wanyu/IteraTeR_v2 huggingface dataset:
Original:  We then present an efficient estimator with theoretical guarantee via studying the variational forms of  f-divergence function.
Revised:  We then present an efficient estimator with theoretical guarantees via studying the variational forms of f-divergence function.
Edit intent: fluency
Original:  We then present an efficient estimator with theoretical guarantee via studying the variational forms of  f-divergence function.
Revised:  We then present an efficient estimator with theoretical guarantee via studying the variational forms of the f-divergence function.
Edit intent: fluency
Original:  Our work complements the literature of information elicitation via introducing\emph{sample elicitation .
Revised:  \emph{sample elicitation .
Edit intent: clarity
Original:  Our work complements the literature of information elicitation via introducing\emph{sample elicitation .
Revised:  Our work complements the literature of information elicitation via introducing\emph{ .
Edit intent: clarity
Original:  Our work complements the literature of information elicitation via introducing\emph{sample elicitation .
Revised:  Our work complements the literature of information elicitation via introducing\emph{sample elicitation 
Edit intent: fluency
Original: Connections of the conjugate gradient (CG) method with other methods in computational mathematics are surveyed, including the connections with the conjugate direction method, the subspace optimization method and the quai-Newton method BFGS in numrical optimization, and the Lanczos method in numerical linear algebra.
Revised: Connections of the conjugate gradient (CG) method with other methods in computational mathematics are surveyed, including the connections with the conjugate direction method, the subspace optimization method and the quasi-Newton method BFGS in numrical optimization, and the Lanczos method in numerical linear algebra.
Edit intent: fluency
Original: Motivation: Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in biology .
Revised:  Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in biology .
Edit intent: coherence
Original: Motivation: Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in biology .
Revised: Motivation: Discovering functional modules in protein-protein interaction networks through optimization remains a longstanding challenge in biology .
Edit intent: clarity
Original: Motivation: Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in biology .
Revised: Motivation: Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in Biology .
Edit intent: fluency
Original:  Traditional algorithms simply consider strong protein complexes that can be found in the original network by optimizing some metrics, which causes obstacles for the discovery of weak and hidden complexes shielded by stronger complexes.
Revised:  Traditional algorithms simply consider strong protein complexes that can be found in the original network by optimizing some metric, which may cause obstacles for the discovery of weak and hidden complexes shielded by stronger complexes.
Edit intent: clarity
Original:  Also , protein complexes are not only in different density but also in a large range of scale, making it extremely difficult to be detected.
Revised:  Also , protein complexes not only have different densities but also a various range of scales, making them extremely difficult to be detected.
Edit intent: clarity
Original:  It is the first community detection algorithm that can find a hierarchical structure as well as hidden structure .
Revised:  It is the first combination of hierarchical structure with hidden structure, which provides a new perspective for finding protein complexes of various strengths and scales .
Edit intent: coherence
Original:  Experimental results show that the HirHide methods using traditional methods as the base algorithms achieve better performance , sometimes even significantly outperform the baselines.
Revised:  Experimental results show that the HirHide versions achieve better performance , sometimes even significantly outperform the baselines.
Edit intent: clarity
Original:  Experimental results show that the HirHide methods using traditional methods as the base algorithms achieve better performance , sometimes even significantly outperform the baselines.
Revised:  Experimental results show that the HirHide methods using traditional methods as the base algorithms achieve better performance and sometimes even significantly outperform the baselines.
Edit intent: coherence
Original:  Discovering functional modules in protein-protein interaction networks through optimization remains a longstanding challenge in Biology .
Revised:  Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in Biology .
Edit intent: clarity
Original:  Discovering functional modules in protein-protein interaction networks through optimization remains a longstanding challenge in Biology .
Revised:  Discovering functional modules in protein-protein interaction networks through optimization remains a longstanding challenge in biology .
Edit intent: fluency
Original:  Additionally , protein complexes not only have different densities but also a various range of scales, making them extremely difficult to be detected.
Revised:  Additionally , protein complexes are not only in different density but also in a large range of scale, making it extremely difficult to be detected.
Edit intent: clarity
Original:  We address these issues and propose a hierarchical hidden community detection approach to accurately predict protein complexes of various strengths and scales.
Revised:  Toward this objective, we propose a hierarchical hidden community detection approach to accurately predict protein complexes of various strengths and scales.
Edit intent: clarity
Original:  We address these issues and propose a hierarchical hidden community detection approach to accurately predict protein complexes of various strengths and scales.
Revised:  We address these issues and propose a hierarchical hidden community approach to predict protein complexes of various strengths and scales.
Edit intent: clarity
Original:  We address these issues and propose a hierarchical hidden community detection approach to accurately predict protein complexes of various strengths and scales.
Revised:  We address these issues and propose a hierarchical hidden community detection approach to accurately predict protein complexes . Results:
Edit intent: clarity
Original:  Experimental results show that the HirHide versions achieve better performance and sometimes even significantly outperform the baselines.
Revised:  Experimental results show that the HirHide versions achieve better performance , sometimes even significantly outperform the baselines.
Edit intent: fluency
Original: Vanilla RNN with ReLU activation have a simple structure that is amenable to systematic dynamical systems analysis and interpretation, but they suffer from the exploding vs. vanishing gradients problem.
Revised: Vanilla RNN with ReLU activation have a simple structure that lends itself to systematic dynamical systems analysis and interpretation, but they suffer from the exploding vs. vanishing gradients problem.
Edit intent: clarity
Original:  {\rm   In addition, our lower bounds - which we show are tracial Cauchy-Schwartz inequalities - are sharp .
Revised:  {\rm rk In addition, our lower bounds - which we show are tracial Cauchy-Schwartz inequalities - are sharp .
Edit intent: fluency
Original:  {\rm   In addition, our lower bounds - which we show are tracial Cauchy-Schwartz inequalities - are sharp .
Revised:  {\rm In addition, our lower bounds -- which we show are tracial Cauchy-Schwartz inequalities - are sharp .
Edit intent: fluency
Original:  In this short note, we affirmatively answer all three questions by extending and refining Vybiral's result  .
Revised:  In this note, we affirmatively answer all three questions by extending and refining Vybiral's result .
Edit intent: clarity
Original:  In addition, our lower bounds -- which we show are tracial Cauchy--Schwartz inequalities -- are sharp.
Revised:  In addition, our lower bounds - which we show are tracial Cauchy--Schwartz inequalities -- are sharp.
Edit intent: fluency
Original:  In addition, our lower bounds -- which we show are tracial Cauchy--Schwartz inequalities -- are sharp.
Revised:  In addition, our lower bounds -- which we show are tracial Cauchy-Schwartz inequalities - are sharp.
Edit intent: fluency
Original:   We end with some consequences for positive definite functions on groups, metric spaces, and Hilbert spaces.
Revised:  We end with consequences for positive definite functions on groups, metric spaces, and Hilbert spaces.
Edit intent: clarity
Original:  Vybiral then asked if one can obtain similar uniform lower bounds for higher entrywise powers of M, or for M \circ N when N \neq M, M. A natural third question is to obtain a tighter lower bound that need not vanish ,\to  over infinite-dimensional Hilbert spaces as well .
Revised:  Vybiral then asked if one can obtain similar uniform lower bounds for higher entrywise powers of M, or for M \circ N when N \neq M, M. A natural third question is to obtain a tighter lower bound that need not vanish as n\to over infinite-dimensional Hilbert spaces as well .
Edit intent: clarity
Original:  Vybiral then asked if one can obtain similar uniform lower bounds for higher entrywise powers of M, or for M \circ N when N \neq M, M. A natural third question is to obtain a tighter lower bound that need not vanish ,\to  over infinite-dimensional Hilbert spaces as well .
Revised:  Vybiral then asked if one can obtain similar uniform lower bounds for higher entrywise powers of M, or for M \circ N when N \neq M, M. A natural third question is to obtain a tighter lower bound that need not vanish ,\to over infinite-dimensional Hilbert spaces .
Edit intent: coherence
Original:  In this note, we affirmatively answer all three questions by extending and refining Vybiral's result to lower bound M \circ N for arbitrary positive M, N. As a special case, the above bound of E_n/n can be improved to E_n /%DIFDELCMD < {\rm %%% rk (M).
Revised:  In this note, we affirmatively answer all three questions by extending and refining Vybiral's result to lower-bound M \circ N for arbitrary positive M, N. As a special case, the above bound of E_n/n can be improved to E_n /%DIFDELCMD < {\rm %%% rk (M).
Edit intent: fluency
Original:  In this note, we affirmatively answer all three questions by extending and refining Vybiral's result to lower bound M \circ N for arbitrary positive M, N. As a special case, the above bound of E_n/n can be improved to E_n /%DIFDELCMD < {\rm %%% rk (M).
Revised:  In this note, we affirmatively answer all three questions by extending and refining Vybiral's result to lower bound M \circ N for arbitrary positive M, N. %DIFDELCMD < {\rm %%% rk (M).
Edit intent: coherence
Original:  In this note, we affirmatively answer all three questions by extending and refining Vybiral's result to lower bound M \circ N for arbitrary positive M, N. As a special case, the above bound of E_n/n can be improved to E_n /%DIFDELCMD < {\rm %%% rk (M).
Revised:  In this note, we affirmatively answer all three questions by extending and refining Vybiral's result to lower bound M \circ N for arbitrary positive M, N. As a special case, the above bound of E_n/n can be improved to E_n /%DIFDELCMD < {\rm %%% (M).
Edit intent: fluency
Original:  In this paper we tackle this task by introducing a notion of temporal core decomposition where each core is associated with two quantities, its coreness, which quantifies how densely it is connected, and its span, which is a temporal interval: we call such cores span-cores .
Revised:  In this paper we tackle this task by introducing a notion of temporal core decomposition where each core is associated with two quantities, its coreness, which quantifies how densely it is connected, and its span, which is a temporal interval: we call such cores span-cores .
Edit intent: fluency
Original:  Then, we focus on the problem of finding only the maximal span-cores , i.e., span-cores that are not dominated by any other span-core by both their coreness property and their span.
Revised:  Then, we focus on the problem of finding only the maximal span-cores , i.e., span-cores that are not dominated by any other span-core by both their coreness property and their span.
Edit intent: fluency
Original:  Finally,  we introduce the problem of temporal community search \emph{ , where a set of query vertices is given as input, and the goal is to find a set of densely-connected subgraphs containing the query vertices and covering the whole underlying temporal domain T.
Revised:  Finally, we introduce the problem of \emph{ , where a set of query vertices is given as input, and the goal is to find a set of densely-connected subgraphs containing the query vertices and covering the whole underlying temporal domain T.
Edit intent: clarity
Original:  In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically non-scalable or even divergent behaviour of these solvers for this problem.
Revised:  In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically non-scalable or even divergent behavior of these solvers for this problem.
Edit intent: fluency
Original:  To overcome these failings, we replace rediscretization on coarse grids with near-optimal coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory.
Revised:  To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory.
Edit intent: clarity
Original:  Our main finding is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behaviour of the hyperbolic problem by tracking the characteristic curves.
Revised:  One of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behaviour of the hyperbolic problem by tracking the characteristic curves.
Edit intent: clarity
Original:  Our main finding is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behaviour of the hyperbolic problem by tracking the characteristic curves.
Revised:  Our main finding is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves.
Edit intent: fluency
Original:  Our approach is tested on discretizations of various orders that use explicit or implicit Runge-Kutta time integration with upwind-finite-difference spatial discretizations , for which we obtain fast and scalable convergence in all cases.
Revised:  Our approach is tested for schemes of various orders that use explicit or implicit Runge-Kutta time integration with upwind-finite-difference spatial discretizations , for which we obtain fast and scalable convergence in all cases.
Edit intent: clarity
Original:  Our approach is tested on discretizations of various orders that use explicit or implicit Runge-Kutta time integration with upwind-finite-difference spatial discretizations , for which we obtain fast and scalable convergence in all cases.
Revised:  Our approach is tested on discretizations of various orders using explicit or implicit Runge-Kutta time integration with upwind-finite-difference spatial discretizations , for which we obtain fast and scalable convergence in all cases.
Edit intent: clarity
Original:  Our approach is tested on discretizations of various orders that use explicit or implicit Runge-Kutta time integration with upwind-finite-difference spatial discretizations , for which we obtain fast and scalable convergence in all cases.
Revised:  Our approach is tested on discretizations of various orders that use explicit or implicit Runge-Kutta methods combined with upwind-finite-difference spatial discretizations , for which we obtain fast and scalable convergence in all cases.
Edit intent: clarity
Original:  Our approach is tested on discretizations of various orders that use explicit or implicit Runge-Kutta time integration with upwind-finite-difference spatial discretizations , for which we obtain fast and scalable convergence in all cases.
Revised:  Our approach is tested on discretizations of various orders that use explicit or implicit Runge-Kutta time integration with upwind-finite-difference spatial discretizations . In all cases, we obtain scalable convergence in all cases.
Edit intent: coherence
Original:  Our insight of tracking characteristics on coarse grids is implemented for linear advection using an optimization approach, but the principle is general, and provides a key idea for solving the long-standing problem of efficient parallel-in-time integration for hyperbolic PDEs.
Revised:  Our insight of tracking characteristics on coarse grids provides a key idea for solving the long-standing problem of efficient parallel-in-time integration for hyperbolic PDEs.
Edit intent: coherence
Original: We consider two graphs, G_{7,3} and G_{7,4},  related to Keller's conjecture in dimension 7.
Revised: We consider two graphs, G_{7,3} , G_{7,4}, related to Keller's conjecture in dimension 7.
Edit intent: fluency
Original:  Since there is a faceshare-free unit cube tiling of R^8  , this completely resolves Keller's conjecture.
Revised:  Since a faceshare-free unit cube tiling of R^8 , this completely resolves Keller's conjecture.
Edit intent: clarity
Original:  The conjecture is true for this dimension if and only if the size of the largest clique in at least one of the graphs is less than 2^7 = 128.
Revised:  The conjecture is false for this dimension if and only if the size of the largest clique in at least one of the graphs is less than 2^7 = 128.
Edit intent: clarity
Original:  The conjecture is true for this dimension if and only if the size of the largest clique in at least one of the graphs is less than 2^7 = 128.
Revised:  The conjecture is true for this dimension if and only if at least one of the graphs is less than 2^7 = 128.
Edit intent: clarity
Original:  Both monads are constructed in terms of double dualization.
Revised:  We construct both monads in a unified way in terms of double dualization.
Edit intent: clarity
Original:  This not only reveals a strong similarity between them, but also allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra.
Revised:  This reveals a close analogy between them, but also allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra.
Edit intent: clarity
Original:  This not only reveals a strong similarity between them, but also allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra.
Revised:  This not only reveals a strong similarity between them, and allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra.
Edit intent: fluency
Original:  By composing these two morphisms of monads, we obtain that taking the support of a \tau-smooth probability measure is also given by a morphism of monads.
Revised:  By composing these two morphisms of monads, we obtain that taking the support of a \tau-smooth probability measure is also a morphism of monads.
Edit intent: clarity
Original:  By composing these two morphisms of monads, we obtain that taking the support of a \tau-smooth probability measure is also a morphism of monads.
Revised:  By composing these two morphisms of monads, we obtain that taking the support of a tau-smooth probability measure is also a morphism of monads.
Edit intent: fluency
Original: While  deep learning (DL)-based networked systems have shown great potential in various applications, a key drawback is that Deep Neural Networks (DNNs) in DL are blackboxes and nontransparent for network operators.
Revised: While many deep learning (DL)-based networked systems have shown great potential in various applications, a key drawback is that Deep Neural Networks (DNNs) in DL are blackboxes and nontransparent for network operators.
Edit intent: clarity
Original: While  deep learning (DL)-based networked systems have shown great potential in various applications, a key drawback is that Deep Neural Networks (DNNs) in DL are blackboxes and nontransparent for network operators.
Revised: While deep learning (DL)-based networking systems have demonstrated superior performance, the underlying Deep Neural Networks (DNNs) in DL are blackboxes and nontransparent for network operators.
Edit intent: clarity
Original: While  deep learning (DL)-based networked systems have shown great potential in various applications, a key drawback is that Deep Neural Networks (DNNs) in DL are blackboxes and nontransparent for network operators.
Revised: While deep learning (DL)-based networked systems have shown great potential in various applications, a key drawback is that Deep Neural Networks (DNNs) remain blackboxes and stay uninterpretable for network operators.
Edit intent: clarity
Original:  The lack of interpretability makes DL-based networked systems challenging to operate and troubleshoot, which further prevents DL-based networked systems from deploying in practice.
Revised:  The lack of interpretability makes DL-based networking systems prohibitive to deploy in practice.
Edit intent: clarity
Original:  We also present three use cases of Transys, which could (i) help network operators troubleshoot DL-based networked systems, (ii) improve the decision latency and resource consumption of DL-based networked systemsby ~10x on different metrics, and (iii) provide suggestions on daily operations for network operators when incidences occur .
Revised:  We also present three use cases of Transys, which could (i) help network operators troubleshoot DL-based networking systems .
Edit intent: coherence
Original:  This approach provides a full FreeSurfer alternative for volumetric analysis (within 1 minute) and surface-based thickness analysis (within only around 1h run time ).
Revised:  This approach provides a full FreeSurfer alternative for volumetric analysis (within 1 minute) and surface-based thickness analysis (within only around 1h runtime ).
Edit intent: clarity
Original:  To this end, we introduce an advanced deep learning architecture capable of whole brain segmentation into 95 classes in under 1 minute, mimicking FreeSurfer's anatomical segmentation and cortical parcellation .
Revised:  To this end, we introduce an advanced deep learning architecture capable of whole brain segmentation into 95 classes .
Edit intent: coherence