wanyu/IteraTeR_v2 huggingface dataset:
Original:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 }  , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Revised:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 } , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Edit intent: coherence
Original:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 }  , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Revised:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 } , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Edit intent: fluency
Original:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 }  , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Revised:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 } , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over\Omega { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Edit intent: fluency
Original:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 }  , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Revised:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 } , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over {2p-1 } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Edit intent: fluency
Original:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 }  , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Revised:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 } , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Edit intent: clarity
Original:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 }  , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Revised:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 } , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order SRF ^{ -2p+1 }\epsilon.
Edit intent: coherence
Original:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 }  , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ -2p+1 }\epsilon.
Revised:  Provided that \epsilon \lessapprox %DIFDELCMD < \left(\Omegah\right)%%% , where SRF=(\Omega\Delta)} ^{ 2p-1 } , we show that the minimax error rate for reconstruction of the cluster nodes is of order (%DIFDELCMD < \Omegah%%% )\SUPERSCRIPT -2p+ 1 \over { } h \epsilon, while for recovering the corresponding amplitudes \{a_j\} the rate is of the order (\Omega h) ^{ 2p-1 }\epsilon.
Edit intent: fluency
Original:  Our numerical experiments show that the well-known Matrix Pencil method achieves the above accuracy bounds.
Edit intent: coherence
Original:  This is the best asymptotic approximation known for this class of diversity maximization and the evidence suggests that it may be tight.
Revised:  This is the best asymptotic approximation known for this class of quadratics and the evidence suggests that it may be tight.
Edit intent: clarity
Original:  Such set functions are called \gamma-meta-submodular .
Revised:  Such set functions are called \gamma-meta-submodular .
Edit intent: fluency
Original: Given a mixture between two populations of coins, "positive" coins that have (unknown and potentially different) probabilities of heads \geq1{2}+\Delta and negative coins with probabilities \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of coins of each type to within additive error \epsilon.
Revised: Given a mixture between two populations of coins, "positive" coins that each have---unknown and potentially different---bias \geq1{2}+\Delta and negative coins with probabilities \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of coins of each type to within additive error \epsilon.
Edit intent: clarity
Original: Given a mixture between two populations of coins, "positive" coins that have (unknown and potentially different) probabilities of heads \geq1{2}+\Delta and negative coins with probabilities \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of coins of each type to within additive error \epsilon.
Revised: Given a mixture between two populations of coins, "positive" coins that have (unknown and potentially different) probabilities of heads \geq1{2}+\Delta and "negative" coins with bias \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of coins of each type to within additive error \epsilon.
Edit intent: clarity
Original: Given a mixture between two populations of coins, "positive" coins that have (unknown and potentially different) probabilities of heads \geq1{2}+\Delta and negative coins with probabilities \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of coins of each type to within additive error \epsilon.
Revised: Given a mixture between two populations of coins, "positive" coins that have (unknown and potentially different) probabilities of heads \geq1{2}+\Delta and negative coins with probabilities \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of positive coins to within additive error \epsilon.
Edit intent: clarity
Original:  We introduce new techniques to show a fully-adaptive lower bound of \Omega (\rho{\epsilon^2\Delta^2}) samples ( for constant probability of success ).
Revised:  We achieve a tight upper and lower bound of \Omega (\rho{\epsilon^2\Delta^2}) samples ( for constant probability of success ).
Edit intent: clarity
Original:  We introduce new techniques to show a fully-adaptive lower bound of \Omega (\rho{\epsilon^2\Delta^2}) samples ( for constant probability of success ).
Revised:  We introduce new techniques to show a fully-adaptive lower bound of \Omega (\rho{\epsilon^2\Delta^2}) samples for constant probability of success ).
Edit intent: fluency
Original:  We achieve almost-matching algorithmic performance of O(\frac{\rho{\epsilon^2\Delta^2}(1+\rho\log1{\epsilon}) ) samples, which matches the lower bound except in the }  regime where \rho= \omega (1{\log 1/\epsilon}).
Revised:  We achieve almost-matching algorithmic performance of O(\frac{\rho{\epsilon^2\Delta^2}(1+\rho\log1{\epsilon}) ) samples, which matches the lower bound except in the } regime where \rho= O (1{\log 1/\epsilon}).
Edit intent: clarity
Original: Given a mixture between two populations of coins, "positive" coins that each have---unknown and potentially different---bias \geq1{2}+\Delta and "negative" coins with bias \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of positive coins to within additive error \epsilon.
Revised: Given a mixture between two populations of coins, "positive" coins that each have -- unknown and potentially different -- bias \geq1{2}+\Delta and "negative" coins with bias \leq1{2}-\Delta, we consider the task of estimating the fraction \rho of positive coins to within additive error \epsilon.
Edit intent: fluency
Original:  We achieve a tight upper and lower bound of \Theta(\rho{\epsilon^2\Delta^2} {\delta}} ) samples for constant probability of success .
Revised:  We achieve an upper and lower bound of \Theta(\rho{\epsilon^2\Delta^2} {\delta}} ) samples for constant probability of success .
Edit intent: clarity
Original:  We present simulation results to demonstrate the practical efficacy of our approach for realistic problem parameters for crowdsourcing applications, focusing on the "rare events" regime where \rho =O(\frac{1{\log 1/\epsilon})}  . The fine-grained adaptive flavor of both our algorithm and lower bound contrasts with much previous work in distributional testing and learning.
Revised:  We present simulation results to demonstrate the practical efficacy of our approach for realistic problem parameters for crowdsourcing applications, focusing on the "rare events" regime where \rho {\log 1/\epsilon})} . The fine-grained adaptive flavor of both our algorithm and lower bound contrasts with much previous work in distributional testing and learning.
Edit intent: clarity
Original:  Episodes also enforce in which order  events are allowed to occur.
Revised:  Episodes also enforce in which order the events are allowed to occur.
Edit intent: fluency
Original:  We show that this closure satisfies the needed Galois connection so that we can use the existing framework for mining closed patterns.
Revised:  We show that this closure satisfies the needed properties so that we can use the existing framework for mining closed patterns.
Edit intent: clarity
Original:  In the area of measurement technology, instruments based on the Photonic Time Stretch have established record real-time measurement throughput in spectroscopy, optical coherence tomography, and imaging flow cytometry.
Revised:  In the area of measurement technology, instruments based on the photonic time stretch have established record real-time measurement throughput in spectroscopy, optical coherence tomography, and imaging flow cytometry.
Edit intent: fluency
Original:  Owing to the abundance of data they generate, time stretch instruments are a natural fit to deep learning classification.
Revised:  Owing to the abundance of data they generate, time-stretch instruments are a natural fit to deep learning classification.
Edit intent: fluency
Original:  Here we describe a new implementation of deep learning which entirely avoids the computationally costly image processing and feature extraction pipeline .
Revised:  Here we describe a new deep learning pipeline, which entirely avoids the computationally costly image processing and feature extraction pipeline .
Edit intent: clarity
Original:  Here we describe a new implementation of deep learning which entirely avoids the computationally costly image processing and feature extraction pipeline .
Revised:  Here we describe a new implementation of deep learning which entirely avoids the slow and computationally costly signal processing and feature extraction pipeline .
Edit intent: clarity
Original:  The improvement in computational efficiency makes this new technology suitable for cell sorting via deep learning.
Revised:  The improvement in computational efficiency enables low-latency inference and makes this pipeline suitable for cell sorting via deep learning.
Edit intent: clarity
Original:  Our neural network takes less than a millisecond to classify the cells, fast enough to provide a decision to a cell sorter  .
Revised:  Our neural network takes less than a few milliseconds to classify the cells, fast enough to provide a decision to a cell sorter .
Edit intent: clarity
Original: Many people rely on online social networks as sources for news and information, and the spread of media content with ideologies across the political spectrum both influences online discussions and impacts actions offline.
Revised: Many people rely on online social networks as sources of news and information, and the spread of media content with ideologies across the political spectrum both influences online discussions and impacts actions offline.
Edit intent: fluency
Original: Many people rely on online social networks as sources for news and information, and the spread of media content with ideologies across the political spectrum both influences online discussions and impacts actions offline.
Revised: Many people rely on online social networks as sources for news and information, and the spread of media content with ideologies across the political spectrum influences online discussions and impacts actions offline.
Edit intent: clarity
Original:  To examine such phenomena , we generalize bounded-confidence models of opinion dynamics on a social network by incorporating media accounts as influencers  .
Revised:  To examine the impact of media in online social networks , we generalize bounded-confidence models of opinion dynamics on a social network by incorporating media accounts as influencers .
Edit intent: clarity
Original:  To examine such phenomena , we generalize bounded-confidence models of opinion dynamics on a social network by incorporating media accounts as influencers  .
Revised:  To examine such phenomena , we generalize bounded-confidence models of opinion dynamics by incorporating media accounts as influencers .
Edit intent: clarity
Original:  To examine such phenomena , we generalize bounded-confidence models of opinion dynamics on a social network by incorporating media accounts as influencers  .
Revised:  To examine such phenomena , we generalize bounded-confidence models of opinion dynamics on a social network by incorporating media accounts as influencers in a network .
Edit intent: clarity
Original:  We quantify partisanship of content as a continuous parameter on an interval, and we present higher-dimensional generalizations to incorporate content quality and increasingly nuanced political positions.
Revised:  We quantify partisanship of content with a continuous parameter on an interval, and we present higher-dimensional generalizations to incorporate content quality and increasingly nuanced political positions.
Edit intent: clarity
Original:  We quantify partisanship of content as a continuous parameter on an interval, and we present higher-dimensional generalizations to incorporate content quality and increasingly nuanced political positions.
Revised:  We quantify partisanship of content as a continuous parameter on an interval, and we formulate higher-dimensional generalizations to incorporate content quality and increasingly nuanced political positions.
Edit intent: clarity
Original:  We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of  non-media account content to the ideologies of media accounts in networks .
Revised:  We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of content from non-media account content to the ideologies of media accounts in networks .
Edit intent: clarity
Original:  We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of  non-media account content to the ideologies of media accounts in networks .
Revised:  We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of non-media accounts to the ideologies of media accounts in networks .
Edit intent: clarity
Original:  We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of  non-media account content to the ideologies of media accounts in networks .
Revised:  We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of non-media account content to the ideologies of media accounts in a network .
Edit intent: clarity
Original:  We maximize media impact over a social network by tuning the number of media accounts that promote the content and the number of followers of the accounts.
Revised:  We maximize media impact in a social network by tuning the number of media accounts that promote the content and the number of followers of the accounts.
Edit intent: clarity
Original:  From our numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of networks, such as size, mean number of followers  , and the receptiveness of  nodes to different opinions.
Revised:  Using numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of networks, such as size, mean number of followers , and the receptiveness of nodes to different opinions.
Edit intent: fluency
Original:  From our numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of networks, such as size, mean number of followers  , and the receptiveness of  nodes to different opinions.
Revised:  From our numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on a network's structural features, including its size, the mean number of followers , and the receptiveness of nodes to different opinions.
Edit intent: clarity
Original:  From our numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of networks, such as size, mean number of followers  , and the receptiveness of  nodes to different opinions.
Revised:  From our numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of networks, such as size, mean number of followers of its nodes , and the receptiveness of nodes to different opinions.
Edit intent: clarity
Original:  From our numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of networks, such as size, mean number of followers  , and the receptiveness of  nodes to different opinions.
Revised:  From our numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on structural features of networks, such as size, mean number of followers , and the receptiveness of its nodes to different opinions.
Edit intent: clarity
Original: Swarm robotics systems are envisioned to become an important component of both academic research and real-world applications.
Revised: Swarm robotics systems are becoming an important component of both academic research and real-world applications.
Edit intent: clarity
Original:  This work proposes a novel model to encapsulate cooperative robotic missions in Merkle trees , one of the fundamental components of blockchain technology .
Revised:  This work proposes a novel model to encapsulate cooperative robotic missions in Merkle trees .
Edit intent: clarity
Original:  With the proposed model, swarm operators can provide the "blueprint" of the swarm's mission without disclosing raw data about the mission itself .
Revised:  With the proposed model, swarm operators can provide the "blueprint" of the swarm's mission without disclosing its raw data .
Edit intent: clarity
Original:  We propose a system where swarm robots have to "prove" their integrity to their peers by exchanging cryptographic proofs.
Revised:  We propose a system where robots in the swarm have to "prove" their integrity to their peers by exchanging cryptographic proofs.
Edit intent: clarity
Original: Swarm robotics systems are becoming an important component of both academic research and real-world applications  .
Revised: The importance of swarm robotics systems in both academic research and real-world applications .
Edit intent: clarity
Original:  However, in order to reach widespread adoption, new models that ensure the secure cooperation of these systems need to be developed.
Revised:  However, to reach widespread adoption, new models that ensure the secure cooperation of these systems need to be developed.
Edit intent: coherence
Original:  However, in order to reach widespread adoption, new models that ensure the secure cooperation of these systems need to be developed.
Revised:  However, in order to reach widespread adoption, new models that ensure the secure cooperation of large groups of robots need to be developed.
Edit intent: clarity
Original:  This work proposes a novel model to encapsulate cooperative robotic missions in Merkle trees.
Revised:  This work introduces a novel method to encapsulate cooperative robotic missions in Merkle trees.
Edit intent: clarity
Original:  This work analyzes and tests the proposed approach for two different robotic missions: foraging (where robots modify the environment) and maze formation (where robots become part of the environment) .
Revised:  We show the implications of this approach for two different robotic missions: foraging (where robots modify the environment) and maze formation (where robots become part of the environment) .
Edit intent: clarity
Original:  This work analyzes and tests the proposed approach for two different robotic missions: foraging (where robots modify the environment) and maze formation (where robots become part of the environment) .
Revised:  This work analyzes and tests the proposed approach for two different robotic missions: foraging and maze formation (where robots become part of the environment) .
Edit intent: clarity
Original:  This work analyzes and tests the proposed approach for two different robotic missions: foraging (where robots modify the environment) and maze formation (where robots become part of the environment) .
Revised:  This work analyzes and tests the proposed approach for two different robotic missions: foraging (where robots modify the environment) and maze formation .
Edit intent: clarity