposed, which introduces cross-subcarrier channel coding to exploit frequency selective fading, and thus can achieve a higher data rate than individual channel coding for each subcarrier .
Edit intent: coherence
Original:  A novel multi-carrier two-way decode-and-forward (DF ) scheme is proposed, which introduces cross-subcarrier channel coding to exploit frequency selective fading, and achieves higher data rate than individual channel coding for each subcarrier .
Revised:  A novel multi-carrier two-way decode-and-forward (DF ) scheme is proposed, which introduces cross-subcarrier channel coding to exploit frequency selective fading, and achieves higher data rate than the conventional per-subcarrier DF relay strategies .
Edit intent: clarity
Original:  We further study the optimal power allocation  to maximize the exchange rate defined for symmetric data traffic.
Revised:  We further study the optimal power allocation strategy to maximize the exchange rate defined for symmetric data traffic.
Edit intent: clarity
Original:  The optimal power allocation is obtained by a dual decomposition algorithm, whose complexity goes in the order of O(N), where N is the number of subcarriers . Simulation results suggest that our scheme obtains substantial gains over conventional per-subcarrier DF scheme, and outperforms the amplify-and-foward (AF) scheme in a wider signal-to-noise-ratio (SNR) region.
Revised:  The optimal power allocation is obtained by a dual decomposition algorithm, whose complexity goes in the order of O(N), where N is the number of subcarriers . Simulation results suggest that our strategy obtains a substantial gain over the per-subcarrier DF scheme, and outperforms the amplify-and-foward (AF) scheme in a wider signal-to-noise-ratio (SNR) region.
Edit intent: clarity
Original:  The optimal power allocation is obtained by a dual decomposition algorithm, whose complexity goes in the order of O(N), where N is the number of subcarriers . Simulation results suggest that our scheme obtains substantial gains over conventional per-subcarrier DF scheme, and outperforms the amplify-and-foward (AF) scheme in a wider signal-to-noise-ratio (SNR) region.
Revised:  The optimal power allocation is obtained by a dual decomposition algorithm, whose complexity goes in the order of O(N), where N is the number of subcarriers . Simulation results suggest that our scheme obtains substantial gains over conventional per-subcarrier DF relay strategies, and also outperforms the amplify-and-forward (AF) scheme in a wider signal-to-noise-ratio (SNR) region.
Edit intent: clarity
Original:  The optimal power allocation is obtained by a dual decomposition algorithm, whose complexity goes in the order of O(N), where N is the number of subcarriers . Simulation results suggest that our scheme obtains substantial gains over conventional per-subcarrier DF scheme, and outperforms the amplify-and-foward (AF) scheme in a wider signal-to-noise-ratio (SNR) region.
Revised:  The optimal power allocation is obtained by a dual decomposition algorithm, whose complexity goes in the order of O(N), where N is the number of subcarriers . Simulation results suggest that our scheme obtains substantial gains over conventional per-subcarrier DF scheme, and outperforms the amplify-and-foward (AF) relay strategy in a wide signal-to-noise-ratio (SNR) region.
Edit intent: clarity
Original: Here is suggested a solution to the accommodation-vergence mismatch problem in the 3D stereoscopic display .
Revised: Here is suggested a solution to the accommodation-vergence mismatch problem in 3D stereoscopic display .
Edit intent: fluency
Original: Here is suggested a solution to the accommodation-vergence mismatch problem in the 3D stereoscopic display .
Revised: Here is suggested a solution to the accommodation-vergence mismatch problem in the 3D stereoscopic displays .
Edit intent: fluency
Original:  The compensation would make the vergence of human eyes match with the virtual stereo-image and reduce the visual fatigue .
Revised:  The compensation would make vergence of human eyes match with the virtual stereo-image and reduce the visual fatigue .
Edit intent: fluency
Original:  The compensation would make the vergence of human eyes match with the virtual stereo-image and reduce the visual fatigue .
Revised:  The compensation would make the vergence of human eyes match with position of virtual stereo-image and reduce the visual fatigue .
Edit intent: clarity
Original:  The compensation would make the vergence of human eyes match with the virtual stereo-image and reduce the visual fatigue .
Revised:  The compensation would make the vergence of human eyes match with the virtual stereo-image , reducing the visual fatigue .
Edit intent: coherence
Original:  The compensation would make vergence of human eyes match with position of virtual stereo-image, reducing the visual fatigue.
Revised:  The compensation would make vergence of human eyes match with position of virtual stereoscopic motion pictures, reducing visual fatigue.
Edit intent: clarity
Original: Given a network infrastructure (e.g., a grid, data-center or on-chip-network) and a distribution on the source-destination requests, the expected path (route) length is an important measure for the performance, efficiency and power consumption of the network.
Revised: Given a network infrastructure (e.g., data-center or on-chip-network) and a distribution on the source-destination requests, the expected path (route) length is an important measure for the performance, efficiency and power consumption of the network.
Edit intent: clarity
Original:  In this work we initiate a study on self-adjusting networks: networks that use local-distributed mechanisms to adjust the position of the nodes  in the network to any distribution of route requests .
Revised:  In this work we initiate a study on self-adjusting networks: networks that use local-distributed mechanisms to adjust the position of the nodes in the network to best fit the route requests distribution .
Edit intent: clarity
Original:  E.g. , we consider grid networks in which the distribution of requests is a symmetric product distribution.
Revised:  In particular , we consider grid networks in which the distribution of requests is a symmetric product distribution.
Edit intent: coherence
Original:  In this setting  we show that simple greedy switches, which locally minimize an objective function, achieve good approximation ratios.
Revised:  In this setting , we show that simple greedy switches, which locally minimize an objective function, achieve good approximation ratios.
Edit intent: fluency
Original:  In this setting  we show that simple greedy switches, which locally minimize an objective function, achieve good approximation ratios.
Revised:  In this setting we show that a simple greedy policy of position switching between neighboring nodes to locally minimize an objective function, achieve good approximation ratios.
Edit intent: clarity
Original:  In this setting  we show that simple greedy switches, which locally minimize an objective function, achieve good approximation ratios.
Revised:  In this setting we show that simple greedy switches, which locally minimize an objective function, achieves good approximation ratios.
Edit intent: fluency
Original: This paper talk about that NP is not AL = P, P is not NC, NC is not NL, and NL is not L.
Revised: This paper talk about that NP is not AL and P, P is not NC, NC is not NL, and NL is not L.
Edit intent: clarity
Original:  The point about this paper is the dependent relation of the problem that need other problem's result to compute it.
Revised:  The point about this paper is the depend relation of the problem that need other problem's result to compute it.
Edit intent: fluency
Original: This paper studies the optimal timing to liquidate defaultable securities in a general intensity-based credit risk model under stochastic interest rate.
Revised: This paper studies the optimal timing to liquidate credit derivatives in a general intensity-based credit risk model under stochastic interest rate.
Edit intent: clarity
Original:  To quantify the value of optimally timing to sell , we introduce the delayed liquidation premium which is closely related to the stochastic bracket between the market price and a pricing kernel.
Revised:  We quantify the value of optimally timing to sell , we introduce the delayed liquidation premium which is closely related to the stochastic bracket between the market price and a pricing kernel.
Edit intent: fluency
Original:  To quantify the value of optimally timing to sell , we introduce the delayed liquidation premium which is closely related to the stochastic bracket between the market price and a pricing kernel.
Revised:  To quantify the value of optimally timing to sell through the concept of delayed liquidation premium which is closely related to the stochastic bracket between the market price and a pricing kernel.
Edit intent: clarity
Original:  Our model serves as the building block for the sequential buying and selling problem .
Revised:  Our model is extended to study the sequential buying and selling problem .
Edit intent: clarity
Original: RNA crystallographic models , our richest sources of RNA structural information, contain pervasive errors due to ambiguities in manually fitting RNA backbones into experimental density maps.
Revised: RNA crystallographic models contain pervasive ambiguities due to the difficulty of manually fitting RNA backbones into experimental density maps.
Edit intent: clarity
Original:  As a rule they degrade endocytosed F content (fragments of bacterial products containing PAMP, including kPAMP) slowly and incompletely, i.e. they are kPAMP-carriers.
Revised:  As a rule they degrade endocytosed F-content (fragments of bacterial products containing PAMP, including kPAMP) slowly and incompletely, i.e. they are kPAMP-carriers.
Edit intent: fluency
Original:  SPP severity predetermines possibility of psoriasis initialization and maintenance because R phagocytes (Mo-R and DC-R) along with normal phagocytes (Mo and DC) participate in homeostatic and inflammatory renewal of pool of dermal non-resident phagocytes (Mo and DC).
Revised:  SPP severity predetermines possibility of psoriasis initialization and maintenance because R-phagocytes (Mo-R and DC-R) along with normal phagocytes (Mo and DC) participate in homeostatic and inflammatory renewal of pool of dermal non-resident phagocytes (Mo and DC).
Edit intent: clarity
Original: Review and analytical study of results of experimental and theoretical works on etiology and pathogenesis of psoriatic disease was conducted.
Revised: Analytical study of results of experimental and theoretical works on etiology and pathogenesis of psoriatic disease was conducted.
Edit intent: coherence
Original: Review and analytical study of results of experimental and theoretical works on etiology and pathogenesis of psoriatic disease was conducted.
Revised: Review and analytical study of results of experimental and theoretical works on pathogenesis of psoriatic disease was conducted.
Edit intent: clarity