wanyu/IteraTeR_v2 huggingface dataset:
Original:  Moreover, we construct the shadow market by the dual optimal process and exhibit the utility based pricing for the random endowment.
Revised:  Moreover, we construct the shadow market by the dual optimal process and consider the utility based pricing for the random endowment.
Edit intent: clarity
Original:  Moreover, we construct the shadow market by the dual optimal process and exhibit the utility based pricing for the random endowment.
Revised:  Moreover, we construct the shadow market by the dual optimal process and exhibit the utility based pricing for random endowment.
Edit intent: fluency
Original:  The coarse-grained simulations quantitatively reproduces the multistep thermal melting  .
Revised:  The coarse-grained simulations quantitatively reproduce the multistep thermal melting .
Edit intent: fluency
Original:  The predicted phase diagram shows that a sequence of structural transitions, populating distinct intermediates, occur as f and C are changed .
Revised:  The predicted phase diagram shows that a sequence of structural transitions, populating distinct intermediate states. As f and C are changed .
Edit intent: clarity
Original:  The stem-loop tertiary interactions rupture first followed by unfolding of the 3^{\prime}-end hairpin (\textrm{ U-I } \textrm{ ).
Revised:  The stem-loop tertiary interactions rupture first followed by unfolding of the 3^{\prime}-end hairpin (\textrm{ I } \textrm{ ).
Edit intent: clarity
Original:  Finally, the 5^{\prime}-end hairpin unravels producing a stretched state ( \textrm{ I-F } \textrm{ ).
Revised:  Finally, the 5^{\prime}-end hairpin unravels producing a extended state ( \textrm{ I-F } \textrm{ ).
Edit intent: clarity
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I%DIFDELCMD < \MBLOCKRIGHTBRACE %%% ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ %DIFDELCMD < \MBLOCKRIGHTBRACE %%% ( \textrm{ \textrm{ I-F } \textrm{ ) transition.
Edit intent: clarity
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I%DIFDELCMD < \MBLOCKRIGHTBRACE %%% ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I%DIFDELCMD < \MBLOCKRIGHTBRACE %%% E \textrm{ \textrm{ I-F } \textrm{ ) transition.
Edit intent: fluency
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I%DIFDELCMD < \MBLOCKRIGHTBRACE %%% ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I%DIFDELCMD < \MBLOCKRIGHTBRACE %%% ( \textrm{I \textrm{ I-F } \textrm{ ) transition.
Edit intent: fluency
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I%DIFDELCMD < \MBLOCKRIGHTBRACE %%% ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I%DIFDELCMD < \MBLOCKRIGHTBRACE %%% ( \textrm{ ( \textrm{ I-F } \textrm{ ) transition.
Edit intent: fluency
Original:  This relation is used to obtain the ion-preferential coefficients, which shows that ion-RNA interactions can be quantitatively measured in single molecule experiments .
Revised:  This relation is used to obtain the preferential ion-RNA interactions can be quantitatively measured in single molecule experiments .
Edit intent: clarity
Original:  This relation is used to obtain the ion-preferential coefficients, which shows that ion-RNA interactions can be quantitatively measured in single molecule experiments .
Revised:  This relation is used to obtain the ion-preferential coefficients, which shows that ion-RNA interaction coefficient, which can be quantitatively measured in single molecule experiments .
Edit intent: clarity
Original:  Finally, the 5^{\prime}-end hairpin unravels producing a extended state (E\rightleftharpoonsI).
Revised:  Finally, the 5^{\prime}-end hairpin unravels , producing an extended state (E\rightleftharpoonsI).
Edit intent: fluency
Original:  This relation is used to obtain the preferential ion-RNA interaction coefficient, which can be quantitatively measured in single molecule experiments, as done previously for DNA hairpins.
Revised:  This relation is used to obtain the preferential ion-RNA interaction coefficient, which can be quantitatively measured in single-molecule experiments, as done previously for DNA hairpins.
Edit intent: fluency
Original:  A by product of our work is the suggestion that the frameshift efficiency is likely determined by the stability of the 5^{\prime}-end hairpin that the ribosome first encounters during translation.
Revised:  A by-product of our work is the suggestion that the frameshift efficiency is likely determined by the stability of the 5^{\prime}-end hairpin that the ribosome first encounters during translation.
Edit intent: fluency
Original:  Our general approach, which employs a pairwise maximum entropy model to infer direct couplings between residues, has been successfully used to predict the three-dimensional structures of proteins from sequences.
Revised:  Our general approach, which employs a pairwise maximum entropy model to infer couplings between residues, has been successfully used to predict the three-dimensional structures of proteins from sequences.
Edit intent: clarity
Original:  Building on this approach , we introduce an iterative algorithm to predict specific interaction partners from among the members of two protein families .
Revised:  Thus inspired , we introduce an iterative algorithm to predict specific interaction partners from among the members of two protein families .
Edit intent: clarity
Original:  Building on this approach , we introduce an iterative algorithm to predict specific interaction partners from among the members of two protein families .
Revised:  Building on this approach , we introduce an iterative algorithm to predict specific interaction partners from two protein families .
Edit intent: clarity
Original:  The algorithm proves successful without any a priori knowledge of interaction partners, yielding a striking 0.93 true positive fraction on our complete dataset  , and we uncover the origin of this surprising success.
Revised:  We obtain a striking 0.93 true positive fraction on our complete dataset , and we uncover the origin of this surprising success.
Edit intent: clarity
Original: Consider a distributed network on a simple graph G=(V,E) where each node has a phase oscillator revolving on S^{1}=R/Z with natural period of 1 second . Pulse-coupling is a class of distributed time evolution rule for such networked clock system inspired by biological oscillators, where local interactions between neighboring nodes are event-triggered and do not depend on any kind of global information.
Revised: Consider a distributed network on a simple graph G=(V,E) where each node has a phase oscillator revolving on S^{1}=R/Z with unit speed . Pulse-coupling is a class of distributed time evolution rule for such networked clock system inspired by biological oscillators, where local interactions between neighboring nodes are event-triggered and do not depend on any kind of global information.
Edit intent: clarity
Original:  In this paper, we propose a novel inhibitory pulse-coupling and prove that arbitrary phase configuration on any tree with maximum degree at most 3 and diameter d synchronizes in at most 24d times .
Revised:  In this paper, we propose a novel inhibitory pulse-coupling and prove that arbitrary phase configuration on any tree with maximum degree at most 3 and diameter d synchronizes in at most 24d time .
Edit intent: fluency
Original:  We extend this pulse-coupling by making each oscillator adjust its phase response curve depending on local events, and show that arbitrary initial configuration on any finite tree with diameter d synchronizes in at most 51d times .
Revised:  We extend this pulse-coupling by making each oscillator adjust its phase response curve depending on local events, and show that arbitrary initial configuration on any finite tree with diameter d synchronizes in at most 51d time .
Edit intent: fluency
Original:  As an application, we obtain a universal Las Vegas self-stabilizing distributed phase clock synchronization algorithm, using O(\log \Delta) memory per node with O( d ^{ O(1) }+ )\log } |V|) expected time complexity, where d and \Delta denote the diameter and the maximum degree of G, respectively .
Revised:  As an application, we obtain a universal randomized distributed clock synchronization algorithm, using O(\log \Delta) memory per node with O( d ^{ O(1) }+ )\log } |V|) expected time complexity, where d and \Delta denote the diameter and the maximum degree of G, respectively .
Edit intent: clarity
Original:  As an application, we obtain a universal Las Vegas self-stabilizing distributed phase clock synchronization algorithm, using O(\log \Delta) memory per node with O( d ^{ O(1) }+ )\log } |V|) expected time complexity, where d and \Delta denote the diameter and the maximum degree of G, respectively .
Revised:  As an application, we obtain a universal Las Vegas self-stabilizing distributed phase clock synchronization algorithm, using O(\log \Delta) memory per node with O( |V|+(d ^{ O(1) }+ )\log } |V|) expected time complexity, where d and \Delta denote the diameter and the maximum degree of G, respectively .
Edit intent: fluency
Original:  Pulse-coupling is a class of distributed time evolution rule for such networked clock system inspired by biological oscillators, where local interactions between neighboring nodes are event-triggered and do not depend on any kind of global information .
Revised:  Pulse-coupling is a class of distributed time evolution rule for such networked phase oscillators inspired by biological oscillators, where local interactions between neighboring nodes are event-triggered and do not depend on any kind of global information .
Edit intent: clarity
Original:  Pulse-coupling is a class of distributed time evolution rule for such networked clock system inspired by biological oscillators, where local interactions between neighboring nodes are event-triggered and do not depend on any kind of global information .
Revised:  Pulse-coupling is a class of distributed time evolution rule for such networked clock system inspired by biological oscillators, which depends only upon event-triggered and do not depend on any kind of global information .
Edit intent: clarity
Original:  Pulse-coupling is a class of distributed time evolution rule for such networked clock system inspired by biological oscillators, where local interactions between neighboring nodes are event-triggered and do not depend on any kind of global information .
Revised:  Pulse-coupling is a class of distributed time evolution rule for such networked clock system inspired by biological oscillators, where local interactions between neighboring nodes are event-triggered local pulse communications .
Edit intent: clarity
Original: \le  We extend this pulse-coupling by letting each oscillator may throttle the input according to an auxiliary state variable.
Revised: \le We extend this pulse-coupling by letting each oscillator throttle the input according to an auxiliary state variable.
Edit intent: clarity
Original:  We show that this adaptive pulse-coupling synchronizes arbitrary initial configuration on G by time 83d if G is a tree.
Revised:  We show that the resulting adaptive pulse-coupling synchronizes arbitrary initial configuration on G by time 83d if G is a tree.
Edit intent: clarity
Original:  As an application, we obtain a universal randomized distributed clock synchronization algorithm, using O(\log \Delta) memory per node with O(|V|+(d^{5}+\Delta^{2})\log |V|) expected worst case running time .
Revised:  As an application, we obtain a universal randomized distributed clock synchronization algorithm, which uses O(\log \Delta) memory per node with O(|V|+(d^{5}+\Delta^{2})\log |V|) expected worst case running time .
Edit intent: coherence
Original:  As an application, we obtain a universal randomized distributed clock synchronization algorithm, using O(\log \Delta) memory per node with O(|V|+(d^{5}+\Delta^{2})\log |V|) expected worst case running time .
Revised:  As an application, we obtain a universal randomized distributed clock synchronization algorithm, using O(\log \Delta) memory per node with O(|V|+(d^{5}+\Delta^{2})\log |V|) .
Edit intent: clarity
Original:  Furthermore, our analysis is general, and it might be extended to other settings , as well .
Revised:  Furthermore, our analysis is general, and it might be extended to other settings .
Edit intent: coherence
Original:  The efficiency of the new algorithm relies on two new theoretical contribution , of independent interest.
Revised:  The efficiency of the new algorithm relies on two new theoretical contributions , of independent interest.
Edit intent: fluency
Original:  Despite the efforts of many researchers, no improvement in the order of magnitude has ever been made on the upper bound over the last 81 years.
Edit intent: coherence
Original: The LFR benchmark is a popular benchmark graph model used to evaluate community detection algorithms.
Revised: LFR is a popular benchmark graph model used to evaluate community detection algorithms.
Edit intent: clarity
Original: The LFR benchmark is a popular benchmark graph model used to evaluate community detection algorithms.
Revised: The LFR benchmark is a popular benchmark graph generator used to evaluate community detection algorithms.
Edit intent: clarity
Original:  We present  the first external memory algorithm that is able to generate massive complex networks following the LFR model .
Revised:  We present the first external memory algorithm able to generate massive complex networks following the LFR model .
Edit intent: clarity
Original:  We present  the first external memory algorithm that is able to generate massive complex networks following the LFR model .
Revised:  We present the first external memory algorithm that is able to generate massive complex networks following the LFR benchmark .
Edit intent: clarity
Original:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided in two steps: They are first materialized as deterministic graphs using the Havel-Hakimi algorithm and then randomized.
Revised:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided into two steps: They are first materialized as deterministic graphs using the Havel-Hakimi algorithm and then randomized.
Edit intent: fluency
Original:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided in two steps: They are first materialized as deterministic graphs using the Havel-Hakimi algorithm and then randomized.
Revised:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided in two steps: the graphs are first materialized as deterministic graphs using the Havel-Hakimi algorithm and then randomized.
Edit intent: fluency
Original:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided in two steps: They are first materialized as deterministic graphs using the Havel-Hakimi algorithm and then randomized.
Revised:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided in two steps: They are first materialized deterministically using the Havel-Hakimi algorithm and then randomized.
Edit intent: clarity
Original:  In an experimental evaluation we demonstrate their performance: our implementation is able to generate graphs with more than 10 billion edges on a single machine, is competitive with a parallel massively distributed algorithm and on smaller instances faster than a state-of-the-art internal memory implementation  .
Revised:  In an experimental evaluation we demonstrate their performance: our implementation is able to handle graphs with more than 10 billion edges on a single machine, is competitive with a parallel massively distributed algorithm and on smaller instances faster than a state-of-the-art internal memory implementation .
Edit intent: clarity
Original:  In an experimental evaluation we demonstrate their performance: our implementation is able to generate graphs with more than 10 billion edges on a single machine, is competitive with a parallel massively distributed algorithm and on smaller instances faster than a state-of-the-art internal memory implementation  .
Revised:  In an experimental evaluation we demonstrate their performance: our implementation is able to generate graphs with more than 10 billion edges on a single machine, is competitive with a massive parallel distributed algorithm and on smaller instances faster than a state-of-the-art internal memory implementation .
Edit intent: fluency
Original:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided into two steps: the graphs are first materialized deterministically using the Havel-Hakimi algorithm  and then randomized.
Revised:  Its most expensive component is the generation of random graphs with prescribed degree sequences which can be divided into two steps: the graphs are first materialized deterministically using the Havel-Hakimi algorithm , and then randomized.
Edit intent: fluency
Original:   In an experimental evaluation we demonstrate their performance : our implementation is able to handle graphs with more than 37 billion edges on a single machine, is competitive with a massive parallel distributed algorithm and on smaller instances faster than a state-of-the-art internal memory implementation .
Revised:  In an experimental evaluation we demonstrate their performance ; our implementation is able to handle graphs with more than 37 billion edges on a single machine, is competitive with a massive parallel distributed algorithm and on smaller instances faster than a state-of-the-art internal memory implementation .
Edit intent: fluency
Original:   In an experimental evaluation we demonstrate their performance : our implementation is able to handle graphs with more than 37 billion edges on a single machine, is competitive with a massive parallel distributed algorithm and on smaller instances faster than a state-of-the-art internal memory implementation .
Revised:  In an experimental evaluation we demonstrate their performance : our implementation is able to handle graphs with more than 37 billion edges on a single machine, is competitive with a massive parallel distributed algorithm , and is faster than a state-of-the-art internal memory implementation .
Edit intent: clarity
Original:  By applying clustering algorithms to generated instances, we give evidence that both implementations yield graphs with matching properties  .
Revised:  We give evidence that both implementations yield graphs with matching properties .
Edit intent: clarity
Original:  Namely, we prove that if G  has at most one crossing per edge (i.e. G is a 1-plane graph ) an OPVR of G always exists while this may not be the case if two crossings per edge are allowed.
Revised:  Namely, we prove that if G is 1-plane (i.e., it has at most one crossing per edge (i.e. G is a 1-plane graph ) an OPVR of G always exists while this may not be the case if two crossings per edge are allowed.
Edit intent: clarity
Original:  Namely, we prove that if G  has at most one crossing per edge (i.e. G is a 1-plane graph ) an OPVR of G always exists while this may not be the case if two crossings per edge are allowed.
Revised:  Namely, we prove that if G has at most one crossing per edge ) an OPVR of G always exists while this may not be the case if two crossings per edge are allowed.
Edit intent: coherence
Original:  In contrast, we describe a family of 2-connected 1-plane graphs for which , in O(n) time, an embedding that guarantees constant vertex complexity can be computed.
Revised:  In contrast, we describe a family of 2-connected 1-plane graphs for which an embedding that guarantees constant vertex complexity can be computed.
Edit intent: clarity
Original:  Finally, we present the results of an experimental study on the vertex complexity of ortho-polygon visibility representations of 1-plane graphs.
Revised:  Finally, we present the results of an experimental study on the vertex complexity of OPVRs of 1-plane graphs.
Edit intent: clarity
Original: An ortho-polygon visibility representation of an n-vertex embedded graph G (OPVR of G) is an embedding preserving drawing of G that maps every vertex to a distinct orthogonal polygon and each edge to a vertical or horizontal visibility between its end-vertices.
Revised: An ortho-polygon visibility representation of an n-vertex embedded graph G (OPVR of G) is an embedding-preserving drawing of G that maps every vertex to a distinct orthogonal polygon and each edge to a vertical or horizontal visibility between its end-vertices.
Edit intent: fluency
Original:  Namely , we prove that if G is 1-plane (i.e., it has at most one crossing per edge ) an OPVR of G always exists while this may not be the case if two crossings per edge are allowed.
Revised:  More precisely , we prove that if G is 1-plane (i.e., it has at most one crossing per edge ) an OPVR of G always exists while this may not be the case if two crossings per edge are allowed.
Edit intent: coherence
Original:  Also, if G is a 3-connected 1-plane graph, we can compute in O(n) time an OPVR of G whose vertex complexity is bounded by a constant  .
Revised:  Also, if G is a 3-connected 1-plane graph, we can compute an OPVR of G whose vertex complexity is bounded by a constant .
Edit intent: clarity
Original:  Also, if G is a 3-connected 1-plane graph, we can compute in O(n) time an OPVR of G whose vertex complexity is bounded by a constant  .
Revised:  Also, if G is a 3-connected 1-plane graph, we can compute in O(n) time an OPVR of G whose vertex complexity is bounded by a constant in O(n) time .
Edit intent: clarity
Original: The increasing power of computer technology does not dispense with the need to extract meaningful information out of data sets of ever growing size, and indeed typically exacerbates the complexity of this task.
Revised: The increasing power of computer technology does not dispense with the need to extract meaningful in- formation out of data sets of ever growing size, and indeed typically exacerbates the complexity of this task.
Edit intent: clarity
Original:  A variety of contexts in which complex network theory and data mining have be used in a synergistic manner are then presented.
Revised:  A variety of contexts in which complex network theory and data mining have been used in a synergistic manner are then presented.
Edit intent: fluency