wanyu/IteraTeR_v2 huggingface dataset:
Original:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a special form of CUR LRA , which is particularly memory efficient, as long as an input matrix admits LRA and is Symmetric Positive Semidefinite or is sufficiently close to a low rank matrix.
Revised:  Adversary argument shows that no algorithm running at sublinear cost can output accurate LRA even of the matrices of small families of our Appendix, but we prove that some deterministic sublinear cost algorithms output reasonably close LRA in a special form of CUR LRA , which is particularly memory efficient, as long as an input matrix admits LRA and is Symmetric Positive Semidefinite or is very close to a low rank matrix.
Edit intent: clarity
Original:  The design and analysis of our algorithms rely on extensive previous study of CUR LRA based on volume maximization .
Revised:  The design and analysis of our algorithms rely on extensive prior study of the link of LRA of a matrix to maximization of its volume .
Edit intent: clarity
Original:  Thus an efficient algorithm for the maximum independent set approximation in the LOCAL model  efficient algorithms for many problems in the LOCAL model including the computation of (polylog n, polylog n) network decompositions.
Revised:  Thus an efficient algorithm for the maximum independent set approximation in the LOCAL model implies efficient algorithms for many problems in the LOCAL model including the computation of (polylog n, polylog n) network decompositions.
Edit intent: coherence
Original:  These are like register automata for data words (introduced by Kaminski and Francez ), with the restriction that every read access to a register destroys the register contents.
Revised:  These are like register automata for data words , in the style of Kaminski and Francez ), with the restriction that every read access to a register destroys the register contents.
Edit intent: clarity
Original:  Independence describes the result of drawing a fresh random sample---a basic operation in all probabilistic languages---and greatly simplifies formal reasoning about collections of random samples .
Revised:  Independence describes the result of random sampling---a basic operation in all probabilistic languages---and greatly simplifies formal reasoning about collections of random samples .
Edit intent: clarity
Original:  Independence describes the result of drawing a fresh random sample---a basic operation in all probabilistic languages---and greatly simplifies formal reasoning about collections of random samples .
Revised:  Independence describes the result of drawing a fresh random sample---a basic operation in all probabilistic languages---and for reasoning about groups of random variables .
Edit intent: clarity
Original:  In this paper, we propose a probabilistic separation logic  where separation models probabilistic independence.
Revised:  We propose a probabilistic separation logic where separation models probabilistic independence.
Edit intent: coherence
Original:  Then, we introduce a program logic based on these assertions  and prove soundness of the proof system.
Revised:  Then, we introduce a program logic based on these assertions , and prove soundness of the proof system.
Edit intent: fluency
Original:  Our logic is able to state and verify two different forms of the standard cryptographic security property, while proofs work in terms of high-level properties  like independence and uniformity.
Revised:  Our logic is able to state and verify two different forms of the standard cryptographic security property, while proofs work in terms of high-level properties , like independence and uniformity.
Edit intent: fluency
Original: In this paper we provide improved algorithms for approximating the girth and producing roundtrip spanners of  n-node m-edge directed graphs with non-negative edge lengths.
Revised: In this paper we provide a n-node m-edge directed graphs with non-negative edge lengths.
Edit intent: clarity
Original: In this paper we provide improved algorithms for approximating the girth and producing roundtrip spanners of  n-node m-edge directed graphs with non-negative edge lengths.
Revised: In this paper we provide improved algorithms for approximating the girth and producing roundtrip spanners of n-node m-edge directed graph with non-negative edge lengths.
Edit intent: fluency
Original:  First, for any integer k \ge 1, we provide a deterministic (m^{1+ 1/k a O(k\log\log n) multiplicative approximation of the girth and a O(k\log\log n) multiplicative roundtrip spanner with O( n^{1+1/k (m\sqrt{n) timealgorithm that with high probability computes a 3-multiplicative approximation to the girth.
Revised:  First, for any integer k \ge 1, we provide a deterministic algorithm for a O(k\log\log n) multiplicative approximation of the girth and a O(k\log\log n) multiplicative roundtrip spanner with O( n^{1+1/k (m\sqrt{n) timealgorithm that with high probability computes a 3-multiplicative approximation to the girth.
Edit intent: fluency
Original:  First, for any integer k \ge 1, we provide a deterministic (m^{1+ 1/k a O(k\log\log n) multiplicative approximation of the girth and a O(k\log\log n) multiplicative roundtrip spanner with O( n^{1+1/k (m\sqrt{n) timealgorithm that with high probability computes a 3-multiplicative approximation to the girth.
Revised:  First, for any integer k \ge 1, we provide a deterministic (m^{1+ 1/k a O(k\log\log n) multiplicative approximation of the girth and a O(k\log\log n) multiplicative roundtrip spanner with O( (m\sqrt{n) timealgorithm that with high probability computes a 3-multiplicative approximation to the girth.
Edit intent: clarity
Original:  Third, we show how to combine these algorithms to obtain for any integer k }%DIFDELCMD < \ge %%% 1 a randomized algorithm which in (m^{1+ 1/k O(k\log k) multiplicative approximation of the girth and O(k \log k) multiplicative roundtrip spanner with high probability\tilde{O} .
Revised:  Third, we show how to combine these algorithms to obtain for any integer k }%DIFDELCMD < \ge %%% (m^{1+ 1/k O(k\log k) multiplicative approximation of the girth and O(k \log k) multiplicative roundtrip spanner with high probability\tilde{O} .
Edit intent: coherence
Original:  Third, we show how to combine these algorithms to obtain for any integer k }%DIFDELCMD < \ge %%% 1 a randomized algorithm which in (m^{1+ 1/k O(k\log k) multiplicative approximation of the girth and O(k \log k) multiplicative roundtrip spanner with high probability\tilde{O} .
Revised:  Third, we show how to combine these algorithms to obtain for any integer k }%DIFDELCMD < \ge %%% 1 a randomized algorithm which in m^{1+1/k O(k\log k) multiplicative approximation of the girth and O(k \log k) multiplicative roundtrip spanner with high probability\tilde{O} .
Edit intent: fluency
Original:  Third, we show how to combine these algorithms to obtain for any integer k }%DIFDELCMD < \ge %%% 1 a randomized algorithm which in (m^{1+ 1/k O(k\log k) multiplicative approximation of the girth and O(k \log k) multiplicative roundtrip spanner with high probability\tilde{O} .
Revised:  Third, we show how to combine these algorithms to obtain for any integer k }%DIFDELCMD < \ge %%% 1 a randomized algorithm which in (m^{1+ 1/k O(k\log k) multiplicative approximation of the girth and O(k \log k) multiplicative roundtrip spanner with high probability\tilde{O}(m^{1+1/k .
Edit intent: fluency
Original:  time, i.e. %DIFDELCMD < \tilde{O}%%%  (mn), or were due Pachocki et al (SODA 2018 ) which provided a randomized algorithm that for any integer k \ge 1 in time \tilde{O}(m^{1+1/k})
Revised:  time, i.e. %DIFDELCMD < \tilde{O}%%% O (mn), or were due Pachocki et al (SODA 2018 ) which provided a randomized algorithm that for any integer k \ge 1 in time \tilde{O}(m^{1+1/k})
Edit intent: clarity
Original:  multiplicative approximation of the girth and a O(k\log n) multiplicative roundtrip spanners with%DIFDELCMD < \tilde{O}%%% (n^{1+1/k . Our first algorithm  removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-offs for obtaining constant approximations.
Revised:  multiplicative approximation of the girth %DIFDELCMD < \tilde{O}%%% (n^{1+1/k . Our first algorithm removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-offs for obtaining constant approximations.
Edit intent: coherence
Original:  multiplicative approximation of the girth and a O(k\log n) multiplicative roundtrip spanners with%DIFDELCMD < \tilde{O}%%% (n^{1+1/k . Our first algorithm  removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-offs for obtaining constant approximations.
Revised:  multiplicative approximation of the girth and a O(k\log n) multiplicative roundtrip spanners with%DIFDELCMD < \tilde{O}%%% . Our first algorithm removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-offs for obtaining constant approximations.
Edit intent: coherence
Original:  multiplicative approximation of the girth and a O(k\log n) multiplicative roundtrip spanners with%DIFDELCMD < \tilde{O}%%% (n^{1+1/k . Our first algorithm  removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-offs for obtaining constant approximations.
Revised:  multiplicative approximation of the girth and a O(k\log n) multiplicative roundtrip spanners with%DIFDELCMD < \tilde{O}%%% (n^{1+1/k . Our first algorithm constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy, our second removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-offs for obtaining constant approximations.
Edit intent: fluency
Original:  multiplicative approximation of the girth and a O(k\log n) multiplicative roundtrip spanners with%DIFDELCMD < \tilde{O}%%% (n^{1+1/k . Our first algorithm  removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-offs for obtaining constant approximations.
Revised:  multiplicative approximation of the girth and a O(k\log n) multiplicative roundtrip spanners with%DIFDELCMD < \tilde{O}%%% (n^{1+1/k . Our first algorithm removes the need for randomness and improves the approximation factor in Pachocki et al (SODA 2018), our second is constitutes the first sub-APSP-time algorithm for approximating the girth to constant accuracy with high probability, and our third is the first time versus quality trade-off for obtaining constant approximations.
Edit intent: fluency
Original:  This makes M-SERPT the only scheduling policy known to be constant-competitive with Gittins.
Revised:  This makes M-SERPT the only scheduling policy known to be a constant-factor approximation of Gittins.
Edit intent: clarity
Original:  When the scheduler knows each job's size, the shortest remaining processing time (SRPT) policy is optimal.
Revised:  When we know each job's size, the shortest remaining processing time (SRPT) policy is optimal.
Edit intent: clarity
Original:  In this setting , the Gittins policy is known to minimize mean response time, but its complex priority structure can be computationally intractable.
Revised:  In this setting the Gittins policy is known to minimize mean response time, but its complex priority structure can be computationally intractable.
Edit intent: fluency
Original:  While SERPT is a natural extension of SRPT to unknown job sizes, it is unknown how close SERPT is to optimal .
Revised:  While SERPT is a natural extension of SRPT to unknown job sizes, it is unknown whether or not SERPT is close to optimal for mean response time .
Edit intent: clarity
Original:  This makes M-SERPT the only  scheduling policy known to be a constant-factor approximation of Gittins .
Revised:  This makes M-SERPT the only scheduling policy known to have a constant-factor approximation of Gittins .
Edit intent: clarity
Original:  This improves on a celebrated 2^{O(\sqrt{\log n})}-time algorithm of Panconesi and Srinivasan [STOC' 93 ] and settles one of the long-standing and central questions in distributed graph algorithms.
Revised:  This improves on a celebrated 2^{O(\sqrt{\log n})}-time algorithm of Panconesi and Srinivasan [STOC' 93 ] and settles a central and long-standing and central questions in distributed graph algorithms.
Edit intent: clarity
Original:  This improves on a celebrated 2^{O(\sqrt{\log n})}-time algorithm of Panconesi and Srinivasan [STOC' 93 ] and settles one of the long-standing and central questions in distributed graph algorithms.
Revised:  This improves on a celebrated 2^{O(\sqrt{\log n})}-time algorithm of Panconesi and Srinivasan [STOC' 93 ] and settles one of the long-standing question in distributed graph algorithms.
Edit intent: clarity
Original:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several  open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87  ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P- RLOCAL = P - LOCAL.
Revised:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other problems, hence resolving several open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87 ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P- RLOCAL = P - LOCAL.
Edit intent: clarity
Original:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several  open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87  ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P- RLOCAL = P - LOCAL.
Revised:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several open problems, including Linial's question about the deterministic complexity of maximal independent set [FOCS'87 ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P- RLOCAL = P - LOCAL.
Edit intent: clarity
Original:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several  open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87  ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P- RLOCAL = P - LOCAL.
Revised:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87 ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P-- RLOCAL = P - LOCAL.
Edit intent: fluency
Original:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several  open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87  ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P- RLOCAL = P - LOCAL.
Revised:  It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87 ] . Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P- RLOCAL = P - LOCAL.
Edit intent: fluency
Original:  That is, for any distributed problem whose solution can be checked  in polylogarithmic-time, any polylogarithmic-time randomized algorithm can be derandomized to a polylogarithmic-time deterministic algorithm.
Revised:  That is, for any problem whose solution can be checked in polylogarithmic-time, any polylogarithmic-time randomized algorithm can be derandomized to a polylogarithmic-time deterministic algorithm.
Edit intent: clarity
Original:   By known connections, our result leads also to substantially faster randomized  algorithms for a number of fundamental problems including (\Delta+1)-coloring, MIS , and Lov\'{a}sz Local Lemma  .
Revised:  By known connections, our result leads also to substantially faster randomized algorithms for a number of well-studied problems including (\Delta+1)-coloring, MIS , and Lov\'{a}sz Local Lemma .
Edit intent: clarity
Original:  Ligands with flexible chemical scaffold may remain longer at the protein target if they need to pass through extended conformations upon unbinding, or if they exhibit strong electrostatic and/or van der Waals interactions with the target.
Revised:  Ligands with flexible chemical scaffold may remain longer at the protein if they exhibit strong electrostatic and/or van der Waals interactions with the target.
Edit intent: clarity
Original:  Ligands with rigid chemical scaffold can exhibit longer residence times if they need to perform any kind of conformational change for unbinding, while electrostatic interactions with the protein can facilitate unbinding.
Revised:  In the case of ligands with rigid chemical scaffold can exhibit longer residence times if they need to perform any kind of conformational change for unbinding, while electrostatic interactions with the protein can facilitate unbinding.
Edit intent: clarity
Original:  Ligands with rigid chemical scaffold can exhibit longer residence times if they need to perform any kind of conformational change for unbinding, while electrostatic interactions with the protein can facilitate unbinding.
Revised:  Ligands with rigid chemical scaffold that exhibit longer residence times if they need to perform any kind of conformational change for unbinding, while electrostatic interactions with the protein can facilitate unbinding.
Edit intent: clarity
Original:  Ligands with rigid chemical scaffold can exhibit longer residence times if they need to perform any kind of conformational change for unbinding, while electrostatic interactions with the protein can facilitate unbinding.
Revised:  Ligands with rigid chemical scaffold can exhibit longer residence times however, transient electrostatic interactions with the protein can facilitate unbinding.
Edit intent: clarity
Original:  Ligands with rigid chemical scaffold can exhibit longer residence times if they need to perform any kind of conformational change for unbinding, while electrostatic interactions with the protein can facilitate unbinding.
Revised:  Ligands with rigid chemical scaffold can exhibit longer residence times if they need to perform any kind of conformational change for unbinding, while electrostatic interactions with the protein appear to facilitate unbinding.
Edit intent: clarity
Original:  Our results show that understanding the unbinding pathway and the protein-ligand interactions along this path is crucial for the prediction of small molecule ligands with defined unbinding kinetics.
Revised:  Our results imply that understanding the unbinding pathway and the protein-ligand interactions along this path is crucial for the prediction of small molecule ligands with defined unbinding kinetics.
Edit intent: clarity
Original:  Our results show that understanding the unbinding pathway and the protein-ligand interactions along this path is crucial for the prediction of small molecule ligands with defined unbinding kinetics.
Revised:  Our results show that understanding the unbinding pathway and the protein-ligand interactions along this path is crucial for the prediction of small molecule ligands with defined unbinding 
Edit intent: clarity
Original:  However, in experiments with an implementation of our algorithm on an industrial benchmark, we find that that tests produced by our algorithm still distinguish more than 99\% of the incompatible state pairs.
Revised:  However, in experiments with an implementation of our algorithm on an industrial benchmark, we find that tests produced by our algorithm still distinguish more than 99\% of the incompatible state pairs.
Edit intent: fluency
Original:  Finally, we present numerical experiments  in two and three dimensional domains .
Revised:  Finally, we present numerical experiments , in two and three dimensional domains .
Edit intent: fluency
Original:  To resolve the problem, a novel graph neural network, namely graph neural lasso (GNL), will be proposed in this paper.
Revised:  To resolve the problem, a novel graph neural network, namely Graph Neural Lasso (GNL), will be proposed in this paper.
Edit intent: fluency
Original:  In conclusion, we believe the present ACC-based measurement of sway offers a patient-friendly, reliable, inexpensive and efficient alternative recording technique that is -- useful together with clinical balance and mobility tests -- in various circumstances, as well as in outcome studies involving diagnosis, follow-up and rehabilitation of UVF patients.
Revised:  In conclusion, we believe the present ACC-based measurement of sway offers a patient-friendly, reliable, inexpensive and efficient alternative recording technique that is useful - together with clinical balance and mobility tests -- in various circumstances, as well as in outcome studies involving diagnosis, follow-up and rehabilitation of UVF patients.
Edit intent: fluency