wanyu/IteraTeR_v2 huggingface dataset:
Original: We introduce a new ] uncapacitated discrete facility location problem , where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Revised: We introduce a new ] uncapacitated discrete facility location problem where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Edit intent: fluency
Original:  To this end, we derive fixed-parameter algorithms for computing weighted representative families for matroid intersections and maximum-weight set packings with multiple matroid constraints.
Revised:  To this end, we derive fixed-parameter algorithms for computing representative families for matroid intersections and maximum-weight set packings with multiple matroid constraints.
Edit intent: clarity
Original: We consider a variant of the matroid median problem introduced by Krishnaswamy et al.
Revised: We 
Edit intent: coherence
Original:  SODA 2011%DIFDELCMD < ]%%% : an uncapacitated discrete facility location problem where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Revised:  %DIFDELCMD < ]%%% : an uncapacitated discrete facility location problem where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Edit intent: coherence
Original:  To illustrate the modeling capabilities of the new problem, we use it to obtain algorithms for a problem in social network analysis.
Edit intent: coherence
Original: Recently Ermon et al. (2013) pioneered an ingenuous way to practically compute approximations to large scale counting or discrete integration problems by using random hashes.
Revised: Recently Ermon et al. (2013) pioneered a way to practically compute approximations to large scale counting or discrete integration problems by using random hashes.
Edit intent: clarity
Original:  The hashes are used to reduce the counting problems into many separate discrete optimization problems.
Revised:  The hashes are used to reduce the counting problem into many separate discrete optimization problems.
Edit intent: fluency
Original:  The optimization problems  can be solved by an NP-oracle , and if they allow some amenable structure then commercial SAT solvers or  linear programming ( LP) solverscan be used in lieu of the NP-oracle .
Revised:  The optimization problems then can be solved by an NP-oracle , and if they allow some amenable structure then commercial SAT solvers or linear programming ( LP) solverscan be used in lieu of the NP-oracle .
Edit intent: coherence
Original:  The optimization problems  can be solved by an NP-oracle , and if they allow some amenable structure then commercial SAT solvers or  linear programming ( LP) solverscan be used in lieu of the NP-oracle .
Revised:  The optimization problems can be solved by an NP-oracle such as commercial SAT solvers or linear programming ( LP) solverscan be used in lieu of the NP-oracle .
Edit intent: clarity
Original:  The optimization problems  can be solved by an NP-oracle , and if they allow some amenable structure then commercial SAT solvers or  linear programming ( LP) solverscan be used in lieu of the NP-oracle .
Revised:  The optimization problems can be solved by an NP-oracle , and if they allow some amenable structure then commercial SAT solvers or linear programming ( ILP) solvers .
Edit intent: clarity
Original:  In particular, Ermon et al. has shown that if the domain of integration is \{0,1\}^n then it is possible to obtain a  16-approximation  by this technique.
Revised:  In particular, Ermon et al. showed that if the domain of integration is \{0,1\}^n then it is possible to obtain a 16-approximation by this technique.
Edit intent: coherence
Original:  In particular, Ermon et al. has shown that if the domain of integration is \{0,1\}^n then it is possible to obtain a  16-approximation  by this technique.
Revised:  In particular, Ermon et al. has shown that if the domain of integration is \{0,1\}^n then it is possible to obtain a 16-approximation ) by this technique.
Edit intent: fluency
Original:  In many crucial counting tasks, such as computation of partition function of ferromagnetic Potts model, the domain of integration is naturally \{0,1,\dots, q-1\}^n, q> 2. A straightforward extension of Ermon et al.'s work would allow a q^2-approximation for this problem , assuming the existence of an optimization oracle .
Revised:  In many crucial counting tasks, such as computation of partition function of ferromagnetic Potts model, the domain of integration is naturally \{0,1,\dots, q-1\}^n, q> 2. A straightforward extension of Ermon et al.'s method allows a q^2-approximation for this problem , assuming the existence of an optimization oracle .
Edit intent: clarity
Original:  Note that, the domain of integration here is the symmetric group .
Revised:  Note that, the domain of integration is the symmetric group .
Edit intent: clarity
Original:  Our method extends to the case when the domain of integration is the symmetric group, and as a result we can obtain a (4+o(1))-approximation of the%DIFDELCMD < {\em %%% permanent of a matrix.
Revised:  %DIFDELCMD < {\em %%% permanent of a matrix.
Edit intent: coherence
Original:  Our method extends to the case when the domain of integration is the symmetric group, and as a result we can obtain a (4+o(1))-approximation of the%DIFDELCMD < {\em %%% permanent of a matrix.
Revised:  Our method extends to the case when the domain of integration is the symmetric group, and as a result we can obtain a (4+o(1))-approximation of the%DIFDELCMD < {\em %%% a matrix.
Edit intent: coherence
Original:  We provide experimental simulation results to support the theoretical guarantees of our algorithms , including comparison to the popular Markov-Chain-Monte-Carlo (MCMC) methods .
Revised:  We provide experimental simulation results to support the theoretical guarantees of our algorithms .
Edit intent: clarity
Original:  In contrast, custom cells that incorporated two structural features, bypassing and gating, were able to boost task accuracy substantially.
Revised:  In contrast, novel cells that incorporated two structural features, bypassing and gating, were able to boost task accuracy substantially.
Edit intent: clarity
Original:  The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc . Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles  .
Revised:  The parity constraints can be extended to label constraints in a group-labeled graph, which is a directed graph with a group label on each arc . Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles .
Edit intent: fluency
Original:  The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc . Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles  .
Revised:  The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with each arc labeled by an element of a group . Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles .
Edit intent: clarity
Original:  The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc . Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles  .
Revised:  The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc . Recently, paths and cycles in group-labeled graphs have been investigated, such as packing non-zero disjoint paths and cycles .
Edit intent: clarity
Original:  The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc . Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths and cycles  .
Revised:  The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc . Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero paths and cycles .
Edit intent: clarity
Original:  In this paper, we present a solution to finding an s--t path in a group-labeled graph with two labels forbidden  .
Revised:  In this paper, we present a solution to finding an s--t path with two labels forbidden .
Edit intent: clarity
Original:  In this paper, we present a solution to finding an s--t path in a group-labeled graph with two labels forbidden  .
Revised:  In this paper, we present a solution to finding an s--t path in a group-labeled graph with two labels forbidden in a group-labeled graph .
Edit intent: coherence
Original:  These dimensions include myriad properties describing genome, epigenome, transcriptome, microbiome, phenotype, and lifestyle.
Revised:  These dimensions include a myriad of properties describing genome, epigenome, transcriptome, microbiome, phenotype, and lifestyle.
Edit intent: fluency
Original:  We evaluated these approaches on simulated data for a repressilator, time-course data from past DREAM challenges, and a HeLa cell cycle dataset to show that they can produce accurate networks that reflect the dynamics and assumptions of the time-lagged Ordered Lasso regression.
Revised:  We evaluated these approaches on simulated data for a repressilator, time-course data from past DREAM challenges, and a HeLa cell cycle dataset to show that they can produce accurate networks subject to the dynamics and assumptions of the time-lagged Ordered Lasso regression.
Edit intent: clarity
Original:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%%  iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right)  for the accelerated randomized dual coordinate ascent.
Revised:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove %DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%% iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right) for the accelerated randomized dual coordinate ascent.
Edit intent: coherence
Original:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%%  iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right)  for the accelerated randomized dual coordinate ascent.
Revised:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%% that the iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right) for the accelerated randomized dual coordinate ascent.
Edit intent: fluency
Original:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%%  iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right)  for the accelerated randomized dual coordinate ascent.
Revised:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%% iteration complexity of the primal solutions and dual solutions have the same O\left({\epsilon}}\right) for the accelerated randomized dual coordinate ascent.
Edit intent: clarity
Original:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%%  iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right)  for the accelerated randomized dual coordinate ascent.
Revised:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%% iteration complexity of the primal solutions and dual solutions \left(\frac{1{\epsilon}}\right) for the accelerated randomized dual coordinate ascent.
Edit intent: fluency
Original:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%%  iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right)  for the accelerated randomized dual coordinate ascent.
Revised:  iterations to achieve an \epsilon-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with T(\epsilon^{-1}) iterations to achieve an \epsilon-optimal dual solution, where T(x) can be x or x. In this paper, we prove the equal O%DIFDELCMD < \left(%%% \frac{1{\epsilon}}%DIFDELCMD < \right) %%% iteration complexity of the primal solutions and dual solutions \left({\epsilon}}\right) order of magnitude for the accelerated randomized dual coordinate ascent.
Edit intent: clarity
Original:  When the dual function further satisfies the weak strong convexity condition, we establish the linear O%DIFDELCMD < \left(%%% \log\frac{1{\epsilon}}%DIFDELCMD < \right) %DIFDELCMD < %%% iteration complexity for both the primal solutions and dual solutions  .
Revised:  When the dual function further satisfies the weak strong convexity condition, we establish the linear %DIFDELCMD < \left(%%% \log\frac{1{\epsilon}}%DIFDELCMD < \right) %DIFDELCMD < %%% iteration complexity for both the primal solutions and dual solutions .
Edit intent: clarity
Original:  When the dual function further satisfies the weak strong convexity condition, we establish the linear O%DIFDELCMD < \left(%%% \log\frac{1{\epsilon}}%DIFDELCMD < \right) %DIFDELCMD < %%% iteration complexity for both the primal solutions and dual solutions  .
Revised:  When the dual function further satisfies the weak strong convexity condition, we establish the linear O%DIFDELCMD < \left(%%% \log\frac{1{\epsilon}}%DIFDELCMD < \right) %DIFDELCMD < %%% iteration complexity for both the primal solutions and dual solutions even if the condition number is unknown .
Edit intent: clarity
Original:  This problem is analyzed in this paper using Whittle index approach.
Revised:  To circumvent this difficulty, we tackle the problem by adopting a Whittle index approach.
Edit intent: clarity
Original:  First, using the Lagrangian relaxation method, we provide a relaxed problem and show that it can be decomposed into simpler one-dimensional subproblems for which the optimal solution is a threshold-based policy .
Revised:  To that extent, we employ a Lagrangian relaxation of the original problem and prove it to be decomposable into multiple one-dimensional subproblems for which the optimal solution is a threshold-based policy .
Edit intent: clarity
Original:  We prove that this heuristic is asymptotically optimal in the infinitely many users regime and provide numerical results that illustrate its remarkably good performance .
Revised:  We prove that this heuristic is asymptotically optimal in the infinitely many users regime . Finally, we provide numerical results that illustrate its remarkably good performance .
Edit intent: coherence
Original: In this paper we demonstrate that state-of-the-art convolutional neural networks can be constructed using a cascade algorithm for deep networks, inspired by the cascade algorithm in wavelet analysis.
Revised: In this paper we demonstrate that state-of-the-art convolutional neural networks can be constructed using a cascade algorithm for deep networks, inspired by the cascade algorithm of wavelet analysis.
Edit intent: clarity
Original:  For each network layer the cascade algorithm creates two streams of features from the previous layer: one streammodulates the existing features producing low-level features, the other stream produces new features of a higher level.
Revised:  ECN employs two feature streams - a low-level features, the other stream produces new features of a higher level.
Edit intent: clarity
Original:  We report new state-of-the-art results for small networks - a consequence of our architecture's simple structure and direct training , without the need for additional treatment such as pruning or compression .
Revised:  We report new state-of-the-art results for small networks , without the need for additional treatment such as pruning or compression .
Edit intent: coherence
Original:  We propose a personalized RT design through the combination of patient multimodal medical scans and state-of-the-art computational tumor models .
Revised:  Here we provide a Bayesian machine learning framework for the rational design of improved, personalized radiotherapy plans using mathematical modeling and patient multimodal medical scans and state-of-the-art computational tumor models .
Edit intent: clarity
Original:  We propose a personalized RT design through the combination of patient multimodal medical scans and state-of-the-art computational tumor models .
Revised:  We propose a personalized RT design through the combination of patient multimodal medical scans .
Edit intent: clarity
Original:  Our method  integrates complementary information from high-resolution MRI scans and highly specific FET-PET metabolic maps to infer tumor cell density in glioma patients.
Revised:  Our method integrates complementary information from high resolution MRI scans and highly specific FET-PET metabolic maps to infer tumor cell density in glioma patients.
Edit intent: fluency
Original:  The Bayesian framework integrates information across multiple imaging modalities, quantifies imaging and modelling uncertainties , and predicts patient-specific tumor cell density with confidence intervals.
Revised:  The Bayesian framework integrates information across multiple imaging modalities, quantifies imaging and modeling uncertainties and predicts patient-specific tumor cell density with confidence intervals.
Edit intent: fluency
Original:  The computational cost of Bayesian inference is reduced by advanced sampling algorithms and parallel software .
Revised:  The proposed methodology relies only on data acquired at a single time point and thus is applicable to standard clinical settings .
Edit intent: clarity
Original:  An initial clinical population study shows that the RT plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard RT protocols.
Revised:  An initial clinical population study shows that the radiotherapy plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard RT protocols.
Edit intent: clarity
Original:  An initial clinical population study shows that the RT plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard RT protocols.
Revised:  An initial clinical population study shows that the RT plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard radiotherapy protocols.
Edit intent: fluency
Original:  Moreover, the inferred regions of high tumor cell density coincide with the tumor radio-resistant areas, providing guidance for personalized dose escalation .
Revised:  Moreover, the inferred regions of high tumor cell densities coincide with the tumor radio-resistant areas, providing guidance for personalized dose escalation .
Edit intent: clarity
Original:  Moreover, the inferred regions of high tumor cell density coincide with the tumor radio-resistant areas, providing guidance for personalized dose escalation .
Revised:  Moreover, the inferred regions of high tumor cell density coincide with the tumor radioresistant areas, providing guidance for personalized dose escalation .
Edit intent: fluency
Original:  Moreover, the inferred regions of high tumor cell density coincide with the tumor radio-resistant areas, providing guidance for personalized dose escalation .
Revised:  Moreover, the inferred regions of high tumor cell density coincide with the tumor radio-resistant areas, providing guidance for personalized dose-escalation .
Edit intent: fluency
Original:  The proposed integration of data and models provides a robust, non-invasive tool to assist personalized RT planning .
Revised:  The proposed integration of multimodal scans and mathematical modeling provides a robust, non-invasive tool to assist personalized RT planning .
Edit intent: clarity
Original:  The proposed integration of data and models provides a robust, non-invasive tool to assist personalized RT planning .
Revised:  The proposed integration of data and models provides a robust, non-invasive tool to assist personalized radiotherapy design .
Edit intent: clarity
Original:  Reducing  action potential onset rapidness can impair the ultrafast population encoding, but it is not clear whether rapid action potential onset is sufficient for ultrafast population encoding.
Revised:  Reducing action potential onset can impair ultrafast population encoding, but it is not clear whether rapid action potential onset is sufficient for ultrafast population encoding.
Edit intent: clarity