wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We further obtain a tight (1-e^{-1-\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (}  0.385- \epsilon )-approximation for non-monotone submodular optimization subject to a constant number of multiple knapsack constraints.
Revised:  -\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (} 0.385- \epsilon )-approximation for non-monotone submodular optimization subject to a constant number of multiple knapsack constraints.
Edit intent: clarity
Original:  We further obtain a tight (1-e^{-1-\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (}  0.385- \epsilon )-approximation for non-monotone submodular optimization subject to a constant number of multiple knapsack constraints.
Revised:  We further obtain a tight (1-e^{-1-\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (} Another example is Non-monotone Submodular Multiple Knapsack, for which we obtain a ( 0.385- \epsilon )-approximation for non-monotone submodular optimization subject to a constant number of multiple knapsack constraints.
Edit intent: meaning-changed
Original:  We further obtain a tight (1-e^{-1-\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (}  0.385- \epsilon )-approximation for non-monotone submodular optimization subject to a constant number of multiple knapsack constraints.
Revised:  We further obtain a tight (1-e^{-1-\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (} 0.385- \varepsilon )-approximation for non-monotone submodular optimization subject to a constant number of multiple knapsack constraints.
Edit intent: clarity
Original:  We further obtain a tight (1-e^{-1-\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (}  0.385- \epsilon )-approximation for non-monotone submodular optimization subject to a constant number of multiple knapsack constraints. At the heart of our algorithms lies a novel representation of a multiple knapsack constraint as a polytope. We consider this key tool as a main technical contribution of this paper .
Revised:  We further obtain a tight (1-e^{-1-\epsilon)-approximation for monotone submodular optimization subject to a constant number of multiple knapsack constraints and a matroid constraint, and a (} 0.385- \epsilon )-approximation , matching the best known ratio for a single knapsack constraint. The robustness of our algorithm is achieved by applying a novel fractional variant of the classical linear grouping technique, which is of independent interest .
Edit intent: meaning-changed
Original:  Due to its highly contagious nature, it has spread rapidly, resulting in major disruption to public health. In addition, it has also had a severe negative impact on the world economy. As a result, it is widely recognized now that widespread testing is key to containing the spread of the disease and opening up the economy. However, the current testing regime  has been unable to keep up with testing demands  .
Revised:  The current testing regime has been unable to keep up with testing demands .
Edit intent: coherence
Original:  The emergence of wearable medical sensors (WMSs) and novel machine learning methods, such as deep neural networks (DNNs), points to a promising approach to address this challenge. WMSs enable continuous and user-transparent monitoring of the physiological signals. However, disease detection based on WMSs/DNNs and their deployment on resource-constrained edge devices remain challenging problems. In this work, we propose CovidDeep, a framework that combines efficient DNNs with commercially available WMSs for pervasive testing of the coronavirus .
Revised:  We propose a framework called CovidDeep that combines efficient DNNs with commercially available WMSs for pervasive testing of the coronavirus .
Edit intent: coherence
Original:  We collected data from 87 individuals, spanning four cohorts including healthy, asymptomatic (but SARS-CoV-2-positive) as well as moderately and severely symptomatic COVID-19 patients.
Revised:  We collected data from 87 individuals, spanning three cohorts including healthy, asymptomatic (but SARS-CoV-2-positive) as well as moderately and severely symptomatic COVID-19 patients.
Edit intent: meaning-changed
Original:  We trained DNNs on various subsets of the features  extracted from six WMS and questionnaire categories to perform ablation studies to determine which subsets are most efficacious in terms of test accuracy for a four-way classification.
Revised:  We trained DNNs on various subsets of the features automatically extracted from six WMS and questionnaire categories to perform ablation studies to determine which subsets are most efficacious in terms of test accuracy for a four-way classification.
Edit intent: meaning-changed
Original:  We trained DNNs on various subsets of the features  extracted from six WMS and questionnaire categories to perform ablation studies to determine which subsets are most efficacious in terms of test accuracy for a four-way classification.
Revised:  We trained DNNs on various subsets of the features extracted from six WMS and questionnaire categories to perform ablation studies to determine which subsets are most efficacious in terms of test accuracy for a three-way classification.
Edit intent: meaning-changed
Original:  The highest test accuracy obtained was 99.4\%. Since different WMS subsets may be more accessible (in terms of cost, availability, etc.) to different sets of people, we hope these DNN models will provide users with ample flexibility. The resultant DNNs can be easily deployed on edge devices, e.g., smartwatch or smartphone, which also has the benefit of preserving patient privacy .
Revised:  The highest test accuracy obtained was 98.1\%. We also augmented the real training dataset with a synthetic training dataset drawn from the same probability distribution to impose a prior on DNN weights and leveraged a grow-and-prune synthesis paradigm to learn both DNN architecture and weights. This boosted the accuracy of the various DNNs further and simultaneously reduced their size and floating-point operations .
Edit intent: meaning-changed
Original:  For the general form (no congestion, general weights, integral routing) {\sc   even the case of unit capacity trees which are stars generalizes the maximum matching problem for which Edmonds provided an exact algorithm.
Revised:  For the general form (no congestion, general weights, integral routing) of edge-disjoint paths ({\sc even the case of unit capacity trees which are stars generalizes the maximum matching problem for which Edmonds provided an exact algorithm.
Edit intent: meaning-changed
Original:  For the general form (no congestion, general weights, integral routing) {\sc   even the case of unit capacity trees which are stars generalizes the maximum matching problem for which Edmonds provided an exact algorithm.
Revised:  For the general form (no congestion, general weights, integral routing) {\sc edp even the case of unit capacity trees which are stars generalizes the maximum matching problem for which Edmonds provided an exact algorithm.
Edit intent: meaning-changed
Original:  For the general form (no congestion, general weights, integral routing) {\sc   even the case of unit capacity trees which are stars generalizes the maximum matching problem for which Edmonds provided an exact algorithm.
Revised:  For the general form (no congestion, general weights, integral routing) {\sc ) even the case of unit capacity trees which are stars generalizes the maximum matching problem for which Edmonds provided an exact algorithm.
Edit intent: fluency
Original: We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general cadlag \cadlag measurable processes.
Revised: We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes.
Edit intent: clarity
Original:  Our key observation is that the general approach from [Heid & Wihler, arXiv:1808.04990v2 ] satisfies an energy contraction property in the context of (abstract) strongly monotone problems.
Revised:  Our key observation is that the general approach from [Heid & Wihler, Math. Comp. 89 (2020), Calcolo 57 (2020) ] satisfies an energy contraction property in the context of (abstract) strongly monotone problems.
Edit intent: meaning-changed
Original:  In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to  linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time.
Revised:  In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to full linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time.
Edit intent: meaning-changed
Original:  3-coloring can be solved in O( 1.4 ^n) time (Beigel and Eppstein, 2005) and 4-coloring can be solved in O( 1.8 ^n) time (Fomin, Gaspers and Saurabh, 2007).
Revised:  3-coloring can be solved in O( 1.33 ^n) time (Beigel and Eppstein, 2005) and 4-coloring can be solved in O( 1.8 ^n) time (Fomin, Gaspers and Saurabh, 2007).
Edit intent: meaning-changed
Original:  3-coloring can be solved in O( 1.4 ^n) time (Beigel and Eppstein, 2005) and 4-coloring can be solved in O( 1.8 ^n) time (Fomin, Gaspers and Saurabh, 2007).
Revised:  3-coloring can be solved in O( 1.4 ^n) time (Beigel and Eppstein, 2005) and 4-coloring can be solved in O( 1.73 ^n) time (Fomin, Gaspers and Saurabh, 2007).
Edit intent: meaning-changed
Original:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Revised:  In particular, for any constants \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Edit intent: fluency
Original:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Revised:  In particular, for any constants k, \Delta,\alpha>0, the chromatic number of graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Edit intent: meaning-changed
Original:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Revised:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be computed in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Edit intent: clarity
Original:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Revised:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Edit intent: coherence
Original:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha As a consequence, for any constant k we can solve k-coloring exponentially faster than O^*(2^n) for sparse graphs.
Revised:  In particular, for any constants k, \Delta,\alpha>0, k-coloring for graphs with at least \alpha\cdot n vertices of degree at most \Delta can be solved in O\left(\left(2-\varepsilon\right)^n\right) time, for some \varepsilon = k, \Delta,\alpha This statement generalizes previous results for bounded-degree graphs (Bj\"orklund, Husfeldt, Kaski, and Koivisto, 2010) and graphs with bounded average degree (Golovnev, Kulikov and Mihajilin, 2016). We generalize the aforementioned statement to List Coloring, for which no previous improvements are known even for the case bounded-degree graphs.
Edit intent: meaning-changed
Original: We consider Gibbs distributions , which are families of probability distributions over a discrete space \Omega with probability mass function of the form \mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)} for \beta in an interval [\min, \max] and H( \omega ) \in \{0 \} \cup [1, n].
Revised: We consider Gibbs distributions , which are families of probability distributions over a discrete space \Omega with probability mass function of the form \mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)} for \beta in an interval [\min, \max] and H( \omega ) \in \{0 \} \cup [1, n].
Edit intent: fluency
Original:  Two important parameters of these distributions are the  partition ratio q = \log Z(\beta_{\max)}{Z(\min)} and the counts c_x = |H^{-1}(x)|.
Revised:  Two important parameters of these distributions are the log partition ratio q = \log Z(\beta_{\max)}{Z(\min)} and the counts c_x = |H^{-1}(x)|.
Edit intent: fluency
Original:  Our first main result is to estimate the values c_x using roughly \tilde O( q{\varepsilon^2}) samples for general Gibbs distributions and \tilde O( n^2{\varepsilon^2} ) samples for integer-valued distributions (ignoring some second-order terms and parameters), and we show this is optimal up to logarithmic factors.
Revised:  Our first main result is to estimate the counts c_x using roughly \tilde O( q{\varepsilon^2}) samples for general Gibbs distributions and \tilde O( n^2{\varepsilon^2} ) samples for integer-valued distributions (ignoring some second-order terms and parameters), and we show this is optimal up to logarithmic factors.
Edit intent: clarity
Original:  A key subroutine we develop is to estimate the partition function Z ; specifically, we generate a data structure capable of estimating Z(\beta) for all \emph{ values \beta, without further samples.
Revised:  A key subroutine we develop is to estimate the partition function Z . Specifically, it generates a data structure capable of estimating Z(\beta) for all \emph{ values \beta, without further samples.
Edit intent: clarity
Original:  Constructing the data structure requires %DIFDELCMD < \tilde %%% O(\frac{q{\varepsilon^2}} {\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% O(\frac{n^2{\varepsilon^2}} {\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Revised:  Constructing the data structure requires %DIFDELCMD < \tilde %%% {\varepsilon^2}} {\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% O(\frac{n^2{\varepsilon^2}} {\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Edit intent: fluency
Original:  Constructing the data structure requires %DIFDELCMD < \tilde %%% O(\frac{q{\varepsilon^2}} {\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% O(\frac{n^2{\varepsilon^2}} {\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Revised:  Constructing the data structure requires %DIFDELCMD < \tilde %%% O(\frac{q{\varepsilon^2}} O(\frac{q \log n{\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% O(\frac{n^2{\varepsilon^2}} {\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Edit intent: meaning-changed
Original:  Constructing the data structure requires %DIFDELCMD < \tilde %%% O(\frac{q{\varepsilon^2}} {\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% O(\frac{n^2{\varepsilon^2}} {\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Revised:  Constructing the data structure requires %DIFDELCMD < \tilde %%% O(\frac{q{\varepsilon^2}} {\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% {\varepsilon^2}} {\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Edit intent: meaning-changed
Original:  Constructing the data structure requires %DIFDELCMD < \tilde %%% O(\frac{q{\varepsilon^2}} {\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% O(\frac{n^2{\varepsilon^2}} {\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Revised:  Constructing the data structure requires %DIFDELCMD < \tilde %%% O(\frac{q{\varepsilon^2}} {\varepsilon^2}} ) samples for general Gibbs distributions and %DIFDELCMD < \tilde %%% O(\frac{n^2{\varepsilon^2}} O(\frac{n^2 \log n{\varepsilon^2} + n \log q} ) samples for integer-valued distributions.
Edit intent: meaning-changed
Original:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}}  ) samples.
Revised:  This improves over a prior algorithm of Huber (2015 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}} ) samples.
Edit intent: meaning-changed
Original:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}}  ) samples.
Revised:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes a single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}} ) samples.
Edit intent: fluency
Original:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}}  ) samples.
Revised:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta ) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}} ) samples.
Edit intent: meaning-changed
Original:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}}  ) samples.
Revised:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% {\varepsilon^2}} ) samples.
Edit intent: meaning-changed
Original:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}}  ) samples.
Revised:  This improves over a prior algorithm of Kolmogorov (2018 ) which computes the single point estimate Z(\beta _{\max) using }%DIFDELCMD < \tilde %%% O( \frac{q{\varepsilon^2}} _\max) using O( q \log n( \log q + \log \log n + \varepsilon^{-2 ) samples.
Edit intent: meaning-changed
Original:  Investigating single nucleotide polymorphisms (SNPs) that correlate with specific diseases needs statistical analysis of associations , considering the huge number of possible disease mutations. The most important drawback of GWAS analysis in addition to its high cost  is the large number of false-positives.
Revised:  Investigating single nucleotide polymorphisms (SNPs) that correlate with specific diseases needs statistical analysis of associations , considering the huge number of possible mutations, in addition to its high cost is the large number of false-positives.
Edit intent: coherence
Original:  We extend this method to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension.
Revised:  We extend the desparsified lasso to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension.
Edit intent: meaning-changed
Original: We consider distributed inference using sequentially interactive protocols. We obtain lower bounds on the minimax sample complexity of interactive protocols under local information constraints, a broad family of resource constraints which captures communication constraints , local differential privacy , and noisy binary queries as special cases .
Revised: We study the role of interactivity in distributed statistical inference under information constraints, a broad family of resource constraints which captures communication constraints , local differential privacy , and noisy binary queries as special cases .
Edit intent: clarity
Original:  We focus on the inference tasks of learning (density estimation) and identity testing ( goodness-of-fit ) for discrete distributionsunder total variation distance, and establish general lower bounds that take into account the local constraints modeled as a channel family.
Revised:  We focus on the tasks of goodness-of-fit ) for discrete distributionsunder total variation distance, and establish general lower bounds that take into account the local constraints modeled as a channel family.
Edit intent: clarity
Original:  We focus on the inference tasks of learning (density estimation) and identity testing ( goodness-of-fit ) for discrete distributionsunder total variation distance, and establish general lower bounds that take into account the local constraints modeled as a channel family. Our main technical contribution is an approach to handle the correlation that builds due to interactivity and quantifies how effectively one can exploit this correlation in spite of the local constraints.
Revised:  We focus on the inference tasks of learning (density estimation) and identity testing ( goodness-of-fit testing and estimation of discrete distributions. From prior work, these tasks are well understood under noninteractive protocols. Extending these approaches directly for interactive protocols is difficult due to correlations that can build due to interactivity and quantifies how effectively one can exploit this correlation in spite of the local constraints.
Edit intent: meaning-changed