wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1]  random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Revised:  We introduce a " Markov chains of Markov chains '' model called multiplex Markov chains (MMCs) such that with probably (1-\omega) \in[0,1] random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Edit intent: meaning-changed
Original:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1]  random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Revised:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Edit intent: meaning-changed
Original:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1]  random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Revised:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1] 0,1 random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Edit intent: meaning-changed
Original:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1]  random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Revised:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1] random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Edit intent: fluency
Original:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1]  random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains .
Revised:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1] random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) .
Edit intent: clarity
Original:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1]  random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains . By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Revised:  We introduce a " Markov chains of Markov chains " model such that with probably (1-\omega) \in[0,1] random walkers remain in the same layer and follow (layer-specific) intralayer Markov chains , whereas with probability \omega they move to different layers following (node-specific) interlayer Markov chains multiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Edit intent: clarity
Original:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Revised:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena including (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Edit intent: clarity
Original:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Revised:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance multiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Edit intent: clarity
Original:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Revised:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) and ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Edit intent: clarity
Original:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Revised:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection interlayer Markov chains. One main finding is the identification of multiplex convection, whereby a stationary distribution exhibits circulating flows that involve multiple layers ).
Edit intent: meaning-changed
Original:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers ). These phenomena (as well as the convergence rate \lambda_2) are found to exhibit optima for intermediate \omega, and we explore their relation to imbalances for the intralayer degrees of nodes .
Revised:  By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena includingmultiplex imbalance (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) andmultiplex convection ( whereby a stationary distribution exhibits circulating flows that involve multiple layers . Convection cycles are well understood in fluids, but are insufficiently explored on networks. Our experiments reveal that one mechanism for convection is the existence of imbalances for the intralayer degrees of nodes .
Edit intent: coherence
Original:  These phenomena (as well as the convergence rate \lambda_2) are found to exhibit optima for intermediate \omega, and we explore their relation to imbalances for the intralayer degrees of nodes .
Revised:  These phenomena (as well as the convergence rate \lambda_2) are found to exhibit optima for intermediate \omega, and we explore their relation to imbalances for the (intralayer) degrees of nodes .
Edit intent: fluency
Original:  These phenomena (as well as the convergence rate \lambda_2) are found to exhibit optima for intermediate \omega, and we explore their relation to imbalances for the intralayer degrees of nodes . To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega%DIFDELCMD < \to0 %%% and \omega%DIFDELCMD < \to1%%% ) .
Revised:  These phenomena (as well as the convergence rate \lambda_2) are found to exhibit optima for intermediate \omega, and we explore their relation to imbalances for the intralayer degrees of nodes in different layers. To gain further insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega%DIFDELCMD < \to0 %%% and \omega%DIFDELCMD < \to1%%% ) .
Edit intent: clarity
Original:  To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega%DIFDELCMD < \to0 %%% and \omega%DIFDELCMD < \to1%%% ) .
Revised:  To provide analytical insight, we %DIFDELCMD < \to0 %%% and \omega%DIFDELCMD < \to1%%% ) .
Edit intent: clarity
Original:  To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega%DIFDELCMD < \to0 %%% and \omega%DIFDELCMD < \to1%%% ) .
Revised:  To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega%DIFDELCMD < \to0 %%% %DIFDELCMD < \to1%%% ) .
Edit intent: meaning-changed
Original:  To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega%DIFDELCMD < \to0 %%% and \omega%DIFDELCMD < \to1%%% ) .
Revised:  To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega%DIFDELCMD < \to0 %%% and \omega%DIFDELCMD < \to1%%% employ spectral perturbation theory to characterize the stationary distribution for the limits of small and large \omega, and we show that MMCs inherently exhibit optimality for intermediate \omega in terms of their convergence rate and the extent of convection. As an application, we conduct an MMC-based analysis of brain-activity data, finding MMCs to differ between healthy persons and those with Alzheimer's disease. Overall, our work suggests MMCs and convection as two important new directions for network-related research .
Edit intent: meaning-changed
Original:  Manual segmentation of the cortical plate, or manual refinement of automatic segmentations is tedious and time consuming, and automatic segmentation of the cortical plate  is challenged by the relatively low resolution of the reconstructed fetal brain MRI scans compared to the thin structure of the cortical plate, partial voluming, and the wide range of variations in the morphology of the cortical plate as the brain matures during gestation.
Revised:  Manual segmentation of the cortical plate, or manual refinement of automatic segmentations is tedious and time-consuming. Automatic segmentation of the cortical plate is challenged by the relatively low resolution of the reconstructed fetal brain MRI scans compared to the thin structure of the cortical plate, partial voluming, and the wide range of variations in the morphology of the cortical plate as the brain matures during gestation.
Edit intent: coherence
Original:  Manual segmentation of the cortical plate, or manual refinement of automatic segmentations is tedious and time consuming, and automatic segmentation of the cortical plate  is challenged by the relatively low resolution of the reconstructed fetal brain MRI scans compared to the thin structure of the cortical plate, partial voluming, and the wide range of variations in the morphology of the cortical plate as the brain matures during gestation.
Revised:  Manual segmentation of the cortical plate, or manual refinement of automatic segmentations is tedious and time consuming, and automatic segmentation of the cortical plate , on the other hand, is challenged by the relatively low resolution of the reconstructed fetal brain MRI scans compared to the thin structure of the cortical plate, partial voluming, and the wide range of variations in the morphology of the cortical plate as the brain matures during gestation.
Edit intent: coherence
Original:  To reduce the burden of manual refinement of segmentations, we have developed a new and powerful deep learning segmentation method that exploits new deep attentive modules with mixed kernel convolutions within a fully convolutional neural network architecture that utilizes deep supervision and residual connections.
Revised:  To reduce the burden of manual refinement of segmentations, we have developed a new and powerful deep learning segmentation method . Our method exploits new deep attentive modules with mixed kernel convolutions within a fully convolutional neural network architecture that utilizes deep supervision and residual connections.
Edit intent: clarity
Original:  Quantitative evaluation based on several performance measures and expert evaluations  show that our method outperformed several state-of-the-art deep models for segmentation, as well as a state-of-the-art multi-atlas segmentation technique.
Revised:  We evaluated our method quantitatively based on several performance measures and expert evaluations show that our method outperformed several state-of-the-art deep models for segmentation, as well as a state-of-the-art multi-atlas segmentation technique.
Edit intent: clarity
Original:  Quantitative evaluation based on several performance measures and expert evaluations  show that our method outperformed several state-of-the-art deep models for segmentation, as well as a state-of-the-art multi-atlas segmentation technique.
Revised:  Quantitative evaluation based on several performance measures and expert evaluations . Results show that our method outperformed several state-of-the-art deep models for segmentation, as well as a state-of-the-art multi-atlas segmentation technique.
Edit intent: clarity
Original:  Quantitative evaluation based on several performance measures and expert evaluations  show that our method outperformed several state-of-the-art deep models for segmentation, as well as a state-of-the-art multi-atlas segmentation technique.
Revised:  Quantitative evaluation based on several performance measures and expert evaluations show that our method outperforms several state-of-the-art deep models for segmentation, as well as a state-of-the-art multi-atlas segmentation technique.
Edit intent: fluency
Original:  In particular, we achieved average Dice similarity coefficient of 0.87, average Hausdroff distance of 0.96 mm, and average symmetric surface difference of 0.28 mm in cortical plate segmentation on reconstructed fetal brain MRI scans of fetuses scanned in the gestational age range of 16 to 39 weeks.
Revised:  We achieved average Dice similarity coefficient of 0.87, average Hausdroff distance of 0.96 mm, and average symmetric surface difference of 0.28 mm in cortical plate segmentation on reconstructed fetal brain MRI scans of fetuses scanned in the gestational age range of 16 to 39 weeks.
Edit intent: coherence
Original:  In particular, we achieved average Dice similarity coefficient of 0.87, average Hausdroff distance of 0.96 mm, and average symmetric surface difference of 0.28 mm in cortical plate segmentation on reconstructed fetal brain MRI scans of fetuses scanned in the gestational age range of 16 to 39 weeks.
Revised:  In particular, we achieved average Dice similarity coefficient of 0.87, average Hausdorff distance of 0.96 mm, and average symmetric surface difference of 0.28 mm in cortical plate segmentation on reconstructed fetal brain MRI scans of fetuses scanned in the gestational age range of 16 to 39 weeks.
Edit intent: fluency
Original:  In particular, we achieved average Dice similarity coefficient of 0.87, average Hausdroff distance of 0.96 mm, and average symmetric surface difference of 0.28 mm in cortical plate segmentation on reconstructed fetal brain MRI scans of fetuses scanned in the gestational age range of 16 to 39 weeks.
Revised:  In particular, we achieved average Dice similarity coefficient of 0.87, average Hausdroff distance of 0.96 mm, and average symmetric surface difference of 0.28 mm on reconstructed fetal brain MRI scans of fetuses scanned in the gestational age range of 16 to 39 weeks.
Edit intent: clarity
Original: Polkadot is a decentralized blockchain platform to be launched in 2020. It will implement nominated proof-of-stake (NPoS), a proof-of-stake based mechanism where k nodes are selected by the network as validators to participate in the consensus protocol, according to the preferences expressed by token holders who take the role of nominators. This setup leads to an approval-based multi-winner election problem, where each nominator submits a list of trusted candidates, and has a vote strength proportional to their stake.
Revised: The property of proportional representation in approval-based multi-winner election problem, where each nominator submits a list of trusted candidates, and has a vote strength proportional to their stake.
Edit intent: clarity
Original:  This setup leads to an approval-based multi-winner election problem, where each nominator submits a list of trusted candidates, and has a vote strength proportional to their stake. A solution consists of a committee of k validators, together with a fractional distribution of each nominator's vote among them. We consider two objectives, both recently studied in the literature of social choice. The first one is ensuring the property of proportional justified representation (PJR).
Revised:  This setup leads to an approval-based committee elections has appeared in the social choice literature for over a century, and is typically understood as avoiding the underrepresentation of minorities. However, we argue that the security of some distributed systems is directly linked to the opposite goal of avoiding the overrepresentation of any minority, a goal which leads us to an optimization objective known as Maximin Support, closely related to the axiom of Proportional Justified Representation (PJR).
Edit intent: coherence
Original:  The second objective, called maximin support, is to maximize the minimum amount of vote support assigned to any elected validator. We argue that the former objective aligns with the notion of decentralization, while the latter aligns with the security level of the consensus protocol. We prove that the maximin support problem is constant-factor approximable, as we present several approximation algorithms for it, and prove a matching hardness result.
Revised:  We provide an inapproximability result for this objective, and propose a new election rule inspired in Phragmen's methods that achieves a) a constant-factor approximable, as we present several approximation algorithms for it, and prove a matching hardness result.
Edit intent: meaning-changed
Original:  We prove that the maximin support problem is constant-factor approximable, as we present several approximation algorithms for it, and prove a matching hardness result. Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Revised:  We prove that the maximin support problem is constant-factor approximation guarantee for the objective, and b) the PJR property. Furthermore, a structural property allows one to quickly verify that the winning committee satisfies the two aforementioned properties, even if the algorithm is executed by an untrusted party who only communicates the output. Finally, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Edit intent: meaning-changed
Original:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Revised:  Furthermore, we present an efficient post-computation that , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Edit intent: fluency
Original:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Revised:  Furthermore, we present an efficient post-computation which , when paired with any approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Edit intent: clarity
Original:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Revised:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for Maximin Support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Edit intent: fluency
Original:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Revised:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies PJR , and c) can be efficiently verified to satisfy PJR by an untrusting third party.
Edit intent: clarity