wanyu/IteraTeR_v2 huggingface dataset:
Original:  Finally, We develop 4 baseline models for the dataset on NER task with several models, including Linear Regression, CRF, LSTM and the state-of-the-art bi-directional LSTM-CRF  . Both CRF and LSTM-CRF outperform human  in both exact-match accuracy and f1 scores.
Revised:  Finally, We develop 4 baseline models for the dataset on NER task with several models, including Linear Regression, CRF, LSTM and the state-of-the-art bi-directional LSTM-CRF . Both CRF and LSTM-CRF outperform human and baselines in both exact-match accuracy and f1 scores.
Edit intent: clarity
Original:   Since common logics like LTL, CTL, or the modal mu-calculus cannot express such hyperproperties, the hyperlogics HyperLTL and HyperCTL* were developed to cure this defect.
Revised:  Since common logics like LTL, CTL, or the modal mu-calculus cannot express hyperproperties, the hyperlogics HyperLTL and HyperCTL* were developed to cure this defect.
Edit intent: clarity
Original:  In this paper  we derive explicit stabilized integrators of orders one and two for the optimal control of stiff systems.
Revised:  In this paper , we derive explicit stabilized integrators of orders one and two for the optimal control of stiff systems.
Edit intent: fluency
Original:  We analyze their favourable stability and symplecticity properties based on the continuous optimality conditions  . Numerical experiments including the optimal control of a nonlinear diffusion-advection PDE illustrate the efficiency of the new approach.
Revised:  We analyze their favorable stability properties based on the continuous optimality conditions . Numerical experiments including the optimal control of a nonlinear diffusion-advection PDE illustrate the efficiency of the new approach.
Edit intent: clarity
Original: Recent model-based congestion control algorithms such as BBR use repeated measurements at the end-point to build a model of the network connection and use it to achieve optimal throughput with low queuing delay.
Revised: Recent model-based congestion control algorithms such as BBR use repeated measurements at the endpoint to build a model of the network connection and use it to achieve optimal throughput with low queuing delay.
Edit intent: fluency
Original:  This is also (up to {\rm polylog}\,n factors, where n is the length of the text) the space used by the state-of-the-art BWT-based indexes, such as the recent r-index [Gagie et al., SODA 2018 ].
Revised:  This is also (up to {\rm polylog}\,n factors, where n is the length of the text) the space used by the state-of-the-art BWT-based indexes, such as the r-index [Gagie et al., SODA 2018 ].
Edit intent: clarity
Original:  The output size of virtually every known compression method is known to be either within a%DIFDELCMD < {\rm %%% polylog \,n factor from z, the size of Lempel-Ziv (LZ77) parsing of the text, or significantly larger (by a n^{\epsilon factor for \epsilon > 0).
Revised:  %DIFDELCMD < {\rm %%% polylog \,n factor from z, the size of Lempel-Ziv (LZ77) parsing of the text, or significantly larger (by a n^{\epsilon factor for \epsilon > 0).
Edit intent: clarity
Original:  The value of r has resisted, however, all attempts and until now, }  no non-trivial upper bounds on r were known.
Revised:  The value of r has resisted, however, all attempts and until now, } no non-trivial bound on the value of r is known.
Edit intent: clarity
Original:  This result has a number of immediate implications : (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel--Ziv indexing and compression, e.g., it is possible to obtain full functionality of the suffix tree and the suffix array in O(z\,{\rm polylog}\,n) space;
Revised:  This result has numerous immediate implications for text indexing and data compression; for example : (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel--Ziv indexing and compression, e.g., it is possible to obtain full functionality of the suffix tree and the suffix array in O(z\,{\rm polylog}\,n) space;
Edit intent: clarity
Original:  This result has a number of immediate implications : (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel--Ziv indexing and compression, e.g., it is possible to obtain full functionality of the suffix tree and the suffix array in O(z\,{\rm polylog}\,n) space;
Revised:  This result has a number of immediate implications : (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel-Ziv indexing and compression, e.g., it is possible to obtain full functionality of the suffix tree and the suffix array in O(z\,{\rm polylog}\,n) space;
Edit intent: fluency
Original:  This result has a number of immediate implications : (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel--Ziv indexing and compression, e.g., it is possible to obtain full functionality of the suffix tree and the suffix array in O(z\,{\rm polylog}\,n) space;
Revised:  This result has a number of immediate implications : (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel--Ziv indexing and compression, e.g., it is possible to obtain functionality of the suffix tree and the suffix array in O(z\,{\rm polylog}\,n) space;
Edit intent: clarity
Original:  (3) it shows that many fundamental text processing tasks can be solved in the optimal time assuming that the text is compressible  by a sufficiently large {\rm polylog}\, n factor using LZ77 \,n) time.
Revised:  (3) it shows that many fundamental text processing tasks can be solved in the optimal time assuming that the text is compressible using LZ77 by a sufficiently large {\rm polylog}\, n factor using LZ77 \,n) time.
Edit intent: fluency
Original:  Burrows-Wheeler Transform (BWT) is an invertible text transformation that permutes symbols of a text according to the lexicographical order of its suffixes.
Revised: The Burrows-Wheeler Transform (BWT) is an invertible text transformation that permutes symbols of a text according to the lexicographical order of its suffixes.
Edit intent: fluency
Original:  BWT is the main component of some of the most popular lossless compression methods as well as of compressed indexes , ] central in modern bioinformatics.
Revised:  BWT is the main component of popular lossless compression methods as well as of compressed indexes , ] central in modern bioinformatics.
Edit intent: clarity
Original:  BWT is the main component of some of the most popular lossless compression methods as well as of compressed indexes , ] central in modern bioinformatics.
Revised:  BWT is the main component of some of the most popular lossless compression methods as well as of compressed indexes , ]), central in modern bioinformatics.
Edit intent: fluency
Original:  The compression ratio of BWT-based compressors, such as bzip2, is quantified by the number r of maximal equal-letter runs in the BWT . This is also (up to {\rm polylog}\,n factors, where n is the length of the text)
Revised:  The compression ratio of BWT is quantified by the number r of maximal equal-letter runs in the BWT . This is also (up to {\rm polylog}\,n factors, where n is the length of the text)
Edit intent: clarity
Original:  The compression ratio of BWT-based compressors, such as bzip2, is quantified by the number r of maximal equal-letter runs in the BWT . This is also (up to {\rm polylog}\,n factors, where n is the length of the text)
Revised:  The compression ratio of BWT-based compressors, such as bzip2, is quantified by the number r of equal-letter runs in the BWT . This is also (up to {\rm polylog}\,n factors, where n is the length of the text)
Edit intent: clarity
Original:  The compression ratio of BWT-based compressors, such as bzip2, is quantified by the number r of maximal equal-letter runs in the BWT . This is also (up to {\rm polylog}\,n factors, where n is the length of the text)
Revised:  The compression ratio of BWT-based compressors, such as bzip2, is quantified by the number r of maximal equal-letter runs in the BWT . This is also (up to {\rm polylog}\,n factor ( where n is the length of the text)
Edit intent: fluency
Original:  the space used by the state-of-the-art BWT-based indexes, such as the r-index Gagie et al., J. ACM, 2020%DIFDELCMD < ]%%% . Despite its practical significance and many years of effort, no non-trivial bound on the value of r is known factor for \varepsilon > 0)} . In this paper, we show that every text satisfies r = O(z \log^2n)  .
Revised:  the space used by the state-of-the-art BWT-based indexes, such as the r-index %DIFDELCMD < ]%%% . Despite its practical significance and many years of effort, no non-trivial bound on the value of r is known factor for \varepsilon > 0)} . In this paper, we show that every text satisfies r = O(z \log^2n) .
Edit intent: clarity
Original:  the space used by the state-of-the-art BWT-based indexes, such as the r-index Gagie et al., J. ACM, 2020%DIFDELCMD < ]%%% . Despite its practical significance and many years of effort, no non-trivial bound on the value of r is known factor for \varepsilon > 0)} . In this paper, we show that every text satisfies r = O(z \log^2n)  .
Revised:  the space used by the state-of-the-art BWT-based indexes, such as the r-index Gagie et al., J. ACM, 2020%DIFDELCMD < ]%%% . Despite its practical significance and many years of effort, no non-trivial bound on the value of r is known factor for \varepsilon > 0)} . In this paper, we show that r = O(z \log^2n) .
Edit intent: clarity
Original:  the space used by the state-of-the-art BWT-based indexes, such as the r-index Gagie et al., J. ACM, 2020%DIFDELCMD < ]%%% . Despite its practical significance and many years of effort, no non-trivial bound on the value of r is known factor for \varepsilon > 0)} . In this paper, we show that every text satisfies r = O(z \log^2n)  .
Revised:  the space used by the state-of-the-art BWT-based indexes, such as the r-index Gagie et al., J. ACM, 2020%DIFDELCMD < ]%%% . Despite its practical significance and many years of effort, no non-trivial bound on the value of r is known factor for \varepsilon > 0)} . In this paper, we show that every text satisfies r = O(z \log^2n) holds for every text .
Edit intent: clarity
Original:  This result has numerous immediate implications for text indexing and data compression;
Revised:  This result has numerous implications for text indexing and data compression;
Edit intent: clarity
Original:  for example: (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel-Ziv indexing and compression , e.g., it is possible to obtain functionality of the suffix tree and the suffix array in \mathcal{O}(z\,{\rm polylog}\,n) space;
Revised:  for example: (1) it proves that many results related to BWT automatically applies to the so-far disjoint field of Lempel-Ziv indexing and compression , e.g., it is possible to obtain functionality of the suffix tree and the suffix array in \mathcal{O}(z\,{\rm polylog}\,n) space;
Edit intent: clarity
Original:  for example: (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel-Ziv indexing and compression , e.g., it is possible to obtain functionality of the suffix tree and the suffix array in \mathcal{O}(z\,{\rm polylog}\,n) space;
Revised:  for example: (1) it proves that a large body of work related to BWT automatically apply to methods based on LZ77 , e.g., it is possible to obtain functionality of the suffix tree and the suffix array in \mathcal{O}(z\,{\rm polylog}\,n) space;
Edit intent: clarity
Original:  for example: (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel-Ziv indexing and compression , e.g., it is possible to obtain functionality of the suffix tree and the suffix array in \mathcal{O}(z\,{\rm polylog}\,n) space;
Revised:  for example: (1) it proves that a large body of work related to BWT automatically applies to the so-far disjoint field of Lempel-Ziv indexing and compression , e.g., it is possible to obtain functionality of the suffix tree in \mathcal{O}(z\,{\rm polylog}\,n) space;
Edit intent: clarity
Original:  (2) it shows that many fundamental text processing tasks can be solved in the optimal time assuming that the text is compressible using LZ77 by a sufficiently large {\rm polylog}\,n factor;
Revised:  (2) it shows that many text processing tasks can be solved in the optimal time assuming that the text is compressible using LZ77 by a sufficiently large {\rm polylog}\,n factor;
Edit intent: clarity
Original:  (2) it shows that many fundamental text processing tasks can be solved in the optimal time assuming that the text is compressible using LZ77 by a sufficiently large {\rm polylog}\,n factor;
Revised:  (2) it shows that many fundamental text processing tasks can be solved in the optimal time assuming the text is compressible using LZ77 by a sufficiently large {\rm polylog}\,n factor;
Edit intent: fluency
Original:  In addition to the existential proof of the bound , we provide an (z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into  run-length compressed BWT running in \mathcal{O(z\,{\rm polylog}\,n) time} .
Revised:  In addition , we provide an (z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into run-length compressed BWT running in \mathcal{O(z\,{\rm polylog}\,n) time} .
Edit intent: clarity
Original:  In addition to the existential proof of the bound , we provide an (z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into  run-length compressed BWT running in \mathcal{O(z\,{\rm polylog}\,n) time} .
Revised:  In addition to the existential proof of the bound , we provide an \mathcal{O(z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into run-length compressed BWT running in \mathcal{O(z\,{\rm polylog}\,n) time} .
Edit intent: fluency
Original:  In addition to the existential proof of the bound , we provide an (z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into  run-length compressed BWT running in \mathcal{O(z\,{\rm polylog}\,n) time} .
Revised:  In addition to the existential proof of the bound , we provide an (z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into the run-length compressed BWT running in \mathcal{O(z\,{\rm polylog}\,n) time} .
Edit intent: fluency
Original:  In addition to the existential proof of the bound , we provide an (z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into  run-length compressed BWT running in \mathcal{O(z\,{\rm polylog}\,n) time} .
Revised:  In addition to the existential proof of the bound , we provide an (z\,{\rm polylog}\,n)-time } algorithm converting the LZ77 parsing into run-length compressed BWT (z\,{\rm polylog}\,n) time} .
Edit intent: clarity
Original:  To achieve this, we develop a number of new data structures and techniques for indexing of compressed data which are of independent interest.
Revised:  To achieve this, we develop a number of new data structures and techniques of independent interest.
Edit intent: clarity
Original:  This allows translating the problem of finding minimal witnesses to the problem of finding vertices with a maximal number of zeros.
Revised:  Using this correspondence we can translate the problem of finding minimal witnesses to the problem of finding vertices with a maximal number of zeros.
Edit intent: clarity
Original:  While computing such vertices is computationally hard in general, we derive new heuristics from our formulations that exhibit competitive performance compared to state-of-the-art techniques and apply to more situations .
Revised:  While computing such vertices is computationally hard in general, we derive new heuristics from our formulations that exhibit competitive performance compared to state-of-the-art techniques .
Edit intent: coherence
Original:  Metamath Zero currently holds the record for fastest verification of the \mathtt{set.mm Metamath library of proofs in ZFC (including 71 of Wiedijk's 100 formalization targets), at less than 200 ms.
Revised:  Metamath Zero currently holds the record for fastest verification of the \mathtt{set .mm Metamath library of proofs in ZFC (including 71 of Wiedijk's 100 formalization targets), at less than 200 ms.
Edit intent: fluency
Original:  We will use the concept of special covering of a set introduced in [9] and study the connection of this concept with the satisfiability of Boolean functions.
Revised:  We will use the concept of special covering of a set introduced in [9] and study the relation of this concept with the satisfiability of Boolean functions.
Edit intent: clarity
Original:  Generally, accepted terminology on set theory, Boolean functions, and graph theory is consistent with the terminology found in the relevant works included in the bibliography 1%DIFDELCMD < ] [%%% 2 3%DIFDELCMD < ]%%% . The newly introduced terms are not found in use by other authors and do not contradict to other terms.
Revised:  Generally, accepted terminology on set theory, Boolean functions, and graph theory is consistent with the terminology found in the relevant works included in the bibliography %DIFDELCMD < ] [%%% 2 3%DIFDELCMD < ]%%% . The newly introduced terms are not found in use by other authors and do not contradict to other terms.
Edit intent: clarity
Original:  Generally, accepted terminology on set theory, Boolean functions, and graph theory is consistent with the terminology found in the relevant works included in the bibliography 1%DIFDELCMD < ] [%%% 2 3%DIFDELCMD < ]%%% . The newly introduced terms are not found in use by other authors and do not contradict to other terms.
Revised:  Generally, accepted terminology on set theory, Boolean functions, and graph theory is consistent with the terminology found in the relevant works included in the bibliography 1%DIFDELCMD < ] [%%% 2 %DIFDELCMD < ]%%% . The newly introduced terms are not found in use by other authors and do not contradict to other terms.
Edit intent: coherence
Original:  We prove that Boolean function represented in conjunctive normal form is satisfable if and only if it is transformed into a function in proportional conjunctive normal form  ] ] ] .
Revised:  Thus, we obtain that the satisfiability of a Boolean function represented in conjunctive normal form is satisfable if and only if it is transformed into a function in proportional conjunctive normal form ] ] ] .
Edit intent: clarity
Original:  We prove that Boolean function represented in conjunctive normal form is satisfable if and only if it is transformed into a function in proportional conjunctive normal form  ] ] ] .
Revised:  We prove that Boolean function represented in conjunctive normal form is equivalent to the possibility of converting it into a function in proportional conjunctive normal form ] ] ] .
Edit intent: clarity
Original:  We prove that Boolean function represented in conjunctive normal form is satisfable if and only if it is transformed into a function in proportional conjunctive normal form  ] ] ] .
Revised:  We prove that Boolean function represented in conjunctive normal form is satisfable if and only if it is transformed into a function in proportional conjunctive normal form ], ] ] .
Edit intent: fluency
Original:  We prove that Boolean function represented in conjunctive normal form is satisfable if and only if it is transformed into a function in proportional conjunctive normal form  ] ] ] .
Revised:  We prove that Boolean function represented in conjunctive normal form is satisfable if and only if it is transformed into a function in proportional conjunctive normal form ] ], ] .
Edit intent: fluency
Original: The paper presents a distributed algorithm, called Prediction-based Opportunistic Sensing for Resilient and Efficient Sensor Networks (POSE.R), where the sensor nodes utilize predictions of the target's positions to probabilistically control their multi-modal operating states to track the target.
Revised: The paper presents a distributed algorithm, called Prediction-based Opportunistic Sensing for Resilient and Efficient Sensor Networks (POSE.R), where the sensor nodes utilize predictions of the targets positions to probabilistically control their multi-modal operating states to track the target.
Edit intent: fluency
Original:  If the target is traveling through a high node density area, then an optimal sensor selection approach is employed that maximizes a joint cost function of remaining energy and geometric diversity around the target's position.
Revised:  If the target is traveling through a high node density area, then an optimal sensor selection approach is employed that maximizes a joint cost function of remaining energy and geometric diversity around the targets position.
Edit intent: clarity
Original:  On the other hand, if the target is traveling through a low node density area or in a coverage gap  , formed by node failures or non-uniform deployment , then a potential game is played amongst the surrounding nodes to optimally expand their sensing ranges via minimizing energy consumption and maximizing target coverage.
Revised:  On the other hand, if the target is traveling through a low node density area or in a coverage gap , formed by node failures or non-uniform node deployment) , then a potential game is played amongst the surrounding nodes to optimally expand their sensing ranges via minimizing energy consumption and maximizing target coverage.
Edit intent: fluency
Original:  The algorithm is validated through extensive Monte Carlo simulations which demonstrate its superior performance as compared to the existing approaches in terms of tracking performance, network-resilience and network-lifetime.
Revised:  The algorithm is comparatively evaluated against existing approaches through Monte Carlo simulations which demonstrate its superior performance as compared to the existing approaches in terms of tracking performance, network-resilience and network-lifetime.
Edit intent: clarity
Original:  The algorithm is validated through extensive Monte Carlo simulations which demonstrate its superior performance as compared to the existing approaches in terms of tracking performance, network-resilience and network-lifetime.
Revised:  The algorithm is validated through extensive Monte Carlo simulations which demonstrate its superiority in terms of tracking performance, network-resilience and network-lifetime.
Edit intent: clarity
Original:  Torque balance also requires each internal vertex to be the orthocentre of the triangle formed by neighbouring edge centroids , and defines vertex locations relative to adjacent cell centres .
Revised:  Torque balance also requires each internal vertex to be the orthocentre of the triangle formed by neighbouring edge centroids .
Edit intent: clarity
Original:  In particular, a recovered numerical flux is shown to be superclose to the Raviart-Thomas interpolant of the exact flux.
Revised:  In particular, a corrected numerical flux is shown to be superclose to the Raviart-Thomas interpolant of the exact flux.
Edit intent: clarity
Original:  In particular, a recovered numerical flux is shown to be superclose to the Raviart-Thomas interpolant of the exact flux.
Revised:  In particular, a recovered numerical flux is shown to be superclose to the Raviart--Thomas interpolant of the exact flux.
Edit intent: fluency
Original:  As a by-product, we obtain a superconvergent recovery estimate of the Crouzeix-Raviart element method for general elliptic equations.
Revised:  As a by-product, we obtain a superconvergent recovery estimate of the Crouzeix--Raviart element method for general elliptic equations.
Edit intent: fluency