wanyu/IteraTeR_v2 huggingface dataset:
Original: Despite the interest in the complexity class MA, the randomized analog of NP, there is just a couple of known natural (promise-) MA-complete problems , the first due to Bravyi and Terhal ( SIAM Journal of Computing 2009) and the second due to Bravyi ( Quantum Information and Computation 2015).
Revised: Despite the interest in the complexity class MA, the randomized analog of NP, just a few natural MA-complete problems , the first due to Bravyi and Terhal ( SIAM Journal of Computing 2009) and the second due to Bravyi ( Quantum Information and Computation 2015).
Edit intent: clarity
Original: Despite the interest in the complexity class MA, the randomized analog of NP, there is just a couple of known natural (promise-) MA-complete problems , the first due to Bravyi and Terhal ( SIAM Journal of Computing 2009) and the second due to Bravyi ( Quantum Information and Computation 2015).
Revised: Despite the interest in the complexity class MA, the randomized analog of NP, there is just a couple of known natural (promise-) MA-complete problems , the first due to Bravyi and Terhal , SIAM Journal of Computing 2009) and the second due to Bravyi ( Quantum Information and Computation 2015).
Edit intent: fluency
Original:  Surprisingly, both problems are stated using terminology from quantum computation .
Revised:  Surprisingly, two of these problems are defined using terminology from quantum computation .
Edit intent: clarity
Original:  This fact makes it hard for classical complexity theorists to study these problems, and prevents possible progress, e.g., on the important question of derandomizing MA . In this note we define a natural combinatorial problem called SetCSP and prove its MA-completeness.
Revised:  This fact makes it hard for classical complexity theorists from studying these problems, and prevents possible progress, e.g., on the important question of derandomizing MA . In this note we define a natural combinatorial problem called SetCSP and prove its MA-completeness.
Edit intent: clarity
Original:  This fact makes it hard for classical complexity theorists to study these problems, and prevents possible progress, e.g., on the important question of derandomizing MA . In this note we define a natural combinatorial problem called SetCSP and prove its MA-completeness.
Revised:  This fact makes it hard for classical complexity theorists to study these problems, delaying potential progress, e.g., on the important question of derandomizing MA . In this note we define a natural combinatorial problem called SetCSP and prove its MA-completeness.
Edit intent: clarity
Original:  The problem generalizes the constraint satisfaction problem (CSP) into constraints on sets of strings.
Revised:  The problem generalizes the constraint satisfaction problem (CSP) into constraints involving sets of strings.
Edit intent: clarity
Original:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019)  that a restricted case of the Bravyi and Terhal's MA complete problem (namely, the uniform case) is already complete, and moreover, that this restricted case can be stated using a classical, combinatorial description.
Revised:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019) , in which it was noted that a restricted case of the Bravyi and Terhal's MA complete problem (namely, the uniform case) is already complete, and moreover, that this restricted case can be stated using a classical, combinatorial description.
Edit intent: coherence
Original:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019)  that a restricted case of the Bravyi and Terhal's MA complete problem (namely, the uniform case) is already complete, and moreover, that this restricted case can be stated using a classical, combinatorial description.
Revised:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019) that a restricted case of Bravyi and Terhal's MA complete problem (namely, the uniform case) is already complete, and moreover, that this restricted case can be stated using a classical, combinatorial description.
Edit intent: fluency
Original:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019)  that a restricted case of the Bravyi and Terhal's MA complete problem (namely, the uniform case) is already complete, and moreover, that this restricted case can be stated using a classical, combinatorial description.
Revised:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019) that a restricted case of the Bravyi and Terhal's problem (namely, the uniform case) is already complete, and moreover, that this restricted case can be stated using a classical, combinatorial description.
Edit intent: coherence
Original:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019)  that a restricted case of the Bravyi and Terhal's MA complete problem (namely, the uniform case) is already complete, and moreover, that this restricted case can be stated using a classical, combinatorial description.
Revised:  This note is, in fact, a combination of previously known works: the brilliant work of Bravyi and Terhal, together with an observation made in our previous work (Aharonov and Grilo, FOCS 2019) that a restricted case of the Bravyi and Terhal's MA complete problem (namely, the uniform case) is already MA-complete; a simple trick allows to state this restricted case can be stated using a classical, combinatorial description.
Edit intent: clarity
Original:  This note, along with a translation of the main result of Aharonov and Grilo  to the SetCSP language, implies that finding a gap-amplification procedure for SetCSP problems (namely a generalization to SetCSPs of the gap-amplification used in Dinur's PCP proof) would imply MA=NP.
Revised:  This note, along with a translation of the main result of Aharonov and Grilo to the SetCSP language, implies that finding a gap-amplification procedure for SetCSP (as in Dinur's PCP proof) would imply MA=NP.
Edit intent: clarity
Original:  This note, along with a translation of the main result of Aharonov and Grilo  to the SetCSP language, implies that finding a gap-amplification procedure for SetCSP problems (namely a generalization to SetCSPs of the gap-amplification used in Dinur's PCP proof) would imply MA=NP.
Revised:  This note, along with a translation of the main result of Aharonov and Grilo to the SetCSP language, implies that finding a gap-amplification procedure for SetCSP problems (namely a generalization to SetCSPs of the gap-amplification used in Dinur's PCP proof) is equivalent to MA=NP.
Edit intent: clarity
Original:  Lastly, we explain how the NNLAD can be used for group testing in the recent COVID-19 crisis and why contamination of specimens may be modeled as peaky noise, which favors \ell_1 based data fidelity terms .
Revised:  Lastly, we explain how the NNLAD can be used for group testing in the recent COVID-19 crisis .
Edit intent: coherence
Original:  We evolve solutions on two very different physical surfaces and analyze the results in terms of both control and morphology.
Revised:  We evolve solutions on two distinct physical surfaces and analyze the results in terms of both control and morphology.
Edit intent: clarity
Original:  A partial triangulation on P is a full triangulation of some subset P' of P containing all extreme points in P.
Revised:  A partial triangulation is a full triangulation of some subset P' of P containing all extreme points in P.
Edit intent: clarity
Original:  The bistellar flip graph has all partial triangulations as vertices ;
Revised:  The bistellar flip graph has all partial triangulations as vertices , and
Edit intent: fluency
Original:  The goal of this paper is to investigate the structure of this graph , with emphasis on  connectivity.
Revised:  The goal of this paper is to investigate these graphs , with emphasis on connectivity.
Edit intent: clarity
Original: In this paper, we study new batch-dynamic algorithms for  k-clique counting  , which are dynamic algorithms where the updates are batches of edge insertions and deletions.
Revised: In this paper, we study new batch-dynamic algorithms for the k-clique counting , which are dynamic algorithms where the updates are batches of edge insertions and deletions.
Edit intent: fluency
Original: In this paper, we study new batch-dynamic algorithms for  k-clique counting  , which are dynamic algorithms where the updates are batches of edge insertions and deletions.
Revised: In this paper, we study new batch-dynamic algorithms for k-clique counting problem , which are dynamic algorithms where the updates are batches of edge insertions and deletions.
Edit intent: clarity
Original:  We study this problem in the parallel setting, where the goal is to obtain algorithms with low ( poly-logarithmic ) depth.
Revised:  We study this problem in the parallel setting, where the goal is to obtain algorithms with low ( polylogarithmic ) depth.
Edit intent: fluency
Original: One of many different hierarchies towards the stability number of a graph is the exact subgraph hierarchy (ESH).
Revised: One of many different hierarchies towards the stability number of G is the exact subgraph hierarchy (ESH).
Edit intent: clarity
Original:  On the first level it starts to compute the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints , where n is the number of vertices and m is the number of edges of a graph G . On the k-th level of the ESH it adds all exact subgraph constraints (ESC) for subgraphs of G with k vertices to the SDP.
Revised:  On the first level it computes the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints , where n is the number of vertices and m is the number of edges of a graph G . On the k-th level of the ESH it adds all exact subgraph constraints (ESC) for subgraphs of G with k vertices to the SDP.
Edit intent: coherence
Original:  On the first level it starts to compute the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints , where n is the number of vertices and m is the number of edges of a graph G . On the k-th level of the ESH it adds all exact subgraph constraints (ESC) for subgraphs of G with k vertices to the SDP.
Revised:  On the first level it starts to compute the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints . On the k-th level of the ESH it adds all exact subgraph constraints (ESC) for subgraphs of G with k vertices to the SDP.
Edit intent: clarity
Original:  On the first level it starts to compute the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints , where n is the number of vertices and m is the number of edges of a graph G . On the k-th level of the ESH it adds all exact subgraph constraints (ESC) for subgraphs of G with k vertices to the SDP.
Revised:  On the first level it starts to compute the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints , where n is the number of vertices and m is the number of edges of a graph G . On the k-th level it adds all exact subgraph constraints (ESC) for subgraphs of G with k vertices to the SDP.
Edit intent: clarity
Original:  On the first level it starts to compute the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints , where n is the number of vertices and m is the number of edges of a graph G . On the k-th level of the ESH it adds all exact subgraph constraints (ESC) for subgraphs of G with k vertices to the SDP.
Revised:  On the first level it starts to compute the Lov\'{a}sz theta function as a semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints , where n is the number of vertices and m is the number of edges of a graph G . On the k-th level of the ESH it adds all exact subgraph constraints (ESC) for subgraphs of order k to the SDP.
Edit intent: clarity
Original:  These ESCs make sure that the submatrix of the matrix variable corresponding to the subgraphs are in the appropriate polytopes.
Revised:  An ESC ensures that the submatrix of the matrix variable corresponding to the subgraphs are in the appropriate polytopes.
Edit intent: clarity
Original:  In this paper we introduce a variant of the ESH that starts with an alternative SDP to compute the Lov\'{a with a matrix variable of order n and only m+1 constraints.
Revised:  In this paper we introduce a variant of the ESH that starts with an alternative SDP to compute the Lov\'{a with a matrix variable of order n and m+1 constraints.
Edit intent: coherence
Original:  We show that it makes sense to include the ESCs into this SDP and build the compressed ESH (CESH) analogously to the ESH. Computationally the CESH seems favorable as the SDP is smaller.
Revised:  We show that it makes sense to include the ESCs into this SDP and introduce the compressed ESH (CESH) analogously to the ESH. Computationally the CESH seems favorable as the SDP is smaller.
Edit intent: clarity
Original:  However, we prove that the bounds obtained with the ESH are always at least as good as those of the CESH.
Revised:  However, we prove that the bounds based on the ESH are always at least as good as those of the CESH.
Edit intent: clarity
Original:  In computations sometimes they are significantly better.
Revised:  In computational experiments sometimes they are significantly better.
Edit intent: clarity
Original:  This theory finds applications in several multi-wave imaging modalities including photo-acoustic tomography, and greedy methods to approximate parameter-dependent elliptic problems  .
Revised:  This theory finds applications in multi-wave imaging modalities including photo-acoustic tomography, and greedy methods to approximate parameter-dependent elliptic problems .
Edit intent: clarity
Original:  This theory finds applications in several multi-wave imaging modalities including photo-acoustic tomography, and greedy methods to approximate parameter-dependent elliptic problems  .
Revised:  This theory finds applications in several multi-wave imaging , greedy methods to approximate parameter-dependent elliptic problems .
Edit intent: clarity
Original:  We predicted structured regions at the 5 prime and 3 prime ends where our calculations also indicate strong propensity to bind  proteins.
Revised:  We predicted structured regions at the 5 and 3 prime ends where our calculations also indicate strong propensity to bind proteins.
Edit intent: fluency
Original:  We predicted structured regions at the 5 prime and 3 prime ends where our calculations also indicate strong propensity to bind  proteins.
Revised:  We predicted structured regions at the 5 prime and 3 prime ends where our calculations indicate strong propensity to bind proteins.
Edit intent: clarity
Original:  Using the catRAPID method, we computed 3500 protein interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1, Zinc Finger Protein ZNF175 and other 20 high-confidence candidate partners.
Revised:  Using the catRAPID method, we calculated 3500 protein interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1, Zinc Finger Protein ZNF175 and other 20 high-confidence candidate partners.
Edit intent: fluency
Original:  Using the catRAPID method, we computed 3500 protein interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1, Zinc Finger Protein ZNF175 and other 20 high-confidence candidate partners.
Revised:  Using the catRAPID method, we computed 3500 interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1, Zinc Finger Protein ZNF175 and other 20 high-confidence candidate partners.
Edit intent: clarity
Original:  Using the CROSS method, we found that the SARS-CoV-2 region encompassing nucleotides 23000 and 24000 is highly conserved at the  structural level, while the region 1000 nucleotides up-stream varies significantly.
Revised:  We found that the SARS-CoV-2 region encompassing nucleotides 23000 and 24000 is highly conserved at the structural level, while the region 1000 nucleotides up-stream varies significantly.
Edit intent: coherence
Original:  Using the CROSS method, we found that the SARS-CoV-2 region encompassing nucleotides 23000 and 24000 is highly conserved at the  structural level, while the region 1000 nucleotides up-stream varies significantly.
Revised:  Using the CROSS method, we found that the SARS-CoV-2 region encompassing nucleotides 23000 and 24000 is highly conserved at the structural level, while the region upstream varies significantly.
Edit intent: clarity
Original:  The two sequences code for a domain of the spike S protein that binds to the host receptor angiotensin-converting enzyme 2 (ACE2) that mediates human infection and in the homologue from Middle East respiratory syndrome coronavirus (MERS-CoV) interacts with sialic acids.
Revised:  Both these sequences code for a domain of the spike S protein that binds to the host receptor angiotensin-converting enzyme 2 (ACE2) that mediates human infection and in the homologue from Middle East respiratory syndrome coronavirus (MERS-CoV) interacts with sialic acids.
Edit intent: clarity
Original:  The two sequences code for a domain of the spike S protein that binds to the host receptor angiotensin-converting enzyme 2 (ACE2) that mediates human infection and in the homologue from Middle East respiratory syndrome coronavirus (MERS-CoV) interacts with sialic acids.
Revised:  The two sequences code for a domain of the viral protein Spike S that interacts with the human receptor angiotensin-converting enzyme 2 (ACE2) that mediates human infection and in the homologue from Middle East respiratory syndrome coronavirus (MERS-CoV) interacts with sialic acids.
Edit intent: clarity
Original:  The two sequences code for a domain of the spike S protein that binds to the host receptor angiotensin-converting enzyme 2 (ACE2) that mediates human infection and in the homologue from Middle East respiratory syndrome coronavirus (MERS-CoV) interacts with sialic acids.
Revised:  The two sequences code for a domain of the spike S protein that binds to the host receptor angiotensin-converting enzyme 2 (ACE2) and could bind to sialic acids, as reported for the homologue from Middle East respiratory syndrome coronavirus (MERS-CoV) interacts with sialic acids.
Edit intent: coherence
Original:  Using the catRAPID method, we calculated 3500 interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1 , Zinc Finger Protein ZNF175 and A-kinase anchor protein 8-like AKAP8L, among 20 high-confidence candidate partners.
Revised:  Using the catRAPID method, we calculated 3500 interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA Helicase DDX1 , Zinc Finger Protein ZNF175 and A-kinase anchor protein 8-like AKAP8L, among 20 high-confidence candidate partners.
Edit intent: fluency
Original:  Using the catRAPID method, we calculated 3500 interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1 , Zinc Finger Protein ZNF175 and A-kinase anchor protein 8-like AKAP8L, among 20 high-confidence candidate partners.
Revised:  Using the catRAPID method, we calculated 3500 interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1 and A-kinase anchor protein 8-like AKAP8L, among 20 high-confidence candidate partners.
Edit intent: coherence
Original:  Using the catRAPID method, we calculated 3500 interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1 , Zinc Finger Protein ZNF175 and A-kinase anchor protein 8-like AKAP8L, among 20 high-confidence candidate partners.
Revised:  Using the catRAPID method, we calculated 3500 interactions with the 5 prime end and identified Cyclin T1 CCNT1, ATP-dependent RNA helicase DDX1 , Zinc Finger Protein ZNF175 and A-kinase anchor protein 8-like AKAP8L, in addition to > 20 high-confidence candidate partners.
Edit intent: coherence
Original:  We propose these proteins , also implicated in HIV replication, to be further investigated for a better understanding of host-virus interaction mechanisms  .
Revised:  These interactions , also implicated in HIV replication, to be further investigated for a better understanding of host-virus interaction mechanisms .
Edit intent: clarity
Original:  We propose these proteins , also implicated in HIV replication, to be further investigated for a better understanding of host-virus interaction mechanisms  .
Revised:  We propose these proteins , also implicated in HIV replication, provide clues on host-virus interaction mechanisms .
Edit intent: clarity
Original: Structural elements of viral genomes regulate interactions in host cells.
Revised: Specific elements of viral genomes regulate interactions in host cells.
Edit intent: clarity
Original: Structural elements of viral genomes regulate interactions in host cells.
Revised: Structural elements of viral genomes regulate interactions within host cells.
Edit intent: clarity
Original:  We found that the 3 and 5 prime ends are highly structured and the 5 prime end especially has strong propensity to associate with proteins involved in replication and transcription .
Revised:  We found that the 3 and 5 prime ends are the most structured elements in the viral genome and the 5 prime end especially has strong propensity to associate with proteins involved in replication and transcription .
Edit intent: clarity
Original:  We found that the 3 and 5 prime ends are highly structured and the 5 prime end especially has strong propensity to associate with proteins involved in replication and transcription .
Revised:  We found that the 3 and 5 prime ends are highly structured and the 5 prime end has the strongest propensity to associate with proteins involved in replication and transcription .
Edit intent: clarity
Original:  We found that the 3 and 5 prime ends are highly structured and the 5 prime end especially has strong propensity to associate with proteins involved in replication and transcription .
Revised:  We found that the 3 and 5 prime ends are highly structured and the 5 prime end especially has strong propensity to associate with human proteins .
Edit intent: clarity
Original:  The domain encompassing nucleotides 23000-24000 is highly conserved  at the sequence and structural level, while the region upstream varies significantly.
Revised:  The domain encompassing nucleotides 23000-24000 is highly conserved both at the sequence and structural level, while the region upstream varies significantly.
Edit intent: clarity
Original:  Both these sequences code for a domain of the viral protein Spike S that interacts with the human receptor angiotensin-converting enzyme 2 (ACE2) and could bind to sialic acids, as reported for the homologue from Middle East respiratory syndrome coronavirus (MERS-CoV) .
Revised:  Both these sequences code for a domain of the viral protein Spike S that interacts with the human receptor angiotensin-converting enzyme 2 (ACE2) and has the potential to bind sialic acids .
Edit intent: clarity