wanyu/IteraTeR_v2 huggingface dataset:
Original:  Moreover, we propose acceleration schemes by utilizing memory-based techniques and randomized, \epsilon-approximate , low-rank projections to speed-up the convergence as well as decrease the computational costs in the recovery process.
Revised:  Moreover, we propose acceleration schemes by utilizing memory-based techniques and randomized, \epsilon-approximate matrix projections to decrease the computational costs in the recovery process.
Edit intent: clarity
Original:  For all these cases , we present theoretical analysis that guarantees convergence under mild problem conditions.
Revised:  For most of the configurations , we present theoretical analysis that guarantees convergence under mild problem conditions.
Edit intent: clarity
Original:  Simulation results demonstrate notable performance improvements  compared to state-of-the-art algorithms both in terms of data reconstruction and computational complexity.
Revised:  Simulation results demonstrate notable performance improvements as compared to state-of-the-art algorithms both in terms of data reconstruction and computational complexity.
Edit intent: fluency
Original:  Simulation results demonstrate notable performance improvements  compared to state-of-the-art algorithms both in terms of data reconstruction and computational complexity.
Revised:  Simulation results demonstrate notable performance improvements compared to state-of-the-art algorithms both in terms of reconstruction accuracy and computational complexity.
Edit intent: clarity
Original: We first talk about the Hamming Distance between two strings.
Revised: We first introduce the Hamming distance between two strings.
Edit intent: coherence
Original:  We claim that a closed-form formula exists that helps us find the sum of all such Hamming Distances.
Revised:  We claim that a simple formula exists for the sum of all such Hamming Distances.
Edit intent: clarity
Original:  We also state and prove other interesting results on the aforementioned topic.
Revised:  We also state and prove other interesting results concerning the aforementioned topic.
Edit intent: clarity
Original: We show that under suitable non-degeneracy conditions, m points and n 2--dimensional algebraic surfaces in R^4 satisfying certain "pseudoflat"
Revised: We show that m points and n 2--dimensional algebraic surfaces in R^4 satisfying certain "pseudoflat"
Edit intent: clarity
Original: We show that under suitable non-degeneracy conditions, m points and n 2--dimensional algebraic surfaces in R^4 satisfying certain "pseudoflat"
Revised: We show that under suitable non-degeneracy conditions, m points and n two-dimensional algebraic surfaces in R^4 satisfying certain "pseudoflat"
Edit intent: fluency
Original:  incidences, provided that m\leq n^{2-\epsilon for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2}  . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, again provided m\leq n ^{2-\epsilon or m\geq n^2}  . As a further special case we recover the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Revised:  incidences, provided that for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2} . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, again provided m\leq n ^{2-\epsilon or m\geq n^2} . As a further special case we recover the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Edit intent: fluency
Original:  incidences, provided that m\leq n^{2-\epsilon for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2}  . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, again provided m\leq n ^{2-\epsilon or m\geq n^2}  . As a further special case we recover the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Revised:  incidences, provided that m\leq n^{2-\epsilon for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2} . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, provided m\leq n ^{2-\epsilon or m\geq n^2} . As a further special case we recover the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Edit intent: clarity
Original:  incidences, provided that m\leq n^{2-\epsilon for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2}  . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, again provided m\leq n ^{2-\epsilon or m\geq n^2}  . As a further special case we recover the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Revised:  incidences, provided that m\leq n^{2-\epsilon for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2} . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, again provided m\leq n or m\geq n^2} . As a further special case we recover the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Edit intent: clarity
Original:  incidences, provided that m\leq n^{2-\epsilon for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2}  . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, again provided m\leq n ^{2-\epsilon or m\geq n^2}  . As a further special case we recover the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Revised:  incidences, provided that m\leq n^{2-\epsilon for any \epsilon>0 (where the implicit constant in the above bound depends on \epsilon), or m\geq n^2} . As a special case, we obtain the Szemer\'edi-Trotter theorem for 2--planes in R^4, again provided m\leq n ^{2-\epsilon or m\geq n^2} . As a further special case , we obtain the Szemer\'edi-Trotter theorem for complex lines in \mathbb{C}^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Edit intent: clarity
Original:  As a special case, we obtain the Szemer\'edi-Trotter  theorem for 2--planes in R^4, provided m\leq n and the planes intersect transversely.
Revised:  As a special case, we obtain a Szemer\'edi-Trotter theorem for 2--planes in R^4, provided m\leq n and the planes intersect transversely.
Edit intent: fluency
Original:  As a further special case, we obtain the Szemer\'edi-Trotter  theorem for complex lines in C^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Revised:  As a further special case, we obtain a Szemer\'edi-Trotter theorem for complex lines in C^2 with no restrictions on m and n (this theorem was originally proved by T\'oth using a different method).
Edit intent: fluency
Original:  As a second special case, we obtain the Szemer\'edi-Trotter  theorem for complex unit circles in C^2 , which has applications to the complex unit distance problem .
Revised:  As a second special case, we obtain a Szemer\'edi-Trotter theorem for complex unit circles in C^2 , which has applications to the complex unit distance problem .
Edit intent: fluency
Original:  As a second special case, we obtain the Szemer\'edi-Trotter  theorem for complex unit circles in C^2 , which has applications to the complex unit distance problem .
Revised:  As a second special case, we obtain the Szemer\'edi-Trotter theorem for complex unit circles in C^2 .
Edit intent: coherence
Original:  We obtain our results by combining several tools, including a " two-level " analogue of the discrete polynomial partitioning theorem and the crossing lemma.
Revised:  We obtain our results by combining several tools, including a two-level " analogue of the discrete polynomial partitioning theorem and the crossing lemma.
Edit intent: fluency
Original:  We obtain our results by combining several tools, including a " two-level " analogue of the discrete polynomial partitioning theorem and the crossing lemma.
Revised:  We obtain our results by combining several tools, including a " two-level analogue of the discrete polynomial partitioning theorem and the crossing lemma.
Edit intent: fluency
Original: We study the problem of designing mechanisms to allocate a heterogeneous set of divisible goods among a set of  agents in a fair manner.
Revised: How does one allocate a collection of resources to a set of agents in a fair manner.
Edit intent: clarity
Original:  To overcome this, in this paper, we give mechanisms which are truthful and achieve proportional fairness in an approximate manner .
Revised:  To overcome this, in this paper, we give mechanisms which are truthful and achieve proportional fairness in an approximate sense .
Edit intent: clarity
Original: \emph{Are analog models of computations more powerful than classical models of computations?
Revised: \emph{
Edit intent: clarity
Original:  From a series of recent papers, it is now clear that many realistic analog models of computations are provably equivalent to classical digital models of computations from acomputability point of view.
Revised:  computability point of view.
Edit intent: clarity
Original:  From a series of recent papers, it is now clear that many realistic analog models of computations are provably equivalent to classical digital models of computations from acomputability point of view.
Revised:  From a series of recent papers, it is now clear that many realistic analog models of computations are provably equivalent to classical digital models of computations from a point of view.
Edit intent: clarity
Original:  The journals containing these publications  are attributed to Web-of-Science Categories other than "Cardiac and Cardiovascular Systems"), perhaps because of the possibility of genetic testing for this syndrome in the clinic.
Revised:  The journals containing these publications , for example, are attributed to Web-of-Science Categories other than "Cardiac and Cardiovascular Systems"), perhaps because of the possibility of genetic testing for this syndrome in the clinic.
Edit intent: coherence
Original:  With this routine, all the instruments available for citation analysis can  be used on the basis of MeSH terms  .
Revised:  With this routine, all the instruments available for citation analysis can now be used on the basis of MeSH terms .
Edit intent: coherence
Original: Deep shotgun sequencing and analysis of genomes, transcriptomes, amplified single-cell genomes, and metagenomes enable the sensitive investigation of a wide range of biological phenomena .
Revised: Deep shotgun sequencing and analysis of genomes, transcriptomes, amplified single-cell genomes, and metagenomes has enabled investigation of a wide range of biological phenomena .
Edit intent: clarity
Original: Deep shotgun sequencing and analysis of genomes, transcriptomes, amplified single-cell genomes, and metagenomes enable the sensitive investigation of a wide range of biological phenomena .
Revised: Deep shotgun sequencing and analysis of genomes, transcriptomes, amplified single-cell genomes, and metagenomes enable the sensitive investigation of a wide range of organisms and ecosystems .
Edit intent: clarity
Original:  However, it is increasingly difficult to deal with the volume of data emerging from deep short-read sequencers, in part because of random and systematic sampling variation as well as a high sequencing error rate .
Revised:  However, sampling variation in short-read sequencers, in part because of random and systematic sampling variation as well as a high sequencing error rate .
Edit intent: coherence
Original:  However, it is increasingly difficult to deal with the volume of data emerging from deep short-read sequencers, in part because of random and systematic sampling variation as well as a high sequencing error rate .
Revised:  However, it is increasingly difficult to deal with the volume of data emerging from deep short-read data sets and high sequencing error rate .
Edit intent: clarity
Original:  These challenges have led to the development of entire new classes of short-read mapping tools , as well as new {\em de novo} assemblers.
Revised:  These challenges have led to the development of new classes of short-read mapping tools , as well as new {\em de novo} assemblers.
Edit intent: clarity
Original:  These challenges have led to the development of entire new classes of short-read mapping tools , as well as new {\em de novo} assemblers.
Revised:  These challenges have led to the development of entire new classes of mapping tools and {\em de novo} assemblers.
Edit intent: clarity
Original:  Despite these advances, algorithms and compute capacity continue to be challenged by the continued improvements in sequencing technology throughput.
Revised:  Despite these advances, algorithms and compute capacity continue to be challenged by the continued improvement in sequencing throughput.
Edit intent: clarity
Original:  We here describe an approach we term digital normalization, a single-pass computational algorithm that discards redundant data and both sampling variationand the number of errorspresent in deep sequencing data sets . Digital normalization substantially reduces the size of  data sets and accordingly decreases the memory and time requirements for {\em de novo} sequence assembly, all without significantly impacting content of the generated contigs.
Revised:  We here describe digital normalization, a single-pass computational algorithm that discards redundant data and both sampling variationand the number of errorspresent in deep sequencing data sets . Digital normalization substantially reduces the size of data sets and accordingly decreases the memory and time requirements for {\em de novo} sequence assembly, all without significantly impacting content of the generated contigs.
Edit intent: clarity
Original:  We here describe an approach we term digital normalization, a single-pass computational algorithm that discards redundant data and both sampling variationand the number of errorspresent in deep sequencing data sets . Digital normalization substantially reduces the size of  data sets and accordingly decreases the memory and time requirements for {\em de novo} sequence assembly, all without significantly impacting content of the generated contigs.
Revised:  We here describe an approach we term digital normalization, a single-pass computational algorithm that discards redundant data and both sampling variationand the number of errorspresent in deep sequencing data sets . Digital normalization substantially reduces the size of shotgun data sets and accordingly decreases the memory and time requirements for {\em de novo} sequence assembly, all without significantly impacting content of the generated contigs.
Edit intent: fluency
Original:  We here describe an approach we term digital normalization, a single-pass computational algorithm that discards redundant data and both sampling variationand the number of errorspresent in deep sequencing data sets . Digital normalization substantially reduces the size of  data sets and accordingly decreases the memory and time requirements for {\em de novo} sequence assembly, all without significantly impacting content of the generated contigs.
Revised:  We here describe an approach we term digital normalization, a single-pass computational algorithm that discards redundant data and both sampling variationand the number of errorspresent in deep sequencing data sets . Digital normalization substantially reduces the size of data sets and decreases the memory and time requirements for {\em de novo} sequence assembly, all without significantly impacting content of the generated contigs.
Edit intent: coherence
Original:  It is particularly useful for reducing the compute requirements for%DIFDELCMD < {\em %%% de novo sequence assembly .
Revised:  It is particularly useful for reducing the compute requirements for%DIFDELCMD < {\em %%% sequence assembly .
Edit intent: clarity
Original: Measurement data , snapshots of a system, and traffic or activity logs are typically collected repeatedly.
Revised: Measurements , snapshots of a system, and traffic or activity logs are typically collected repeatedly.
Edit intent: clarity
Original: Measurement data , snapshots of a system, and traffic or activity logs are typically collected repeatedly.
Revised: Measurement data , snapshots of a system, traffic matrices, and activity logs are typically collected repeatedly.
Edit intent: clarity
Original:  When the data is sampled, as is often necessary to meet resource constraints, queries need to be processed over the sampled data.
Revised:  When the data is sampled, as is often done to meet resource constraints, queries need to be processed over the sampled data.
Edit intent: clarity
Original:  When the data is sampled, as is often necessary to meet resource constraints, queries need to be processed over the sampled data.
Revised:  When the data is sampled, as is often necessary to meet resource constraints, queries are processed over the sampled data.
Edit intent: clarity
Original:  Surprisingly, however, we are not aware of pre-existing satisfactory estimators even for Euclidean distances .
Revised:  We are not aware of pre-existing satisfactory estimators even for Euclidean distances .
Edit intent: coherence
Original:  We derive estimators for L_p (p-norm) distances that are nonnegative and variance optimal in a Pareto sense  .
Revised:  We derive estimators for L_p distances that are nonnegative and variance optimal in a Pareto sense .
Edit intent: clarity
Original:  Our estimators are suitable for independent or coordinated samples of the data and have provable strong properties .
Revised:  Our estimators are applicable both when samples are independent or coordinated samples of the data and have provable strong properties .
Edit intent: clarity
Original:  Our estimators are suitable for independent or coordinated samples of the data and have provable strong properties .
Revised:  Our estimators are suitable for independent or coordinated .
Edit intent: clarity
Original:  For coordinated sampling we present two estimators that tradeoff variance according to similarity of the data.
Revised:  For coordinated samples we present two estimators that tradeoff variance according to similarity of the data.
Edit intent: fluency
Original:  We study performance of our estimators for Manhattan and Euclidean distances (p=1,2)  on diverse datasets, demonstrating scalability and accuracy  .
Revised:  We study performance of our Manhattan and Euclidean distances (p=1,2) on diverse datasets, demonstrating scalability and accuracy .
Edit intent: clarity
Original:  We study performance of our estimators for Manhattan and Euclidean distances (p=1,2)  on diverse datasets, demonstrating scalability and accuracy  .
Revised:  We study performance of our estimators for Manhattan and Euclidean distance (p=1,2) on diverse datasets, demonstrating scalability and accuracy .
Edit intent: fluency
Original: Measurements, snapshots of a system,  traffic matrices, and activity logs are typically collected repeatedly. %DIFDELCMD < {\em %%% Difference queries are then used to detect and localize changes for anomaly detection, monitoring, and planning.
Revised: Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as measurements, snapshots of a system, traffic matrices, and activity logs are typically collected repeatedly. %DIFDELCMD < {\em %%% Difference queries are then used to detect and localize changes for anomaly detection, monitoring, and planning.
Edit intent: clarity
Original: Measurements, snapshots of a system,  traffic matrices, and activity logs are typically collected repeatedly. %DIFDELCMD < {\em %%% Difference queries are then used to detect and localize changes for anomaly detection, monitoring, and planning.
Revised: Measurements, snapshots of a system, traffic matrices, and activity logs are collected repeatedly. %DIFDELCMD < {\em %%% Difference queries are then used to detect and localize changes for anomaly detection, monitoring, and planning.
Edit intent: clarity
Original: Measurements, snapshots of a system,  traffic matrices, and activity logs are typically collected repeatedly. %DIFDELCMD < {\em %%% Difference queries are then used to detect and localize changes for anomaly detection, monitoring, and planning.
Revised: Measurements, snapshots of a system, traffic matrices, and activity logs are typically collected repeatedly. %DIFDELCMD < {\em %%% are then used to detect and localize changes for anomaly detection, monitoring, and planning.
Edit intent: clarity
Original:  We are not aware ,  however, of previously known estimators for L_p (p-norm) distances which are accurate when only a small fraction of the data is sampled .
Revised:  We are not aware , however, hinges on the estimators we have .
Edit intent: clarity
Original:  We derive estimators for L_p distances that are nonnegative and variance optimal in a Pareto sense, building on our recent work on estimating general functions .
Revised:  We derive novel estimators for estimating L_p distance from sampled data .
Edit intent: clarity
Original:  We study  performance of our Manhattan and Euclidean distance (p=1,2) estimators on diverse datasets, demonstrating scalability and accuracy -- we obtain accurate estimates even when a small fraction of the data is sampled.
Revised:  We study the performance of our Manhattan and Euclidean distance (p=1,2) estimators on diverse datasets, demonstrating scalability and accuracy -- we obtain accurate estimates even when a small fraction of the data is sampled.
Edit intent: fluency
Original:  We study  performance of our Manhattan and Euclidean distance (p=1,2) estimators on diverse datasets, demonstrating scalability and accuracy -- we obtain accurate estimates even when a small fraction of the data is sampled.
Revised:  We study performance of our Manhattan and Euclidean distance (p=1,2) estimators on diverse datasets, demonstrating scalability and accuracy even when a small fraction of the data is sampled.
Edit intent: clarity
Original:  We also demonstrate the benefit of tailoring the estimator to characteristics of the dataset .
Revised:  Our work, for the first time, facilitates effective distance estimation over sampled data .
Edit intent: clarity
Original:  While previous literatures study them almost independently, in this paper , we combine CA and CF innovatively and present a new spectrum sharing strategy named CAF (Channel Aggregation and Fragmentation).
Revised:  While most of the literature studies CA and CF independently, in this paper , we combine CA and CF innovatively and present a new spectrum sharing strategy named CAF (Channel Aggregation and Fragmentation).
Edit intent: clarity
Original:  While previous literatures study them almost independently, in this paper , we combine CA and CF innovatively and present a new spectrum sharing strategy named CAF (Channel Aggregation and Fragmentation).
Revised:  While previous literatures study them almost independently, in this paper we combine CA and CF innovatively and present a new spectrum sharing strategy named CAF (Channel Aggregation and Fragmentation).
Edit intent: fluency