wanyu/IteraTeR_v2 huggingface dataset:
Original:  Recently, tractable algorithms have been proposed to solve this optimisation problemunder different cost criteria.
Revised:  While tractable algorithms do exist to solve this optimisation problemunder different cost criteria.
Edit intent: clarity
Original:  Specifically, we provide three novel schemes for online estimation of page change rates .
Revised:  We provide three novel schemes for online estimation of page change rates .
Edit intent: coherence
Original:  All these schemes only need partial information about the page change process, i.e., they only need to know if the page has changed or not since the last crawl instance.
Revised:  All these schemes only need partial information about the page change process, i.e., they only need to know if the page has changed or not since the last crawled instance.
Edit intent: fluency
Original:  Finally, we provide some numerical experiments ( on real as well as synthetic data) to compare the performance of our proposed estimators with the existing ones (e.g., MLE) .
Revised:  Finally, we provide some numerical experiments ( based on real and synthetic data) to compare the performance of our proposed estimators with the existing ones (e.g., MLE) .
Edit intent: clarity
Original:  Finally, we provide some numerical experiments ( on real as well as synthetic data) to compare the performance of our proposed estimators with the existing ones (e.g., MLE) .
Revised:  Finally, we provide some numerical experiments ( on real as well as synthetic data) to demonstrate the superiority of our proposed estimators with the existing ones (e.g., MLE) .
Edit intent: clarity
Original: We consider extended mean field control (extended MFC) problems, which seek optimal control of McKean-Vlasov dynamics whose coefficients involve mean field interactions both on the state and actions, and where objectives are optimized over open-loop strategies .
Revised: We consider the control of McKean-Vlasov dynamics whose coefficients involve mean field interactions both on the state and actions, and where objectives are optimized over open-loop strategies .
Edit intent: clarity
Original: We consider extended mean field control (extended MFC) problems, which seek optimal control of McKean-Vlasov dynamics whose coefficients involve mean field interactions both on the state and actions, and where objectives are optimized over open-loop strategies .
Revised: We consider extended mean field control (extended MFC) problems, which seek optimal control of McKean-Vlasov dynamics whose coefficients have mean field interactions both on the state and actions, and where objectives are optimized over open-loop strategies .
Edit intent: clarity
Original: We consider extended mean field control (extended MFC) problems, which seek optimal control of McKean-Vlasov dynamics whose coefficients involve mean field interactions both on the state and actions, and where objectives are optimized over open-loop strategies .
Revised: We consider extended mean field control (extended MFC) problems, which seek optimal control of McKean-Vlasov dynamics whose coefficients involve mean field interactions in the state and actions, and where objectives are optimized over open-loop strategies .
Edit intent: clarity
Original: We consider extended mean field control (extended MFC) problems, which seek optimal control of McKean-Vlasov dynamics whose coefficients involve mean field interactions both on the state and actions, and where objectives are optimized over open-loop strategies .
Revised: We consider extended mean field control (extended MFC) problems, which seek optimal control of McKean-Vlasov dynamics whose coefficients involve mean field interactions both on the state and control .
Edit intent: clarity
Original:  We show that for a large class of linear-convex extended MFC problems, the unique optimal open-loop control admits the optimal 1/2-H\"{o}lder regularity in time.
Revised:  We show that for a class of linear-convex extended MFC problems, the unique optimal open-loop control admits the optimal 1/2-H\"{o}lder regularity in time.
Edit intent: clarity
Original:  We show that for a large class of linear-convex extended MFC problems, the unique optimal open-loop control admits the optimal 1/2-H\"{o}lder regularity in time.
Revised:  We show that for a large class of linear-convex mean field control problems, the unique optimal open-loop control admits the optimal 1/2-H\"{o}lder regularity in time.
Edit intent: clarity
Original:  Based on the solution regularity , we prove that the value functions of such extended MFC problems can be approximated by those with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping  up to an order 1/2 error, which is optimal in our setting.
Revised:  Consequently , we prove that the value functions of such extended MFC problems can be approximated by those with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping up to an order 1/2 error, which is optimal in our setting.
Edit intent: coherence
Original:  Based on the solution regularity , we prove that the value functions of such extended MFC problems can be approximated by those with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping  up to an order 1/2 error, which is optimal in our setting.
Revised:  Based on the solution regularity , we prove that the value function can be approximated by those with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping up to an order 1/2 error, which is optimal in our setting.
Edit intent: clarity
Original:  Based on the solution regularity , we prove that the value functions of such extended MFC problems can be approximated by those with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping  up to an order 1/2 error, which is optimal in our setting.
Revised:  Based on the solution regularity , we prove that the value functions of such extended MFC problems can be approximated by one with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping up to an order 1/2 error, which is optimal in our setting.
Edit intent: clarity
Original:  Based on the solution regularity , we prove that the value functions of such extended MFC problems can be approximated by those with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping  up to an order 1/2 error, which is optimal in our setting.
Revised:  Based on the solution regularity , we prove that the value functions of such extended MFC problems can be approximated by those with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping , up to an order 1/2 error, which is optimal in our setting.
Edit intent: fluency
Original:  In this work, we present and analyze an online tomography algorithm that is designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy.
Revised:  In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy.
Edit intent: fluency
Original:  The protocol is the first to give  optimal performance in terms of rank and dimension for state copies, measurement settings and memory.
Revised:  The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory.
Edit intent: clarity
Original: We consider the onlineBipartite Caching problem where n users are connected to m caches in the form of a bipartite network.
Revised: We consider Bipartite Caching problem where n users are connected to m caches in the form of a bipartite network.
Edit intent: clarity
Original: We consider the onlineBipartite Caching problem where n users are connected to m caches in the form of a bipartite network.
Revised: We consider the online problem where n users are connected to m caches in the form of a bipartite network.
Edit intent: fluency
Original: We consider the onlineBipartite Caching problem where n users are connected to m caches in the form of a bipartite network.
Revised: We consider the onlineBipartite Caching problem where n users are connected to a number of caches via a bipartite network.
Edit intent: clarity
Original:  A user's request at a time slot is satisfied if the requested file is already hosted on at least one of the caches connected to the user at that time slot.
Revised:  A user's request is met if the requested file is already hosted on at least one of the caches connected to the user at that time slot.
Edit intent: clarity
Original:  A user's request at a time slot is satisfied if the requested file is already hosted on at least one of the caches connected to the user at that time slot.
Revised:  A user's request at a time slot is satisfied if the requested file is cached in at least one of the caches connected to the user at that time slot.
Edit intent: clarity
Original:  In this paper, we proposeLeadCache,  an online caching policy based on the Follow the Perturbed Leader (FTPL) paradigm.
Revised:  In this paper, we proposeLeadCache, - an online caching policy based on the Follow the Perturbed Leader (FTPL) paradigm.
Edit intent: fluency
Original:  In this paper, we proposeLeadCache,  an online caching policy based on the Follow the Perturbed Leader (FTPL) paradigm.
Revised:  In this paper, we proposeLeadCache, an online caching policy based on the (FTPL) paradigm.
Edit intent: coherence
Original:  In this paper, we proposeLeadCache,  an online caching policy based on the Follow the Perturbed Leader (FTPL) paradigm.
Revised:  In this paper, we proposeLeadCache, an online caching policy based on the Follow the Perturbed Leader Follow-the-Perturbed-Leader paradigm.
Edit intent: clarity
Original:  Moreover , we show the surprising result that under mild Strong-Law-type assumptions on the file request sequence, the rate of file fetches to the caches approaches to zero under the\textsf{LeadCache policy.
Revised:  Moreover , we show that the total number of file fetches to the caches approaches to zero under the\textsf{LeadCache policy.
Edit intent: clarity
Original:  Moreover , we show the surprising result that under mild Strong-Law-type assumptions on the file request sequence, the rate of file fetches to the caches approaches to zero under the\textsf{LeadCache policy.
Revised:  Moreover , we show the surprising result that under mild Strong-Law-type assumptions on the file request sequence, the rate of file fetches \textsf{LeadCache policy.
Edit intent: clarity
Original:  Assume that  users are connected to a number of caches via a bipartite network.
Revised:  Assume that multiple users are connected to a number of caches via a bipartite network.
Edit intent: clarity
Original:  Assume that  users are connected to a number of caches via a bipartite network.
Revised:  Assume that users are connected to several caches via a bipartite network.
Edit intent: clarity
Original:  At any time slot, each user requests some file chosen from a large catalog.
Revised:  At any time slot, each user requests an arbitrary file chosen from a large catalog.
Edit intent: clarity
Original:  The objective is to predict and optimally store the files on the caches to maximize the total number of cache hits .
Revised:  Our objective is to predict and optimally store the files on the caches to maximize the total number of cache hits .
Edit intent: fluency
Original:  The objective is to predict and optimally store the files on the caches to maximize the total number of cache hits .
Revised:  The objective is to predict , prefetch, and optimally distribute the files on the caches to maximize the total number of cache hits .
Edit intent: clarity
Original:  Our conclusion is that the proposed learning-based caching \texttt{ policy decisively outperforms the classical policies both theoretically and empirically.
Revised:  We conclude that the learning-based caching \texttt{ policy decisively outperforms the classical policies both theoretically and empirically.
Edit intent: clarity
Original:  Our conclusion is that the proposed learning-based caching \texttt{ policy decisively outperforms the classical policies both theoretically and empirically.
Revised:  Our conclusion is that the proposed learning-based \texttt{ policy decisively outperforms the classical policies both theoretically and empirically.
Edit intent: clarity
Original:  Our conclusion is that the proposed learning-based caching \texttt{ policy decisively outperforms the classical policies both theoretically and empirically.
Revised:  Our conclusion is that the proposed learning-based caching \texttt{ policy decisively outperforms the known caching policies both theoretically and empirically.
Edit intent: clarity
Original:  At any time slot, each user requests an arbitrary file chosen from a large catalog.
Revised:  At any time slot, each user may request an arbitrary file chosen from a large catalog.
Edit intent: clarity
Original:  Our objective is to predict, prefetch, and optimally distribute the files on the caches  to maximize the total number of cache hits in an online setting .
Revised:  Our objective is to predict, prefetch, and optimally distribute the files on the caches to maximize the total number of cache hits .
Edit intent: clarity
Original:  In this paper, we propose LeadCache - an  online caching policy based on the Follow-the-Perturbed-Leader paradigm.
Revised:  In this paper, we propose LeadCache - an efficient online caching policy based on the Follow-the-Perturbed-Leader paradigm.
Edit intent: clarity
Original:  With a Strong-Law-type assumption, we show that the total number of file fetches under LeadCache remains almost surely finite over an infinite horizon.
Revised:  Furthermore, with a Strong-Law-type assumption, we show that the total number of file fetches under LeadCache remains almost surely finite over an infinite horizon.
Edit intent: coherence
Original:  Finally, we derive a tight regret lower bound using results from graph coloring.
Revised:  Finally, we derive an approximately tight regret lower bound using results from graph coloring.
Edit intent: clarity
Original: In an increasing connected world, resilience is an important ability for a system to retain its original function when perturbations happen.
Revised: Resilience characterizes a system's ability to retain its original function when perturbations happen.
Edit intent: clarity
Original:  Even though we understand small-scale resilience well, our understanding of  large-scale networked resilience is limited.
Revised:  Even though we understand small-scale resilience , yet our understanding of large-scale networked resilience is limited.
Edit intent: coherence
Original:  Even though we understand small-scale resilience well, our understanding of  large-scale networked resilience is limited.
Revised:  Even though we understand small-scale resilience well, our understanding of resilience in large-scale networked resilience is limited.
Edit intent: clarity
Original:  Recent research in network-level resilience and node-level resilience pattern has advanced our understanding of the relationship between topology and dynamics across network scales.
Revised:  Recent research in network-level resilience and node-level resilience pattern has developed analytical tools to analyze the relationship between topology and dynamics across network scales.
Edit intent: clarity
Original:  However, the effect of uncertainty in a large-scale networked system is not clear, especially when uncertainties cascade between connected nodes.
Revised:  The effect of uncertainty in a large-scale networked system is not clear, especially when uncertainties cascade between connected nodes.
Edit intent: coherence
Original:  In order to quantify resilience uncertainty across the network resolutions (macro to micro), we develop an arbitrary polynomial chaos (aPC) expansion method  to estimate the resilience subject to parameter uncertainties with arbitrary distributions.
Revised:  In order to quantify resilience uncertainty across the network resolutions (macro to micro), an arbitrary polynomial chaos (aPC) expansion method to estimate the resilience subject to parameter uncertainties with arbitrary distributions.
Edit intent: clarity
Original:  For the first time, by leveraging methods from optimal control theory, we are able to backpropagate errors through spike discontinuities and avoid approximations or smoothing operations.
Revised:  For the first time, by leveraging methods from optimal control theory, we are able to backpropagate errors through spike discontinuities without approximations or smoothing operations.
Edit intent: clarity
Original:  Our work supports the rigorous study of gradient-based methods to train spiking neural networks while providing insights toward the development of learning algorithms in neuromorphic hardware.
Revised:  Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks while providing insights toward the development of learning algorithms in neuromorphic hardware.
Edit intent: clarity
Original:  Our work supports the rigorous study of gradient-based methods to train spiking neural networks while providing insights toward the development of learning algorithms in neuromorphic hardware.
Revised:  Our work supports the rigorous study of gradient-based methods to train spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.
Edit intent: clarity
Original: We provide new algorithms for maintaining approximate distances in a weighted undirected graph G=(V,E ) subject to edge deletions.
Revised: Given a weighted undirected graph G=(V,E ) subject to edge deletions.
Edit intent: clarity
Original:  This }  matches the best known static algorithm , up to polylogarithmic factors for a wide range of settings.
Revised:  This } that matches the best known static algorithm , up to polylogarithmic factors for a wide range of settings.
Edit intent: fluency
Original:  This }  matches the best known static algorithm , up to polylogarithmic factors for a wide range of settings.
Revised:  This } matches the best known static algorithm up to polylogarithmic factors for a wide range of settings.
Edit intent: fluency
Original:  The currently best known algorithm for the problem is obtained by running the single-source algorithm of Henzinger, Krinninger and Nanongkai, FOCS'14%DIFDELCMD < ] %DIFDELCMD < %%% independently from each source.
Revised:  The currently best known algorithm for the problem is obtained by running the single-source algorithm of %DIFDELCMD < ] %DIFDELCMD < %%% independently from each source.
Edit intent: coherence
Original:  Our decremental hopset algorithm allows us to obtain the following improved decremental algorithms for maintaining shortest paths. -} (1+\epsilon)-approximate single-source shortest paths with amortized update time of 2^{O(\log n)} , when 0< \epsilon<1 is a constant and |E|= n2^{\Omega(\sqrt{\log n . This improves  over the best known  update time of 2^{\tilde{O}(\log^{3/4} n)} by [ Henzinger, Krinninger and Nanongkai, FOCS'14].
Revised:  Our decremental hopset algorithm allows us to obtain the following improved decremental algorithms for maintaining shortest paths. -} (1+\epsilon)-approximate single source shortest paths in amortized update time of 2^{O(\log n)} , when 0< \epsilon<1 is a constant and |E|= n2^{\Omega(\sqrt{\log n . This improves over the best known update time of 2^{\tilde{O}(\log^{3/4} n)} by [ Henzinger, Krinninger and Nanongkai, FOCS'14].
Edit intent: clarity
Original:  Our decremental hopset algorithm allows us to obtain the following improved decremental algorithms for maintaining shortest paths. -} (1+\epsilon)-approximate single-source shortest paths with amortized update time of 2^{O(\log n)} , when 0< \epsilon<1 is a constant and |E|= n2^{\Omega(\sqrt{\log n . This improves  over the best known  update time of 2^{\tilde{O}(\log^{3/4} n)} by [ Henzinger, Krinninger and Nanongkai, FOCS'14].
Revised:  Our decremental hopset algorithm allows us to obtain the following improved decremental algorithms for maintaining shortest paths. -} (1+\epsilon)-approximate single-source shortest paths with amortized update time of 2^{O(\log n)} , when 0< \epsilon<1 is a constant and |E|= n2^{\Omega(\sqrt{\log n . This improves over the best known amortized update time of 2^{\tilde{O}(\log^{3/4} n)} by [ Henzinger, Krinninger and Nanongkai, FOCS'14].
Edit intent: fluency
Original:  Furthermore, for any integer k \geq 1 we give an algorithmfor maintaining\tilde{O}, and |E|= n^{1+\Omega(1)}.
Revised:  -( 1 we give an algorithmfor maintaining\tilde{O}, and |E|= n^{1+\Omega(1)}.
Edit intent: coherence
Original:  This improves over the best-known amortized update time of (n^{1/k)\cdot(1/\epsilon)^{O(\sqrt{\log n})} }  [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.
Revised:  This (n^{1/k)\cdot(1/\epsilon)^{O(\sqrt{\log n})} } [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.
Edit intent: clarity
Original:  This improves over the best-known amortized update time of (n^{1/k)\cdot(1/\epsilon)^{O(\sqrt{\log n})} }  [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.
Revised:  This improves over the best-known amortized update time of )\cdot(1/\epsilon)^{O(\sqrt{\log n})} } [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.
Edit intent: clarity
Original:  This improves over the best-known amortized update time of (n^{1/k)\cdot(1/\epsilon)^{O(\sqrt{\log n})} }  [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.
Revised:  This improves over the best-known amortized update time of (n^{1/k)\cdot(1/\epsilon)^{O(\sqrt{\log n})} } [Chechik, FOCS'18] that has a query time of O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.
Edit intent: coherence
Original:  MIDAS-F introduces two modifications: 1) We modify the anomaly scoring function, aiming to reduce the ' poisoning' effect of newly arriving edges;
Revised:  MIDAS-F introduces two modifications: 1) We modify the anomaly scoring function, aiming to reduce the ` poisoning' effect of newly arriving edges;
Edit intent: fluency
Original:  (c) it provides 41\% to 55\% higher accuracy (in terms of ROC-AUC ) than state-of-the-art approaches.
Revised:  (c) it provides 41\% to 55\% higher accuracy (in terms of ROC-AUC than state-of-the-art approaches.
Edit intent: fluency
Original: Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields (e. g. perceptual and categorical judgement, expert risk assessment, attitudinal measurement, consumer and public opinion research).
Revised: Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields .
Edit intent: coherence